0.07/0.15 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.16 % Command : do_cvc5 %s %d 0.13/0.37 % Computer : n019.cluster.edu 0.13/0.37 % Model : x86_64 x86_64 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.37 % Memory : 8042.1875MB 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.37 % CPULimit : 960 0.13/0.37 % WCLimit : 120 0.13/0.37 % DateTime : Tue Aug 9 04:21:21 EDT 2022 0.13/0.38 % CPUTime : 1.12/1.35 %----Proving TF0_NAR, FOF, or CNF 7.03/7.36 ------- cvc5-fof casc J11 : /export/starexec/sandbox/benchmark/theBenchmark.p at /export/starexec/sandbox/benchmark/theBenchmark.p... 7.03/7.36 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 7.03/7.36 % SZS status Theorem for theBenchmark 7.03/7.36 % SZS output start Proof for theBenchmark 7.03/7.36 (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (let ((_let_2 (hAPP_int_int bit1 pls))) (let ((_let_3 (hAPP_int_int bit0 _let_2))) (let ((_let_4 (hAPP_int_nat number_number_of_nat _let_3))) (let ((_let_5 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex ii) ii))) (let ((_let_6 (hAPP_complex_complex uminus473333897omplex one_one_complex))) (let ((_let_7 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (let ((_let_8 (hAPP_int_real number267125858f_real _let_3))) (let ((_let_9 (hAPP_r1250527377l_real inverse_divide_real pi))) (let ((_let_10 (hAPP_real_real _let_9 _let_8))) (let ((_let_11 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_12 (hAPP_nat_nat suc _let_1))) (let ((_let_13 (hAPP_int_int bit0 _let_3))) (let ((_let_14 (hAPP_int_real number267125858f_real _let_13))) (let ((_let_15 (hAPP_r1134773055l_bool ord_less_real pi))) (let ((_let_16 (hAPP_i1948725293t_bool ord_less_int min))) (let ((_let_17 (hAPP_int_int number_number_of_int min))) (let ((_let_18 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_13)) m)) one_one_int))) (let ((_let_19 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes _let_18) _let_17)))) (let ((_let_20 (hAPP_int_nat number_number_of_nat _let_2))) (let ((_let_21 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (let ((_let_22 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int s1) _let_4))) (let ((_let_23 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int s) _let_4))) (let ((_let_24 (zcong _let_23))) (let ((_let_25 (hAPP_int_complex number528085621omplex _let_2))) (let ((_let_26 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (let ((_let_27 (hAPP_i1948725293t_bool ord_less_eq_int one_one_int))) (let ((_let_28 (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat))) (let ((_let_29 (hAPP_r1250527377l_real inverse_divide_real one_one_real))) (let ((_let_30 (hAPP_real_real _let_29 _let_8))) (let ((_let_31 (hAPP_int_int bit1 _let_2))) (let ((_let_32 (hAPP_int_real number267125858f_real _let_31))) (let ((_let_33 (hAPP_real_real _let_9 _let_32))) (let ((_let_34 (hAPP_int_nat number_number_of_nat _let_31))) (let ((_let_35 (hAPP_f229349961t_bool cOMBC_nat_nat_bool fequal_nat))) (let ((_let_36 (hAPP_int_rat number_number_of_rat _let_2))) (let ((_let_37 (hAPP_int_int number_number_of_int _let_3))) (let ((_let_38 (hAPP_real_real uminus_uminus_real one_one_real))) (let ((_let_39 (hAPP_i1948725293t_bool ord_less_int t))) (let ((_let_40 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (let ((_let_41 (hAPP_i1948725293t_bool ord_less_int pls))) (let ((_let_42 (hAPP_int_fun_int_int times_times_int _let_18))) (let ((_let_43 (hAPP_int_int _let_42 zero_zero_int))) (let ((_let_44 (hAPP_int_int _let_42 t))) (let ((_let_45 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_44) _let_43)))) (let ((_let_46 (hAPP_real_real _let_9 _let_14))) (let ((_let_47 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (let ((_let_48 (hAPP_real_real cos _let_8))) (let ((_let_49 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (let ((_let_50 (hAPP_real_real sqrt _let_32))) (let ((_let_51 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real _let_50) _let_8))) (let ((_let_52 (hAPP_real_real _let_9 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 _let_31))))) (let ((_let_53 (hAPP_r1250527377l_real times_times_real _let_8))) (let ((_let_54 (hAPP_real_real _let_53 pi))) (let ((_let_55 (hAPP_int_fun_int_int times_times_int _let_37))) (let ((_let_56 (hAPP_f1629352853nt_int cOMBB_1496585939nt_int plus_plus_int))) (let ((_let_57 (hAPP_f735247205t_bool cOMBC_983868720t_bool (hAPP_f1251097615t_bool (hAPP_f1475822739t_bool cOMBB_2027861294ol_int cOMBB_int_bool_int) fequal_int)))) (let ((_let_58 (hAPP_f423804115t_bool cOMBB_1418110531ol_int fEx_int))) (let ((_let_59 (hAPP_r265291036omplex complex zero_zero_real))) (let ((_let_60 (hAPP_i1948725293t_bool ord_less_eq_int min))) (let ((_let_61 (forall ((A_203 $$unsorted)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_203) zero_zero_int))))) (let ((_let_62 (hAPP_int_nat nat _let_37))) (let ((_let_63 (hAPP_int_int number_number_of_int pls))) (let ((_let_64 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (let ((_let_65 (hAPP_int_complex number528085621omplex min))) (let ((_let_66 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_23) one_one_int))) (let ((_let_67 (= _let_44 _let_66))) (let ((_let_68 (= (hAPP_int_int (legendre _let_17) _let_18) one_one_int))) (let ((_let_69 (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real _let_32) _let_8)) pi))) (let ((_let_70 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat one_one_rat) one_one_rat))) (let ((_let_71 (hAPP_nat_int semiri1621563631at_int zero_zero_nat))) (let ((_let_72 (hAPP_real_real sqrt _let_8))) (let ((_let_73 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real _let_72) _let_8))) (let ((_let_74 (hAPP_int_nat nat one_one_int))) (let ((_let_75 (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int))) (let ((_let_76 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat one_one_nat) one_one_nat))) (let ((_let_77 (hAPP_int_real number267125858f_real pls))) (let ((_let_78 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int one_one_int) one_one_int))) (let ((_let_79 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) one_one_int))) (let ((_let_80 (hAPP_int_real number267125858f_real _let_2))) (let ((_let_81 (hAPP_i1948725293t_bool dvd_dvd_int _let_18))) (let ((_let_82 (hAPP_int_complex number528085621omplex pls))) (let ((_let_83 (hAPP_f1485493409l_bool cOMBB_624415285l_real fconj))) (let ((_let_84 (the_real (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_83 _let_21)) (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_83 (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool ord_less_eq_real) _let_8))) (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool (hAPP_f1393328161l_bool (hAPP_f1900646853l_bool cOMBB_430461877l_real fequal_real) cos)) zero_zero_real)))))) (let ((_let_85 (hAPP_int_int number_number_of_int _let_2))) (let ((_let_86 (hAPP_f1352333353l_real (hAPP_f318350629l_real cOMBB_1946221070al_int inverse_divide_real) real_int))) (let ((_let_87 (hAPP_f1925507189l_bool cOMBB_1121934354l_real fEx_int))) (let ((_let_88 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_66) zero_zero_int)))) (let ((_let_89 (not _let_88))) (let ((_let_90 (hAPP_int_real number267125858f_real min))) (let ((_let_91 (hAPP_int_int number_number_of_int _let_31))) (let ((_let_92 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int _let_23) _let_17))) (let ((_let_93 (hAPP_nat_fun_int_int (hAPP_f2105620693nt_int cOMBC_int_nat_int power_power_int) _let_4))) (let ((_let_94 (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral))) (let ((_let_95 (not (forall ((T $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (=> (is_int T) (not (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int s) (hAPP_int_nat number_number_of_nat _let_1))) one_one_int) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 _let_1))) m)) one_one_int)) T))))))))) (let ((_let_96 (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj))) (let ((_let_97 (hAPP_int_nat number_number_of_nat pls))) (let ((_let_98 (hAPP_int_complex number528085621omplex _let_3))) (let ((_let_99 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) one_one_real))) (let ((_let_100 (hAPP_int_rat number_number_of_rat pls))) (let ((_let_101 (hAPP_complex_complex uminus473333897omplex ii))) (let ((_let_102 (hAPP_f1855025978nt_int (hAPP_f1038672605nt_int cOMBB_1506897658nt_int times_times_int) product_fst_int_int))) (let ((_let_103 (hAPP_f214467655t_bool cOMBB_182850971nt_int fequal_int))) (let ((_let_104 (hAPP_f365317245l_bool (hAPP_f1961001761l_bool cOMBB_1550063917nt_int fconj) (hAPP_f237669397t_bool (hAPP_f513299955t_bool cOMBB_1344650379nt_int fNot) (hAPP_i119638232t_bool (hAPP_f2018027565t_bool cOMBC_33652895t_bool (hAPP_f291087797t_bool _let_103 product_snd_int_int)) zero_zero_int))))) (let ((_let_105 (hAPP_int_int _let_42 skv_2))) (let ((_let_106 (= _let_66 _let_105))) (let ((_let_107 (= zero_zero_int _let_43))) (let ((_let_108 (ASSUME :args (_let_89)))) (let ((_let_109 (ASSUME :args (_let_45)))) (let ((_let_110 (ASSUME :args (_let_67)))) (let ((_let_111 (not _let_106))) (let ((_let_112 (not (is_int skv_2)))) (let ((_let_113 (or _let_112 _let_111))) (let ((_let_114 (forall ((T $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (or (not (is_int T)) (not (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 _let_1))) m)) one_one_int)) T) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int s) (hAPP_int_nat number_number_of_nat _let_1))) one_one_int)))))))) (let ((_let_115 (not _let_113))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_95)) (MACRO_SR_EQ_INTRO :args (_let_95 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (OR))) (let ((_let_118 (not _let_114))) (let ((_let_119 (_let_61))) (let ((_let_120 (ASSUME :args _let_119))) (let ((_let_121 (APPLY_UF hBOOL))) (let ((_let_122 (APPLY_UF hAPP_int_bool))) (let ((_let_123 (ASSUME :args (_let_107)))) (let ((_let_124 (APPLY_UF hAPP_i1948725293t_bool))) (let ((_let_125 (SYMM _let_110))) (let ((_let_126 (REFL :args (ord_less_int)))) (let ((_let_127 (CONG _let_126 (SYMM _let_125) :args _let_124))) (let ((_let_128 (ASSUME :args (_let_106)))) (let ((_let_129 (TRANS (CONG _let_126 (TRANS (SYMM _let_128) _let_125) :args _let_124) _let_127))) (let ((_let_130 (REFL :args (_let_43)))) (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_108 _let_110 _let_128 _let_123 _let_109) :args (_let_89 _let_45 _let_67 _let_106 _let_107)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_109)) (CONG (CONG _let_127 _let_130 :args _let_122) :args _let_121) (CONG (TRANS (CONG (SYMM _let_129) _let_130 :args _let_122) (CONG _let_129 (SYMM _let_123) :args _let_122)) :args _let_121) (FALSE_INTRO _let_108))) :args (_let_89 _let_67 _let_106 _let_107 _let_45)) :args ((not (and _let_89 _let_45 _let_67 _let_106 _let_107)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_88))) (REFL :args ((not _let_45))) (REFL :args ((not _let_67))) (REFL :args (_let_111)) (REFL :args ((not _let_107))) :args _let_117)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (_let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((hAPP_int_fun_int_int times_times_int A_203)))) :args _let_119)) _let_120 :args (_let_107 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 1)) (CONG (REFL :args (_let_113)) (MACRO_SR_PRED_INTRO :args ((= (not _let_111) _let_106))) :args _let_117)) :args ((or _let_106 _let_113))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_116) :args (_let_118)) (REWRITE :args ((=> _let_118 (not (or _let_112 (not (= _let_105 _let_66))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_118) _let_114))) (REFL :args (_let_115)) :args _let_117)) _let_116 :args (_let_115 true _let_114)) :args (_let_106 true _let_113)) _let_110 _let_109 _let_108 :args (false false _let_107 false _let_106 false _let_67 false _let_45 true _let_88)) :args ((forall ((B_94 $$unsorted) (C_52 $$unsorted) (A_116 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat B_94))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_116)) (=> (hBOOL (hAPP_nat_bool _let_1 C_52)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_116) C_52))))))) (= (hAPP_nat_real real_nat _let_1) one_one_real) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)) (hBOOL (hAPP_int_bool nat_is_nat X_1)))) (forall ((A_218 $$unsorted) (B_161 $$unsorted) (C_90 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_218) C_90)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_161) C_90)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_218) B_161)) C_90))) (forall ((Z_2 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_int_nat nat (hAPP_int_int abs_abs_int Z_2))) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Z_2) (hAPP_nat_int semiri1621563631at_int Ma))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int P R) Q) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int (hAPP_f465821005nt_int cOMBC_1964283556nt_int P) Q) R))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B))))))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat M))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 N)) K_2)))) (forall ((A_3 $$unsorted)) (let ((_let_1 (hAPP_real_real sgn_sgn_real A_3))) (let ((_let_2 (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_3)))) (and (=> (not (= A_3 zero_zero_real)) (and (=> (not _let_2) (= _let_1 (hAPP_real_real uminus_uminus_real one_one_real))) (=> _let_2 (= _let_1 one_one_real)))) (=> (= zero_zero_real A_3) (= zero_zero_real _let_1)))))) (forall ((B_93 $$unsorted) (A_115 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_115) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_93) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_115) B_93)) zero_zero_real))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) X)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Y) (hAPP_int_int (hAPP_int_fun_int_int times_times_int N_2) X))))) X)) (is_int N_2))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_nat (div_mod_nat M) N))) (let ((_let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)))) (and (=> _let_2 (= M _let_1)) (=> (not _let_2) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) N) _let_1)))))) (forall ((A_21 $$unsorted) (B_17 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_21) B_17)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int B_17) A_21)) A_21) B_17))) (= pls (hAPP_int_int uminus_uminus_int pls)) (forall ((Z_14 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_14) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Z_14) Z_14))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 W_1)) zero_zero_int)))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral Lx_6))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral _let_1 Rx_6)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral Ly_4) Ry_4)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral _let_1 Ly_4)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral Rx_6) Ry_4))))) (forall ((A_208 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_208) zero_z891286103de_int))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X)) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat X))) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat suc X)) _let_1))))) (forall ((M_18 $$unsorted) (N_38 $$unsorted) (A_128 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_128))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_128)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int _let_1 M_18)) (hAPP_nat_int _let_1 N_38))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_18) N_38)))))) (forall ((P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (= (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int)) (hAPP_int_nat phi P_3)))) (forall ((A_230 $$unsorted) (C_96 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_230) C_96) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat C_96) A_230))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B))) (exists ((Y_1 $$unsorted)) (and (hBOOL (hAPP_real_bool (deriv_real F X_2) Y_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y_1)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real F A)) (hAPP_real_real F B)))))) (forall ((A $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) A)) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) zero_zero_rat)))) (forall ((A_184 $$unsorted) (M_23 $$unsorted) (N_58 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_184))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_23) N_58)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat _let_1 M_23)) (hAPP_nat_nat _let_1 N_58)))))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (= (hBOOL (hAPP_rat_bool _let_1 A)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) A)))))) (forall ((Z_12 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Z_12) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Z_12) Z_12))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int) A)) (= (= N_1 Ma) (= (hAPP_n522471361de_int _let_1 N_1) (hAPP_n522471361de_int _let_1 Ma)))))) (forall ((A_35 $$unsorted)) (=> (is_int A_35) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_35) one_one_int) A_35))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_bool P (hAPP_real_real Q R)) (hAPP_real_bool (hAPP_f1402056515l_bool (hAPP_f824790735l_bool cOMBB_real_bool_real P) Q) R))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int bit1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_2) L_2)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit1 K_2)) (hAPP_int_int bit0 L_2)))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (= (hAPP_int_int (legacy_zgcd (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int M) (hAPP_int_int (hAPP_int_fun_int_int times_times_int N) K_2))) N) (hAPP_int_int (legacy_zgcd M) N))) (forall ((C_46 $$unsorted) (A_104 $$unsorted) (B_86 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat C_46))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A_104)) (hAPP_rat_rat _let_1 B_86))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_104) B_86))))) (hBOOL (hAPP_int_bool _let_60 min)) (forall ((B_2 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (log B_2))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y)) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real powr X) Y)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y) (hAPP_real_real _let_1 X))))))) (forall ((A_145 $$unsorted) (M_20 $$unsorted) (N_48 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_145))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral _let_1 M_20)) (hAPP_n1108039445umeral _let_1 N_48)) (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_20) N_48))))) (forall ((A_110 $$unsorted) (B_88 $$unsorted) (C_48 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_110))) (=> (= (hAPP_C498520661umeral _let_1 B_88) (hAPP_C498520661umeral _let_1 C_48)) (= C_48 B_88)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2))) (let ((_let_2 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) X)) (not (hBOOL (hAPP_nat_bool _let_2 A_3)))) (and (not (hBOOL (hAPP_nat_bool _let_2 _let_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_1) X))))))) (forall ((X_1 $$unsorted)) (= (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sqrt X_1)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_1) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (hAPP_int_int abs_abs_int L_2))) (let ((_let_2 (hAPP_int_int abs_abs_int K_2))) (= (pdivmod K_2 L_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int _let_2) _let_1)) (hAPP_int_int (div_mod_int _let_2) _let_1)))))) (forall ((N $$unsorted)) (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc N)))))) (forall ((W $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W) W))) (forall ((X_4 $$unsorted) (Y_4 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X_4) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_4) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_4) _let_1)))))) (= (hAPP_real_real sin (hAPP_real_real arccos _let_2)) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_2) _let_1))))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat N)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_nat_real real_nat (hAPP_nat_nat suc N)))) (= N (hAPP_int_nat nat (archim1246769320r_real X)))))) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat L) X_2)))) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_nat_bool P_1 X_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat L) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_2) zero_zero_nat))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) B)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A)) (hAPP_rat_rat _let_1 B))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int _let_1 Y)) (hAPP_nat_int _let_1 Z_1)) (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Y) Z_1))))) (forall ((Nat $$unsorted)) (= (hAPP_nat_nat size_size_nat (hAPP_nat_nat suc Nat)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat size_size_nat Nat)) (hAPP_nat_nat suc zero_zero_nat)))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y)) (=> (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) N) X) (= (hAPP_real_real (hAPP_n546711566l_real root N) X) Y))))) (forall ((W_5 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_5))) (let ((_let_2 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat zero_zero_rat) _let_1))) (and (=> (= _let_1 zero_zero_nat) (= one_one_rat _let_2)) (=> (not (= zero_zero_nat _let_1)) (= zero_zero_rat _let_2)))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_1)) (hBOOL (hAPP_int_bool even_odd_even_int X_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= (hAPP_real_real sqrt X_1) (hAPP_real_real sqrt Y_2)) (= Y_2 X_1))) (forall ((N_56 $$unsorted)) (= one_one_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_int_complex number528085621omplex min)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_56)))) (forall ((B_95 $$unsorted) (C_53 $$unsorted) (A_117 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_117)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_95) C_53)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B_95) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_117) C_53)))))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_3)) (hAPP_real_real _let_1 B_2))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_3) B_2)))))) (forall ((A_226 $$unsorted) (B_163 $$unsorted) (C_92 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_226))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 C_92)) B_163) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 B_163)) C_92)))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (hAPP_real_real arcsin Y))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_1)) _let_2)) (= (hAPP_real_real sin _let_2) Y) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_2) _let_1)))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real G X_1) Ma)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real cos) G) X_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real uminus_uminus_real (hAPP_real_real sin (hAPP_real_real G X_1)))) Ma))))) (forall ((C_34 $$unsorted) (D_6 $$unsorted) (A_80 $$unsorted) (B_68 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_80) B_68)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C_34) D_6)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_80) C_34)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_68) D_6)))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) K_2))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hAPP_n1699378549t_bool (ord_at238088361st_nat Ma) N_1) (image_int_nat nat (hAPP_i1948725293t_bool (ord_at875362053st_int (hAPP_nat_int semiri1621563631at_int Ma)) (hAPP_nat_int semiri1621563631at_int N_1))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (not (= N_1 Ma)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) Ma)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1))))) (forall ((A_15 $$unsorted) (B_11 $$unsorted)) (=> (is_int B_11) (=> (not (= B_11 zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_15) B_11)) one_one_int) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_15) B_11)) B_11))))) (forall ((Z_12 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real Z_12) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Z_12) Z_12))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_int (hAPP_f659380387ol_int B_1_1 B_2_1))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_int_int (div_mod_int X_1) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (= (= _let_1 one_one_int) (not (= zero_zero_int _let_1))))) (forall ((C_78 $$unsorted) (D_14 $$unsorted) (A_178 $$unsorted) (B_138 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_178) B_138)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C_78) D_14)) (=> (hBOOL (hAPP_real_bool _let_1 A_178)) (=> (hBOOL (hAPP_real_bool _let_1 C_78)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_178) C_78)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_138) D_14))))))))) (forall ((B_1_1 $$unsorted)) (is_int (code_int_of B_1_1))) (forall ((X_33 $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_33) zero_zero_nat) one_one_complex)) (forall ((A_230 $$unsorted) (C_96 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_230) C_96) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral C_96) A_230))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_rat_bool B_1_1 B_2_1))) (forall ((A_59 $$unsorted) (B_50 $$unsorted) (C_29 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_59) C_29)) B_50)) C_29) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_59) B_50)) C_29))) (forall ((P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int P_5) zOdd)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5))))) (forall ((A_228 $$unsorted) (C_94 $$unsorted) (D_19 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_228))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 C_94)) D_19) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat C_94) D_19))))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat Lx_1))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat _let_1 Rx_1)) Ry_1) (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Rx_1) Ry_1))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1948725293t_bool (hAPP_f351634443t_bool (hAPP_f1576199059t_bool cOMBB_95956018ol_int P) Q) R) (hAPP_f429384717t_bool P (hAPP_i627165055t_real Q R)))) (forall ((N_33 $$unsorted) (A_123 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_123)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_33)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_123) N_33))))))) (forall ((Ma $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= (= Ma _let_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Ma) _let_1))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract K_2) L_2) (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat (hAPP_int_rat ring_1_of_int_rat K_2)) (hAPP_int_rat ring_1_of_int_rat L_2)))) (forall ((X_1 $$unsorted)) (= (= X_1 zero_zero_complex) (= zero_zero_complex X_1))) (= negateSnd (produc713050258nt_int uminus_uminus_int)) (forall ((X $$unsorted) (N $$unsorted)) (=> (not (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int N)))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (natceiling X)) (hAPP_int_nat number_number_of_nat N)) (natceiling (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_int_real number267125858f_real N))))))) (forall ((N_26 $$unsorted)) (let ((_let_1 (hAPP_nat_int semiri1621563631at_int N_26))) (= _let_1 (hAPP_int_int number_number_of_int _let_1)))) (forall ((X $$unsorted)) (=> (is_int X) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) zero_zero_int)) (exists ((N_2 $$unsorted)) (= X (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc N_2)))))))) (forall ((A_196 $$unsorted) (N_63 $$unsorted)) (let ((_let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_196) N_63))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_196) _let_1) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral _let_1) A_196)))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat suc X_1))) (not (hBOOL (hAPP_nat_bool even_odd_even_nat X_1))))) (forall ((V_23 $$unsorted)) (= (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_23) (hAPP_int_int bit1 pls))) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex V_23)) one_one_complex))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sqrt X)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X))) (forall ((R_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_int_real real_int (archim856651990g_real R_3))) one_one_real)) R_3))) (forall ((A_148 $$unsorted) (N_51 $$unsorted) (N_50 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_148))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_51) N_50)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral one_on1645066479umeral) A_148)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral _let_1 N_51)) (hAPP_n1108039445umeral _let_1 N_50))))))) (forall ((A_225 $$unsorted) (B_162 $$unsorted) (C_91 $$unsorted) (D_18 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_225))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 B_162)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int C_91) D_18)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 C_91)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_162) D_18))))) (not (= one_one_real zero_zero_real)) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex ii) (hAPP_real_complex (hAPP_r265291036omplex complex A_3) B_2)) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real uminus_uminus_real B_2)) A_3))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) N))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= X_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X_1) Y_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (posDivAlg A B))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) zero_zero_int)))) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int posDivAlg_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A) B))) (and (=> (or _let_2 _let_3) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) A) _let_1)) (=> (not (or _let_3 _let_2)) (= _let_1 (hAPP_P1975530577nt_int (adjust B) (posDivAlg A (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) B))))))))))) (forall ((V_18 $$unsorted) (W_14 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int V_18)) (hAPP_int_int number_number_of_int W_14)) (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_18) W_14)))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_i1948725293t_bool (ord_at641636577an_int L) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int U) one_one_int)) (hAPP_i1948725293t_bool (ord_at875362053st_int L) U))) (forall ((L $$unsorted)) (=> (is_int L) (= (= pls L) (= (hAPP_int_int bit0 L) pls)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (or (hBOOL (hAPP_int_bool even_odd_even_int Y_2)) (hBOOL (hAPP_int_bool even_odd_even_int X_1))) (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) Y_2))))) (forall ((A_228 $$unsorted) (C_94 $$unsorted) (D_19 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex A_228))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 C_94)) D_19) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex C_94) D_19))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int A_3))) (= (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int B_2) C_1))) C_1) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 B_2)) C_1)))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (= Z_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int zero_zero_int) Z_1)))) (forall ((X_9 $$unsorted)) (let ((_let_1 (hAPP_nat_complex semiri2020571505omplex (hAPP_int_nat nat X_9)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_9)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex _let_1) _let_1) (hAPP_nat_complex semiri2020571505omplex (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_9))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool even_odd_even_nat X_1)))) (let ((_let_2 (hBOOL (hAPP_nat_bool even_odd_even_nat Y_2)))) (= (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat X_1) Y_2))) (or (and (not _let_1) (not _let_2)) (and _let_2 _let_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (nat_tsub (hAPP_nat_int semiri1621563631at_int X)) (hAPP_nat_int semiri1621563631at_int Y)) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat X) Y)))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (let ((_let_2 (hAPP_n1699378549t_bool dvd_dvd_nat Y))) (=> (and (not (hBOOL (hAPP_nat_bool _let_2 X))) (hBOOL (hAPP_nat_bool _let_1 Y))) (=> (hBOOL (hAPP_nat_bool _let_2 Z_1)) (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Z_1) X))) (hBOOL (hAPP_nat_bool _let_1 Z_1)))))))) (forall ((C_64 $$unsorted) (A_142 $$unsorted) (B_111 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_64))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A_142)) (hAPP_rat_rat _let_1 B_111))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_64)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_142) B_111)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (cis (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_3) B_2)) (hAPP_complex_complex (hAPP_c172932010omplex invers1025623611omplex (cis A_3)) (cis B_2)))) (forall ((C_75 $$unsorted) (A_175 $$unsorted) (B_135 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_75))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_175) B_135)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_75)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int _let_1 A_175)) (hAPP_Q1762011733de_int _let_1 B_135))))))) (hBOOL (hAPP_int_bool _let_39 zero_zero_int)) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_1) W) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int W) Z_1))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (hAPP_P1860904029l_real (hAPP_P1982799375l_real (hAPP_b1482221219l_real if_Pro313124157l_real fTrue) X) Y))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f237669397t_bool (hAPP_P877703507t_bool P R) (hAPP_P989584703t_bool Q R)) (hAPP_P989584703t_bool (hAPP_f1781059817t_bool (hAPP_f125837377t_bool cOMBS_1610675060t_bool P) Q) R))) (forall ((C_74 $$unsorted) (A_174 $$unsorted) (B_134 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_74))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_174) B_134)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_74)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A_174)) (hAPP_real_real _let_1 B_134))))))) (forall ((A_44 $$unsorted) (B_35 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_44) B_35)) B_35) (hAPP_C498520661umeral (div_mo1740067990umeral A_44) B_35))) (forall ((K_2 $$unsorted)) (= (frct (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int K_2) zero_zero_int)) zero_zero_rat)) (forall ((P_5 $$unsorted)) (=> (is_int P_5) (= (hBOOL (hAPP_int_bool zprime P_5)) (and (forall ((M_1 $$unsorted)) (=> (is_int M_1) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int M_1) P_5)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) M_1))) (or (= M_1 P_5) (= M_1 one_one_int))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) P_5)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool d22set A)))))) (forall ((X $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real _let_1 X)) K_2) (hAPP_real_real _let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) K_2)))))) (forall ((N $$unsorted)) (= (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat suc N))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) N))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_n1699378549t_bool (ord_gr660468384an_nat L) U) (hAPP_n1699378549t_bool (ord_at4362885an_nat (hAPP_nat_nat suc L)) U))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_bool (hAPP_f800510211t_bool (hAPP_f1722879237t_bool cOMBC_226598744l_bool P) Q) R) (hAPP_f54304608l_bool (hAPP_n215258509l_bool P R) Q))) (forall ((N $$unsorted)) (= N (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat zero_zero_nat) N))) (forall ((P $$unsorted)) (=> (is_bool P) (or (= P fFalse) (= P fTrue)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (bezw X Y))) (let ((_let_2 (= zero_zero_nat Y))) (let ((_let_3 (bezw Y (hAPP_nat_nat (div_mod_nat X) Y)))) (let ((_let_4 (hAPP_P1175774780nt_int product_snd_int_int _let_3))) (and (=> (not _let_2) (= _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int _let_4) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_P1175774780nt_int product_fst_int_int _let_3)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_4) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X) Y))))))) (=> _let_2 (= _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int one_one_int) zero_zero_int))))))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (z3mod K_2) L_2))) (let ((_let_2 (div_mod_int K_2))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) L_2)))) (and (=> (not _let_3) (= (hAPP_int_int _let_2 (hAPP_int_int uminus_uminus_int L_2)) _let_1)) (=> _let_3 (= (hAPP_int_int _let_2 L_2) _let_1))))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_nat_int semiri1621563631at_int N))) (= (hAPP_int_int ring_1_of_int_int _let_1) _let_1))) (forall ((B_115 $$unsorted) (C_67 $$unsorted) (A_153 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat B_115))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_153)) (=> (hBOOL (hAPP_rat_bool _let_1 C_67)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_153) C_67))))))) (= _let_99 _let_8) (forall ((C_44 $$unsorted) (D_8 $$unsorted) (A_102 $$unsorted) (B_84 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_102) B_84)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C_44) D_8)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_102) C_44)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_84) D_8)))))) (forall ((A_59 $$unsorted) (B_50 $$unsorted) (C_29 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_59) C_29)) B_50)) C_29) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_59) B_50)) C_29))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc M)) N) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real ln X)) X)))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int bit0 K_2) (hAPP_int_int pred (hAPP_int_int bit1 K_2)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_1))) (= (= Y_2 X_1) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_2) _let_1))))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_i1732201573de_int quickcheck_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (quickcheck_int_of N)) (quickcheck_int_of M))) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int N) M))) (forall ((W $$unsorted)) (= (hAPP_int_nat number_number_of_nat W) (hAPP_int_nat nat (hAPP_int_int number_number_of_int W)))) (forall ((U_1 $$unsorted) (X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real U_1) U_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) X)))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int uminus_uminus_int X_1))) (hBOOL (hAPP_int_bool even_odd_even_int X_1)))) (forall ((B_72 $$unsorted) (C_35 $$unsorted) (A_84 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat B_72))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_84)) (=> (hBOOL (hAPP_nat_bool _let_1 C_35)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_84) C_35))))))) (forall ((X $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) X))) (forall ((B_121 $$unsorted) (A_160 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_160) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) B_121)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_160) B_121)) zero_zero_real))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (or (not (= X_1 zero_zero_real)) (not (= Y_2 zero_zero_real))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_1) X_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_2) Y_2)))))) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat zero_zero_rat) _let_4) zero_zero_rat) (forall ((A_182 $$unsorted)) (= A_182 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_182) one_one_nat))) (forall ((C_34 $$unsorted) (D_6 $$unsorted) (A_80 $$unsorted) (B_68 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_80) B_68)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int C_34) D_6)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_80) C_34)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_68) D_6)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_i1948725293t_bool P R) Q) (hAPP_int_bool (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool P) Q) R))) (forall ((A_233 $$unsorted)) (=> (is_int A_233) (= A_233 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int pls)) A_233)))) (forall ((P_2 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)))) (let ((_let_2 (hBOOL P_1))) (let ((_let_3 (hBOOL P_2))) (=> (=> _let_1 (= _let_2 _let_3)) (= (and _let_3 _let_1) (and _let_2 _let_1))))))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (= Z_1 (hAPP_int_int uminus_uminus_int (hAPP_int_int uminus_uminus_int Z_1))))) _let_68 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int A) B))) (hBOOL (hAPP_int_bool _let_1 A)))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int semiri1621563631at_int M)) N))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) N_1)) (or (= Ma zero_zero_nat) (= zero_zero_nat N_1)))) (forall ((L $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (divmod_int K_1 L))) (let ((_let_2 (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int))) (let ((_let_3 (pdivmod K_1 L))) (let ((_let_4 (hAPP_f2054677283nt_int cOMBB_782625832nt_int product_Pair_int_int))) (=> (and (is_int L) (is_int K_1)) (and (=> (not (= zero_zero_int K_1)) (and (=> (= L zero_zero_int) (= (hAPP_i1524277240nt_int _let_2 K_1) _let_1)) (=> (not (= zero_zero_int L)) (= (hAPP_P1975530577nt_int (produc713050258nt_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int sgn_sgn_int L))) (hAPP_P1975530577nt_int (hAPP_P1145851913nt_int (hAPP_b40753821nt_int if_Pro1731782967nt_int (fdisj (hAPP_bool_bool (hAPP_b589554111l_bool fconj (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) L)) (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_1)) (hAPP_bool_bool (hAPP_b589554111l_bool fconj (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int L) zero_zero_int)) (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) zero_zero_int)))) _let_3) (hAPP_P1975530577nt_int (produc1518849193nt_int (hAPP_f465821005nt_int (hAPP_f1081447804nt_int cOMBS_1470252563nt_int (hAPP_f617310012nt_int (hAPP_f197974549nt_int cOMBB_638531587nt_int cOMBS_1891347093nt_int) (hAPP_f1148171384nt_int (hAPP_f334321603nt_int cOMBB_1484610687nt_int (hAPP_f1582586579nt_int cOMBC_707974837nt_int (hAPP_f251264923nt_int (hAPP_f279307923nt_int cOMBB_662120866nt_int if_Pro1731782967nt_int) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool fequal_int) zero_zero_int)))) (hAPP_i1584592887nt_int (hAPP_f465821005nt_int cOMBC_1964283556nt_int (hAPP_f1574055885nt_int _let_4 uminus_uminus_int)) zero_zero_int)))) (hAPP_f1574055885nt_int (hAPP_f960630521nt_int cOMBC_1805044090nt_int (hAPP_f142232355nt_int (hAPP_f1377453843nt_int cOMBB_320287386nt_int cOMBB_1846624359nt_int) (hAPP_f1574055885nt_int _let_4 (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int (hAPP_f1760145644nt_int (hAPP_f1629352853nt_int cOMBB_1496585939nt_int minus_minus_int) uminus_uminus_int)) one_one_int)))) (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int abs_abs_int L))))) _let_3))) _let_1)))) (=> (= K_1 zero_zero_int) (= (hAPP_i1524277240nt_int _let_2 zero_zero_int) _let_1))))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) M)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)) M))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat suc M)) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) (hAPP_nat_nat suc N)))) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (=> (is_int X_1) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) (hAPP_i1948725293t_bool sRStar P_5))) (= (hAPP_int_int (standardRes P_5) X_1) X_1)))) (forall ((M_9 $$unsorted) (N_23 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_9) N_23)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral semiri1619134803umeral M_9)) (hAPP_n1108039445umeral semiri1619134803umeral N_23))))) (forall ((B_5 $$unsorted) (A_5 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2))) (=> (not (= _let_1 zero_zero_int)) (=> (= A_3 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_5) _let_1)) (=> (= B_2 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_5) _let_1)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_5) B_5) one_one_int)))))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_int_int bit1 pls))) (let ((_let_2 (hAPP_int_int bit0 _let_1))) (let ((_let_3 (hAPP_nat_nat (div_mod_nat M) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_2))))) (or (= _let_3 one_one_nat) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 _let_1)) _let_3) (= (hAPP_int_nat number_number_of_nat _let_2) _let_3) (= zero_zero_nat _let_3)))))) (forall ((X_36 $$unsorted) (Y_28 $$unsorted) (Z_9 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex X_36))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 Y_28)) (hAPP_complex_complex _let_1 Z_9)) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex Y_28) Z_9))))) (forall ((M_25 $$unsorted) (A_185 $$unsorted) (N_60 $$unsorted) (B_142 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_185))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat _let_1 N_60)) B_142)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_25) N_60)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat _let_1 M_25)) B_142)))))) (forall ((C_63 $$unsorted) (A_141 $$unsorted) (B_110 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_63))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 A_141)) (hAPP_nat_nat _let_1 B_110))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_63)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_141) B_110)))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (= (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat _let_1)) N)))) pi)) (hAPP_int_real number267125858f_real _let_1))) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)) N)))) (forall ((N $$unsorted)) (= (hAPP_nat_real real_nat (hAPP_nat_nat suc N)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real real_nat N)) one_one_real))) (forall ((C_57 $$unsorted) (D_10 $$unsorted) (A_135 $$unsorted) (B_104 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_135) B_104)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int C_57) D_10)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) B_104)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_57)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_135) C_57)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_104) D_10)))))))) (forall ((R_3 $$unsorted)) (= (rcis R_3 zero_zero_real) (of_real_complex R_3))) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_rat number_number_of_rat W_1))) (= (= X_1 _let_1) (= _let_1 X_1)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1216375074nt_int (hAPP_f1375227553nt_int (hAPP_f1311564564nt_int cOMBS_1640193733nt_int P) Q) R) (hAPP_P1145851913nt_int (hAPP_i2104874254nt_int P R) (hAPP_i1524277240nt_int Q R)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_real real_int N))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) one_one_real))) (= (archim856651990g_real X) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int N) one_one_int)))))) (forall ((A_93 $$unsorted)) (= A_93 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_93) zero_zero_real))) (forall ((N_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real A N_2)))) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real A (hAPP_nat_nat suc N_2))) (hAPP_nat_real A N_2)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real _let_1) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_1)))) (hAPP_f352196356l_real suminf_real _let_1)))))))) (forall ((C_69 $$unsorted) (A_163 $$unsorted) (B_124 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_69))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_163) B_124)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) C_69)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int _let_1 A_163)) (hAPP_Q1762011733de_int _let_1 B_124))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y) _let_1))) zero_zero_rat))))) (forall ((S $$unsorted)) (= (exists ((K $$unsorted)) (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le1568362934t_bool S) (hAPP_n1699378549t_bool ord_atMost_nat K)))) (hBOOL (hAPP_f54304608l_bool finite_finite_nat S)))) (forall ((M_11 $$unsorted)) (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat semiri151668891at_rat M_11)) zero_zero_rat)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Z1) Z2)) W) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real Z1) W)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Z2) W)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_real real_int N))) (=> (is_int N) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) one_one_real))) (= (archim1246769320r_real X) N)))))) (forall ((X_6 $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X_6))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_6) (hAPP_nat_int _let_1 Q_5)) (hAPP_nat_int _let_1 (hAPP_nat_nat suc Q_5))))) (forall ((A $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool norRRset Ma))) (let ((_let_2 (zcong A))) (let ((_let_3 (hilbert_Eps_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool _let_2) Ma))) (hAPP_f1805168059t_bool (hAPP_f202917053t_bool cOMBC_94739984l_bool member_int) _let_1))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Ma)) (=> (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) A_1)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_2 _let_3) Ma)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int _let_3) _let_1)))))))))) (forall ((A_225 $$unsorted) (B_162 $$unsorted) (C_91 $$unsorted) (D_18 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A_225))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 B_162)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat C_91) D_18)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 C_91)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_162) D_18))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real exp_real X)) (hAPP_real_real exp_real Y))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)))) (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat one_one_rat) zero_zero_rat))) (forall ((Ma $$unsorted) (Ta $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int K_1))) (=> (is_int K_1) (=> (not (= zero_zero_int K_1)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int _let_1 Ma)) (hAPP_int_int _let_1 Ta))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Ma) Ta))))))) (forall ((V_12 $$unsorted) (W_10 $$unsorted)) (= (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_12) W_10)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real V_12)) (hAPP_int_real number267125858f_real W_10)))) (forall ((P_3 $$unsorted) (Q_2 $$unsorted)) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int P_3) Q_2)) (hAPP_int_int (div_mod_int P_3) Q_2)) (divmod_int P_3 Q_2))) (forall ((B_117 $$unsorted) (A_156 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_156)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_117) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_156) B_117)) zero_zero_int))))) (forall ((P_5 $$unsorted)) (= (archim791455193or_rat P_5) (hAPP_P1175774780nt_int (produc1298267108nt_int div_div_int) (quotient_of P_5)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real uminus_uminus_real Y))) (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Y) (hAPP_real_real uminus_uminus_real X))))) (= (hAPP_complex_complex cnj zero_zero_complex) zero_zero_complex) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) zero_zero_real)) (= (hAPP_int_real number267125858f_real min) (hAPP_real_real sgn_sgn_real X)))) (forall ((N $$unsorted) (M $$unsorted)) (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) M)) N))) (forall ((W_5 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_5))) (let ((_let_2 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int zero_zero_int) _let_1))) (and (=> (not (= _let_1 zero_zero_nat)) (= _let_2 zero_zero_int)) (=> (= zero_zero_nat _let_1) (= one_one_int _let_2)))))) (forall ((S $$unsorted)) (= (forall ((M_1 $$unsorted)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_1) N_2)) (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat N_2) S))))) (not (hBOOL (hAPP_f54304608l_bool finite_finite_nat S))))) (forall ((Ma $$unsorted)) (let ((_let_1 (hAPP_nat_nat (div_mod_nat Ma) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (= (= one_one_nat _let_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) _let_1))))) (forall ((I $$unsorted) (U_1 $$unsorted) (J_2 $$unsorted) (K_2 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I) U_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J_2) U_1)) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) J_2)) U_1)) K_2))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f352196356l_real P (hAPP_r474017924t_real Q R)) (hAPP_real_real (hAPP_f1122023986l_real (hAPP_f1786887945l_real cOMBB_1896127834l_real P) Q) R))) (forall ((L_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int minus_minus_int min))) (= (hAPP_int_int bit0 (hAPP_int_int _let_1 L_2)) (hAPP_int_int _let_1 (hAPP_int_int bit1 L_2))))) (not (hBOOL (hAPP_real_bool _let_15 zero_zero_real))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real B_2))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real A_3))) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real _let_2 C_1)) (hAPP_real_real _let_1 D_3))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_2 D_3)) (hAPP_real_real _let_1 C_1))) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_real_complex (hAPP_r265291036omplex complex A_3) B_2)) (hAPP_real_complex (hAPP_r265291036omplex complex C_1) D_3)))))) (= (hAPP_real_real tan _let_33) _let_50) (forall ((N $$unsorted) (M $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2) one_one_int) (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_2) M))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real ln X))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X))))) (forall ((X $$unsorted) (M $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int uminus_uminus_int X)) M) (hAPP_int_int (div_mod_int (hAPP_int_int uminus_uminus_int (hAPP_int_int (div_mod_int X) M))) M))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_f429384717t_bool (hAPP_f1173902867t_bool cOMBB_real_bool_int P) Q) R) (hAPP_real_bool P (hAPP_int_real Q R)))) (forall ((X_1 $$unsorted)) (= (= X_1 one_one_rat) (= one_one_rat X_1))) (forall ((X $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real exp_real X)) zero_zero_real)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat semiri984289939at_nat Ma)) (hAPP_nat_nat semiri984289939at_nat N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (and (is_int A_3) (is_int B_2)) (=> (not (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2) zero_zero_int)) (exists ((A_4 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2))) (and (is_int A_4) (= B_2 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_3) _let_1)) (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_4) B_3)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_4) _let_1) A_3) (is_int B_3))))))) (forall ((A_105 $$unsorted)) (=> (is_int A_105) (= A_105 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int zero_zero_int) A_105)))) (= (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real _let_90))) one_one_real))) (hAPP_f1676298106t_real _let_28 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat times_times_nat) _let_4))) one_one_nat)))) _let_46) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real exp_real one_one_real)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real ln Y)) Y)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real ln X)) X)))))) (forall ((A_219 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_219) zero_zero_complex) A_219)) (forall ((M $$unsorted) (K_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int fact_fact_int M)) (hAPP_int_int fact_fact_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int M) K_2)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int abs_abs_int X)) Y))) (forall ((Y $$unsorted) (X $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_3)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3)) (hAPP_real_real (hAPP_r1250527377l_real powr Y) A_3))))))) (forall ((F $$unsorted)) (=> (hBOOL (summable_real F)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real F N_2)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_f352196356l_real suminf_real F)))))) (forall ((M $$unsorted)) (= (hAPP_int_int (legacy_zgcd one_one_int) M) one_one_int)) (forall ((N_55 $$unsorted) (A_152 $$unsorted) (B_114 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_152) B_114)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_152)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_152) N_55)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat B_114) N_55)))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (is_int X) (= X (hAPP_int_int (hAPP_int_fun_int_int (hAPP_b1463609396nt_int if_int fTrue) X) Y)))) (forall ((C $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real C)) one_one_real)) (hBOOL (tendsto_nat_real (hAPP_r474017924t_real power_power_real C) zero_zero_real sequentially)))) (forall ((Ta $$unsorted) (A_1 $$unsorted) (D_1 $$unsorted)) (=> (is_int Ta) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Ta) A_1)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa))))))))) (=> (not (= X_2 Ta)) (not (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) D_1) Ta)))))))))) (forall ((A_140 $$unsorted) (C_62 $$unsorted) (B_109 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_140) C_62)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_109) C_62))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_62)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_140) B_109))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int bit1 pls))) (let ((_let_2 (hAPP_int_int bit1 _let_1))) (let ((_let_3 (hAPP_int_nat number_number_of_nat _let_2))) (let ((_let_4 (hAPP_int_fun_nat_int power_power_int B_2))) (let ((_let_5 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_1)))) (let ((_let_6 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_2)))) (let ((_let_7 (hAPP_int_fun_nat_int power_power_int A_3))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2)) _let_3) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int _let_7 _let_3)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_6 (hAPP_nat_int _let_7 _let_5))) B_2))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_6 A_3)) (hAPP_nat_int _let_4 _let_5)))) (hAPP_nat_int _let_4 _let_3))))))))))) (forall ((N_41 $$unsorted)) (let ((_let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int zero_zero_int) N_41))) (and (=> (not (= zero_zero_nat N_41)) (= _let_1 zero_zero_int)) (=> (= N_41 zero_zero_nat) (= _let_1 one_one_int))))) (forall ((M_6 $$unsorted) (N_20 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat semiri984289939at_nat M_6)) N_20) (hAPP_nat_nat semiri984289939at_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M_6) N_20)))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1))) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))))) (forall ((B_121 $$unsorted) (A_160 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_160) zero_z891286103de_int)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) B_121)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_160) B_121)) zero_z891286103de_int))))) (forall ((A_3 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) zero_zero_nat))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat D) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_2) Sa))))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat Z) X_2)) (= _let_1 _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A) B)) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat B) A)))) (= _let_73 (hAPP_real_real sin _let_46)) (forall ((A_98 $$unsorted) (C_40 $$unsorted) (B_80 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_98) C_40)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_80) C_40))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_98) B_80)))) (forall ((B_65 $$unsorted)) (= zero_zero_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex zero_zero_complex) B_65))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool (ord_gr1297742076an_int L) U)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int U) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int L) one_one_int))))) (forall ((X $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (multInv P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int _let_1 (hAPP_int_int _let_1 X))) X) P_3))))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (is_int Y) (= Y (hAPP_int_int (hAPP_int_fun_int_int (hAPP_b1463609396nt_int if_int fFalse) X) Y)))) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat one_one_nat) _let_4)) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) (hAPP_int_rat number_number_of_rat Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 pls)) Y_2)))) (forall ((B_120 $$unsorted) (A_159 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_120) A_159))) (=> (hBOOL (hAPP_real_bool _let_1 A_159)) (hBOOL (hAPP_real_bool _let_1 B_120)))))) (forall ((D $$unsorted) (F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real F X_1) L)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D)) (=> (forall ((Y_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_1) Y_1))) D)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real F Y_1)) (hAPP_real_real F X_1))))) (= zero_zero_real L))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int Y) (hAPP_int_int (div_mod_int X) Y)) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y))) (forall ((A_46 $$unsorted) (B_37 $$unsorted) (C_18 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_46))) (= (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int B_37) C_18))) C_18) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 B_37)) C_18)))) (forall ((A_68 $$unsorted) (B_56 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_68) B_56)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_68) B_56)) B_56)) A_68)) (forall ((A_239 $$unsorted) (B_167 $$unsorted) (V_15 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat V_15))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_239) B_167)) _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_239) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_167) _let_1))))) (forall ((A_37 $$unsorted)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_37) zero_zero_int))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (bolzano_bisect P_1 A B))) (let ((_let_2 (hAPP_r337325687l_real (hAPP_f1644353557l_real cOMBC_1508019322l_real (hAPP_f1644353557l_real (hAPP_f1874145443l_real cOMBB_1768400739l_real cOMBC_real_real_real) (hAPP_f1732848529l_real (hAPP_f1310479593l_real cOMBB_2092576745l_real (hAPP_f1960414057l_real cOMBB_882763271l_real inverse_divide_real)) plus_plus_real))) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_3 (hAPP_f320596107l_real (hAPP_f850851693l_real cOMBS_193881978l_real (hAPP_f1119546819l_real (hAPP_f555557763l_real cOMBB_422423973l_real cOMBB_2107848501l_real) produc865579683l_real)) _let_2))) (= (hAPP_n332733730l_real _let_1 (hAPP_nat_nat suc N_1)) (hAPP_P1860904029l_real (produc595218619l_real (hAPP_f2072293513l_real (hAPP_f1763467369l_real cOMBS_163651580l_real (hAPP_f1663701695l_real (hAPP_f774948957l_real cOMBB_3698607l_real cOMBS_902912708l_real) (hAPP_f324002831l_real (hAPP_f677014621l_real cOMBS_107495110l_real (hAPP_f1161935955l_real (hAPP_f328572565l_real cOMBB_520243667l_real cOMBS_794971624l_real) (hAPP_f517738447l_real (hAPP_f1879982819l_real cOMBB_731595089l_real (hAPP_f1076489843l_real cOMBB_415306361l_real if_Pro313124157l_real)) (hAPP_f1884005689l_bool (hAPP_f172451459l_bool cOMBB_421479067l_real (hAPP_f940061907l_bool cOMBB_1795223523l_real P_1)) _let_3)))) (hAPP_f1591894897l_real (hAPP_f644105375l_real cOMBC_467724138l_real (hAPP_f1108539711l_real (hAPP_f1109256153l_real cOMBB_44084907l_real cOMBS_511527878l_real) (hAPP_f823702159l_real (hAPP_f1040184293l_real cOMBB_557258983l_real (hAPP_f2114902373l_real cOMBB_237479429l_real produc865579683l_real)) _let_2))) cOMBI_real)))) _let_3)) (hAPP_n332733730l_real _let_1 N_1))))))) (forall ((X_44 $$unsorted) (Y_32 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_44) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_32) _let_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y_32)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_44) Y_32)))))) (forall ((X_24 $$unsorted) (N_32 $$unsorted)) (=> (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32)) (= X_24 one_one_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_24) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_24) N_32))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat nat X_1))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int uminus_uminus_int A)) _let_1) (hAPP_int_int uminus_uminus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) _let_1))))))) (forall ((B_148 $$unsorted) (A_192 $$unsorted) (C_84 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat A_192))) (=> (hBOOL (hAPP_nat_bool _let_1 C_84)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_148) C_84)))))) (forall ((A_15 $$unsorted) (B_11 $$unsorted)) (=> (not (= zero_z126310315umeral B_11)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_15) B_11)) one_on1645066479umeral) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_15) B_11)) B_11)))) (forall ((U_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real U_1) _let_1))) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1))))) (forall ((C_83 $$unsorted) (D_16 $$unsorted) (A_191 $$unsorted) (B_147 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat A_191) B_147)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat C_83) D_16)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_191) C_83)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_147) D_16)))))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_int_real number267125858f_real Y_2))))) (forall ((Z_2 $$unsorted) (P_1 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_int_bool P_1 (hAPP_nat_int semiri1621563631at_int N_2)))) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc N_2)))))) (hBOOL (hAPP_int_bool P_1 Z_2))))) (= _let_38 (hAPP_real_real sin _let_69)) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_nat_real real_nat M)) (hAPP_nat_real real_nat N)) (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))))) (forall ((P_1 $$unsorted)) (=> (and (forall ((A_2 $$unsorted) (B_4 $$unsorted) (C_3 $$unsorted)) (let ((_let_1 (hAPP_r2019696015l_real produc865579683l_real A_2))) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_2) B_4)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_4) C_3)) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real B_4) C_3))) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real _let_1 B_4)))) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real _let_1 C_3)))))) (forall ((X_2 $$unsorted)) (exists ((D_2 $$unsorted)) (and (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B_4) A_2)) D_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B_4)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_2) X_2))) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real A_2) B_4))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D_2)))))) (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_2) B_4)) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real A_2) B_4))))))) (forall ((A_3 $$unsorted)) (= (rcis zero_zero_real A_3) zero_zero_complex)) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N)) (= (hAPP_int_int (legacy_zgcd N) (hAPP_int_int (div_mod_int M) N)) (hAPP_int_int (legacy_zgcd M) N)))) (forall ((K_1 $$unsorted) (N_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (ord_at4362885an_nat zero_zero_nat))) (let ((_let_2 (hAPP_f1509287679l_real big_co604158596t_real F_2))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat F_2) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat plus_plus_nat) K_1))) (hAPP_n1699378549t_bool _let_1 N_2))) (hAPP_f1406902706l_real _let_2 (hAPP_n1699378549t_bool _let_1 K_1))) (hAPP_f1406902706l_real _let_2 (hAPP_n1699378549t_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N_2) K_1))))))) (forall ((X_1 $$unsorted)) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) sin_coeff)) (hAPP_r474017924t_real power_power_real X_1))))) (forall ((N_66 $$unsorted) (A_210 $$unsorted) (B_158 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_210) B_158)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_210)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_66)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_210) N_66)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral B_158) N_66))))))) (= (hAPP_nat_nat semiri984289939at_nat one_one_nat) one_one_nat) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (= M (hAPP_nat_nat (div_mod_nat M) N)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P1975530577nt_int (hAPP_i1216375074nt_int P R) (hAPP_i1524277240nt_int Q R)) (hAPP_i1524277240nt_int (hAPP_f1735705551nt_int (hAPP_f713949180nt_int cOMBS_1891347093nt_int P) Q) R))) (forall ((K_5 $$unsorted) (M_15 $$unsorted) (N_28 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral K_5))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (div_mo1740067990umeral M_15) N_28))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 N_28)) (hBOOL (hAPP_C24501650l_bool _let_1 M_15)))))) (forall ((L_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat minus_minus_nat L_2))) (let ((_let_2 (hAPP_n1699378549t_bool ord_less_nat M))) (=> (hBOOL (hAPP_nat_bool _let_2 N)) (=> (hBOOL (hAPP_nat_bool _let_2 L_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 N)) (hAPP_nat_nat _let_1 M)))))))) (forall ((W_12 $$unsorted)) (= (hAPP_int_rat number_number_of_rat (hAPP_int_int bit0 W_12)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat one_one_rat) one_one_rat)) (hAPP_int_rat number_number_of_rat W_12)))) (forall ((M $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong M) zero_zero_int) M))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f203520653l_real P (hAPP_r337325687l_real Q R)) (hAPP_r337325687l_real (hAPP_f1644353557l_real (hAPP_f1874145443l_real cOMBB_1768400739l_real P) Q) R))) (forall ((Ta $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) D_1)) (forall ((X_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int D))) (= (not (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K) D_1))) Ta)))) (not (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) Ta))))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (forall ((N_2 $$unsorted)) (let ((_let_1 (bolzano_bisect P_1 A B))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_P731461727l_real produc1935615926l_real (hAPP_n332733730l_real _let_1 N_2))) (hAPP_P731461727l_real produc1935615926l_real (hAPP_n332733730l_real _let_1 (hAPP_nat_nat suc N_2))))))))) (forall ((W_7 $$unsorted)) (let ((_let_1 (hAPP_int_complex number528085621omplex W_7))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex zero_zero_complex) _let_1)) _let_1) (hAPP_int_complex number528085621omplex (hAPP_int_int bit0 W_7))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1153444985nt_int (hAPP_f55007289nt_int (hAPP_f747475781nt_int cOMBB_222539774nt_int P) Q) R) (hAPP_f1375227553nt_int P (hAPP_i1584592887nt_int Q R)))) (forall ((X_35 $$unsorted) (Y_27 $$unsorted) (Q_11 $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_35) Y_27)) Q_11) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_35) Q_11)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex Y_27) Q_11)))) (forall ((X_41 $$unsorted) (Y_29 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_41) Y_29)) _let_2) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_41) _let_2)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_29) _let_2))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat _let_1)) X_41)) Y_29)))))) (forall ((X_46 $$unsorted) (Y_34 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (let ((_let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_34) _let_2) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_46) _let_2)) (=> (hBOOL (hAPP_rat_bool _let_1 X_46)) (=> (hBOOL (hAPP_rat_bool _let_1 Y_34)) (= X_46 Y_34))))))) (forall ((X $$unsorted)) (= (hAPP_complex_real re (hAPP_complex_complex cnj X)) (hAPP_complex_real re X))) (forall ((X_21 $$unsorted) (N_31 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex X_21))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_31)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_31) one_one_nat))) X_21) (hAPP_nat_complex _let_1 N_31))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r474017924t_real (hAPP_f1993765077t_real (hAPP_f895854793t_real cOMBB_1948233853l_real P) Q) R) (hAPP_f1888375463t_real P (hAPP_r474017924t_real Q R)))) (forall ((B_92 $$unsorted) (A_114 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_114) zero_zero_rat)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B_92) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_114) B_92)) zero_zero_rat))))) (forall ((M_17 $$unsorted) (N_30 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral M_17))) (let ((_let_2 (hAPP_n1108039445umeral _let_1 N_30))) (and (=> (not (= zero_zero_nat N_30)) (= _let_2 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral M_17) (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_30) one_one_nat))))) (=> (= N_30 zero_zero_nat) (= _let_2 one_on1645066479umeral)))))) (forall ((X_1 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real F N_2)))) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real F) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_2))) X_1))) (hBOOL (summable_real F))))) (forall ((A $$unsorted) (B $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted) (C_3 $$unsorted)) (let ((_let_1 (hAPP_r2019696015l_real produc865579683l_real A_2))) (=> (and (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real _let_1 B_4))) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real B_4) C_3))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_4) C_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_2) B_4))) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real _let_1 C_3)))))) (=> (forall ((X_2 $$unsorted)) (exists ((D_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D_2)) (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B_4)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B_4) A_2)) D_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_2) X_2))) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real A_2) B_4)))))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real A) B))))))) (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) (hAPP_nat_nat suc M)))) (forall ((X1_2 $$unsorted) (X2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (standardRes Ma))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (= (= (hAPP_int_int _let_1 X1_2) (hAPP_int_int _let_1 X2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X1_2) X2) Ma)))))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat _let_1) _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 W))))) (forall ((Q_2 $$unsorted) (R_3 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat Q_2) R_3) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat Q_2) (hAPP_rat_rat uminus_uminus_rat R_3)))) (= zero_zero_real (hAPP_complex_real re zero_zero_complex)) (hBOOL (hAPP_int_bool zprime _let_37)) (= _let_97 zero_zero_nat) (forall ((N $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat zero_zero_nat) N))) (forall ((C_89 $$unsorted) (D_17 $$unsorted) (A_213 $$unsorted) (B_159 $$unsorted) (R_8 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int R_8))) (=> (and (is_int R_8) (is_int D_17) (is_int C_89)) (=> (not (= zero_zero_int R_8)) (=> (and (not (= C_89 D_17)) (= A_213 B_159)) (not (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_159) (hAPP_int_int _let_1 D_17)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_213) (hAPP_int_int _let_1 C_89))))))))) (forall ((A_158 $$unsorted) (B_119 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_158) B_119))) (=> (hBOOL (hAPP_int_bool _let_1 A_158)) (hBOOL (hAPP_int_bool _let_1 B_119)))))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_real norm_norm_complex (hAPP_complex_complex cnj Z_1)) (hAPP_complex_real norm_norm_complex Z_1))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1566856189t_real P (hAPP_r474017924t_real Q R)) (hAPP_r50993370t_real (hAPP_f1163894827t_real (hAPP_f1998755145t_real cOMBB_421464275l_real P) Q) R))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_1))) (=> (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat K_1) N_1)) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) N_1))) (hBOOL (hAPP_nat_bool _let_1 Ma)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (div_mod_int A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int M) B_2)) (= (hAPP_int_int _let_1 M) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 B_2)) M)))))) (= (hAPP_complex_complex invers1449016382omplex ii) _let_101) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int bit1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int K_2) L_2)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int bit1 K_2)) (hAPP_int_int bit0 L_2)))) (= (hAPP_nat_real semiri132038758t_real zero_zero_nat) zero_zero_real) (forall ((A_110 $$unsorted) (B_88 $$unsorted) (C_48 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real A_110))) (=> (= (hAPP_real_real _let_1 C_48) (hAPP_real_real _let_1 B_88)) (= B_88 C_48)))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat U) L) (hAPP_f22106695ol_nat finite_card_nat (hAPP_n1699378549t_bool (ord_at4362885an_nat L) U)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (A_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) A_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_5) B_2)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (expi (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_3) B_2)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (expi A_3)) (expi B_2)))) (forall ((A_207 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real A_207) A_207))) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (hBOOL (hAPP_rat_bool P_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat L) X_2)))) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_rat_bool P_1 X_2)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat L) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_2) zero_zero_rat))))))) (exists ((K_4 $$unsorted)) (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real norm_norm_real (hAPP_complex_real im X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4))))) (forall ((A_25 $$unsorted) (B_20 $$unsorted)) (=> (not (= zero_z891286103de_int B_20)) (= A_25 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_25) B_20)) B_20)))) (forall ((A $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (tendsto_nat_real X_3 X_1 sequentially)) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_3) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real X_3 N_2)) A))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) A))))) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Lx_5) Ly_3)))) (let ((_let_2 (hAPP_c172932010omplex times_times_complex Rx_5))) (= (hAPP_complex_complex _let_1 (hAPP_complex_complex _let_2 Ry_3)) (hAPP_complex_complex _let_2 (hAPP_complex_complex _let_1 Ry_3)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (and (is_int Y_2) (is_int X_1)) (= (or (not (= zero_zero_int X_1)) (not (= zero_zero_int Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_1) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_2) _let_1)))))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat N_1)) (exists ((M_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) M_1) N_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2)) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) Y_2)) (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) field_1210416355s_real)))))) (forall ((Z_13 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_13) Z_13) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_13))) (forall ((C_75 $$unsorted) (A_175 $$unsorted) (B_135 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_75))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_175) B_135)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_75)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A_175)) (hAPP_int_int _let_1 B_135))))))) (forall ((A_129 $$unsorted) (N_40 $$unsorted) (N_39 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_129))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_40) N_39)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral) A_129)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral _let_1 N_40)) (hAPP_n1108039445umeral _let_1 N_39))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (= (quotient_of A_3) (quotient_of B_2)) (= B_2 A_3))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (not (= zero_zero_nat N_1)))) (forall ((K_2 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat K_2) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) N))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N)) (=> (= (hAPP_int_int (legacy_zgcd A_3) N) one_one_int) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) N)) (forall ((Y_1 $$unsorted)) (=> (is_int Y_1) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) Y_1)) B_2) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_1) N))) (= Y_1 X_2)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) X_2)) B_2) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2)) (is_int X_2)))))) (forall ((B_1_1 $$unsorted)) (is_bool (trivial_limit_nat B_1_1))) (forall ((A $$unsorted) (B $$unsorted)) (= (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) (= A B))) (forall ((A_217 $$unsorted) (M_29 $$unsorted) (B_160 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_217) B_160)) M_29) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_217) M_29)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_160) M_29)))) (forall ((X $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_3))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X) N))) (hBOOL (hAPP_nat_bool _let_1 X)))))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex one_one_complex) one_one_complex) _let_98) (forall ((F $$unsorted) (J $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H)) (exists ((B_6 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real H))) (= (hAPP_real_real F H) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) J)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_6) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real _let_1 N_1)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))))))))) (forall ((A_71 $$unsorted) (B_60 $$unsorted) (B_59 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real A_71))) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real _let_1 B_60)) (hAPP_real_real _let_1 B_59)) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B_60) B_59))))) (forall ((N_61 $$unsorted) (X_29 $$unsorted) (Y_23 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int X_29) Y_23)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_29) N_61)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int Y_23) N_61))))) (forall ((A_68 $$unsorted) (B_56 $$unsorted)) (= A_68 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (div_mod_nat A_68) B_56)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_68) B_56)) B_56)))) (= _let_82 zero_zero_complex) (forall ((A_194 $$unsorted) (B_150 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat A_194) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_150) A_194)))) (= zero_zero_rat _let_100) (forall ((N_27 $$unsorted) (Y_7 $$unsorted) (X_10 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_7) X_10)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X_10) Y_7)) N_27) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_10) N_27)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_7) N_27))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real C))) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (= (divmod_nat M N) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat zero_zero_nat) M)))) (forall ((A_227 $$unsorted) (B_164 $$unsorted) (C_93 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_227))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 B_164)) C_93) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_164) C_93))))) (forall ((N $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int N) (archim1246769320r_real (hAPP_nat_real real_nat N)))) (forall ((N $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)))) (let ((_let_3 (hAPP_real_real _let_2 X))) (let ((_let_4 (hAPP_real_real tan X))) (=> (not (= (hAPP_real_real cos X) zero_zero_real)) (=> (not (= zero_zero_real (hAPP_real_real cos _let_3))) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real _let_2 _let_4)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_4) (hAPP_int_nat number_number_of_nat _let_1)))) (hAPP_real_real tan _let_3))))))))) (forall ((N_1 $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_eq_int) N_1)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_rat P (hAPP_int_int Q R)) (hAPP_int_rat (hAPP_f1900950721nt_rat (hAPP_f1270196437nt_rat cOMBB_int_rat_int P) Q) R))) (forall ((N $$unsorted) (K_2 $$unsorted)) (=> (is_int K_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_2)) (= (hAPP_int_int (legacy_zgcd (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) N)) K_2) K_2)))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat Lx_2))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ly) Rx_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 Ly)) Rx_2)))) (forall ((N_25 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) (hAPP_nat_nat semiri984289939at_nat N_25)))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (exists ((X_2 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_1)) X_2)) (= Y (hAPP_real_real sin X_2)) (forall ((Y_1 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_1)) Y_1)) (= Y (hAPP_real_real sin Y_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_1) _let_1))) (= Y_1 X_2)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) _let_1)))))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real sin X))) one_one_real))) (forall ((N_59 $$unsorted) (M_24 $$unsorted) (X_28 $$unsorted) (Y_22 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int X_28) Y_22)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_59) M_24)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_28) N_59)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_22) M_24)))))) (forall ((A_188 $$unsorted) (B_144 $$unsorted) (C_81 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_188) B_144)) C_81)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral B_144) C_81)))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_real im (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Z_1) (hAPP_complex_complex cnj Z_1))) zero_zero_real)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (or (not (= N_1 zero_zero_nat)) (not (= Ma zero_zero_nat))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Ma) N_1))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int bit1 K_2) (hAPP_int_int succ (hAPP_int_int bit0 K_2)))) (forall ((B $$unsorted) (A $$unsorted)) (= (= zero_zero_complex A) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B) A) B))) (forall ((X_1 $$unsorted)) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) (hAPP_r474017924t_real power_power_real X_1))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Z_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Z_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y))))))) (forall ((A_103 $$unsorted) (C_45 $$unsorted) (B_85 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_103) C_45)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_85) C_45))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_103) B_85)))) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral Rx_4) Ry_2))) (let ((_let_2 (hAPP_C1594335432umeral times_1655362735umeral Lx_4))) (= (hAPP_C498520661umeral _let_2 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral Ly_2) _let_1)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral _let_2 Ly_2)) _let_1))))) (forall ((C_37 $$unsorted) (A_95 $$unsorted) (B_77 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_95) B_77)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_95) C_37)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_77) C_37))))) (forall ((B_28 $$unsorted) (A_34 $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_28) A_34)) B_28))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 K_1)) min)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) min)))) (not (= one_one_complex zero_zero_complex)) (= _let_66 _let_92) (forall ((Y $$unsorted) (U_1 $$unsorted) (X1_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool _let_1 X1_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X1_1) Y)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) U_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real inverse_inverse_real X)) Y)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real inverse_inverse_real X1_1)) U_1)))))))) (forall ((N $$unsorted)) (=> (not (= zero_zero_nat N)) (exists ((M_1 $$unsorted)) (= N (hAPP_nat_nat suc M_1))))) (forall ((M $$unsorted) (R_3 $$unsorted) (S_1 $$unsorted) (T_1 $$unsorted) (N $$unsorted)) (=> (is_int R_3) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N)) (=> (= (xzgcd M N) (hAPP_P408881810nt_int (hAPP_i1730167831nt_int produc282740534nt_int R_3) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int S_1) T_1))) (= R_3 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int S_1) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int T_1) N))))))) (forall ((B_2 $$unsorted)) (= (posDivAlg zero_zero_int B_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) zero_zero_int))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int X_1))) (let ((_let_2 (hAPP_int_int number_number_of_int Y_2))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int _let_1) _let_2)) (= zero_zero_int (hAPP_int_int (div_mod_int _let_2) _let_1)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_real_real cos X_1))) (=> (not (= zero_zero_real _let_1)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real inverse_divide_real) sin)) cos) X_1) (hAPP_real_real inverse_inverse_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) E_2)) C)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) E_2)) D))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B)) E_2)) C)) D)))) (forall ((C_66 $$unsorted) (A_144 $$unsorted) (B_113 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_66))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A_144)) (hAPP_int_int _let_1 B_113))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_66)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_144) B_113)))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool _let_1 X)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_n546711566l_real root N) X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_real im (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X) Y)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real re X)) (hAPP_complex_real im Y))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real im X)) (hAPP_complex_real re Y))))) (forall ((N $$unsorted) (J_2 $$unsorted) (K_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat J_2) K_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) N)) K_2)))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C))) (= (or (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real A) B)) (= zero_zero_real C)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B)))))) (forall ((N $$unsorted)) (= N (natceiling (hAPP_nat_real real_nat N)))) (forall ((P_1 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_2) X_1)))) (let ((_let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2)))) (=> (and _let_2 (not _let_1)) (=> (and (not _let_2) _let_1) (hBOOL P_1)))))) (= zero_zero_real (hAPP_complex_real im one_one_complex)) (forall ((C_7 $$unsorted) (A_22 $$unsorted) (B_18 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_22) B_18)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_18) C_7)) A_22) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_18) A_22)) C_7)))) (forall ((I_1 $$unsorted) (J $$unsorted) (K_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J) K_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_1) K_1)) J)))) (forall ((K_2 $$unsorted)) (=> (is_int K_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_2)) (not (forall ((N_2 $$unsorted)) (not (= K_2 (hAPP_nat_int semiri1621563631at_int N_2)))))))) (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) zero_zero_rat))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int number_number_of_int K_2) (quickcheck_int_of (hAPP_i1732201573de_int number1226105091de_int K_2)))) (forall ((A_41 $$unsorted) (B_32 $$unsorted) (C_16 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (div_mod_int A_41) C_16)) (hAPP_int_int (div_mod_int B_32) C_16))) C_16) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_41) B_32)) C_16))) (forall ((A_124 $$unsorted) (N_34 $$unsorted) (B_102 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_124) N_34) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_102) N_34)) (=> (hBOOL (hAPP_real_bool _let_1 A_124)) (=> (hBOOL (hAPP_real_bool _let_1 B_102)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_34)) (= B_102 A_124))))))) (forall ((B $$unsorted) (A $$unsorted)) (= (= zero_zero_nat A) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B) A) B))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real real_nat M)) (hAPP_nat_real real_nat N)) (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N)))) (forall ((A_61 $$unsorted)) (= zero_z891286103de_int (hAPP_Q1762011733de_int (div_mo231679042de_int zero_z891286103de_int) A_61))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_P880235623l_bool B_1_1 B_2_1))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_3)) (=> (hBOOL (hAPP_real_bool _let_1 B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (archim1246769320r_real A_3)) (archim1246769320r_real B_2))) (archim1246769320r_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_3) B_2)))))))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) one_one_nat)) N))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (=> (forall ((N_2 $$unsorted)) (not (= Z_1 (hAPP_nat_int semiri1621563631at_int N_2)))) (not (forall ((N_2 $$unsorted)) (not (= Z_1 (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc N_2)))))))))) (forall ((F $$unsorted) (L $$unsorted) (C $$unsorted)) (=> (hBOOL (tendsto_real_real F L (at_real C))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real L) zero_zero_real)) (exists ((R_1 $$unsorted)) (and (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real C) X_2))) R_1)) (not (= C X_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F X_2)) zero_zero_real)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) R_1))))))) (= (hAPP_i1732201573de_int quickcheck_of_int one_one_int) one_on1684967323de_int) (forall ((N $$unsorted) (M $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2)) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_3) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_2) M))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat B_2) A_3) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2))) (forall ((B_115 $$unsorted) (C_67 $$unsorted) (A_153 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int B_115))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_153)) (=> (hBOOL (hAPP_int_bool _let_1 C_67)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_153) C_67))))))) (= zero_zero_real (hAPP_real_real inverse_inverse_real zero_zero_real)) (forall ((V $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_i1732201573de_int number1226105091de_int V))) (let ((_let_2 (hAPP_i1732201573de_int number1226105091de_int W_1))) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int _let_1) _let_2)) (not (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int _let_2) _let_1))))))) (forall ((A_111 $$unsorted) (B_89 $$unsorted) (C_49 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A_111))) (=> (= (hAPP_rat_rat _let_1 B_89) (hAPP_rat_rat _let_1 C_49)) (= B_89 C_49)))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat) zero_zero_nat))) (forall ((V_14 $$unsorted) (B_166 $$unsorted) (C_97 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat V_14)))) (= (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_166) C_97)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 B_166)) (hAPP_rat_rat _let_1 C_97))))) (forall ((X_38 $$unsorted) (P_8 $$unsorted) (Q_12 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_38))) (= (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_8) Q_12)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_nat_real _let_1 P_8)) Q_12)))) (forall ((D_1 $$unsorted) (X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N_1))) (let ((_let_2 (hAPP_real_real inverse_inverse_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real _let_1 X_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) (hAPP_nat_nat suc zero_zero_nat))))))) (let ((_let_3 (hBOOL (hAPP_nat_bool even_odd_even_nat N_1)))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (=> (not (= X_1 zero_zero_real)) (=> (=> _let_3 (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (= _let_2 D_1))) (=> (=> _let_3 (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) zero_zero_real)) (= D_1 (hAPP_real_real uminus_uminus_real _let_2)))) (=> (=> (not _let_3) (= D_1 _let_2)) (hBOOL (hAPP_real_bool (deriv_real _let_1 X_1) D_1))))))))))) (forall ((K_5 $$unsorted) (M_15 $$unsorted) (N_28 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_5))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (div_mod_nat M_15) N_28))) (=> (hBOOL (hAPP_nat_bool _let_1 N_28)) (hBOOL (hAPP_nat_bool _let_1 M_15)))))) (not (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral) zero_z126310315umeral))) (forall ((X $$unsorted)) (= (archim791455193or_rat X) (archim1246769320r_real (ratreal X)))) (forall ((N $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat N))) (exists ((X_2 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_1))) X_2)) one_one_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat N) (hAPP_int_nat number_number_of_nat _let_1))))))) (forall ((A_231 $$unsorted) (B_165 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_231) B_165) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_165) A_231))) (forall ((B $$unsorted) (D $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat D))) (= (= D (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A) B)) (and (hBOOL (hAPP_nat_bool _let_1 A)) (hBOOL (hAPP_nat_bool _let_1 B)) (forall ((E $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat E))) (=> (and (hBOOL (hAPP_nat_bool _let_1 A)) (hBOOL (hAPP_nat_bool _let_1 B))) (hBOOL (hAPP_nat_bool _let_1 D))))))))) (forall ((P_1 $$unsorted)) (= P_1 (collect_nat P_1))) (forall ((I $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (nat_aux I) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat nat I)) N))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat K_1))) (= (= Ma N_1) (= (hAPP_nat_nat _let_1 Ma) (hAPP_nat_nat _let_1 N_1))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real R_3))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real _let_2 (hAPP_real_real cos A_3))) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real _let_2 (hAPP_real_real sin A_3))) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real R_3) _let_1))))) (forall ((X_31 $$unsorted) (Y_25 $$unsorted)) (=> (and (is_int Y_25) (is_int X_31)) (=> (not (= Y_25 X_31)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_31) Y_25))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_25) X_31)))))) (forall ((A_30 $$unsorted) (B_25 $$unsorted) (C_11 $$unsorted)) (= (hAPP_int_int (div_mod_int A_30) B_25) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_30) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_25) C_11))) B_25))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N)) K_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) K_2)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int uminus_uminus_int A_3)) B_2) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) (hAPP_int_int uminus_uminus_int B_2)))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hAPP_int_int (legacy_zgcd K_1) L) (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int (hAPP_b1463609396nt_int if_int (hAPP_int_bool (hAPP_i1948725293t_bool fequal_int L) zero_zero_int)) K_1) (hAPP_int_int (legacy_zgcd L) (hAPP_int_int (div_mod_int (hAPP_int_int abs_abs_int K_1)) (hAPP_int_int abs_abs_int L))))))) (forall ((Y $$unsorted) (X $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_3) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real powr Y) A_3)) (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3))))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted)) (= (hAPP_complex_real norm_norm_complex (rcis R_3 A_3)) (hAPP_real_real abs_abs_real R_3))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i614188481l_bool (hAPP_f252743847l_bool (hAPP_f643658017l_bool cOMBB_2046938128ol_int P) Q) R) (hAPP_f1146629647l_bool P (hAPP_i418383825t_bool Q R)))) (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N)) N))) (forall ((A_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Ma)) (=> (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)) (= (hAPP_i1948725293t_bool norRRset Ma) (image_int_int (rRset2norRR A_1 Ma) A_1))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real real_nat N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) Ma)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc N_1)) Ma)))) (forall ((X_1 $$unsorted)) (let ((_let_1 (= X_1 one_one_int))) (=> (is_int X_1) (= _let_1 _let_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_f1501066425l_bool B_1_1 B_2_1))) (forall ((A_3 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A_3) one_one_nat))) (forall ((R1 $$unsorted) (A_3 $$unsorted) (R2 $$unsorted) (B_2 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex invers1025623611omplex (rcis R1 A_3)) (rcis R2 B_2)) (rcis (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real R1) R2) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_3) B_2)))) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) X)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y) Y)))))) (forall ((N_1 $$unsorted)) (= (big_co1705425894at_nat cOMBI_nat (hAPP_n1699378549t_bool (ord_at238088361st_nat one_one_nat) N_1)) (hAPP_nat_nat fact_fact_nat N_1))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (G $$unsorted) (X_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real F (hAPP_real_real G X_1)) D_1)) (=> (not (= D_1 zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) B)) (=> (forall ((Y_1 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_1) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) Y_1))) (= (hAPP_real_real F (hAPP_real_real G Y_1)) Y_1))) (=> (hBOOL (hAPP_real_bool (isCont_real_real G) X_1)) (hBOOL (hAPP_real_bool (deriv_real G X_1) (hAPP_real_real inverse_inverse_real D_1)))))))))) (forall ((A_1 $$unsorted) (P_2 $$unsorted) (P_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z) X_2)) (= (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P_2 X_2))))))) (=> (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa) X_2)))))) (=> (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) D_1))))))) (=> (forall ((X_2 $$unsorted) (K $$unsorted)) (=> (and (is_int K) (is_int X_2)) (= (hBOOL (hAPP_int_bool P_2 X_2)) (hBOOL (hAPP_int_bool P_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K) D_1))))))) (= (exists ((X1 $$unsorted)) (and (hBOOL (hAPP_int_bool P_1 X1)) (is_int X1))) (or (exists ((X_2 $$unsorted)) (and (exists ((Xa $$unsorted)) (and (is_int Xa) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) A_1)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xa) X_2))))) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_2) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (is_int X_2))) (exists ((X_2 $$unsorted)) (and (is_int X_2) (hBOOL (hAPP_int_bool P_2 X_2)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_2) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1)))))))))))) (forall ((A_9 $$unsorted) (N_14 $$unsorted) (B_7 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_14))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_9) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_7) _let_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) B_7)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_9) B_7)))))) (forall ((N $$unsorted)) (=> (not (= one_one_nat N)) (exists ((P_4 $$unsorted)) (and (hBOOL (hAPP_nat_bool prime P_4)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_4) N)))))) (forall ((N_26 $$unsorted)) (= (hAPP_int_complex number528085621omplex (hAPP_nat_int semiri1621563631at_int N_26)) (hAPP_nat_complex semiri2020571505omplex N_26))) (forall ((A_87 $$unsorted) (B_75 $$unsorted)) (=> (is_int A_87) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_87) B_75)) B_75) A_87))) (forall ((N $$unsorted) (M $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc N)))) (hAPP_nat_int semiri1621563631at_int M)))) (forall ((A_125 $$unsorted) (N_36 $$unsorted) (N_35 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_125))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_36) N_35)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_125)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_125) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int _let_1 N_35)) (hAPP_nat_int _let_1 N_36)))))))) (forall ((X_5 $$unsorted) (Y_5 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_5) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_5) _let_1)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat X_5) Y_5)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_5) Y_5))))) (forall ((A_202 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real zero_zero_real) A_202) zero_zero_real)) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (= (hAPP_real_real (hAPP_n546711566l_real root M) (hAPP_real_real (hAPP_n546711566l_real root N) X)) (hAPP_real_real (hAPP_n546711566l_real root (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) X)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real semiri132038758t_real Ma)) (hAPP_nat_real semiri132038758t_real N_1))))) (forall ((A_220 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real zero_zero_real) A_220) A_220)) (forall ((X $$unsorted) (A_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (= (and (hBOOL (hAPP_nat_bool _let_1 N_1)) (hBOOL (hAPP_nat_bool _let_1 Ma))) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) N_1)))))) (= (hAPP_real_real tan pi) zero_zero_real) (forall ((X $$unsorted) (N_5 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) N_5)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_n546711566l_real root N_5) X)) (hAPP_real_real (hAPP_n546711566l_real root N) X))))))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int N) (hAPP_int_int fact_fact_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int N) one_one_int))) (hAPP_int_int fact_fact_int N)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1948725293t_bool (hAPP_i345030060t_bool (hAPP_f791698359t_bool cOMBC_241247961t_bool P) Q) R) (hAPP_i1948725293t_bool (hAPP_i345030060t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1671359920t_real (hAPP_f74147283t_real (hAPP_f1169087445t_real cOMBB_2129825580al_int P) Q) R) (hAPP_f766218899t_real P (hAPP_i371647666l_real Q R)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool fequal_nat X) Y))) (= X Y))) (forall ((A_133 $$unsorted) (N_46 $$unsorted) (N_45 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_133))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_46) N_45)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_133)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_133) one_one_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 N_45)) (hAPP_nat_nat _let_1 N_46)))))))) (forall ((A_205 $$unsorted) (B_156 $$unsorted)) (=> (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_205) B_156)) (or (= zero_zero_rat B_156) (= A_205 zero_zero_rat)))) (forall ((A_27 $$unsorted) (B_22 $$unsorted) (C_9 $$unsorted)) (=> (is_int C_9) (=> (not (= C_9 zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_27) B_22) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_27) C_9)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_22) C_9)))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat A_3))) (=> (and (hBOOL (hAPP_nat_bool _let_1 B_2)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) A_3)))) (=> (= B_2 C_1) (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat C_1) A_3))) (hBOOL (hAPP_nat_bool _let_1 C_1))))))) (forall ((U $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (hAPP_i1948725293t_bool (ord_at641636577an_int zero_zero_int) U)))) (forall ((A_190 $$unsorted) (B_146 $$unsorted) (K_7 $$unsorted)) (=> (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_146) K_7) A_190) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral B_146) A_190)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)))) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) Q_2)) R_3) A_3) (=> (and (=> _let_1 (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_3) B_2)))) (=> (not _let_1) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) R_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int R_3) zero_zero_int))))) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) K_2)) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)))) (forall ((A_103 $$unsorted) (C_45 $$unsorted) (B_85 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_103) C_45)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_85) C_45))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_103) B_85)))) (forall ((X_8 $$unsorted) (Q_7 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat X_8))) (= (hAPP_nat_rat _let_1 (hAPP_nat_nat suc Q_7)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat _let_1 Q_7)) X_8)))) (forall ((A_236 $$unsorted)) (= A_236 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_236) (hAPP_int_rat number_number_of_rat (hAPP_int_int bit1 pls))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) (hAPP_int_real number267125858f_real _let_1)) (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat _let_1)) N))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (=> (not (= zero_zero_int (hAPP_int_int (div_mod_int (hAPP_int_int uminus_uminus_int K_2)) L_2))) (not (= (hAPP_int_int (div_mod_int K_2) L_2) zero_zero_int)))) (forall ((X_3 $$unsorted)) (=> (forall ((R_1 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) R_1)) (exists ((K $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K) N_2)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat abs_abs_rat (hAPP_nat_rat X_3 N_2))) R_1))))))) (hBOOL (vanishes X_3)))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_2))) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat K_2) N) one_one_nat) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N))) (hBOOL (hAPP_nat_bool _let_1 M)))))) (forall ((A_224 $$unsorted) (N_68 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_Q125967240de_int power_881366806de_int A_224))) (= (hAPP_n522471361de_int _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_68)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int (hAPP_n522471361de_int _let_2 N_68)) _let_1))))) (forall ((B_155 $$unsorted) (A_204 $$unsorted)) (=> (not (= zero_zero_rat A_204)) (=> (not (= zero_zero_rat B_155)) (not (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_204) B_155)))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= X (hAPP_real_real (hAPP_n546711566l_real root N) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) N)))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Y)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int Y) (hAPP_int_int (div_mod_int X) Y)) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1576199059t_bool P (hAPP_r847664445t_bool Q R)) (hAPP_r1392521531t_bool (hAPP_f332806115t_bool (hAPP_f1177545951t_bool cOMBB_1459832681l_real P) Q) R))) (forall ((A_220 $$unsorted)) (= A_220 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral zero_z126310315umeral) A_220))) (forall ((P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)) P_3)))) (forall ((Y_6 $$unsorted) (P_6 $$unsorted) (N_10 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex Y_6))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_6) N_10)) (= (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc N_10)) P_6)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_10) P_6))) Y_6))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i2104874254nt_int (hAPP_f251264923nt_int (hAPP_f279307923nt_int cOMBB_662120866nt_int P) Q) R) (hAPP_b40753821nt_int P (hAPP_int_bool Q R)))) (forall ((A_222 $$unsorted)) (= zero_z891286103de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int zero_z891286103de_int) A_222))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sin X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_real norm_norm_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X) Y)) (hAPP_complex_real (dist_dist_complex X) Y))) (forall ((R $$unsorted) (S_4 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real R) (hAPP_real_real inverse_inverse_real S_4)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real R) S_4))) (forall ((W $$unsorted)) (= (hAPP_int_int ring_1_of_int_int W) (hAPP_int_int number_number_of_int W))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) Ma)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat N_1)) (hAPP_nat_real real_nat Ma))))) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (=> (hBOOL (vanishes X_3)) (=> (hBOOL (vanishes Y_3)) (hBOOL (vanishes (hAPP_f2062659861at_rat (hAPP_f1131305186at_rat cOMBS_nat_rat_rat (hAPP_f1830834240at_rat (hAPP_f1073644437at_rat cOMBB_1926947at_nat minus_minus_rat) X_3)) Y_3)))))) (forall ((B_90 $$unsorted) (A_112 $$unsorted) (C_50 $$unsorted)) (=> (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int C_50) A_112) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_90) A_112)) (= B_90 C_50))) (forall ((X_5 $$unsorted) (Y_5 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_5) Y_5)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_5) Y_5)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_5) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_5) _let_1))))) (forall ((B_2 $$unsorted) (B_5 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int div_div_int A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_5) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 B_5)) (hAPP_int_int _let_1 B_2)))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_2) _let_1))) (and (= zero_zero_real X_1) (= Y_2 zero_zero_real))))) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X_1) zero_zero_int) P_5)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_5) X_1)))) (forall ((N_26 $$unsorted)) (= (hAPP_int_real number267125858f_real (hAPP_nat_int semiri1621563631at_int N_26)) (hAPP_nat_real semiri132038758t_real N_26))) (hBOOL (hAPP_real_bool _let_21 _let_72)) (forall ((A_224 $$unsorted) (N_68 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_c1088319240omplex power_power_complex A_224))) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_nat_complex _let_2 N_68)) _let_1) (hAPP_nat_complex _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_68)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) X))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) one_one_real)) (= (hAPP_real_real uminus_uminus_real (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) _let_1)))) (hAPP_real_real ln _let_1))))) (forall ((N_29 $$unsorted) (K_6 $$unsorted) (M_16 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_6))) (=> (hBOOL (hAPP_int_bool _let_1 M_16)) (=> (hBOOL (hAPP_int_bool _let_1 N_29)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (div_mod_int M_16) N_29))))))) (forall ((A_207 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_207) A_207))) (forall ((A_50 $$unsorted) (C_22 $$unsorted) (B_41 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_50) B_41)) C_22) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_50) C_22)) B_41)) C_22))) (forall ((M_7 $$unsorted) (N_21 $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_7) N_21)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int semiri1621563631at_int M_7)) (hAPP_nat_int semiri1621563631at_int N_21)))) (forall ((A_234 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_234) A_234) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_234) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((A_202 $$unsorted)) (= zero_zero_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex zero_zero_complex) A_202))) (forall ((A_158 $$unsorted) (B_119 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_158) B_119))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_158)) (hBOOL (hAPP_Q2096512830t_bool _let_1 B_119)))))) (forall ((N_55 $$unsorted) (A_152 $$unsorted) (B_114 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_152) B_114)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_152)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_152) N_55)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_114) N_55)))))) (forall ((P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (hAPP_i1948725293t_bool sRStar P_5))))) (hBOOL (hAPP_rat_bool _let_47 _let_70)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (= (hAPP_int_nat nat (hAPP_int_int (div_mod_int X) Y)) (hAPP_nat_nat (div_mod_nat (hAPP_int_nat nat X)) (hAPP_int_nat nat Y))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP_f115998247l_bool (hAPP_P1876494581l_bool member180897546at_nat X_1) A_1)) (hBOOL (hAPP_P1463840893t_bool A_1 X_1)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat N_1))) (=> (not (hBOOL (hAPP_nat_bool _let_1 Ma))) (= (= Ma N_1) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat suc Ma))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r632163725t_bool (hAPP_f956464319t_bool (hAPP_f422375781t_bool cOMBC_243356514t_bool P) Q) R) (hAPP_f351634443t_bool (hAPP_r1392521531t_bool P R) Q))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) L)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int K_1) L)) zero_zero_int)))) (forall ((A $$unsorted) (B $$unsorted) (K_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int K_1))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Ma)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd K_1) Ma)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B)) Ma))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M N) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Z_2)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_1) Z_2)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_2) Z_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2))))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_nat_nat fact_fact_nat M))) (let ((_let_2 (= zero_zero_nat M))) (and (=> (not _let_2) (= _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) (hAPP_nat_nat fact_fact_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) one_one_nat))))) (=> _let_2 (= _let_1 one_one_nat)))))) (forall ((A_71 $$unsorted) (B_60 $$unsorted) (B_59 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex A_71))) (= (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex B_60) B_59)) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex _let_1 B_60)) (hAPP_complex_complex _let_1 B_59))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (and (= Ma zero_zero_nat) (= N_1 zero_zero_nat)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int semiri1621563631at_int N_1)) (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int Ma)))))) (forall ((B_36 $$unsorted) (A_45 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_36) A_45)) B_36) (hAPP_int_int (div_mod_int A_45) B_36))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat K_2) N)))) (forall ((A_232 $$unsorted)) (=> (is_int A_232) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_232) (hAPP_int_int number_number_of_int pls)) A_232))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat nat (hAPP_int_int abs_abs_int W))) (hAPP_int_nat nat (hAPP_int_int abs_abs_int Z_1))) (hAPP_int_nat nat (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int W) Z_1))))) (forall ((W_1 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat X_1))) (let ((_let_2 (hAPP_rat_fun_rat_rat times_times_rat W_1))) (= (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_2 Y_2)) (hAPP_rat_rat _let_1 Z_2)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_2 Z_2)) (hAPP_rat_rat _let_1 Y_2))) (or (= Y_2 Z_2) (= W_1 X_1)))))) (forall ((A_63 $$unsorted)) (= zero_z891286103de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_63) A_63))) (forall ((B_96 $$unsorted) (A_118 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_118)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_96)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_118) B_96))))))) (forall ((N_55 $$unsorted) (A_152 $$unsorted) (B_114 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_152) B_114)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_152)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_152) N_55)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int B_114) N_55)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (isCont_real_real (hAPP_n546711566l_real root N_1)) X_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) Y_2)) (= (hAPP_real_real uminus_uminus_real X_1) Y_2))) (forall ((A_188 $$unsorted) (B_144 $$unsorted) (C_81 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_188) B_144)) C_81)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat B_144) C_81)))) (forall ((P $$unsorted) (Q $$unsorted)) (= (hAPP_f957591787ol_nat (cOMBK_1643584600t_bool P) Q) P)) (forall ((B_72 $$unsorted) (C_35 $$unsorted) (A_84 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real B_72))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_84)) (=> (hBOOL (hAPP_real_bool _let_1 C_35)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_84) C_35))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) Y_2)) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) N))) (forall ((X $$unsorted)) (= (hAPP_complex_complex cnj (hAPP_complex_complex invers1449016382omplex X)) (hAPP_complex_complex invers1449016382omplex (hAPP_complex_complex cnj X)))) (forall ((Z_8 $$unsorted) (X_23 $$unsorted) (Y_18 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool dvd_dvd_real X_23))) (=> (hBOOL (hAPP_real_bool _let_1 Y_18)) (=> (hBOOL (hAPP_real_bool _let_1 Z_8)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Y_18) Z_8))))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat K_2) N)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat K_2) M)) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) B)) zOdd)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) zEven))))) (forall ((A_11 $$unsorted) (N_17 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_11))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_11) (hAPP_n522471361de_int _let_1 N_17)) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat suc N_17))))) (forall ((N_37 $$unsorted) (A_126 $$unsorted)) (let ((_let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_126) N_37))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_126)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_126) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_126) _let_1)) _let_1)))))) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real L) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_2) zero_zero_real))) (hBOOL (hAPP_real_bool P_1 X_2)))) (exists ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool P_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real L) X_2)))))) (forall ((A_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_rat fract zero_zero_int))) (= (hAPP_int_rat _let_1 C_1) (hAPP_int_rat _let_1 A_3)))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real times_times_real) sin)) sin) X_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_real_real cos X_1))) (hAPP_real_real sin X_1))))) (forall ((A_200 $$unsorted) (B_153 $$unsorted) (C_86 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_200) C_86)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_153) C_86)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_200) B_153)) C_86))) (forall ((A_3 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls))))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int uminus_uminus_int A_3)) _let_1) (hAPP_int_int uminus_uminus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) _let_1))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_complex_real re X)) (hAPP_complex_real norm_norm_complex X)))) (forall ((C_39 $$unsorted) (D_7 $$unsorted) (A_97 $$unsorted) (B_79 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_97) B_79)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int C_39) D_7)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_97) C_39)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_79) D_7)))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real cos X_1) (hAPP_real_real uminus_uminus_real (hAPP_real_real sin X_1))))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) N))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (exists ((K $$unsorted)) (= N_1 (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) K)))))) (forall ((X_3 $$unsorted)) (=> (hBOOL (summable_complex X_3)) (hBOOL (summable_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat im) X_3))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)) (not (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool d22set A)))))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) (hAPP_int_int (inv P_3) A_3))) one_one_int) P_3)))))) (forall ((W $$unsorted)) (= (hAPP_int_int number_number_of_int (hAPP_int_int uminus_uminus_int W)) (hAPP_int_int uminus_uminus_int (hAPP_int_int number_number_of_int W)))) (forall ((N_52 $$unsorted) (A_150 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_150)) (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_150) N_52)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) B_2)) (= (hAPP_int_int (div_mod_int A_3) B_2) (hAPP_P1175774780nt_int product_snd_int_int (posDivAlg A_3 B_2)))))) (hBOOL (tendsto_real_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real inverse_divide_real) cos)) sin) zero_zero_real (at_real _let_10))) (forall ((A $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) A)) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) zero_zero_real)))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A) B)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) zero_zero_rat)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_1) N_1))) (and (hBOOL (hAPP_int_bool even_odd_even_int X_1)) (not (= zero_zero_nat N_1))))) (forall ((N $$unsorted)) (= zero_zero_real (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_nat_real real_nat N))) pi)))) (forall ((B_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int zero_zero_int) B_2) zero_zero_int)) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_f526364711l_bool B_1_1 B_2_1))) (forall ((A_92 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_92) one_one_complex) A_92)) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int B_2))) (=> (is_int B_2) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))) (=> (not (= zero_zero_int B_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_1)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 (hAPP_int_int _let_1 C_1)) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int Q_2) C_1)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int Q_2) C_1))) R_3)))))))))) (= (hAPP_nat_int semiri1621563631at_int _let_1) one_one_int) (forall ((C_74 $$unsorted) (A_174 $$unsorted) (B_134 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_74))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_174) B_134)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_74)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int _let_1 A_174)) (hAPP_Q1762011733de_int _let_1 B_134))))))) (forall ((P_5 $$unsorted)) (= (hAPP_P1975530577nt_int (produc1518849193nt_int (hAPP_f1574055885nt_int (hAPP_f2054677283nt_int cOMBB_782625832nt_int product_Pair_int_int) abs_abs_int)) (quotient_of P_5)) (quotient_of (hAPP_rat_rat abs_abs_rat P_5)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) B_2)))) (=> (not (= A_3 B_2)) (=> _let_1 (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) A_3))) _let_1))))) (forall ((X_8 $$unsorted) (Q_7 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int X_8))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int _let_1 Q_7)) X_8) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat suc Q_7))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (is_int X) (is_int Y)) (or (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool fequal_int X) Y))) (= X Y)))) (forall ((V_2 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int V_2)) (hAPP_int_int number_number_of_int W)) (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_2) W)))) (forall ((X_20 $$unsorted) (Y_16 $$unsorted) (A_120 $$unsorted) (B_98 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int X_20))) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int _let_1 Y_16)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_120) B_98)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Y_16) B_98))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_20) A_120)) B_98))))) (forall ((A_231 $$unsorted) (B_165 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_165) A_231) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_231) B_165))) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Rx_4) Ry_2))) (let ((_let_2 (hAPP_nat_fun_nat_nat times_times_nat Lx_4))) (= (hAPP_nat_nat _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ly_2) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_2 Ly_2)) _let_1))))) (forall ((R_3 $$unsorted) (P_3 $$unsorted) (Q_2 $$unsorted)) (=> (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2) (normalize R_3)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int P_3) Q_2) one_one_int))) (forall ((A_108 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_108) zero_zero_complex) A_108)) (forall ((M_6 $$unsorted) (N_20 $$unsorted)) (= (hAPP_nat_complex semiri2020571505omplex (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M_6) N_20)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_nat_complex semiri2020571505omplex M_6)) N_20))) (forall ((M $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) (hAPP_nat_nat suc zero_zero_nat)) M)) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_n546711566l_real root N_1) X_1))) (let ((_let_2 (hAPP_f695504873l_bool cOMBC_real_real_bool (hAPP_f1393328161l_bool (hAPP_f1900646853l_bool cOMBB_430461877l_real fequal_real) (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real power_power_real) N_1))))) (let ((_let_3 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (let ((_let_4 (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool (hAPP_f1485493409l_bool cOMBB_624415285l_real fconj) _let_3)))) (let ((_let_5 (hBOOL (hAPP_real_bool _let_3 X_1)))) (let ((_let_6 (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) zero_zero_real)))) (and (=> (not _let_5) (and (=> (not _let_6) (= zero_zero_real _let_1)) (=> _let_6 (= _let_1 (hAPP_real_real uminus_uminus_real (the_real (hAPP_f1861673493l_bool _let_4 (hAPP_r1134773055l_bool _let_2 (hAPP_real_real uminus_uminus_real X_1))))))))) (=> _let_5 (= (the_real (hAPP_f1861673493l_bool _let_4 (hAPP_r1134773055l_bool _let_2 X_1))) _let_1)))))))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat D) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_2) Sa)))))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat X_2) Z)) (= _let_1 _let_1)))))) (forall ((M_12 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_nat_rat semiri151668891at_rat M_12)))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y)) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) Y)))))) (forall ((Nat_3 $$unsorted)) (not (= (hAPP_nat_nat suc Nat_3) zero_zero_nat))) (forall ((X_34 $$unsorted) (P_7 $$unsorted) (Q_10 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex X_34))) (= (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat P_7) Q_10)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex _let_1 P_7)) (hAPP_nat_complex _let_1 Q_10))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat P) Q) R) (hAPP_complex_real P (hAPP_nat_complex Q R)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 B)) (= (hBOOL (hAPP_int_bool _let_1 A)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B))))))) (forall ((A_18 $$unsorted) (C_5 $$unsorted) (B_14 $$unsorted)) (=> (not (= B_14 zero_zero_nat)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat C_5) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_18) B_14)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_18) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat C_5) B_14))) B_14)))) (forall ((Ta $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (=> (is_int Ta) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Ta) one_one_int)) B_1)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa))))))))) (=> (= X_2 Ta) (= Ta (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B)) one_one_rat)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) B))))) (forall ((A $$unsorted) (N_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B) _let_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A) B))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2))) (exists ((Y_1 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Y_1)) (hBOOL (hAPP_real_bool (deriv_real F X_2) Y_1)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F A)) (hAPP_real_real F B)))))) (forall ((B_5 $$unsorted) (A_5 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2))) (=> (not (= zero_zero_nat _let_1)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_5) _let_1) A_3) (=> (= B_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_5) _let_1)) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_5) B_5))))))) (= ratrel (collec50511176nt_int (produc973645403t_bool (hAPP_f1781059817t_bool (hAPP_f125837377t_bool cOMBS_1610675060t_bool (hAPP_f1965248563t_bool (hAPP_f1273270095t_bool cOMBB_595786433nt_int cOMBB_1344650379nt_int) _let_104)) (hAPP_f1781059817t_bool (hAPP_f326728547t_bool cOMBB_2086486755nt_int (hAPP_f461489489t_bool cOMBS_400904860l_bool _let_104)) (hAPP_f1187443546t_bool (hAPP_f11709033t_bool cOMBS_1676841879t_bool (hAPP_f223623489t_bool (hAPP_f1815301987t_bool cOMBB_650041899nt_int cOMBS_480885903t_bool) (hAPP_f1198736473t_bool (hAPP_f2042071795t_bool cOMBB_773384995nt_int _let_103) (hAPP_f167782601nt_int (hAPP_f1769710159nt_int cOMBC_2037038898nt_int (hAPP_f301246617nt_int (hAPP_f1151807883nt_int cOMBB_563965291nt_int cOMBB_47643171nt_int) _let_102)) product_snd_int_int)))) (hAPP_f167782601nt_int (hAPP_f400538607nt_int cOMBB_866192175nt_int (hAPP_f578362681nt_int cOMBC_1417754532nt_int _let_102)) product_snd_int_int))))))) (hBOOL (hAPP_C24501650l_bool _let_94 one_on1645066479umeral)) (forall ((K_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int min))) (= (hBOOL (hAPP_int_bool _let_1 K_1)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int bit1 K_1)))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real real_nat N)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_nat_real real_nat (hAPP_nat_nat suc N)))) (= N (hAPP_int_nat nat (archim1246769320r_real X)))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) zOdd)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) B)) zEven))))) (forall ((X_43 $$unsorted) (Y_31 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_43) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_31) _let_1)))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real min)) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) one_one_real)) (hBOOL (hAPP_real_bool (isCont_real_real arccos) X_1))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_complex (hAPP_n1983812447omplex P R) (hAPP_nat_real Q R)) (hAPP_nat_complex (hAPP_f219720582omplex (hAPP_f1052840010omplex cOMBS_696648398omplex P) Q) R))) (forall ((M $$unsorted) (K_2 $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) J_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) K_2)) (hAPP_nat_nat suc J_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) K_2)))))) (forall ((C_68 $$unsorted) (A_162 $$unsorted) (B_123 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_162) B_123)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_68)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_162) C_68)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_123) C_68)))))) (forall ((N_1 $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_eq_int) N_1)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat C) D) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) (= (= D C) (= A B)))) (forall ((A_11 $$unsorted) (N_17 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex A_11))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_11) (hAPP_nat_complex _let_1 N_17)) (hAPP_nat_complex _let_1 (hAPP_nat_nat suc N_17))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat minus_minus_nat Ma))) (= (hAPP_nat_nat (nat_case_nat zero_zero_nat cOMBI_nat) (hAPP_nat_nat _let_1 N_1)) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc N_1))))) (forall ((A_205 $$unsorted) (B_156 $$unsorted)) (=> (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_205) B_156)) (or (= zero_zero_real B_156) (= zero_zero_real A_205)))) (forall ((N $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc N)))) zero_zero_int))) (forall ((A_222 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real zero_zero_real) A_222) zero_zero_real)) (forall ((C_80 $$unsorted) (A_187 $$unsorted) (B_143 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_187))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_143)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C_80)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_143) C_80))))))) (forall ((A_16 $$unsorted) (B_12 $$unsorted)) (=> (not (= zero_z891286103de_int B_12)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_12) A_16)) B_12) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_16) B_12)) one_on1684967323de_int)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int X_1)) (hAPP_int_real real_int Y_2))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int C))) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A) B)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int _let_1 A)) (hAPP_Q1762011733de_int _let_1 B)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real ln X)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) one_one_real))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zEven)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X_1) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int Y_2) _let_1))))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (= (hAPP_i1948725293t_bool (wset _let_1) P_5) (hAPP_i1948725293t_bool d22set _let_1))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int N_1)) Ma)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real N_1)) (hAPP_int_real real_int Ma))))) (hBOOL fTrue) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= X_1 Y_2) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_2) X_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2))))) (forall ((X $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real abs_abs_real X)) one_one_real)) X)))) (forall ((A_200 $$unsorted) (B_153 $$unsorted) (C_86 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_200) C_86)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_153) C_86)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_200) B_153)) C_86))) (forall ((C_43 $$unsorted) (A_101 $$unsorted) (B_83 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat C_43))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_101) B_83)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A_101)) (hAPP_rat_rat _let_1 B_83)))))) (forall ((A_76 $$unsorted) (B_64 $$unsorted) (B_63 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real A_76))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 B_64)) (hAPP_real_real _let_1 B_63)) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_64) B_63))))) (forall ((A_108 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_108) zero_zero_real) A_108)) (forall ((S $$unsorted)) (=> (hBOOL (hAPP_f54304608l_bool finite_finite_nat S)) (exists ((K $$unsorted)) (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le1568362934t_bool S) (hAPP_n1699378549t_bool ord_lessThan_nat K)))))) (forall ((A_143 $$unsorted) (C_65 $$unsorted) (B_112 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_143) C_65)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_112) C_65))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) C_65)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_143) B_112))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (isCont_real_real sin) X_1))) (forall ((C_57 $$unsorted) (D_10 $$unsorted) (A_135 $$unsorted) (B_104 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_135) B_104)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C_57) D_10)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) B_104)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_57)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_135) C_57)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_104) D_10)))))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (exists ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real inverse_inverse_real (hAPP_nat_real real_nat (hAPP_nat_nat suc N_2)))) X))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_i2112223885l_bool member_int X_1))) (or (hBOOL (hAPP_f448129468l_bool _let_1 zOdd)) (hBOOL (hAPP_f448129468l_bool _let_1 zEven))))) (forall ((X_41 $$unsorted) (Y_29 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_41) _let_2)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex Y_29) _let_2))) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex _let_1)) X_41)) Y_29)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X_41) Y_29)) _let_2))))) (forall ((P $$unsorted)) (=> (is_int P) (= P (hAPP_int_int cOMBI_int P)))) (not (= zero_zero_real _let_10)) (forall ((K_2 $$unsorted) (L_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I) J_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) L_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) L_2)))))) (forall ((A_3 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool _let_1 Y)) (= (hAPP_real_real (hAPP_r1250527377l_real powr (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) Y)) A_3) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3)) (hAPP_real_real (hAPP_r1250527377l_real powr Y) A_3))))))) (forall ((A_88 $$unsorted) (B_76 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_88) B_76)) B_76) A_88)) (forall ((B_1_1 $$unsorted)) (is_int (archim856651990g_real B_1_1))) (forall ((N_33 $$unsorted) (A_123 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat one_one_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_123)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_33)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_123) N_33))))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int K_2))) (= (hAPP_int_int (legacy_zgcd (hAPP_int_int _let_1 M)) (hAPP_int_int _let_1 N)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int abs_abs_int K_2)) (hAPP_int_int (legacy_zgcd M) N))))) (forall ((B_2 $$unsorted) (X $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 A_3)) (=> (hBOOL (hAPP_nat_bool _let_1 B_2)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2))))))) (forall ((N_49 $$unsorted) (A_147 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral one_on1645066479umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_147)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_147) N_49)))))) (forall ((Z_1 $$unsorted)) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_complex_real re Z_1)) (hAPP_real_real uminus_uminus_real (hAPP_complex_real im Z_1))) (hAPP_complex_complex cnj Z_1))) (forall ((X_34 $$unsorted) (P_7 $$unsorted) (Q_10 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral X_34))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral _let_1 P_7)) (hAPP_n1108039445umeral _let_1 Q_10)) (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat P_7) Q_10))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int K_2) N) one_one_int) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) M)) N) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int M) N)))) (forall ((Ma $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int Ma)) Z_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) (hAPP_int_nat nat Z_2))))) (forall ((N_13 $$unsorted) (A_8 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_8)) (hBOOL (hAPP_real_bool _let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_8) (hAPP_nat_nat suc N_13))))))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real one_one_real))) (= (hBOOL (hAPP_real_bool _let_1 Y_2)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sqrt Y_2)))))) (forall ((D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool coprime D_3))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))) (hBOOL (hAPP_nat_bool _let_1 A_3))))) (forall ((A_121 $$unsorted) (C_54 $$unsorted) (B_99 $$unsorted) (D_9 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_121) B_99)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int C_54) D_9)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_121) C_54)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_99) D_9)))) (forall ((A_107 $$unsorted)) (= A_107 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_107) zero_z891286103de_int))) (forall ((N_43 $$unsorted) (A_131 $$unsorted)) (let ((_let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_131) N_43))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A_131)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_131) _let_1)))))) (forall ((A_3 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_nat_real real_nat A_3))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) X)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (natceiling X)) A_3) (natceiling (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) _let_1)))))) (forall ((X_6 $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat X_6))) (= (hAPP_nat_rat _let_1 (hAPP_nat_nat suc Q_5)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_6) (hAPP_nat_rat _let_1 Q_5))))) (forall ((C_1 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong C_1) D_3) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) C_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) D_3)) M))))) (forall ((A $$unsorted) (Ma $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool (bnorRset A) Ma))) (=> (is_int X_1) (=> (not (= zero_zero_int X_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) Ma)) (= (big_co1548731110nt_int cOMBI_int (image_int_int (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int times_times_int) X_1) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (big_co1548731110nt_int cOMBI_int _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_1) (hAPP_f957591787ol_nat finite_card_int _let_1))))))))) (forall ((A $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (hAPP_i1948725293t_bool d22set A)))) (forall ((C_38 $$unsorted) (A_96 $$unsorted) (B_78 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int C_38))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_96) B_78)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A_96)) (hAPP_int_int _let_1 B_78)))))) (forall ((F $$unsorted) (K_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (not (= B A)) (=> (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real F X_2) K_1))) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real F B)) (hAPP_real_real F A)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B) A)) K_1))))) (= _let_63 zero_zero_int) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_1))) (let ((_let_2 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real T)) (hAPP_real_real abs_abs_real X_1))) (= (hAPP_real_real cos X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real (hAPP_f451358433l_real (hAPP_f335634176l_real cOMBS_337378985l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min))) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat div_div_nat) (hAPP_int_nat number_number_of_nat _let_2))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) zero_zero_real))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real T) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) (hAPP_int_real number267125858f_real _let_2))) (hAPP_nat_real real_nat N_1))) pi)))) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1))))))))) (forall ((A_220 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat zero_zero_nat) A_220) A_220)) (forall ((A_3 $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_3))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_3) N))) (hBOOL (hAPP_nat_bool _let_1 A_3)))))) (forall ((A_47 $$unsorted) (B_38 $$unsorted) (C_19 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (div_mod_nat A_47) C_19)) B_38)) C_19) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_47) B_38)) C_19))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc (hAPP_nat_nat suc M))) _let_1) (hAPP_nat_nat (div_mod_nat M) _let_1)))) (forall ((X $$unsorted) (Y $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (multInv P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) Y) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int _let_1 X)) (hAPP_int_int _let_1 Y)) P_3)))))) (forall ((X_33 $$unsorted)) (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_33) zero_zero_nat) one_on1645066479umeral)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))))))) (forall ((K_2 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat suc zero_zero_nat)) K_2))) (forall ((A_196 $$unsorted) (N_63 $$unsorted)) (let ((_let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_196) N_63))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat _let_1) A_196) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_196) _let_1)))) (forall ((N_61 $$unsorted) (X_29 $$unsorted) (Y_23 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral X_29) Y_23)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_29) N_61)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral Y_23) N_61))))) (forall ((M $$unsorted) (N $$unsorted) (R_5 $$unsorted) (S_3 $$unsorted) (S_1 $$unsorted) (T_2 $$unsorted) (T_1 $$unsorted) (Rn $$unsorted) (Sn_1 $$unsorted) (Tn_1 $$unsorted) (R_3 $$unsorted)) (=> (is_int Rn) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) R_3)) (=> (= (hAPP_P408881810nt_int (hAPP_i1730167831nt_int produc282740534nt_int Rn) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Sn_1) Tn_1)) (xzgcda M N R_5 R_3 S_3 S_1 T_2 T_1)) (=> (= R_5 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int S_3) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int T_2) N))) (=> (= R_3 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int S_1) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int T_1) N))) (= Rn (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Sn_1) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Tn_1) N))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_int (hAPP_P2110489235nt_int P R) (hAPP_P1175774780nt_int Q R)) (hAPP_P1175774780nt_int (hAPP_f521271395nt_int (hAPP_f1914742907nt_int cOMBS_2019229620nt_int P) Q) R))) (forall ((P_5 $$unsorted)) (hBOOL (hAPP_f448129468l_bool (resSet P_5) (hAPP_i1948725293t_bool sRStar P_5)))) (forall ((M $$unsorted) (N $$unsorted) (R_5 $$unsorted) (R_3 $$unsorted) (S_3 $$unsorted) (S_1 $$unsorted) (T_2 $$unsorted) (T_1 $$unsorted) (K_2 $$unsorted)) (=> (is_int K_2) (=> (exists ((Sn $$unsorted) (Tn $$unsorted)) (= (hAPP_P408881810nt_int (hAPP_i1730167831nt_int produc282740534nt_int K_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Sn) Tn)) (xzgcda M N R_5 R_3 S_3 S_1 T_2 T_1))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) R_3)) (= (hAPP_int_int (legacy_zgcd R_5) R_3) K_2))))) (forall ((A_167 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_167) A_167)))) (forall ((X_45 $$unsorted) (Y_33 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_45) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_33) _let_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y_33)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_45) Y_33)))))) (forall ((A_69 $$unsorted) (B_57 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_69) B_57)) B_57))) (forall ((B_69 $$unsorted) (A_81 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_81)) (=> (hBOOL (hAPP_real_bool _let_1 B_69)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_81) B_69))))))) (forall ((M_7 $$unsorted) (N_21 $$unsorted)) (= (hAPP_nat_nat semiri984289939at_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_7) N_21)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat semiri984289939at_nat M_7)) (hAPP_nat_nat semiri984289939at_nat N_21)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc M)) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N))))))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Lx_2))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 Ly)) Rx_2) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real Ly) Rx_2))))) (forall ((A_182 $$unsorted)) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_182) one_one_nat) A_182)) (forall ((X_37 $$unsorted)) (=> (is_int X_37) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_37) one_one_nat) X_37))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A) B)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) zero_zero_int))))) (forall ((A $$unsorted)) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (hBOOL (monoseq_real A)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real A zero_zero_nat))) (forall ((N_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_2))) (let ((_let_2 (ord_at4362885an_nat zero_zero_nat))) (let ((_let_3 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))) (let ((_let_4 (hAPP_f1509287679l_real big_co604158596t_real _let_3))) (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real (hAPP_f352196356l_real suminf_real _let_3)) (hAPP_r1134773055l_bool (ord_at1589558736t_real (hAPP_f1406902706l_real _let_4 (hAPP_n1699378549t_bool _let_2 _let_1))) (hAPP_f1406902706l_real _let_4 (hAPP_n1699378549t_bool _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat _let_1) one_one_nat))))))))))))))) (forall ((K_2 $$unsorted)) (not (= pls (hAPP_int_int bit1 K_2)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_P1463840893t_bool B_1_1 B_2_1))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_1) L)) (exists ((N_2 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat K_1) N_2) L)))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int Lx_6))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int _let_1 Ly_4)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int Rx_6) Ry_4)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int _let_1 Rx_6)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int Ly_4) Ry_4))))) (forall ((N_11 $$unsorted) (A_7 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_7)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_7) one_one_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_7) (hAPP_nat_nat suc N_11))) one_one_nat))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_n546711566l_real P (hAPP_nat_nat Q R)) (hAPP_n546711566l_real (hAPP_f1904307534l_real (hAPP_f224989205l_real cOMBB_1419615765al_nat P) Q) R))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real X)) one_one_real)) (exists ((Z $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)) Z)) (= X (hAPP_real_real tan Z)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Z) _let_1))))))) (forall ((V_13 $$unsorted) (W_11 $$unsorted) (Z_10 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_13) W_11))) Z_10) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex V_13)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex W_11)) Z_10)))) (forall ((N_1 $$unsorted)) (= (hAPP_nat_real (diffs_real sin_coeff) N_1) (hAPP_nat_real cos_coeff N_1))) (forall ((N $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)) N) (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) pi)))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N))) (let ((_let_2 (= M zero_zero_nat))) (and (=> (not _let_2) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) one_one_nat)) N)) _let_1)) (=> _let_2 (= N _let_1)))))) (forall ((B_117 $$unsorted) (A_156 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) A_156)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int B_117) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_156) B_117)) zero_z891286103de_int))))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (legendre A_3) P_3))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_3) A_3)))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) zero_zero_int) P_3)))) (and (=> _let_3 (= _let_1 zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= one_one_int _let_1)) (=> (not _let_2) (= _let_1 (hAPP_int_int number_number_of_int min)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y)) X))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_complex_complex P (hAPP_nat_complex Q R)) (hAPP_nat_complex (hAPP_f1646117269omplex (hAPP_f1457396693omplex cOMBB_117013006ex_nat P) Q) R))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real sqrt X_1)) zero_zero_real)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (ratreal X)) (ratreal Y)) (ratreal (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X) Y)))) (forall ((A_189 $$unsorted) (B_145 $$unsorted) (C_82 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_189) B_145)) C_82)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_189) C_82)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (div_mod_int X) Y))))))) (forall ((C_44 $$unsorted) (D_8 $$unsorted) (A_102 $$unsorted) (B_84 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_102) B_84)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C_44) D_8)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_102) C_44)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_84) D_8)))))) (forall ((B_74 $$unsorted) (A_86 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_86) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_74) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_86) B_74)) zero_zero_int))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) E_2)) C)) D)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) E_2)) C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B) E_2)) D))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat semiri151668891at_rat Ma)) (hAPP_nat_rat semiri151668891at_rat N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)))) (forall ((B_73 $$unsorted) (A_85 $$unsorted) (C_36 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int B_73))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_36)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_85)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_85) C_36))))))) (forall ((M $$unsorted) (N $$unsorted)) (= (divmod_nat M N) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)) (hAPP_nat_nat (div_mod_nat M) N)))) (forall ((P $$unsorted) (X $$unsorted)) (or (hBOOL (hAPP_f448129468l_bool fEx_int P)) (not (hBOOL (hAPP_int_bool P X))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (legacy_zgcd I) J_2)) J_2))) (=> (= t zero_zero_int) (= _let_66 zero_zero_int)) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_3) B_2)) _let_1)) A_3) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B_2) A_3)) _let_1)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (and (= N_1 zero_zero_nat) (= zero_zero_nat Ma)) (= (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int N_1)) (hAPP_nat_int semiri1621563631at_int Ma)))) (forall ((C_39 $$unsorted) (D_7 $$unsorted) (A_97 $$unsorted) (B_79 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_97) B_79)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral C_39) D_7)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_97) C_39)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_79) D_7)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) C_1)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_2) C_1))) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (div_mod_int A_3) C_1)) (hAPP_int_int (div_mod_int B_2) C_1))) C_1)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2)) C_1))) (forall ((P_5 $$unsorted) (A $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) (hAPP_i1948725293t_bool (wset A) P_5))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P1145851913nt_int (hAPP_i2104874254nt_int P R) Q) (hAPP_i1216375074nt_int (hAPP_P621635040nt_int (hAPP_f1582586579nt_int cOMBC_707974837nt_int P) Q) R))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc M)) (hAPP_nat_nat suc N))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (div_mod_int (hAPP_int_int uminus_uminus_int A_3)) B_2))) (let ((_let_2 (hAPP_int_int (div_mod_int A_3) B_2))) (let ((_let_3 (= _let_2 zero_zero_int))) (and (=> (not _let_3) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B_2) _let_2) _let_1)) (=> _let_3 (= zero_zero_int _let_1))))))) (forall ((A $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_1))) (= (= zero_zero_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A) _let_1)) (and (= A zero_zero_rat) (not (= zero_zero_nat _let_1)))))) (forall ((Ma $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Ma) (hAPP_int_nat nat (hAPP_int_int abs_abs_int Z_2)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int semiri1621563631at_int Ma)) Z_2)))) (forall ((Ma $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)) (not (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool (bnorRset A) Ma)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_int_rat number_number_of_rat X_1)) (hAPP_int_rat number_number_of_rat Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) Y_2)))) (forall ((C_27 $$unsorted) (A_57 $$unsorted) (B_48 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_27))) (= (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int A_57) B_48)) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 A_57)) (hAPP_int_int _let_1 B_48))))) (= (hAPP_int_int uminus_uminus_int one_one_int) min) (forall ((A_202 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral zero_z126310315umeral) A_202))) (forall ((A_200 $$unsorted) (B_153 $$unsorted) (C_86 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_200) B_153)) C_86) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_200) C_86)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_153) C_86)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real sin X))) (let ((_let_2 (hAPP_real_real cos X))) (= one_one_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_2) _let_2)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_1) _let_1)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (K_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) K_2) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2))) (hAPP_int_int (div_mod_int A_3) B_2))) K_2))) (forall ((C_79 $$unsorted) (D_15 $$unsorted) (A_179 $$unsorted) (B_139 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_179) B_139)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat C_79) D_15)) (=> (hBOOL (hAPP_nat_bool _let_1 B_139)) (=> (hBOOL (hAPP_nat_bool _let_1 C_79)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_179) C_79)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_139) D_15))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (=> (= F (hAPP_n546711566l_real Diff zero_zero_nat)) (=> (forall ((M_1 $$unsorted) (X_2 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) X_2) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) X_2)))) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_1))) (and (= (hAPP_real_real F X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real T)) (hAPP_real_real abs_abs_real X_1))))))))) (forall ((V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_int_nat number_number_of_nat V_2)) one_one_nat))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int V_2) pls)))) (and (=> (not _let_2) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int pred V_2)) _let_1)) (=> _let_2 (= zero_zero_nat _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_1 (standardRes M))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 X)) (hAPP_int_int _let_1 Y))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y)) M))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N))) (let ((_let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (and (=> _let_2 (= zero_zero_nat _let_1)) (=> (not _let_2) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) N)) _let_1))))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (= (or (= Ma N_1) (= zero_zero_nat K_1)) (= (hAPP_nat_nat _let_1 Ma) (hAPP_nat_nat _let_1 N_1))))) (forall ((L $$unsorted) (U $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (hAPP_i1948725293t_bool (ord_at875362053st_int L) U)))) (forall ((A_89 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real one_one_real) A_89) A_89)) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B)) zero_zero_rat)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) zero_zero_int))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) Y)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (natceiling X)) (natceiling Y))))) (forall ((K_2 $$unsorted)) (=> (is_int K_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) K_2)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_2)) (= (hAPP_nat_int semiri1621563631at_int N_2) K_2)))))) (= (hAPP_nat_nat nat_size zero_zero_nat) zero_zero_nat) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i371647666l_real (hAPP_f1352333353l_real (hAPP_f318350629l_real cOMBB_1946221070al_int P) Q) R) (hAPP_r1250527377l_real P (hAPP_int_real Q R)))) (forall ((C_41 $$unsorted) (A_99 $$unsorted) (B_81 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat C_41))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 A_99)) (hAPP_nat_nat _let_1 B_81))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_99) B_81))))) (forall ((K_1 $$unsorted) (F $$unsorted) (N_1 $$unsorted)) (=> (is_int K_1) (=> (forall ((I_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_2) N_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int F (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_2) one_one_nat))) (hAPP_nat_int F I_2)))) one_one_int)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int F zero_zero_nat)) K_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) (hAPP_nat_int F N_1))) (exists ((I_2 $$unsorted)) (and (= (hAPP_nat_int F I_2) K_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_2) N_1))))))))) (forall ((A_73 $$unsorted) (A_72 $$unsorted) (B_61 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_73) B_61)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_72) B_61)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_73) A_72)) B_61))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_2) one_one_int)) A_3))) one_one_int) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) (hAPP_int_int _let_1 B_2))) (hAPP_int_int _let_1 A_3)))))) (forall ((Z_1 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int uminus_uminus_int Z_1)) Z_1) zero_zero_int)) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X)) (= (hAPP_int_nat nat (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_int_nat nat X)) N)))) (forall ((X_22 $$unsorted) (Y_17 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_22) _let_2)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_17) _let_2))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat _let_1)) X_22)) Y_17)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat X_22) Y_17)) _let_2))))) (forall ((D $$unsorted)) (= (collec1347809874nt_int (produc93441119t_bool (hAPP_f428220345t_bool (hAPP_f654702867t_bool cOMBB_591320580ol_int (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int D)))) ord_less_int))) (int_ge_less_than2 D))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos Y)) (hAPP_real_real sin X))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real sin Y)) (hAPP_real_real cos X))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat times_times_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) one_one_nat))) (let ((_let_2 (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X_1)) one_one_real)) (= (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_2 (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_2 (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real inverse_divide_real one_one_real)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) _let_1)))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1)))) (hAPP_real_real arctan X_1)))))) (forall ((B_65 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real zero_zero_real) B_65) zero_zero_real)) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat I))) (=> (hBOOL (hAPP_nat_bool _let_1 J_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat J_2) K_2)) (hBOOL (hAPP_nat_bool _let_1 K_2)))))) (forall ((A_188 $$unsorted) (B_144 $$unsorted) (C_81 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_188) B_144)) C_81)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_144) C_81)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) B)))))) (forall ((Z_2 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real Y_2))) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_1) X_3)) (=> (hBOOL (hAPP_real_bool _let_1 X_1)) (=> (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) X_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) Z_2)))) (hBOOL (hAPP_real_bool _let_1 (comple124823625p_real X_3)))))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (is_bool B_2_1) (is_bool (hAPP_bool_bool B_1_1 B_2_1)))) (forall ((X_22 $$unsorted) (Y_17 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_22) Y_17)) _let_2) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_22) _let_2)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_17) _let_2))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_1)) X_22)) Y_17)))))) (not (hBOOL (hAPP_int_bool _let_26 min))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P731461727l_real P (hAPP_n332733730l_real Q R)) (hAPP_nat_real (hAPP_f73570213t_real (hAPP_f918606171t_real cOMBB_64450052al_nat P) Q) R))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral semiri1619134803umeral Ma)) (hAPP_n1108039445umeral semiri1619134803umeral N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))) (forall ((X_40 $$unsorted) (N_69 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int X_40))) (let ((_let_2 (hAPP_n522471361de_int _let_1 N_69))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int _let_2) _let_2) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_69)))))) (forall ((W_1 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex X_1))) (let ((_let_2 (hAPP_c172932010omplex times_times_complex W_1))) (= (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_2 Y_2)) (hAPP_complex_complex _let_1 Z_2)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_2 Z_2)) (hAPP_complex_complex _let_1 Y_2))) (or (= Z_2 Y_2) (= X_1 W_1)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (= zero_zero_real (hAPP_real_real sin X)) (exists ((N_2 $$unsorted)) (and (= X (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_2)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hBOOL (hAPP_nat_bool even_odd_even_nat N_2))))))) (forall ((A $$unsorted)) (= (= zero_zero_real A) (= zero_zero_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_rat ring_1_of_int_rat K_2) (hAPP_int_rat (hAPP_int_fun_int_rat fract K_2) one_one_int))) (forall ((A_216 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real one_one_real) A_216) A_216)) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real sin X)) (hAPP_real_real cos Y))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos X)) (hAPP_real_real sin Y))) (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y)))) (forall ((N_1 $$unsorted)) (= (= zero_zero_nat N_1) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int semiri1621563631at_int N_1)) zero_zero_int)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) (hAPP_real_real uminus_uminus_real A))) (= X_1 A))) (= (of_real_complex _let_90) _let_5) (forall ((Y $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_real_real arctan Y)))) (forall ((B_122 $$unsorted) (A_161 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_161) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B_122) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_161) B_122)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= (hAPP_nat_int semiri1621563631at_int X_1) (hAPP_nat_int semiri1621563631at_int Y_2)) (= Y_2 X_1))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real X_1)) zero_zero_real)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) pls)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool fequal_real X) Y))) (= X Y))) (forall ((A_125 $$unsorted) (N_36 $$unsorted) (N_35 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_125))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_36) N_35)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) A_125)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_125) one_on1645066479umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral _let_1 N_35)) (hAPP_n1108039445umeral _let_1 N_36)))))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_nat_complex semiri2020571505omplex N))) (= _let_1 (hAPP_complex_complex cnj _let_1)))) (forall ((C_41 $$unsorted) (A_99 $$unsorted) (B_81 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real C_41))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_99)) (hAPP_real_real _let_1 B_81))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_99) B_81))))) (forall ((A_27 $$unsorted) (B_22 $$unsorted) (C_9 $$unsorted)) (=> (not (= C_9 zero_z891286103de_int)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_27) C_9)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_22) C_9)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_27) B_22)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) C)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) C))) (or (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B) A)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C) zero_zero_real))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)))))) (forall ((D $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat D))) (= (and (= (hAPP_nat_nat _let_1 B) one_one_nat) (= (hAPP_nat_nat _let_1 A) one_one_nat)) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A) B)) one_one_nat)))) (forall ((C $$unsorted)) (let ((_let_1 (hAPP_real_real abs_abs_real C))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) one_one_real)) (hBOOL (tendsto_nat_real (hAPP_r474017924t_real power_power_real _let_1) zero_zero_real sequentially))))) (forall ((N_61 $$unsorted) (X_29 $$unsorted) (Y_23 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int X_29) Y_23)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_29) N_61)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_23) N_61))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat M) N)) (hBOOL (hAPP_nat_bool _let_1 M)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A)) (= (= (hAPP_nat_int _let_1 Ma) (hAPP_nat_int _let_1 N_1)) (= Ma N_1))))) (forall ((A_145 $$unsorted) (M_20 $$unsorted) (N_48 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_145))) (= (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_20) N_48)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real _let_1 M_20)) (hAPP_nat_real _let_1 N_48))))) (forall ((M_19 $$unsorted) (N_44 $$unsorted) (A_132 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_132))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A_132)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real _let_1 M_19)) (hAPP_nat_real _let_1 N_44))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_19) N_44)))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X)))) (not (= Y X)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (=> (hBOOL (hAPP_nat_bool even_odd_even_nat N_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (deriv_real _let_1 X_1) (hAPP_real_real inverse_inverse_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real uminus_uminus_real (hAPP_nat_real real_nat N_1))) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real _let_1 X_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) (hAPP_nat_nat suc zero_zero_nat)))))))))))) (forall ((Diff $$unsorted) (F $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (=> (= (hAPP_n546711566l_real Diff zero_zero_nat) F) (=> (forall ((M_1 $$unsorted) (T $$unsorted)) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) T)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) H))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) T) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) T))))) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real H))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) T)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real T) H)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1))) (hAPP_real_real F H)))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool _let_1 Y)) (= (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real ln X)) (hAPP_real_real ln Y))))))) (forall ((N_65 $$unsorted) (A_199 $$unsorted)) (=> (not (= A_199 zero_zero_rat)) (not (= zero_zero_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_199) N_65))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (= C (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat B) A)) E_2)) D)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B) E_2)) D) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) E_2)) C)))) (forall ((X_30 $$unsorted) (Y_24 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_30) Y_24)) (=> (not (= Y_24 X_30)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_30) Y_24))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_fun_int_int P (hAPP_int_int Q R)) (hAPP_int_fun_int_int (hAPP_f1760145644nt_int (hAPP_f1629352853nt_int cOMBB_1496585939nt_int P) Q) R))) (forall ((C_33 $$unsorted) (D_5 $$unsorted) (A_79 $$unsorted) (B_67 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_79) B_67)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat C_33) D_5)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_79) C_33)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_67) D_5)))))) (forall ((A_62 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int A_62) zero_z891286103de_int) A_62)) (forall ((B_72 $$unsorted) (C_35 $$unsorted) (A_84 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral B_72))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_84)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C_35)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_84) C_35))))))) (forall ((N $$unsorted)) (= (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real times_times_real pi) (hAPP_nat_real real_nat N))) zero_zero_real)) (forall ((Ta $$unsorted) (A_1 $$unsorted) (D_1 $$unsorted)) (=> (is_int Ta) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Ta) one_one_int)) A_1)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa) X_2)))))))) (=> (= X_2 Ta) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) D_1) Ta))))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (= (and (or (hBOOL (hAPP_real_bool _let_1 X_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_2) zero_zero_real))) (or (hBOOL (hAPP_real_bool _let_1 Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) zero_zero_real)))) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X_1) Y_2)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_1)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) _let_1)) (= (hAPP_real_real arcsin (hAPP_real_real sin X)) X))))) (forall ((C_38 $$unsorted) (A_96 $$unsorted) (B_78 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int C_38))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_96) B_78)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int _let_1 A_96)) (hAPP_Q1762011733de_int _let_1 B_78)))))) (forall ((C_85 $$unsorted) (A_193 $$unsorted) (B_149 $$unsorted)) (let ((_let_1 (hAPP_c1403687985x_bool dvd_dvd_complex A_193))) (=> (hBOOL (hAPP_complex_bool _let_1 B_149)) (hBOOL (hAPP_complex_bool _let_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_149) C_85)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc X))) (= (hAPP_nat_nat fact_fact_nat _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) (hAPP_nat_nat fact_fact_nat X))))) (forall ((A_18 $$unsorted) (C_5 $$unsorted) (B_14 $$unsorted)) (=> (is_int B_14) (=> (not (= zero_zero_int B_14)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_18) (hAPP_int_int (hAPP_int_fun_int_int times_times_int C_5) B_14))) B_14) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int C_5) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_18) B_14)))))) (forall ((I $$unsorted) (M $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) I))))) (forall ((A_227 $$unsorted) (B_164 $$unsorted) (C_93 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_227))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 B_164)) C_93) (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_164) C_93))))) (forall ((M_17 $$unsorted) (N_30 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex M_17))) (let ((_let_2 (hAPP_nat_complex _let_1 N_30))) (let ((_let_3 (= zero_zero_nat N_30))) (and (=> (not _let_3) (= _let_2 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex M_17) (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_30) one_one_nat))))) (=> _let_3 (= one_one_complex _let_2))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C))) (=> (is_int C) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B))) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A) B)) (= zero_zero_int C)))))) (forall ((B_45 $$unsorted) (B_44 $$unsorted) (A_54 $$unsorted) (C_24 $$unsorted) (A_53 $$unsorted)) (=> (= (hAPP_int_int (div_mod_int A_53) C_24) (hAPP_int_int (div_mod_int A_54) C_24)) (=> (= (hAPP_int_int (div_mod_int B_45) C_24) (hAPP_int_int (div_mod_int B_44) C_24)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_53) B_44)) C_24) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_54) B_45)) C_24))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B))) (exists ((Y_1 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_1) zero_zero_real)) (hBOOL (hAPP_real_bool (deriv_real F X_2) Y_1)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real F B)) (hAPP_real_real F A)))))) (forall ((A_196 $$unsorted) (N_63 $$unsorted)) (let ((_let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_196) N_63))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int _let_1) A_196) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_196) _let_1)))) (forall ((N_1 $$unsorted) (Diff $$unsorted) (F $$unsorted) (H $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H)) (forall ((M_1 $$unsorted) (T $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) T)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) H)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) T) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) T))))) (= (hAPP_n546711566l_real Diff zero_zero_nat) F)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real H))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) T)) (= (hAPP_real_real F H) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) H))))))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_nat_nat suc N)))) (forall ((V_22 $$unsorted) (V_21 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_21)) (=> (hBOOL (hAPP_int_bool _let_1 V_22)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex V_21)) (hAPP_int_complex number528085621omplex V_22)) (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_21) V_22))))))) (forall ((C_88 $$unsorted) (A_206 $$unsorted) (B_157 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool dvd_dvd_rat A_206))) (=> (hBOOL (hAPP_rat_bool _let_1 B_157)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat B_157) C_88)) (hBOOL (hAPP_rat_bool _let_1 C_88)))))) (forall ((A_49 $$unsorted) (B_40 $$unsorted) (C_21 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_49))) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat B_40) C_21))) C_21) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 B_40)) C_21)))) (forall ((A_56 $$unsorted) (C_26 $$unsorted) (B_47 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (div_mod_int A_56) B_47)) C_26) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_56) C_26)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_47) C_26)))) (forall ((N $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real inverse_inverse_real (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N)))))) (forall ((P_1 $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool P_1 zero_zero_nat))) (=> (exists ((X1 $$unsorted)) (hBOOL (hAPP_nat_bool P_1 X1))) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat suc N_2))) (not (hBOOL (hAPP_nat_bool P_1 N_2)))))))) (forall ((A_1 $$unsorted)) (= (image_int_nat nat (image_nat_int semiri1621563631at_int A_1)) A_1)) (forall ((C_43 $$unsorted) (A_101 $$unsorted) (B_83 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real C_43))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_101) B_83)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A_101)) (hAPP_real_real _let_1 B_83)))))) (forall ((A_228 $$unsorted) (C_94 $$unsorted) (D_19 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_228))) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int C_94) D_19)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 C_94)) D_19)))) (forall ((V $$unsorted) (K_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (not (= A B)) (=> (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real V X_2) K_1))) (= (hAPP_real_real V (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) B)) _let_1)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real V A)) (hAPP_real_real V B))) _let_1)))))) (forall ((F $$unsorted) (X_1 $$unsorted) (F_1 $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool (ord_at4362885an_nat Ma) N_1))) (=> (forall ((R_1 $$unsorted)) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) R_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat R_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) N_1)))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real F R_1) X_1) (hAPP_real_real (hAPP_n546711566l_real F_1 R_1) X_1))))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f2119584768l_real (hAPP_f59594445l_real cOMBC_2010481033l_real (hAPP_f1523861863l_real (hAPP_f1067681227l_real cOMBB_1934313333l_real big_co604158596t_real) (hAPP_f42270917t_real cOMBC_nat_real_real F))) _let_1) X_1) (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real F_1) X_1)) _let_1)))))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_3) A_3))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int zfact _let_2)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int _let_2) _let_1)))) P_3))))))))) (forall ((A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_3)) (exists ((P_4 $$unsorted)) (and (is_int P_4) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_4) A_3)) (hBOOL (hAPP_int_bool zprime P_4)))))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) M)) one_one_int))) (=> (hBOOL (hAPP_int_bool zprime _let_1)) (= one_one_int (hAPP_int_int (legendre (hAPP_int_int number_number_of_int min)) _let_1))))) (forall ((B_140 $$unsorted) (A_180 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (or (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_140) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_180) zero_zero_rat))) (and (hBOOL (hAPP_rat_bool _let_1 A_180)) (hBOOL (hAPP_rat_bool _let_1 B_140)))) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_180) B_140)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2)))) (= (or (and _let_1 (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_2) X_1)))) (= X_1 Y_2)) _let_1))) (forall ((A_229 $$unsorted) (C_95 $$unsorted) (D_20 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex C_95))) (let ((_let_2 (hAPP_c172932010omplex plus_plus_complex A_229))) (= (hAPP_complex_complex _let_1 (hAPP_complex_complex _let_2 D_20)) (hAPP_complex_complex _let_2 (hAPP_complex_complex _let_1 D_20)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (=> (= F (hAPP_n546711566l_real Diff zero_zero_nat)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (=> (not (= X_1 zero_zero_real)) (=> (forall ((M_1 $$unsorted) (X_2 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) X_2) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) X_2)))) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_real_real abs_abs_real T))) (let ((_let_2 (hAPP_r474017924t_real power_power_real X_1))) (and (= (hAPP_real_real F X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_2)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_2 N_1)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) (hAPP_real_real abs_abs_real X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) _let_1))))))))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X_1)) (hBOOL (hAPP_f448129468l_bool nat_nat_set (hAPP_i1948725293t_bool (ord_at875362053st_int X_1) Y_2))))) (forall ((X $$unsorted) (N_5 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) N_5)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_n546711566l_real root N) X)) (hAPP_real_real (hAPP_n546711566l_real root N_5) X)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) Y)) (hAPP_real_real (dist_dist_real X) Y))) (forall ((A_90 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex one_one_complex) A_90) A_90)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r373117745t_bool (hAPP_f1459420095t_bool (hAPP_f693283245t_bool cOMBC_1113900202t_bool P) Q) R) (hAPP_f1222178131t_bool (hAPP_r2052264067t_bool P R) Q))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (divmod_nat Ma N_1))) (let ((_let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))) (and (=> (or (= zero_zero_nat N_1) _let_2) (= _let_1 (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat zero_zero_nat) Ma))) (=> (not (or _let_2 (= N_1 zero_zero_nat))) (= _let_1 (hAPP_P1586233937at_nat (produc1391996073at_nat (hAPP_f837737749at_nat (hAPP_f999082675at_nat cOMBB_348438404at_nat product_Pair_nat_nat) suc)) (divmod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat Ma) N_1) N_1)))))))) (forall ((A_10 $$unsorted) (N_15 $$unsorted) (B_8 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (let ((_let_2 (hAPP_nat_nat suc N_15))) (=> (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral B_8) _let_2) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_10) _let_2)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_10)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A $$unsorted) (C $$unsorted) (D $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) D))) (=> (and (is_int B) (is_int D)) (=> (not (= B zero_zero_int)) (=> (not (= D zero_zero_int)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B)) (hAPP_int_rat (hAPP_int_fun_int_rat fract C) D))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) D)) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int C) B)) _let_1))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r2019696015l_real (hAPP_f2072293513l_real (hAPP_f1763467369l_real cOMBS_163651580l_real P) Q) R) (hAPP_f1736103445l_real (hAPP_r224952523l_real P R) (hAPP_r2019696015l_real Q R)))) (forall ((A_211 $$unsorted) (M_26 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_211) one_one_rat)) M_26) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_211) M_26)) M_26))) (forall ((A_234 $$unsorted)) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_234) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_234) A_234))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B) _let_1) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) _let_1)) (= (hAPP_int_int abs_abs_int B) (hAPP_int_int abs_abs_int A))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N) zero_zero_nat) (=> (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) M)) (= N M)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i447943416t_real (hAPP_f1295083291t_real (hAPP_f212164053t_real cOMBB_929094628al_int P) Q) R) (hAPP_f1690286043t_real P (hAPP_i371647666l_real Q R)))) (forall ((M_17 $$unsorted) (N_30 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int M_17))) (let ((_let_2 (hAPP_nat_int _let_1 N_30))) (and (=> (not (= zero_zero_nat N_30)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int M_17) (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_30) one_one_nat))) _let_2)) (=> (= N_30 zero_zero_nat) (= one_one_int _let_2)))))) (forall ((A_32 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat A_32) one_one_nat) zero_zero_nat)) (= (natceiling zero_zero_real) zero_zero_nat) (forall ((U $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) U)) (= (image_nat_int semiri1621563631at_int (hAPP_n1699378549t_bool ord_lessThan_nat (hAPP_int_nat nat U))) (hAPP_i1948725293t_bool (ord_at641636577an_int zero_zero_int) U)))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 K1)) (hAPP_int_int bit1 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K1) K2)))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) (hAPP_real_real sin X)))) (forall ((A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (= (hAPP_f22106695ol_nat finite_card_nat (image_int_nat nat A_1)) (hAPP_f957591787ol_nat finite_card_int A_1)))) (= _let_85 one_one_int) (forall ((B_73 $$unsorted) (A_85 $$unsorted) (C_36 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat B_73))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_36)) (=> (hBOOL (hAPP_nat_bool _let_1 A_85)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_85) C_36))))))) (forall ((C_75 $$unsorted) (A_175 $$unsorted) (B_135 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_75))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_175) B_135)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_75)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A_175)) (hAPP_real_real _let_1 B_135))))))) (forall ((X_1 $$unsorted)) (= (not (hBOOL (hAPP_int_bool nat_neg X_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)))) (forall ((N_59 $$unsorted) (M_24 $$unsorted) (X_28 $$unsorted) (Y_22 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral X_28) Y_22)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_59) M_24)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_28) N_59)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral Y_22) M_24)))))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat Lx_2))) (= (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Ly) Rx_2)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat _let_1 Ly)) Rx_2)))) (forall ((N_41 $$unsorted)) (let ((_let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real zero_zero_real) N_41))) (and (=> (= zero_zero_nat N_41) (= _let_1 one_one_real)) (=> (not (= N_41 zero_zero_nat)) (= _let_1 zero_zero_real))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (= K_1 L) (= (quickcheck_int_of K_1) (quickcheck_int_of L)))) (forall ((V $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (= (=> (not (hBOOL (hAPP_int_bool nat_neg _let_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat nat _let_1)) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat number_number_of_nat V)) (hAPP_nat_nat suc N_1)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (not (= B_2 zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2)) B_2)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X) Y)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int semiri1621563631at_int X)) (hAPP_nat_int semiri1621563631at_int Y)))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit0 K_1)) (hAPP_int_int bit1 L))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) L)))) (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool P_1 zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool P_1 N_1)) (exists ((K $$unsorted)) (and (forall ((I_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_2) K)) (not (hBOOL (hAPP_nat_bool P_1 I_2))))) (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat K) one_one_nat))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat K) N_1))))))) (forall ((A_25 $$unsorted) (B_20 $$unsorted)) (=> (not (= zero_zero_nat B_20)) (= A_25 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_25) B_20)) B_20)))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (forall ((N_2 $$unsorted)) (let ((_let_1 (bolzano_bisect P_1 A B))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_P731461727l_real produc556554744l_real (hAPP_n332733730l_real _let_1 (hAPP_nat_nat suc N_2)))) (hAPP_P731461727l_real produc556554744l_real (hAPP_n332733730l_real _let_1 N_2)))))))) (forall ((A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (div_mod_int A) Ma)) (hAPP_int_int (div_mod_int B) Ma)) Ma)))) (forall ((N_43 $$unsorted) (A_131 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_131) N_43))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) A_131)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_131) _let_1)))))) (forall ((C $$unsorted) (D $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real B))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real A))) (= (and (not (= D C)) (not (= B A))) (not (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_2 D)) (hAPP_real_real _let_1 C)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_2 C)) (hAPP_real_real _let_1 D)))))))) (forall ((A_3 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) A_3) A_3)) (forall ((B_148 $$unsorted) (A_192 $$unsorted) (C_84 $$unsorted)) (let ((_let_1 (hAPP_c1403687985x_bool dvd_dvd_complex A_192))) (=> (hBOOL (hAPP_complex_bool _let_1 C_84)) (hBOOL (hAPP_complex_bool _let_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_148) C_84)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real ln X))))) (forall ((A_3 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) (hAPP_int_int number_number_of_int min)) (hAPP_int_int uminus_uminus_int A_3))) (forall ((N $$unsorted) (I $$unsorted)) (let ((_let_1 (hAPP_nat_nat (code_nat_of_aux I) N))) (and (=> (not (= I zero_z126310315umeral)) (= _let_1 (hAPP_nat_nat (code_nat_of_aux (hAPP_C498520661umeral (hAPP_C1594335432umeral minus_1690775515umeral I) one_on1645066479umeral)) (hAPP_nat_nat suc N)))) (=> (= zero_z126310315umeral I) (= _let_1 N))))) (forall ((A_62 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat A_62) zero_zero_nat) A_62)) (forall ((X_43 $$unsorted) (Y_31 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_43) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_31) _let_1)))))) (forall ((N $$unsorted) (X $$unsorted)) (= (hAPP_real_real exp_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) X)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real exp_real X)) N))) (forall ((A_30 $$unsorted) (B_25 $$unsorted) (C_11 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral A_30) B_25) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_30) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_25) C_11))) B_25))) (forall ((X $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_3) X)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int)) _let_1)))) one_one_int) P_3)))))))) (forall ((N_25 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_nat_rat semiri151668891at_rat N_25)))) (forall ((A_12 $$unsorted) (N_18 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex A_12))) (= (hAPP_nat_complex _let_1 (hAPP_nat_nat suc N_18)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex _let_1 N_18)) A_12)))) (forall ((X $$unsorted)) (= (hAPP_real_real uminus_uminus_real (hAPP_real_real arctan X)) (hAPP_real_real arctan (hAPP_real_real uminus_uminus_real X)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_bool_bool (hAPP_P921862901l_bool P R) (hAPP_P603027463t_bool Q R)) (hAPP_P603027463t_bool (hAPP_f237669397t_bool (hAPP_f461489489t_bool cOMBS_400904860l_bool P) Q) R))) (forall ((Z_1 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_complex_real re Z_1)) (hAPP_complex_real norm_norm_complex Z_1)) (hAPP_complex_real re (hAPP_complex_complex sgn_sgn_complex Z_1)))) (forall ((X $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (multInv P_3))) (let ((_let_2 (hAPP_int_int _let_1 X))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) _let_2)) (hAPP_int_int _let_1 _let_2))) X) P_3)))))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) one_one_real)) (hBOOL (tendsto_nat_real (hAPP_r474017924t_real power_power_real X_1) zero_zero_real sequentially))))) (forall ((A_230 $$unsorted) (C_96 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real C_96) A_230) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_230) C_96))) (forall ((A_3 $$unsorted)) (let ((_let_1 (hAPP_real_real abs_abs_real A_3))) (let ((_let_2 (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_3) zero_zero_real)))) (and (=> _let_2 (= _let_1 (hAPP_real_real uminus_uminus_real A_3))) (=> (not _let_2) (= A_3 _let_1)))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real X_1)) one_one_real)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) (hAPP_int_int bit1 pls))))) (forall ((M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int M) zero_zero_int)) (= (hAPP_int_int fact_fact_int M) zero_zero_int))) (forall ((I_1 $$unsorted)) (=> (is_int I_1) (=> (not (= I_1 zero_zero_int)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (collect_int (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool dvd_dvd_int) I_1))))))) (forall ((N_37 $$unsorted) (A_126 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_126) N_37))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_126)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_126) one_one_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_126) _let_1)) _let_1)))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (hBOOL (hAPP_f448129468l_bool (nat_tr876908586nt_nat F) A_1))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real tan Y)) (hAPP_real_real tan X)))))))) (forall ((C $$unsorted) (D $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int B))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int A))) (=> (and (is_int D) (is_int B) (is_int A) (is_int C)) (= (not (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_2 C)) (hAPP_int_int _let_1 D)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_2 D)) (hAPP_int_int _let_1 C)))) (and (not (= B A)) (not (= D C)))))))) (forall ((X $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat one_one_nat) X) one_one_nat)) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B_2) A_3)) _let_1) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_2) A_3)) _let_1)) A_3)))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat B) A)) E_2)) D))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) E_2)) C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B) E_2)) D))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)) (or (= Y_2 X_1) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2))))) (forall ((A_26 $$unsorted) (B_21 $$unsorted)) (=> (not (= zero_zero_nat B_21)) (= A_26 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_21) A_26)) B_21)))) (forall ((N_65 $$unsorted) (A_199 $$unsorted)) (=> (not (= zero_zero_real A_199)) (not (= zero_zero_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_199) N_65))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (is_int A) (is_int D) (is_int C) (is_int B)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int C) D)) (= (= A B) (= D C))))) (forall ((A_111 $$unsorted) (B_89 $$unsorted) (C_49 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_111))) (=> (= (hAPP_Q1762011733de_int _let_1 B_89) (hAPP_Q1762011733de_int _let_1 C_49)) (= B_89 C_49)))) (forall ((C_57 $$unsorted) (D_10 $$unsorted) (A_135 $$unsorted) (B_104 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_135) B_104)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C_57) D_10)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) B_104)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_57)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_135) C_57)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_104) D_10)))))))) (forall ((A $$unsorted) (B $$unsorted) (N_1 $$unsorted)) (=> (not (= zero_zero_nat N_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A) N_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A) B))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real D) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_2) Sa)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) Z)) (= _let_1 _let_1)))))) (forall ((X $$unsorted)) (= (bezw X zero_zero_nat) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int one_one_int) zero_zero_int))) (exists ((K_4 $$unsorted)) (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_complex_real norm_norm_complex (hAPP_complex_complex cnj X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4))))) (forall ((A_205 $$unsorted) (B_156 $$unsorted)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_205) B_156) zero_zero_nat) (or (= B_156 zero_zero_nat) (= A_205 zero_zero_nat)))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (forall ((N_2 $$unsorted)) (let ((_let_1 (hAPP_n332733730l_real (bolzano_bisect P_1 A B) N_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_P731461727l_real produc1935615926l_real _let_1)) (hAPP_P731461727l_real produc556554744l_real _let_1))))))) (forall ((M $$unsorted) (N $$unsorted)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)))) (forall ((A_39 $$unsorted) (B_30 $$unsorted) (C_14 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int minus_minus_int A_39))) (= (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 B_30)) C_14) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int B_30) C_14))) C_14)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A))) (= (= C B) (= (hAPP_nat_nat _let_1 B) (hAPP_nat_nat _let_1 C))))) (forall ((A_3 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted) (B_2 $$unsorted)) (=> (and (is_int B_2) (is_int D_3)) (=> (not (= zero_zero_int B_2)) (=> (not (= D_3 zero_zero_int)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) D_3)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int C_1) B_2))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) D_3)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)) (hAPP_int_rat (hAPP_int_fun_int_rat fract C_1) D_3))))))) (forall ((Ta $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex D) D_1)) (forall ((X_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_c1403687985x_bool dvd_dvd_complex D))) (= (hBOOL (hAPP_complex_bool _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X_2) Ta))) (hBOOL (hAPP_complex_bool _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_2) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex K) D_1))) Ta)))))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y)))))) (forall ((A_61 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (div_mo1740067990umeral zero_z126310315umeral) A_61))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_real (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat P) Q) R) (hAPP_nat_real P (hAPP_nat_nat Q R)))) (forall ((A $$unsorted) (N_1 $$unsorted)) (= (and (= A zero_zero_rat) (not (= N_1 zero_zero_nat))) (= zero_zero_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A) N_1)))) (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP_complex_real re (of_real_complex Z_1)))) (forall ((A $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_1))) (= (and (= zero_z891286103de_int A) (not (= zero_zero_nat _let_1))) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A) _let_1) zero_z891286103de_int)))) (forall ((B $$unsorted) (P_5 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_i2112223885l_bool member_int B))) (=> (and (is_int B) (is_int A)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A)) (=> (not (hBOOL (hAPP_f448129468l_bool _let_1 (hAPP_i1948725293t_bool (wset (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) one_one_int)) P_5)))) (=> (hBOOL (hAPP_f448129468l_bool _let_1 (hAPP_i1948725293t_bool (wset A) P_5))) (or (= A B) (= (hAPP_int_int (inv P_5) A) B)))))))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int K_1))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 N_1)) (= (hBOOL (hAPP_Q2096512830t_bool _let_1 Ma)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int Ma) N_1))))))) (forall ((A_89 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral one_on1645066479umeral) A_89) A_89)) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N)) N) M)) (forall ((N $$unsorted)) (=> (not (= N zero_zero_nat)) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) one_one_nat)) N)))) (forall ((X $$unsorted) (M $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) (hAPP_int_int (div_mod_int X) M)) M))) (forall ((A_3 $$unsorted) (M $$unsorted) (B_2 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) M)) M))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real power_power_real) N_1) X_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) (hAPP_nat_nat suc zero_zero_nat))))))) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int Rx_4) Ry_2))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int Lx_4))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_2 Ly_2)) _let_1) (hAPP_int_int _let_2 (hAPP_int_int (hAPP_int_fun_int_int times_times_int Ly_2) _let_1)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int B))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int) B)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_1) Y_2)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int _let_1 X_1)) (hAPP_n522471361de_int _let_1 Y_2))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y) _let_1))) zero_zero_int))))) (forall ((I $$unsorted) (M $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) M))))) (forall ((A_90 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral one_on1645066479umeral) A_90) A_90)) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (norm_frac A_3 B_2))) (let ((_let_2 (hAPP_int_int (hAPP_int_fun_int_int int_gcd A_3) B_2))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) zero_zero_int)))) (=> (and (is_int B_2) (is_int A_3)) (and (=> _let_3 (= _let_1 (norm_frac (hAPP_int_int uminus_uminus_int A_3) (hAPP_int_int uminus_uminus_int B_2)))) (=> (not _let_3) (and (=> (not (or (= zero_zero_int B_2) (= zero_zero_int A_3))) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) _let_2)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_2) _let_2)) _let_1)) (=> (or (= B_2 zero_zero_int) (= A_3 zero_zero_int)) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) one_one_int) _let_1)))))))))) (forall ((N $$unsorted) (P_3 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) M)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N))) (or (hBOOL (hAPP_int_bool _let_1 M)) (hBOOL (hAPP_int_bool _let_1 N)))))))) (forall ((N $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat N) zero_zero_nat))) (forall ((X $$unsorted)) (= (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) pi)) (hAPP_real_real uminus_uminus_real (hAPP_real_real sin X)))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_1)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat nat Z_1)) (hAPP_int_nat nat Z_4)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z_1) Z_4))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int lazy_small_lazy_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A0) A1))) (=> (forall ((D_2 $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool P_1 D_2))) (=> (and (is_int D_2) (is_int I_2)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int lazy_small_lazy_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int D_2) I_2))) (=> (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int D_2) I_2))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int I_2) one_one_int)))) (hBOOL (hAPP_int_bool _let_1 I_2))))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int div_div_int A_3))) (let ((_let_2 (hAPP_int_int _let_1 (hAPP_int_int uminus_uminus_int B_2)))) (let ((_let_3 (hAPP_int_int uminus_uminus_int (hAPP_int_int _let_1 B_2)))) (let ((_let_4 (= (hAPP_int_int (div_mod_int A_3) B_2) zero_zero_int))) (=> (is_int B_2) (=> (not (= zero_zero_int B_2)) (and (=> _let_4 (= _let_2 _let_3)) (=> (not _let_4) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int _let_3) one_one_int) _let_2)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int fact_fact_int X))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X)))) (and (=> (not _let_2) (= _let_1 zero_zero_int)) (=> _let_2 (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat fact_fact_nat (hAPP_int_nat nat X))) _let_1)))))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int (hAPP_int_int bit0 W_1)))) (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int W_1))))) (forall ((C_66 $$unsorted) (A_144 $$unsorted) (B_113 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_66))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int _let_1 A_144)) (hAPP_Q1762011733de_int _let_1 B_113))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) C_66)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_144) B_113)))))) (forall ((C_57 $$unsorted) (D_10 $$unsorted) (A_135 $$unsorted) (B_104 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_135) B_104)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral C_57) D_10)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) B_104)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_57)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_135) C_57)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_104) D_10)))))))) (forall ((N_33 $$unsorted) (A_123 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_123)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_33)) (hBOOL (hAPP_real_bool _let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_123) N_33))))))) (forall ((K_2 $$unsorted)) (= zero_zero_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract K_2) zero_zero_int))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X) Y)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X) Y)))) (forall ((N_56 $$unsorted)) (= one_one_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int number_number_of_int min)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_56)))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) E_2)) C)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) E_2)) D))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B)) E_2)) C)) D)))) (forall ((V_14 $$unsorted) (B_166 $$unsorted) (C_97 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real V_14)))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 B_166)) (hAPP_real_real _let_1 C_97)) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_166) C_97))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X_1) Y_2) zero_zero_nat) (and (= zero_zero_nat X_1) (= Y_2 zero_zero_nat)))) (forall ((A_92 $$unsorted)) (= A_92 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_92) one_one_nat))) (forall ((X_45 $$unsorted) (Y_33 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_45) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_33) _let_1))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) Y_33)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat X_45) Y_33)))))) (= (hAPP_n522471361de_int semiri1424489471de_int one_one_nat) one_on1684967323de_int) (forall ((D_3 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int abs_abs_int D_3)) D_3))) (forall ((A $$unsorted)) (= (not (= A zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))) (forall ((C_38 $$unsorted) (A_96 $$unsorted) (B_78 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral C_38))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_96) B_78)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral _let_1 A_96)) (hAPP_C498520661umeral _let_1 B_78)))))) (forall ((V_2 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int number_number_of_int V_2)) (hAPP_int_int number_number_of_int W)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 V_2))) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 W))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (quotient_of A) (quotient_of B)) (= A B))) (forall ((X_3 $$unsorted) (A $$unsorted)) (=> (hBOOL (tendsto_nat_complex X_3 A sequentially)) (hBOOL (tendsto_nat_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat re) X_3) (hAPP_complex_real re A) sequentially)))) (forall ((A_3 $$unsorted)) (=> (= one_one_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_int_int abs_abs_int A_3) one_one_int))) (hBOOL (hAPP_real_bool _let_64 _let_10)) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (posDivAlg A_3 B_2))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) B_2)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (and (=> _let_2 (= _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) A_3))) (=> (not _let_2) (= (hAPP_P1975530577nt_int (adjust B_2) (posDivAlg A_3 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) B_2))) _let_1))))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit0 K1)) (hAPP_int_int bit1 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K1) K2)))) (forall ((A_92 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_92) one_one_real) A_92)) (forall ((A_133 $$unsorted) (N_46 $$unsorted) (N_45 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_133))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_46) N_45)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_133)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_133) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int _let_1 N_45)) (hAPP_nat_int _let_1 N_46)))))))) (forall ((B_2 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat D_3))) (=> (hBOOL (hAPP_nat_bool _let_1 A_3)) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_3) B_2))) (hBOOL (hAPP_nat_bool _let_1 B_2)))))) (forall ((C_43 $$unsorted) (A_101 $$unsorted) (B_83 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int C_43))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_101) B_83)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A_101)) (hAPP_int_int _let_1 B_83)))))) (forall ((X_15 $$unsorted) (Y_12 $$unsorted) (Ya_2 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_15) Y_12)) Ya_2) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_15) Ya_2)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_12) Ya_2)))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit0 K1)) (hAPP_int_int bit0 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K1) K2)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))) zero_zero_real))))) (forall ((A_197 $$unsorted) (B_152 $$unsorted) (N_64 $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_197) B_152)) N_64) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_197) N_64)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_152) N_64)))) (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral one_on1645066479umeral) _let_4) one_on1645066479umeral) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N))) (let ((_let_2 (hAPP_nat_nat fact_fact_nat _let_1))) (and (=> (= zero_zero_nat _let_1) (= one_one_nat _let_2)) (=> (not (= _let_1 zero_zero_nat)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) (hAPP_nat_nat fact_fact_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_1) one_one_nat))) _let_2)))))) (forall ((M_13 $$unsorted)) (= (hAPP_nat_rat semiri151668891at_rat (hAPP_nat_nat suc M_13)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat one_one_rat) (hAPP_nat_rat semiri151668891at_rat M_13)))) (= _let_4 _let_76) (forall ((A_3 $$unsorted)) (not (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat one_one_nat) A_3))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) one_one_nat))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int uminus_uminus_int A_3)) (hAPP_int_int uminus_uminus_int B_2)) (hAPP_int_int uminus_uminus_int (hAPP_int_int (div_mod_int A_3) B_2)))) (forall ((A_3 $$unsorted) (J_2 $$unsorted) (K_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (multInv P_3))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong J_2) K_2) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int _let_2 (hAPP_int_int _let_1 J_2))) (hAPP_int_int _let_2 (hAPP_int_int _let_1 K_2))) P_3))))))) (forall ((M_13 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat one_one_nat) (hAPP_nat_nat semiri984289939at_nat M_13)) (hAPP_nat_nat semiri984289939at_nat (hAPP_nat_nat suc M_13)))) (= (hAPP_int_int bit0 min) (hAPP_int_int pred min)) (= one_one_complex (cis zero_zero_real)) (forall ((Ta $$unsorted) (B_1 $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) D_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int D))) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa))))))))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) Ta))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1)) Ta)))))))))) (forall ((A_194 $$unsorted) (B_150 $$unsorted)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex A_194) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_150) A_194)))) (forall ((A $$unsorted)) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (hBOOL (monoseq_real A)) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A)))))) (forall ((C_57 $$unsorted) (D_10 $$unsorted) (A_135 $$unsorted) (B_104 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_135) B_104)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat C_57) D_10)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) B_104)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_57)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_135) C_57)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_104) D_10)))))))) (forall ((A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) P_5)) (= (hAPP_int_nat nat A) (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool (bnorRset A) P_5)))))) (forall ((C_59 $$unsorted) (D_12 $$unsorted) (A_137 $$unsorted) (B_106 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_137) B_106)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C_59) D_12)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_137)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C_59)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_137) C_59)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_106) D_12)))))))) (forall ((A_197 $$unsorted) (B_152 $$unsorted) (N_64 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_197) N_64)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_152) N_64)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_197) B_152)) N_64))) (forall ((K_2 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_nat_int semiri1621563631at_int K_2)) one_one_int) (hAPP_nat_rat semiri151668891at_rat K_2))) (forall ((A_198 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat zero_zero_nat) A_198)) (= zero_zero_nat A_198))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat D) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_2) Sa)))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Z) X_2)) (= _let_1 _let_1)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) X)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2)) X)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A))) (= (= (hAPP_C498520661umeral _let_1 C) (hAPP_C498520661umeral _let_1 B)) (= B C)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat B))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) B)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_1) Y_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 X_1)) (hAPP_nat_nat _let_1 Y_2))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (is_int Y_2) (is_int X_1)) (= (= X_1 Y_2) (= (hAPP_int_rat number_number_of_rat X_1) (hAPP_int_rat number_number_of_rat Y_2))))) (forall ((X $$unsorted)) (= (hAPP_real_real sin (hAPP_real_real uminus_uminus_real X)) (hAPP_real_real uminus_uminus_real (hAPP_real_real sin X)))) (= _let_8 _let_99) (forall ((X_1 $$unsorted)) (= (archim791455193or_rat X_1) (the_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_r1900510169t_bool (hAPP_f1480506641t_bool cOMBC_int_rat_bool (hAPP_f601898971t_bool (hAPP_f857296063t_bool cOMBB_214503962ol_int ord_less_eq_rat) ring_1_of_int_rat)) X_1))) (hAPP_f1241350704t_bool (hAPP_f1131424617t_bool cOMBB_rat_bool_int (hAPP_r2115560837t_bool ord_less_rat X_1)) (hAPP_f1900950721nt_rat (hAPP_f1270196437nt_rat cOMBB_int_rat_int ring_1_of_int_rat) (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int plus_plus_int) one_one_int))))))) (forall ((V_22 $$unsorted) (V_21 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_21)) (=> (hBOOL (hAPP_int_bool _let_1 V_22)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int V_21)) (hAPP_int_int number_number_of_int V_22)) (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_21) V_22))))))) (forall ((B_73 $$unsorted) (A_85 $$unsorted) (C_36 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat B_73))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_36)) (=> (hBOOL (hAPP_rat_bool _let_1 A_85)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_85) C_36))))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_complex_real re X))) (hAPP_complex_real norm_norm_complex X)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Y)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y) (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) Y))) X)))) (forall ((B_1_1 $$unsorted)) (is_bool (cauchy_real B_1_1))) (forall ((A $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Ma)) (=> (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) A_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (rRset2norRR A_1 Ma) A)) (hAPP_i1948725293t_bool norRRset Ma))))))) (forall ((A_233 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real pls)) A_233) A_233)) (forall ((A_113 $$unsorted) (B_91 $$unsorted) (C_51 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat A_113))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 B_91)) C_51) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_91) C_51))))) (forall ((N $$unsorted)) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)) N)) (not (hBOOL (hAPP_nat_bool prime N)))) (exists ((M_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)))) (and (hBOOL (hAPP_nat_bool _let_1 M_1)) (hBOOL (hAPP_nat_bool _let_1 K)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_1) K) N) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat K) N))))))) (forall ((Ta $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Ta) B_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int Ta))) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa))))))))) (=> (hBOOL (hAPP_int_bool _let_1 X_2)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1))))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (and (is_int M) (is_int N)) (=> (hBOOL (hAPP_int_bool _let_1 M)) (=> (hBOOL (hAPP_int_bool _let_1 N)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int M) N)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N) M)) (= N M)))))))) (forall ((A_208 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_208) zero_zero_nat))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat X_1)) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat X_1) (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 Z_1)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Y) Z_1)))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int bit0 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int K_2) L_2)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int bit0 K_2)) (hAPP_int_int bit0 L_2)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int A)) one_one_real))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (archim1246769320r_real X_1)) A)))) (forall ((A $$unsorted)) (= (not (= A one_one_nat)) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat one_one_nat) A)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A) one_one_nat)))))) (forall ((X $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) (hAPP_int_int (multInv P_3) X))) one_one_int) P_3)))))) (forall ((Y $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int P_3))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y) N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (hBOOL (hAPP_int_bool _let_1 Y))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r2052264067t_bool (hAPP_f77155443t_bool (hAPP_f403082607t_bool cOMBB_984071017l_real P) Q) R) (hAPP_f743790483t_bool P (hAPP_r279757445t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f183342685l_real P (hAPP_r794344869l_real Q R)) (hAPP_r1043989325l_real (hAPP_f1161935955l_real (hAPP_f328572565l_real cOMBB_520243667l_real P) Q) R))) (forall ((K_1 $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_1))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int N_1) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) Ma)))) (hBOOL (hAPP_int_bool _let_1 N_1))))) (forall ((R_3 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real R_3))) (= (hAPP_complex_complex (scaleR1652505878omplex R_3) X) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real _let_1 (hAPP_complex_real re X))) (hAPP_real_real _let_1 (hAPP_complex_real im X)))))) (forall ((A_227 $$unsorted) (B_164 $$unsorted) (C_93 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_227))) (= (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_164) C_93)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 B_164)) C_93)))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_eq_nat) X_1))))) (forall ((X $$unsorted)) (= (hAPP_real_real (log (hAPP_real_real exp_real one_one_real)) X) (hAPP_real_real ln X))) (forall ((Ma $$unsorted)) (=> (not (= zero_zero_nat Ma)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool dvd_dvd_nat) Ma)))))) (forall ((N $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N))))) (= one_one_nat _let_74) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 Y)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y) (hAPP_nat_nat suc N))))))) (forall ((A_198 $$unsorted)) (=> (is_int A_198) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int zero_zero_int) A_198)) (= zero_zero_int A_198)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat B))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) B)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 X_1)) (hAPP_nat_nat _let_1 Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)))))) (forall ((N_54 $$unsorted) (A_151 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_151)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_151) N_54)))))) (forall ((A_23 $$unsorted)) (=> (not (= zero_zero_nat A_23)) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_23) A_23)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat A_3))) (let ((_let_2 (hAPP_nat_nat _let_1 R_3))) (=> (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel B_2 C_1) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat Q_2) R_3))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_1)) (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel (hAPP_nat_nat _let_1 B_2) C_1) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 Q_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat _let_2) C_1))) (hAPP_nat_nat (div_mod_nat _let_2) C_1))))))))) (forall ((E_1 $$unsorted) (B_2 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D_3) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int E_1) B_2)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2) one_one_int) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int D_3) E_1) one_one_int))))) (forall ((C_83 $$unsorted) (D_16 $$unsorted) (A_191 $$unsorted) (B_147 $$unsorted)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex A_191) B_147)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex C_83) D_16)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_191) C_83)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_147) D_16)))))) (forall ((B_141 $$unsorted) (A_181 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (or (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_181) zero_zero_nat)) (hBOOL (hAPP_nat_bool _let_1 B_141))) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat B_141) zero_zero_nat)) (hBOOL (hAPP_nat_bool _let_1 A_181)))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_181) B_141)) zero_zero_nat))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_rat_rat abs_abs_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)) (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int abs_abs_int A_3)) (hAPP_int_int abs_abs_int B_2)))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_complex_real norm_norm_complex Z_1) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_complex_real re Z_1)) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_complex_real im Z_1)) _let_1)))))) (forall ((A $$unsorted) (B $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_5))) (=> (hBOOL (hAPP_nat_bool prime P_5)) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A) B))) (or (hBOOL (hAPP_nat_bool _let_1 A)) (hBOOL (hAPP_nat_bool _let_1 B))))))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int N) M) (hAPP_i1732201573de_int quickcheck_of_int (hAPP_int_int (div_mod_int (quickcheck_int_of N)) (quickcheck_int_of M))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (div_mod_nat A_3) B_2)) (hAPP_int_int (div_mod_int (hAPP_nat_int semiri1621563631at_int A_3)) (hAPP_nat_int semiri1621563631at_int B_2)))) (forall ((C_75 $$unsorted) (A_175 $$unsorted) (B_135 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_75))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_175) B_135)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_75)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral _let_1 A_175)) (hAPP_C498520661umeral _let_1 B_135))))))) (forall ((N $$unsorted) (M $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int N))) (hAPP_nat_int semiri1621563631at_int M)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat number_number_of_nat pls)) N)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc M)) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 pls))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_real number267125858f_real _let_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) _let_2))) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X))) X))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_2) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat _let_1)))))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int bit1 pls))) (let ((_let_2 (hAPP_int_int bit1 _let_1))) (let ((_let_3 (hAPP_int_nat number_number_of_nat _let_2))) (let ((_let_4 (hAPP_int_fun_nat_int power_power_int B_2))) (let ((_let_5 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_1)))) (let ((_let_6 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_2)))) (let ((_let_7 (hAPP_int_fun_nat_int power_power_int A_3))) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int _let_7 _let_3)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_6 (hAPP_nat_int _let_7 _let_5))) B_2))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_6 A_3)) (hAPP_nat_int _let_4 _let_5)))) (hAPP_nat_int _let_4 _let_3)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_3) B_2)) _let_3)))))))))) (forall ((J $$unsorted) (I_1 $$unsorted) (P_1 $$unsorted) (P_5 $$unsorted)) (=> (forall ((I_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_2) P_5)) (=> (hBOOL (hAPP_nat_bool P_1 I_2)) (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc I_2)) P_5)))))) (=> (hBOOL (hAPP_nat_bool P_1 I_1)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_1) P_5)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat J) P_5)) (hBOOL (hAPP_nat_bool P_1 J))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int int_gcd X) Y) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (nat_gcd (hAPP_int_nat nat (hAPP_int_int abs_abs_int X))) (hAPP_int_nat nat (hAPP_int_int abs_abs_int Y)))))) (forall ((G $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D)) (=> (forall ((Z $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (= Z (hAPP_real_real G (hAPP_real_real F Z))))) (=> (forall ((Z $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (hBOOL (hAPP_real_bool (isCont_real_real F) Z)))) (hBOOL (hAPP_real_bool (isCont_real_real G) (hAPP_real_real F X_1))))))) (forall ((A $$unsorted) (Ma $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (hAPP_i1948725293t_bool (bnorRset A) Ma)))) (forall ((Ta $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (=> (is_int Ta) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Ta) B_1)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa) X_2)))))))) (=> (not (= X_2 Ta)) (not (= Ta (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1))))))))))) (forall ((R_2 $$unsorted) (X_3 $$unsorted)) (=> (hBOOL (vanishes X_3)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) R_2)) (exists ((K $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K) N_2)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat abs_abs_rat (hAPP_nat_rat X_3 N_2))) R_2)))))))) (hBOOL (hAPP_int_bool nat_is_nat _let_91)) (= _let_101 (hAPP_complex_complex cnj ii)) (forall ((A_11 $$unsorted) (N_17 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_11))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat suc N_17)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_11) (hAPP_nat_nat _let_1 N_17))))) (forall ((X $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real powr X) zero_zero_real) one_one_real)) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_int_real real_int A)) one_one_real))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (archim856651990g_real X_1)) A)))) (forall ((A_145 $$unsorted) (M_20 $$unsorted) (N_48 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_145))) (= (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_20) N_48)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int _let_1 M_20)) (hAPP_n522471361de_int _let_1 N_48))))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 W)))) (let ((_let_2 (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int W))))) (let ((_let_3 (hAPP_int_nat number_number_of_nat W))) (and (=> (not _let_2) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat _let_3) _let_3)) _let_1)) (=> _let_2 (= _let_1 zero_zero_nat))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP_f1469637905l_bool (hAPP_P1681069257l_bool member308914164t_bool X_1) A_1)) (hBOOL (hAPP_P880235623l_bool A_1 X_1)))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) K_2)) K_2) (hAPP_int_int bit1 K_2))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i688218208l_bool (hAPP_f801032407l_bool (hAPP_f499530369l_bool cOMBB_1317819104ol_int P) Q) R) (hAPP_r1134773055l_bool P (hAPP_int_real Q R)))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int _let_1 Y)) Z_1) (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Y) Z_1))))) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (= (hAPP_int_nat number_number_of_nat W_1) X_1))) (= _let_1 _let_1))) (forall ((B_115 $$unsorted) (C_67 $$unsorted) (A_153 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat B_115))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_153)) (=> (hBOOL (hAPP_nat_bool _let_1 C_67)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_153) C_67))))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= Y zero_zero_nat)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Y) (hAPP_nat_nat (div_mod_nat X) Y)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y)))) (= _let_62 _let_4) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) Y))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int B))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int _let_1 X_1)) (hAPP_nat_int _let_1 Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (posDivAlg A_3 B_2))) (let ((_let_2 (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) zero_zero_int))))) (and (=> _let_2 (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) A_3) _let_1)) (=> (not _let_2) (= _let_1 (hAPP_P1975530577nt_int (adjust B_2) (posDivAlg A_3 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) B_2))))))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_f215623910l_bool B_1_1 B_2_1))) (forall ((V_7 $$unsorted) (B_101 $$unsorted) (C_56 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real V_7)))) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B_101) C_56)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real _let_1 B_101)) (hAPP_real_real _let_1 C_56))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_1) Y_2)) zEven))))) (forall ((C_66 $$unsorted) (A_144 $$unsorted) (B_113 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_66))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 A_144)) (hAPP_nat_nat _let_1 B_113))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_66)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_144) B_113)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C) zero_zero_real)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B) A)))))) (forall ((Y_6 $$unsorted) (P_6 $$unsorted) (N_10 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real Y_6))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_6) N_10)) (= (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc N_10)) P_6)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_10) P_6))) Y_6))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X_1)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real ln X_1))))))) (forall ((A_49 $$unsorted) (B_40 $$unsorted) (C_21 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_49))) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (div_mo1740067990umeral B_40) C_21))) C_21) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral _let_1 B_40)) C_21)))) (forall ((Z_1 $$unsorted)) (= zero_zero_real (hAPP_complex_real im (hAPP_int_complex ring_11397209091omplex Z_1)))) (forall ((C_68 $$unsorted) (A_162 $$unsorted) (B_123 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_162) B_123)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) C_68)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_162) C_68)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_123) C_68)))))) (forall ((A_148 $$unsorted) (N_51 $$unsorted) (N_50 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_148))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_51) N_50)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) A_148)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real _let_1 N_51)) (hAPP_nat_real _let_1 N_50))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (is_int B_2) (=> (not (= B_2 zero_zero_int)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (divmod_int A_3 B_2)))))) (forall ((V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat V_2)) one_one_nat))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int V_2) pls)))) (and (=> _let_2 (= one_one_nat _let_1)) (=> (not _let_2) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int succ V_2)) _let_1)))))) (forall ((A_239 $$unsorted) (B_167 $$unsorted) (V_15 $$unsorted)) (let ((_let_1 (hAPP_int_complex number528085621omplex V_15))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_239) B_167)) _let_1) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_239) _let_1)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_167) _let_1))))) (forall ((A $$unsorted)) (= (= A zero_zero_nat) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat zero_zero_nat) A)))) (forall ((B_53 $$unsorted) (A_65 $$unsorted) (C_32 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_65) C_32) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_53) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_65) B_53))) (hAPP_int_int (div_mod_int A_65) B_53))) C_32))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) B_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_2) C_1))))) (forall ((A $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) Ma)) (= one_one_int (hAPP_int_int (legacy_zgcd (big_co1548731110nt_int cOMBI_int (hAPP_i1948725293t_bool (bnorRset A) Ma))) Ma)))) (forall ((N_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 N_1)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat nat N_1)) one_one_nat) (hAPP_f957591787ol_nat finite_card_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) _let_1)) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_eq_int) N_1)))))))) (forall ((N_11 $$unsorted) (A_7 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_7)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_7) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_7) (hAPP_nat_nat suc N_11))) one_one_real))))) (forall ((X $$unsorted) (Z_1 $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int minus_minus_int X))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int abs_abs_int (hAPP_int_int _let_1 Z_1))) one_one_int)) D_3))) Z_1))))) (forall ((X $$unsorted)) (= (hAPP_real_real uminus_uminus_real (hAPP_complex_real re X)) (hAPP_complex_real re (hAPP_complex_complex uminus473333897omplex X)))) (forall ((B_55 $$unsorted) (A_67 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_55) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_67) B_55))) (hAPP_C498520661umeral (div_mo1740067990umeral A_67) B_55)) A_67)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2))) (=> (or (not (= zero_zero_nat A_3)) (not (= B_2 zero_zero_nat))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_3) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B_2) _let_1)) one_one_nat)))) (forall ((A_148 $$unsorted) (N_51 $$unsorted) (N_50 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_148))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_51) N_50)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) A_148)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int _let_1 N_51)) (hAPP_nat_int _let_1 N_50))))))) (forall ((A $$unsorted)) (hBOOL (hAPP_complex_bool (isCont_complex_real re) A))) (forall ((C_43 $$unsorted) (A_101 $$unsorted) (B_83 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral C_43))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_101) B_83)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral _let_1 A_101)) (hAPP_C498520661umeral _let_1 B_83)))))) (forall ((A_58 $$unsorted) (B_49 $$unsorted) (C_28 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_58) B_49)) C_28) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (div_mod_int A_58) C_28)) (hAPP_int_int (div_mod_int B_49) C_28))) C_28))) (forall ((A_32 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_32) one_on1645066479umeral))) (forall ((Y_8 $$unsorted) (Z_6 $$unsorted) (X_11 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int Z_6))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 X_11)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 Y_8)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int X_11) Y_8)) Z_6) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int X_11) Z_6)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int Y_8) Z_6))))))) (forall ((X $$unsorted)) (= (ratreal (hAPP_rat_rat inverse_inverse_rat X)) (hAPP_real_real inverse_inverse_real (ratreal X)))) (forall ((N $$unsorted)) (= (hAPP_int_int uminus_uminus_int N) (archim1246769320r_real (hAPP_real_real uminus_uminus_real (hAPP_int_real real_int N))))) (forall ((X_1 $$unsorted)) (= (or (exists ((N_2 $$unsorted)) (and (not (hBOOL (hAPP_nat_bool even_odd_even_nat N_2))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_2)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X_1))) (exists ((N_2 $$unsorted)) (and (= X_1 (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_2)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (not (hBOOL (hAPP_nat_bool even_odd_even_nat N_2)))))) (= zero_zero_real (hAPP_real_real cos X_1)))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_1) zero_zero_int) Z_1))) (forall ((B_2 $$unsorted) (Bq $$unsorted) (Br $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted) (Aq $$unsorted) (Ar $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ar) Br))) (=> (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel A_3 C_1) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat Aq) Ar))) (=> (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel B_2 C_1) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat Bq) Br))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_1)) (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_3) B_2) C_1) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Aq) Bq)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat _let_1) C_1))) (hAPP_nat_nat (div_mod_nat _let_1) C_1))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real plus_plus_real) (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real _let_2 sin)) _let_1))) (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real _let_2 cos)) _let_1)) X_2) zero_zero_real))))) (forall ((X $$unsorted)) (= (hAPP_complex_real im (hAPP_complex_complex uminus473333897omplex X)) (hAPP_real_real uminus_uminus_real (hAPP_complex_real im X)))) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) one_on1684967323de_int)) (forall ((X_37 $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_37) one_one_nat) X_37)) (forall ((A_224 $$unsorted) (N_68 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_r474017924t_real power_power_real A_224))) (= (hAPP_nat_real _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_68)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_nat_real _let_2 N_68)) _let_1))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted)) (= (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int C) A) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B) A)) (= C B))) (forall ((B_71 $$unsorted) (A_83 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_83)) (=> (hBOOL (hAPP_rat_bool _let_1 B_71)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_83) B_71))))))) (forall ((C_88 $$unsorted) (A_206 $$unsorted) (B_157 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int A_206))) (=> (hBOOL (hAPP_int_bool _let_1 B_157)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int B_157) C_88)) (hBOOL (hAPP_int_bool _let_1 C_88)))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zEven)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_1) Y_2)) _let_1) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X_1) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int Y_2) _let_1))))))) (forall ((A_198 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral zero_z126310315umeral) A_198)) (= A_198 zero_z126310315umeral))) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real powr X) Y)))) (forall ((N $$unsorted)) (= (hAPP_real_real tan (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) pi)) zero_zero_real)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f237669397t_bool P (hAPP_P989584703t_bool Q R)) (hAPP_P989584703t_bool (hAPP_f1781059817t_bool (hAPP_f326728547t_bool cOMBB_2086486755nt_int P) Q) R))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (= (or (hBOOL (hAPP_nat_bool _let_1 X_1)) (= N_1 zero_zero_nat)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) N_1)))))) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (=> (is_int X_1) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) (hAPP_i1948725293t_bool sr P_5))) (= (hAPP_int_int (standardRes P_5) X_1) X_1)))) (forall ((A_3 $$unsorted)) (let ((_let_1 (hAPP_int_int bit1 pls))) (let ((_let_2 (hAPP_int_fun_nat_int power_power_int A_3))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) (hAPP_nat_int _let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_1)))) (hAPP_nat_int _let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (K_2 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_3) K_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X) Y)) (exists ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat P_3))) (and (= (hAPP_nat_nat _let_1 I_2) X) (= (hAPP_nat_nat _let_1 J_1) Y))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_P1175774780nt_int product_fst_int_int (divmod_int A_3 B_2)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) J_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) K_2))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool _let_1 X_2)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int F X_2))))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (big_co1548731110nt_int F A_1)))))) (forall ((V_4 $$unsorted)) (let ((_let_1 (hAPP_nat_rat semiri151668891at_rat (hAPP_int_nat number_number_of_nat V_4)))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int number_number_of_int V_4))))) (and (=> (not _let_2) (= _let_1 zero_zero_rat)) (=> _let_2 (= (hAPP_int_rat number_number_of_rat V_4) _let_1)))))) (forall ((Y $$unsorted) (X $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y)))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat A_3))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B_2) C_1))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat B_2) C_1))) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat _let_1 B_2)) C_1)))) (forall ((C_78 $$unsorted) (D_14 $$unsorted) (A_178 $$unsorted) (B_138 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_178) B_138)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral C_78) D_14)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_178)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C_78)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_178) C_78)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_138) D_14))))))))) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Lx_5) Ly_3)))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int Rx_5))) (= (hAPP_int_int _let_1 (hAPP_int_int _let_2 Ry_3)) (hAPP_int_int _let_2 (hAPP_int_int _let_1 Ry_3)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real P) Q) R) (hAPP_real_real (hAPP_n546711566l_real P R) Q))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex Z_1) (hAPP_complex_complex cnj Z_1)) (of_real_complex (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_complex_real re Z_1))))) (forall ((W $$unsorted)) (= (hAPP_int_rat number_number_of_rat W) (hAPP_int_rat (hAPP_int_fun_int_rat fract W) one_one_int))) (forall ((B_131 $$unsorted) (A_171 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_171) zero_z891286103de_int)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) B_131)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_171) B_131)) zero_z891286103de_int))))) (forall ((N $$unsorted)) (= (hAPP_nat_real semiri132038758t_real N) (hAPP_complex_real re (hAPP_nat_complex semiri2020571505omplex N)))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (zcong A_3))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) A_3)) one_one_int) P_3)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int)) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 one_one_int) P_3)))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2))) (hBOOL (hAPP_real_bool (isCont_real_real F) X_2)))) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) X_2))) (hBOOL (hAPP_real_bool (deriv_real F X_2) zero_zero_real)))) (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B))) (= (hAPP_real_real F A) (hAPP_real_real F X_2)))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real A) B) (hAPP_n332733730l_real (bolzano_bisect P_1 A B) zero_zero_nat))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) K_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N_1) K_1))) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1))))) (forall ((A_109 $$unsorted) (B_87 $$unsorted) (C_47 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A_109))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 B_87)) C_47) (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_87) C_47))))) (forall ((I_1 $$unsorted) (J $$unsorted)) (= (hAPP_n1699378549t_bool (ord_at4362885an_nat (hAPP_nat_nat suc I_1)) (hAPP_nat_nat suc J)) (image_nat_nat suc (hAPP_n1699378549t_bool (ord_at4362885an_nat I_1) J)))) (forall ((N_1 $$unsorted)) (= zero_zero_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real (hAPP_f451358433l_real (hAPP_f335634176l_real cOMBS_337378985l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min))) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat div_div_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) (hAPP_r474017924t_real power_power_real zero_zero_real)))) zero_zero_real)) (hAPP_n1699378549t_bool (ord_at4362885an_nat one_one_nat) N_1)))) (forall ((A $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_5)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) P_5))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_5) A))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (big_co1548731110nt_int cOMBI_int (comple219730294t_bool (setS A P_5)))) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int)) _let_1)))) P_5)))))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real cos X))) one_one_real))) (forall ((X_21 $$unsorted) (N_31 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_21))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_31)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_31) one_one_nat))) X_21) (hAPP_nat_real _let_1 N_31))))) (forall ((A_62 $$unsorted)) (=> (is_int A_62) (= A_62 (hAPP_int_int (div_mod_int A_62) zero_zero_int)))) (forall ((C_66 $$unsorted) (A_144 $$unsorted) (B_113 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_66))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A_144)) (hAPP_rat_rat _let_1 B_113))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C_66)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_144) B_113)))))) (forall ((N_61 $$unsorted) (X_29 $$unsorted) (Y_23 $$unsorted)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex X_29) Y_23)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_29) N_61)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex Y_23) N_61))))) (forall ((X $$unsorted)) (=> (= (hAPP_real_real cos X) one_one_real) (= zero_zero_real (hAPP_real_real sin X)))) (forall ((X $$unsorted)) (=> (not (= X zero_zero_real)) (= (hAPP_real_real arctan (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) X)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real sgn_sgn_real X)) pi)) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hAPP_real_real arctan X))))) (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)) M))) (forall ((M_28 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex M_28) M_28) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex one_one_complex) one_one_complex)) M_28))) (forall ((C_59 $$unsorted) (D_12 $$unsorted) (A_137 $$unsorted) (B_106 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_137) B_106)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C_59) D_12)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_137)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C_59)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_137) C_59)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_106) D_12)))))))) (forall ((P_3 $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int P_3))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y) N))))))) (forall ((V $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V_1))) (let ((_let_2 (hAPP_int_int number_number_of_int V))) (let ((_let_3 (hBOOL (hAPP_int_bool nat_neg _let_2)))) (let ((_let_4 (hBOOL (hAPP_int_bool nat_neg _let_1)))) (=> (and (is_int V) (is_int V_1)) (= (= (hAPP_int_nat number_number_of_nat V_1) (hAPP_int_nat number_number_of_nat V)) (and (=> (not _let_3) (and (=> _let_4 (= _let_2 zero_zero_int)) (=> (not _let_4) (= V V_1)))) (=> _let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int _let_1) zero_zero_int))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X) Y)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_int_real real_int X)) (hAPP_int_real real_int Y)))) (forall ((A_234 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_234) A_234) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_234) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((Q_2 $$unsorted)) (let ((_let_1 (hAPP_rat_rat sgn_sgn_rat Q_2))) (let ((_let_2 (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) Q_2)))) (let ((_let_3 (= Q_2 zero_zero_rat))) (and (=> _let_3 (= zero_zero_rat _let_1)) (=> (not _let_3) (and (=> _let_2 (= one_one_rat _let_1)) (=> (not _let_2) (= (hAPP_rat_rat uminus_uminus_rat one_one_rat) _let_1))))))))) (forall ((A_203 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_203) zero_zero_real) zero_zero_real)) (forall ((A_3 $$unsorted)) (= (hAPP_int_int (div_mod_int A_3) A_3) zero_zero_int)) (forall ((C_37 $$unsorted) (A_95 $$unsorted) (B_77 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_95) B_77)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_95) C_37)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_77) C_37))))) (forall ((X_40 $$unsorted) (N_69 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_40))) (let ((_let_2 (hAPP_nat_real _let_1 N_69))) (= (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_69)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_2) _let_2))))) (forall ((A_19 $$unsorted) (B_15 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_19) B_15)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_19) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral B_15) A_19)) B_15))) (forall ((Z_14 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Z_14) Z_14) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_14))) (forall ((N_12 $$unsorted) (R_6 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) R_6)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat R_6) one_one_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat R_6) (hAPP_nat_nat suc N_12))) R_6))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_Q2096512830t_bool B_1_1 B_2_1))) (forall ((N $$unsorted)) (=> (not (= zero_zero_nat N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) one_one_nat)) N)))) (forall ((A_38 $$unsorted) (C_13 $$unsorted) (B_29 $$unsorted)) (let ((_let_1 (div_mo231679042de_int A_38))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int C_13) B_29)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int _let_1 B_29)) C_13) (hAPP_Q1762011733de_int _let_1 C_13))))) (= (hAPP_int_int uminus_uminus_int zero_zero_int) zero_zero_int) (forall ((A_200 $$unsorted) (B_153 $$unsorted) (C_86 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_200) B_153)) C_86) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_200) C_86)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_153) C_86)))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int upto_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A0) A1))) (=> (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (and (is_int J_1) (is_int I_2)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int upto_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int I_2) J_1))) (=> (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I_2) J_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int I_2) one_one_int)) J_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 I_2) J_1)))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((X_39 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_39) X_39) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_39) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((M $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc M)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) (hAPP_nat_int semiri1621563631at_int M)))) (forall ((D $$unsorted)) (= (= D one_one_nat) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime zero_zero_nat) D)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (and (= one_one_real Y_2) (= zero_zero_real X_1)) (= (hAPP_real_complex (hAPP_r265291036omplex complex X_1) Y_2) ii))) (forall ((C_37 $$unsorted) (A_95 $$unsorted) (B_77 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_95) B_77)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_95) C_37)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_77) C_37))))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) K_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N_1) K_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real semiri132038758t_real Ma)) (hAPP_nat_real semiri132038758t_real N_1))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat) (natfloor X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X_1)))) (forall ((N $$unsorted) (M $$unsorted) (R_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int M) R_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N) R_3)) (=> (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int M) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N)) R_3)))))) (forall ((B_90 $$unsorted) (A_112 $$unsorted) (C_50 $$unsorted)) (=> (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral C_50) A_112) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_90) A_112)) (= B_90 C_50))) (forall ((A_233 $$unsorted)) (= A_233 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat pls)) A_233))) (= _let_20 _let_1) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1948725293t_bool (hAPP_f720654810t_bool (hAPP_f908327869t_bool cOMBB_1290694363ol_int P) Q) R) (hAPP_f429935748t_bool P (hAPP_int_fun_int_int Q R)))) (forall ((A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) P_5))) (= (hAPP_int_int zfact (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int)) (big_co1548731110nt_int cOMBI_int (comple219730294t_bool (setS A P_5)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Xa_2 $$unsorted) (Ya $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real Xa_2) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Ya) _let_1)))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (div_mod_int A_3) B_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) B_2)))))) (forall ((V_22 $$unsorted) (V_21 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_21)) (=> (hBOOL (hAPP_int_bool _let_1 V_22)) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_21) V_22)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat V_21)) (hAPP_int_nat number_number_of_nat V_22))))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real D) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_2) Sa))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) Z)) (= _let_1 _let_1)))))) (forall ((A_139 $$unsorted) (C_61 $$unsorted) (B_108 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_139) C_61)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_108) C_61))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_61)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_139) B_108))))) (forall ((X_21 $$unsorted) (N_31 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral X_21))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_31)) (= (hAPP_n1108039445umeral _let_1 N_31) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_31) one_one_nat))) X_21))))) (not (= one_one_nat zero_zero_nat)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_f284875647l_bool ord_le951220754t_bool X_1) Y_2)) (=> (not (= Y_2 X_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_f284875647l_bool ord_le1912455174t_bool X_1) Y_2))))) (forall ((A_146 $$unsorted)) (= one_one_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_146) zero_zero_nat))) (forall ((C_38 $$unsorted) (A_96 $$unsorted) (B_78 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real C_38))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_96) B_78)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_96)) (hAPP_real_real _let_1 B_78)))))) (forall ((A_3 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_3)) (exists ((R_1 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) R_1)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real R_1) N) A_3)))))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral Lx_1))) (= (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral Rx_1) Ry_1)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral _let_1 Rx_1)) Ry_1)))) (forall ((X_33 $$unsorted)) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_33) zero_zero_nat) one_on1684967323de_int)) (forall ((M_27 $$unsorted) (A_212 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_212) one_one_int)) M_27) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int M_27) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_212) M_27)))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real exp_real X)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (div_mod_int A_3) B_2)) B_2)))) (forall ((F $$unsorted)) (=> (forall ((I_2 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat F (hAPP_nat_nat suc I_2))) (hAPP_nat_nat F I_2)))) (exists ((I_2 $$unsorted)) (forall ((K $$unsorted)) (= (hAPP_nat_nat F I_2) (hAPP_nat_nat F (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_2) K))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat N) M)) (or (= M N) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N)) M)) (= zero_zero_nat M)))) (forall ((I_1 $$unsorted) (M_2 $$unsorted)) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat zero_zero_nat) M_2)) (not (= (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_f800510211t_bool (hAPP_f561022312t_bool cOMBS_nat_bool_bool (hAPP_f1146629647l_bool (hAPP_f1080886329l_bool cOMBB_1015721476ol_nat fconj) (hAPP_f800510211t_bool (hAPP_f1722879237t_bool cOMBC_226598744l_bool member_nat) M_2))) (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_nat) (hAPP_nat_nat suc I_1))))) zero_zero_nat)))) (forall ((A_10 $$unsorted) (N_15 $$unsorted) (B_8 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (let ((_let_2 (hAPP_nat_nat suc N_15))) (=> (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_10) _let_2) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat B_8) _let_2)) (=> (hBOOL (hAPP_rat_bool _let_1 A_10)) (=> (hBOOL (hAPP_rat_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A_208 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat A_208) zero_zero_rat))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) A)) (= (= Ma N_1) (= (hAPP_nat_nat _let_1 Ma) (hAPP_nat_nat _let_1 N_1)))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (log A))) (let ((_let_2 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A)) (=> (hBOOL (hAPP_real_bool _let_2 X_1)) (=> (hBOOL (hAPP_real_bool _let_2 Y_2)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 X_1)) (hAPP_real_real _let_1 Y_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2))))))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_8) pi)) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_real number267125858f_real _let_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) _let_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X))) X))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_2) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat _let_1))))))))) (forall ((Z_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Z_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)) (hAPP_int_nat nat Z_2))))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) zero_zero_real)) (= (hAPP_real_real cos (arg (hAPP_real_complex (hAPP_r265291036omplex complex zero_zero_real) Y))) zero_zero_real))) (forall ((A_202 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int zero_z891286103de_int) A_202) zero_z891286103de_int)) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat B) A)) E_2)) D))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) E_2)) C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B) E_2)) D))))) (forall ((W_6 $$unsorted)) (let ((_let_1 (hAPP_int_rat number_number_of_rat W_6))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat one_one_rat) _let_1)) _let_1) (hAPP_int_rat number_number_of_rat (hAPP_int_int bit1 W_6))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral C))) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral _let_1 A)) (hAPP_C498520661umeral _let_1 B))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A) B))))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int min) (hAPP_int_int bit0 K_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int min) K_1)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) C)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B) C))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2))) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2) (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_2) _let_1))))) (forall ((X_1 $$unsorted)) (= (comple124823625p_real (hAPP_r1134773055l_bool ord_lessThan_real X_1)) X_1)) (forall ((Z_1 $$unsorted) (W $$unsorted)) (=> (and (is_int W) (is_int Z_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_1) W)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W) Z_1)) (= Z_1 W))))) (forall ((X_3 $$unsorted)) (=> (hBOOL (cauchy_complex X_3)) (hBOOL (cauchy_complex (hAPP_f1646117269omplex (hAPP_f1457396693omplex cOMBB_117013006ex_nat cnj) X_3))))) (forall ((A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (=> (is_int B) (= (exists ((K $$unsorted)) (and (is_int K) (= B (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Ma) K))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma))))) (forall ((A_208 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_208) zero_zero_int))) (forall ((K_1 $$unsorted) (Xa_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real sin) (hAPP_r1250527377l_real (hAPP_f203520653l_real cOMBC_real_real_real plus_plus_real) K_1)) Xa_1) (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Xa_1) K_1))))) (forall ((B_1_1 $$unsorted)) (is_bool (summable_complex B_1_1))) (forall ((X $$unsorted)) (= (hAPP_real_real tan (hAPP_real_real uminus_uminus_real X)) (hAPP_real_real uminus_uminus_real (hAPP_real_real tan X)))) (forall ((A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (big_co1548731110nt_int cOMBI_int (hAPP_i1948725293t_bool (wset A) P_5))) one_one_int) P_5)))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (hAPP_int_complex ring_11397209091omplex Z_1))) (= _let_1 (hAPP_complex_complex cnj _let_1)))) (forall ((A_19 $$unsorted) (B_15 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_19) B_15)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_19) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B_15) A_19)) B_15))) (not (= one_on1684967323de_int zero_z891286103de_int)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real Y)) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (=> (not (= zero_zero_nat N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X) N)) Y)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y))))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (= (hAPP_real_real (hAPP_r1250527377l_real powr (hAPP_real_real _let_1 B_2)) A_3) (hAPP_real_real (hAPP_r1250527377l_real powr (hAPP_real_real _let_1 A_3)) B_2)))) (forall ((A_143 $$unsorted) (C_65 $$unsorted) (B_112 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_143) C_65)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_112) C_65))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_65)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_143) B_112))))) (forall ((X $$unsorted)) (= (hAPP_real_real cos X) (hAPP_real_real cos (hAPP_real_real uminus_uminus_real X)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (is_int B_2_1) (is_int (hAPP_int_int B_1_1 B_2_1)))) (forall ((C_89 $$unsorted) (D_17 $$unsorted) (A_213 $$unsorted) (B_159 $$unsorted) (R_8 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex R_8))) (=> (not (= R_8 zero_zero_complex)) (=> (and (not (= C_89 D_17)) (= A_213 B_159)) (not (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_213) (hAPP_complex_complex _let_1 C_89)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_159) (hAPP_complex_complex _let_1 D_17)))))))) (= one_one_real (hAPP_complex_real re one_one_complex)) (forall ((N_54 $$unsorted) (A_151 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_151)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_151) N_54)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_rat_fun_rat_rat P (hAPP_nat_rat Q R)) (hAPP_nat_fun_rat_rat (hAPP_f1830834240at_rat (hAPP_f1073644437at_rat cOMBB_1926947at_nat P) Q) R))) (forall ((A_167 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_167) A_167)))) (forall ((N $$unsorted)) (= N (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc N)) one_one_nat))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real arccos Y)) pi))))) (forall ((X_9 $$unsorted)) (let ((_let_1 (hAPP_nat_nat semiri984289939at_nat (hAPP_int_nat nat X_9)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_9)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat _let_1) _let_1) (hAPP_nat_nat semiri984289939at_nat (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_9))))))) (forall ((A_143 $$unsorted) (C_65 $$unsorted) (B_112 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_143) C_65)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_112) C_65))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) C_65)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_143) B_112))))) (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real sin Y_2))) (let ((_let_3 (hAPP_f1960414057l_real cOMBB_882763271l_real times_times_real))) (let ((_let_4 (hAPP_f203520653l_real cOMBC_real_real_real (hAPP_f556082547l_real _let_3 sin)))) (let ((_let_5 (hAPP_real_real cos Y_2))) (let ((_let_6 (hAPP_f203520653l_real cOMBC_real_real_real (hAPP_f556082547l_real _let_3 cos)))) (let ((_let_7 (hAPP_f1960414057l_real cOMBB_882763271l_real minus_minus_real))) (let ((_let_8 (hAPP_r1250527377l_real (hAPP_f203520653l_real cOMBC_real_real_real plus_plus_real) Y_2))) (let ((_let_9 (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real))) (let ((_let_10 (hAPP_f1960414057l_real cOMBB_882763271l_real plus_plus_real))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real _let_10 (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real _let_9 (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real _let_7 (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real sin) _let_8))) (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real _let_10 (hAPP_r1250527377l_real _let_4 _let_5))) (hAPP_r1250527377l_real _let_6 _let_2))))) _let_1))) (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real _let_9 (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real _let_7 (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real cos) _let_8))) (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real _let_7 (hAPP_r1250527377l_real _let_6 _let_5))) (hAPP_r1250527377l_real _let_4 _let_2))))) _let_1)) X_2) zero_zero_real))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int P_3))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N))) (or (hBOOL (hAPP_int_bool _let_1 M)) (hBOOL (hAPP_int_bool _let_1 N))))))) (forall ((A_18 $$unsorted) (C_5 $$unsorted) (B_14 $$unsorted)) (=> (not (= zero_z891286103de_int B_14)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int C_5) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_18) B_14)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_18) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int C_5) B_14))) B_14)))) (forall ((Ta $$unsorted) (A_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int Ta))) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa))))))))) (=> (hBOOL (hAPP_int_bool _let_1 X_2)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) D_1)))))))))) (forall ((B_70 $$unsorted) (A_82 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_82) zero_z126310315umeral)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral B_70) zero_z126310315umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_82) B_70)) zero_z126310315umeral))))) (forall ((P_3 $$unsorted)) (= (frct P_3) (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_P1175774780nt_int product_fst_int_int P_3)) (hAPP_P1175774780nt_int product_snd_int_int P_3)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real pi)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real cos Y)) (hAPP_real_real cos X))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= (= (hAPP_nat_nat (div_mod_nat X_1) (hAPP_nat_nat suc _let_1)) _let_1) (not (hBOOL (hAPP_nat_bool even_odd_even_nat X_1)))))) (forall ((A_140 $$unsorted) (C_62 $$unsorted) (B_109 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_140) C_62)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_109) C_62))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_62)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_140) B_109))))) (forall ((A_232 $$unsorted)) (= A_232 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_232) (hAPP_int_rat number_number_of_rat pls)))) (= one_one_real (hAPP_real_real sin _let_10)) (forall ((Ta $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real D) D_1)) (forall ((X_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool dvd_dvd_real D))) (= (not (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_2) (hAPP_real_real (hAPP_r1250527377l_real times_times_real K) D_1))) Ta)))) (not (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_2) Ta))))))))) (forall ((C $$unsorted) (X_1 $$unsorted) (Ta $$unsorted) (A $$unsorted) (D $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int X_1))) (let ((_let_2 (hAPP_i1948725293t_bool dvd_dvd_int A))) (=> (hBOOL (hAPP_int_bool _let_2 D)) (= (hBOOL (hAPP_int_bool _let_2 (hAPP_int_int _let_1 Ta))) (hBOOL (hAPP_int_bool _let_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int C) D))) Ta)))))))) (forall ((A $$unsorted) (B $$unsorted) (K_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Ma)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd K_1) Ma)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) K_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) K_1)) Ma)))))) (forall ((C_58 $$unsorted) (D_11 $$unsorted) (A_136 $$unsorted) (B_105 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_136) B_105)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C_58) D_11)) (=> (hBOOL (hAPP_rat_bool _let_1 A_136)) (=> (hBOOL (hAPP_rat_bool _let_1 C_58)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_136) C_58)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_105) D_11))))))))) (forall ((A $$unsorted)) (= (big_co1548731110nt_int cOMBI_int (hAPP_i1948725293t_bool d22set A)) (hAPP_int_int zfact A))) (forall ((Q_2 $$unsorted) (B_2 $$unsorted) (R_3 $$unsorted) (C_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) R_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int R_3) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) (hAPP_int_int (div_mod_int Q_2) C_1))) R_3)) zero_zero_int)))))) (forall ((A_189 $$unsorted) (B_145 $$unsorted) (C_82 $$unsorted)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_189) B_145)) C_82)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex A_189) C_82)))) (forall ((A_10 $$unsorted) (N_15 $$unsorted) (B_8 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (let ((_let_2 (hAPP_nat_nat suc N_15))) (=> (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_10) _let_2) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_8) _let_2)) (=> (hBOOL (hAPP_real_bool _let_1 A_10)) (=> (hBOOL (hAPP_real_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_bool (hAPP_f101635158l_bool (hAPP_f1925507189l_bool cOMBB_1121934354l_real P) Q) R) (hAPP_f448129468l_bool P (hAPP_r481142414t_bool Q R)))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A) B)) (exists ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat B))) (let ((_let_2 (hAPP_nat_fun_nat_nat times_times_nat A))) (or (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 X_2)) (hAPP_nat_nat _let_2 Y_1))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_2 X_2)) (hAPP_nat_nat _let_1 Y_1)) one_one_nat))))))) (forall ((A_143 $$unsorted) (C_65 $$unsorted) (B_112 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_143) C_65)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_112) C_65))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C_65)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_143) B_112))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (nat_tsub X) Y))))))) (= (hAPP_real_real ln one_one_real) zero_zero_real) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat Ma) (hAPP_nat_nat suc N_1)) (hAPP_nat_nat (nat_case_nat zero_zero_nat (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat suc) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat ord_min_nat) N_1))) Ma))) (forall ((N $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real real_nat N)) zero_zero_real)))) (forall ((Ma $$unsorted) (X_1 $$unsorted)) (= (hAPP_i1948725293t_bool (noXRRset Ma) X_1) (image_int_int (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int times_times_int) X_1) (hAPP_i1948725293t_bool norRRset Ma)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_real number267125858f_real _let_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) _let_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real uminus_uminus_real X)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_2) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat _let_1))))) (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) X))))))))) (forall ((A_198 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat zero_zero_rat) A_198)) (= zero_zero_rat A_198))) (not (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int) zero_z891286103de_int))) (forall ((A_235 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_235) A_235)) A_235) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_235) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))))) (forall ((P_1 $$unsorted)) (= (forall ((X1 $$unsorted)) (hBOOL (hAPP_nat_bool P_1 X1))) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2)) (hBOOL (hAPP_nat_bool P_1 (hAPP_int_nat nat X_2)))))))) (= _let_100 zero_zero_rat) (forall ((A_134 $$unsorted) (N_47 $$unsorted) (B_103 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_134) N_47)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int B_103) N_47))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) B_103)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_134) B_103))))) (forall ((V_2 $$unsorted) (W $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W))) (let ((_let_2 (hAPP_int_int number_number_of_int V_2))) (let ((_let_3 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_4 (hAPP_int_int (div_mod_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 V_2))) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 W))))) (let ((_let_5 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_1)))) (and (=> _let_5 (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_3 (hAPP_int_int (div_mod_int _let_2) _let_1))) one_one_int) _let_4)) (=> (not _let_5) (= _let_4 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int _let_3 (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_2) one_one_int)) _let_1))) one_one_int)))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_b646336293l_real P (hAPP_nat_bool Q R)) (hAPP_n682674106l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat P) Q) R))) (forall ((A_229 $$unsorted) (C_95 $$unsorted) (D_20 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat C_95))) (let ((_let_2 (hAPP_nat_fun_nat_nat plus_plus_nat A_229))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_2 D_20)) (hAPP_nat_nat _let_2 (hAPP_nat_nat _let_1 D_20)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int B_2) A_3) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (or (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real A) B)) (= zero_zero_real C)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) C)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) C))))) (forall ((N $$unsorted) (X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real real_nat N)) (hAPP_nat_real real_nat X))) (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) X)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int P R) Q) (hAPP_int_int (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int P) Q) R))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P1668131738nt_int (hAPP_f167782601nt_int (hAPP_f1769710159nt_int cOMBC_2037038898nt_int P) Q) R) (hAPP_f521271395nt_int (hAPP_P752050971nt_int P R) Q))) (forall ((A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (natceiling (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_nat_real real_nat A_3))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (natceiling X)) A_3)))) (forall ((N $$unsorted)) (= zero_zero_real (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) pi)))) (forall ((A_21 $$unsorted) (B_17 $$unsorted)) (=> (is_int B_17) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_21) B_17)) (= B_17 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_17) A_21)) A_21))))) (forall ((Diff $$unsorted) (F $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real H) zero_zero_real)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (forall ((M_1 $$unsorted) (T $$unsorted)) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real H) T)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) zero_zero_real))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) T) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) T))))) (= (hAPP_n546711566l_real Diff zero_zero_nat) F)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real H))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real H) T)) (= (hAPP_real_real F H) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real T) zero_zero_real))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) C)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) C))) (or (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) A)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C) zero_zero_int))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)))))) (forall ((A_36 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral zero_z126310315umeral) A_36) zero_z126310315umeral)) (forall ((A_143 $$unsorted) (C_65 $$unsorted) (B_112 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_143) C_65)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_112) C_65))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_65)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_143) B_112))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) (hAPP_int_real real_int A))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (archim1246769320r_real X_1)) A)))) (forall ((R_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) zero_zero_real)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int N_2)) R_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int N_2) one_one_int)))) (is_int N_2))))) (forall ((N_62 $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real one_one_real) N_62) one_one_real)) (forall ((N $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) zero_zero_nat)))) (hBOOL (hAPP_int_bool nat_is_nat zero_zero_int)) (forall ((Diff $$unsorted) (N_1 $$unsorted) (X_1 $$unsorted)) (=> (= X_1 zero_zero_real) (=> (not (= N_1 zero_zero_nat)) (= (hAPP_real_real (hAPP_n546711566l_real Diff zero_zero_nat) zero_zero_real) (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) (hAPP_r474017924t_real power_power_real X_1))) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1)))))) (forall ((B_93 $$unsorted) (A_115 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_115) zero_zero_nat)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat B_93) zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_115) B_93)) zero_zero_nat))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (zcong A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 B_2) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong B_2) C_1) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 C_1) M)))))) (forall ((A_110 $$unsorted) (B_88 $$unsorted) (C_48 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_110))) (=> (= (hAPP_Q1762011733de_int _let_1 B_88) (hAPP_Q1762011733de_int _let_1 C_48)) (= B_88 C_48)))) (forall ((A_239 $$unsorted) (B_167 $$unsorted) (V_15 $$unsorted)) (let ((_let_1 (hAPP_i1732201573de_int number1226105091de_int V_15))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_239) _let_1)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_167) _let_1)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_239) B_167)) _let_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le1568362934t_bool X_1) Y_2)) (=> (not (= Y_2 X_1)) (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le382113706t_bool X_1) Y_2))))) (forall ((A_218 $$unsorted) (B_161 $$unsorted) (C_90 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_218) B_161)) C_90) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_218) C_90)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_161) C_90)))) (forall ((A_93 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A_93) zero_zero_complex) A_93)) (forall ((A_33 $$unsorted) (B_27 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_33) B_27)) B_27) zero_z891286103de_int)) (= zero_zero_int pls) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real uminus_uminus_real X))) (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real sin _let_2)) (hAPP_real_real sin X))) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real cos _let_2)) (hAPP_real_real cos X))) _let_1)))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) N) (hAPP_real_real (hAPP_r1250527377l_real powr X) (hAPP_nat_real real_nat N))))) (not (= min pls)) (forall ((N $$unsorted) (X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_int_real real_int N)) (hAPP_int_real real_int X))) (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int N) X)))) one_one_real))) (forall ((V_13 $$unsorted) (W_11 $$unsorted) (Z_10 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_13) W_11))) Z_10) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat V_13)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat W_11)) Z_10)))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_1)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int one_one_int) _let_1) (hAPP_P1175774780nt_int product_fst_int_int (posDivAlg one_one_int _let_1)))))) (forall ((B_69 $$unsorted) (A_81 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_81)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_69)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_81) B_69))))))) (forall ((N $$unsorted) (M_4 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc N)) M_4)) (exists ((M_1 $$unsorted)) (= M_4 (hAPP_nat_nat suc M_1))))) (forall ((B_128 $$unsorted) (A_168 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_168)) (=> (hBOOL (hAPP_rat_bool _let_1 B_128)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_168) B_128))))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc (hAPP_nat_nat (div_mod_nat M) N))) N) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc M)) N))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))))))) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_i769753017umeral number1443263063umeral W_1))) (= (= X_1 _let_1) (= _let_1 X_1)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) N))) (let ((_let_2 (= zero_zero_real X))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (and (=> _let_2 (= zero_zero_real _let_1)) (=> (not _let_2) (= _let_1 (hAPP_real_real (hAPP_r1250527377l_real powr X) (hAPP_nat_real real_nat N)))))))))) (forall ((A_3 $$unsorted)) (=> (is_int A_3) (and (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) zero_zero_int)) (= A_3 (hAPP_int_int (div_mod_int A_3) zero_zero_int))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (P_3 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int B_2))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int A_3))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_P1175774780nt_int twoSqu1907779896sum2sq (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A_3) B_2))) (hAPP_P1175774780nt_int twoSqu1907779896sum2sq (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2))) (hAPP_P1175774780nt_int twoSqu1907779896sum2sq (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_2 P_3)) (hAPP_int_int _let_1 Q_2))) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int _let_2 Q_2)) (hAPP_int_int _let_1 P_3)))))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (= C (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B) A)) E_2)) D)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) E_2)) D) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) E_2)) C)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (log A))) (let ((_let_2 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A)) (=> (hBOOL (hAPP_real_bool _let_2 X_1)) (=> (hBOOL (hAPP_real_bool _let_2 Y_2)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 X_1)) (hAPP_real_real _let_1 Y_2)))))))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_10) _let_8)) (forall ((M $$unsorted) (A_3 $$unsorted)) (=> (is_int A_3) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) zero_zero_int) M)) (= zero_zero_int A_3)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (deriv_real _let_1 X_1) (hAPP_real_real inverse_inverse_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real _let_1 X_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) (hAPP_nat_nat suc zero_zero_nat))))))))))) (forall ((N_1 $$unsorted)) (= (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real (hAPP_f451358433l_real (hAPP_f335634176l_real cOMBS_337378985l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min))) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat div_div_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) zero_zero_real))) (hAPP_r474017924t_real power_power_real zero_zero_real))) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) (hAPP_nat_nat suc N_1))) one_one_real)) (forall ((N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat suc N)) N) one_one_nat)) (forall ((M $$unsorted)) (=> (is_int M) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) M)) (= M (hAPP_int_int (legacy_zgcd M) M))))) (forall ((V_20 $$unsorted) (W_16 $$unsorted) (Z_15 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_20) W_16))) Z_15) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat V_20)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat W_16)) Z_15)))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat I))) (=> (hBOOL (hAPP_nat_bool _let_1 J_2)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) J_2)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_bool (hAPP_f800510211t_bool (hAPP_f561022312t_bool cOMBS_nat_bool_bool P) Q) R) (hAPP_bool_bool (hAPP_n1006566506l_bool P R) (hAPP_nat_bool Q R)))) (forall ((V_3 $$unsorted) (K_2 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat V_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat V_3)) K_2)))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int V_2) pls)))) (and (=> (not _let_2) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_2) V_3))) K_2) _let_1)) (=> _let_2 (= _let_1 zero_zero_nat)))))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat Lx_6))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat _let_1 Ly_4)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Rx_6) Ry_4)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat _let_1 Rx_6)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Ly_4) Ry_4))))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_3) B_2)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 A_3)) (hAPP_real_real _let_1 B_2))))) (forall ((A_125 $$unsorted) (N_36 $$unsorted) (N_35 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_125))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_36) N_35)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_125)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_125) one_one_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 N_35)) (hAPP_nat_nat _let_1 N_36)))))))) (forall ((N_1 $$unsorted)) (= (hAPP_real_real uminus_uminus_real (hAPP_nat_real sin_coeff N_1)) (hAPP_nat_real (diffs_real cos_coeff) N_1))) true (forall ((Z_1 $$unsorted)) (exists ((R_1 $$unsorted) (A_2 $$unsorted)) (= Z_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (of_real_complex R_1)) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real cos A_2)) (hAPP_real_real sin A_2)))))) (forall ((N_1 $$unsorted) (G $$unsorted) (X_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real G X_1) Ma)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real) G)) N_1) X_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real G X_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) one_one_nat)))) Ma))))) (forall ((N_1 $$unsorted) (S $$unsorted)) (=> (hBOOL (hAPP_f215623910l_bool finite1395289673t_bool S)) (=> (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool X_2) S)) (hBOOL (hAPP_f448129468l_bool finite_finite_int X_2)))) (=> (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool X_2) S)) (= N_1 (hAPP_f957591787ol_nat finite_card_int X_2)))) (= (hAPP_f521865025ol_nat (hAPP_f93439879ol_nat big_co1758102091ol_nat (cOMBK_1643584600t_bool N_1)) S) (hAPP_f521865025ol_nat (hAPP_f93439879ol_nat big_co1758102091ol_nat finite_card_int) S)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) M)) N)))) (forall ((A_146 $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A_146) zero_zero_nat) one_one_complex)) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (divmod_int A_3 B_2))) (let ((_let_2 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_3 (hBOOL (hAPP_int_bool _let_2 B_2)))) (let ((_let_4 (hAPP_int_int uminus_uminus_int B_2))) (let ((_let_5 (hAPP_int_int uminus_uminus_int A_3))) (let ((_let_6 (= A_3 zero_zero_int))) (let ((_let_7 (hBOOL (hAPP_int_bool _let_2 A_3)))) (let ((_let_8 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)))) (=> (is_int A_3) (and (=> (not _let_7) (and (=> (not _let_8) (= (hAPP_P1975530577nt_int negateSnd (posDivAlg _let_5 _let_4)) _let_1)) (=> _let_8 (= _let_1 (negDivAlg A_3 B_2))))) (=> _let_7 (and (=> (not _let_3) (and (=> _let_6 (= _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) zero_zero_int))) (=> (not _let_6) (= (hAPP_P1975530577nt_int negateSnd (negDivAlg _let_5 _let_4)) _let_1)))) (=> _let_3 (= _let_1 (posDivAlg A_3 B_2)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) zero_zero_int)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A) B)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A))))) (forall ((N_19 $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real zero_zero_real) (hAPP_nat_nat suc N_19)) zero_zero_real)) (forall ((N_41 $$unsorted)) (let ((_let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral zero_z126310315umeral) N_41))) (let ((_let_2 (= N_41 zero_zero_nat))) (and (=> _let_2 (= _let_1 one_on1645066479umeral)) (=> (not _let_2) (= zero_z126310315umeral _let_1)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X)) (hAPP_real_real exp_real X))))) (forall ((A_215 $$unsorted)) (= A_215 (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_215) one_one_real))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_real real_int N))) (=> (is_int N) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real _let_1) one_one_real)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) _let_1)) (= N (archim856651990g_real X))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_int (hAPP_f1139079189at_int (hAPP_f1431025877at_int cOMBB_int_int_nat P) Q) R) (hAPP_int_int P (hAPP_nat_int Q R)))) (forall ((A_31 $$unsorted) (C_12 $$unsorted) (B_26 $$unsorted)) (= (hAPP_int_int (div_mod_int A_31) B_26) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_31) (hAPP_int_int (hAPP_int_fun_int_int times_times_int C_12) B_26))) B_26))) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) X)) one_one_real)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) one_one_real)) N))))) (forall ((N_49 $$unsorted) (A_147 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int one_one_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_147)) (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_147) N_49)))))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (or (= N zero_zero_nat) (= (hAPP_nat_nat suc zero_zero_nat) N)))) (forall ((K_2 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_i1732201573de_int number1226105091de_int _let_1))) (let ((_let_3 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_1)) (quickcheck_int_of (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int K_2) _let_2))))) (let ((_let_4 (quickcheck_int_of K_2))) (let ((_let_5 (= (hAPP_Q1762011733de_int (div_mo231679042de_int K_2) _let_2) zero_z891286103de_int))) (and (=> (= K_2 zero_z891286103de_int) (= _let_4 zero_zero_int)) (=> (not (= zero_z891286103de_int K_2)) (and (=> _let_5 (= _let_3 _let_4)) (=> (not _let_5) (= _let_4 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_3) one_one_int)))))))))))) (forall ((R_3 $$unsorted) (X $$unsorted)) (= (hAPP_real_real (scaleR_scaleR_real R_3) (hAPP_complex_real im X)) (hAPP_complex_real im (hAPP_complex_complex (scaleR1652505878omplex R_3) X)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_bool (hAPP_r1134773055l_bool P R) Q) (hAPP_real_bool (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool P) Q) R))) (forall ((C_76 $$unsorted) (B_136 $$unsorted) (A_176 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_136) A_176)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C_76) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_176) C_76)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_136) C_76)))))) (forall ((Ta $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat D) D_1)) (forall ((X_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool dvd_dvd_rat D))) (= (not (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat X_2) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat K) D_1))) Ta)))) (not (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_2) Ta))))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat fact_fact_nat N)) (hAPP_nat_nat fact_fact_nat M))))) (forall ((D $$unsorted) (B $$unsorted) (C $$unsorted) (A $$unsorted)) (=> (not (= zero_z891286103de_int A)) (=> (not (= zero_z891286103de_int C)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A) B)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int C) D)) (= (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A) D) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B) C)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int D) C) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int B) A)))))))) (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool P_1 zero_zero_nat)) (=> (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool P_1 N_2)) (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat suc N_2))))) (hBOOL (hAPP_nat_bool P_1 N_1))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real cos X)) one_one_real))) (forall ((A_88 $$unsorted) (B_76 $$unsorted)) (= A_88 (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_88) B_76)) B_76))) (forall ((N $$unsorted) (X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int N) X))) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_int_real real_int N)) (hAPP_int_real real_int X))))) (forall ((Y $$unsorted) (X $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (let ((_let_3 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real U_1) (hAPP_real_real sqrt (hAPP_int_real number267125858f_real _let_1))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real X)) _let_3)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real Y)) _let_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_2)))) U_1)))))))) (forall ((M $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) zero_zero_nat) zero_zero_nat)) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted)) (= (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B) A) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real C) A)) (= C B))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat semiri151668891at_rat Ma)) (hAPP_nat_rat semiri151668891at_rat N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int X_1))) (let ((_let_2 (hAPP_int_int number_number_of_int Y_2))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int _let_1) _let_2)) (= zero_zero_int (hAPP_int_int (div_mod_int _let_2) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat Y))) (let ((_let_2 (hAPP_nat_fun_nat_nat gcd_gcd_nat X))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_2 Z_1)) (hAPP_nat_nat _let_2 (hAPP_nat_nat _let_1 Z_1)))))) (forall ((A_231 $$unsorted) (B_165 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_231) B_165) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_165) A_231))) (forall ((X $$unsorted) (A_3 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3) (hAPP_real_real exp_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_3) (hAPP_real_real ln X))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) M) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (and (is_int Ma) (is_int N_1)) (= (= Ma N_1) (= (hAPP_i1732201573de_int quickcheck_of_int N_1) (hAPP_i1732201573de_int quickcheck_of_int Ma))))) (forall ((B_129 $$unsorted) (A_169 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_169)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat B_129) zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_169) B_129)) zero_zero_nat))))) (forall ((A_3 $$unsorted)) (=> (is_int A_3) (=> (not (= A_3 zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) A_3) one_one_int)))) (forall ((A_98 $$unsorted) (C_40 $$unsorted) (B_80 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_98) C_40)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_80) C_40))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_98) B_80)))) (forall ((N_29 $$unsorted) (K_6 $$unsorted) (M_16 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int K_6))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 M_16)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 N_29)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int M_16) N_29))))))) (forall ((A_222 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex zero_zero_complex) A_222) zero_zero_complex)) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int _let_1) zero_zero_int)) (= _let_1 (hAPP_int_int (div_mod_int A_3) B_2)))))) (forall ((A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Ma) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)))) (forall ((A_35 $$unsorted)) (= A_35 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_35) one_on1684967323de_int))) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_f1469637905l_bool (hAPP_P1681069257l_bool member308914164t_bool (hAPP_f538843494t_bool (hAPP_f1418982953t_bool produc713279741t_bool A_1) B_1)) (bijR_int_int (zcongm Ma)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (big_co1548731110nt_int cOMBI_int A_1)) (big_co1548731110nt_int cOMBI_int B_1)) Ma)))) (forall ((X $$unsorted) (N_5 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) N_5)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_n546711566l_real root N_5) X)) (hAPP_real_real (hAPP_n546711566l_real root N) X))))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) K_2)) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) N)))) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int W_1))) (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int (hAPP_int_int bit1 W_1)))))) (forall ((X_1 $$unsorted)) (= (= X_1 zero_z126310315umeral) (= zero_z126310315umeral X_1))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_int_nat nat X)) (hAPP_int_nat nat Y)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) Y))))) (forall ((X $$unsorted)) (=> (= zero_zero_real (hAPP_real_real sin X)) (= (hAPP_real_real abs_abs_real (hAPP_real_real cos X)) one_one_real))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (not (= (hAPP_int_int bit0 L_2) (hAPP_int_int bit1 K_2)))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real arctan Y))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_2)) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) _let_2)) (= Y (hAPP_real_real tan _let_1)))))) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real W_1))) (= (= X_1 _let_1) (= _let_1 X_1)))) (forall ((M_19 $$unsorted) (N_44 $$unsorted) (A_132 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_132))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_132)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int _let_1 M_19)) (hAPP_nat_int _let_1 N_44))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_19) N_44)))))) (forall ((C_85 $$unsorted) (A_193 $$unsorted) (B_149 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat A_193))) (=> (hBOOL (hAPP_nat_bool _let_1 B_149)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_149) C_85)))))) (forall ((X_1 $$unsorted)) (= (= one_on1684967323de_int X_1) (= X_1 one_on1684967323de_int))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (is_int X_1) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (= X_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_1) (hAPP_int_int (hAPP_int_fun_int_int div_div_int X_1) _let_1))))))) (forall ((A_196 $$unsorted) (N_63 $$unsorted)) (let ((_let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_196) N_63))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_196) _let_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_1) A_196)))) (forall ((A_225 $$unsorted) (B_162 $$unsorted) (C_91 $$unsorted) (D_18 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real A_225))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 C_91)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_162) D_18)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 B_162)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real C_91) D_18))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime X) Y)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X) Y)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y) _let_1))))))) (forall ((A_133 $$unsorted) (N_46 $$unsorted) (N_45 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_133))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_46) N_45)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_133)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_133) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real _let_1 N_45)) (hAPP_nat_real _let_1 N_46)))))))) (forall ((A_232 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_232) (hAPP_int_complex number528085621omplex pls)) A_232)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat nat X_1))) (=> (is_int A) (=> (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) B) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int C) _let_1)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) _let_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd A) B)) (exists ((K $$unsorted)) (and (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int K) (hAPP_int_nat nat X_1)) A) (is_int K)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_f1961001761l_bool cOMBB_1550063917nt_int fconj))) (= (the_Pr2103884470nt_int (hAPP_f237669397t_bool (hAPP_f461489489t_bool cOMBS_400904860l_bool (hAPP_f365317245l_bool _let_1 (hAPP_f1084724746t_bool (hAPP_f374502857t_bool cOMBB_569260360nt_int (hAPP_r2115560837t_bool fequal_rat X_1)) (hAPP_f1065357839nt_rat (hAPP_f1120137083nt_rat cOMBS_549334880nt_rat (hAPP_f1547007718nt_rat (hAPP_f382317021nt_rat cOMBB_170828966nt_int fract) product_fst_int_int)) product_snd_int_int)))) (hAPP_f237669397t_bool (hAPP_f461489489t_bool cOMBS_400904860l_bool (hAPP_f365317245l_bool _let_1 (hAPP_f892584630t_bool (hAPP_f492612297t_bool cOMBB_798864284nt_int (hAPP_i1948725293t_bool ord_less_int zero_zero_int)) product_snd_int_int))) (hAPP_i119638232t_bool (hAPP_f2018027565t_bool cOMBC_33652895t_bool (hAPP_f291087797t_bool (hAPP_f214467655t_bool cOMBB_182850971nt_int fequal_int) (hAPP_f521271395nt_int (hAPP_f1914742907nt_int cOMBS_2019229620nt_int (hAPP_f1855025978nt_int (hAPP_f1038672605nt_int cOMBB_1506897658nt_int gcd_gcd_int) product_fst_int_int)) product_snd_int_int))) one_one_int)))) (quotient_of X_1)))) (forall ((P_1 $$unsorted)) (hBOOL (hAPP_f448129468l_bool nat_nat_set (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) P_1))))) (forall ((X $$unsorted)) (let ((_let_1 (of_real_complex X))) (= _let_1 (hAPP_complex_complex cnj _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_nat_real real_nat X))) (= (hAPP_real_real abs_abs_real _let_1) _let_1))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (not (= (hAPP_int_int bit0 K_2) (hAPP_int_int bit1 L_2)))) (forall ((N_9 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real semiri132038758t_real N_9)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_9)))) (forall ((N_52 $$unsorted) (A_150 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_150)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_150) N_52)))))) (forall ((X_30 $$unsorted) (Y_24 $$unsorted)) (=> (and (is_int X_30) (is_int Y_24)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_30) Y_24)) (=> (not (= X_30 Y_24)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_30) Y_24)))))) (forall ((Z_14 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_14) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat Z_14) Z_14))) (forall ((N $$unsorted) (K_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_2))) (=> (hBOOL (hAPP_int_bool _let_1 M)) (=> (hBOOL (hAPP_int_bool _let_1 N)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (legacy_zgcd M) N))))))) (forall ((A_16 $$unsorted) (B_12 $$unsorted)) (=> (not (= zero_zero_nat B_12)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_12) A_16)) B_12) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_16) B_12)) one_one_nat)))) (forall ((A_121 $$unsorted) (C_54 $$unsorted) (B_99 $$unsorted) (D_9 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_121) C_54)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_99) D_9)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A_121) B_99)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat C_54) D_9)))) (forall ((M_7 $$unsorted) (N_21 $$unsorted)) (= (hAPP_n522471361de_int semiri1424489471de_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_7) N_21)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int semiri1424489471de_int M_7)) (hAPP_n522471361de_int semiri1424489471de_int N_21)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_fun_int_int P (hAPP_P1175774780nt_int Q R)) (hAPP_P2110489235nt_int (hAPP_f1855025978nt_int (hAPP_f1038672605nt_int cOMBB_1506897658nt_int P) Q) R))) (forall ((R_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int (archim856651990g_real R_3))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real R_3) one_one_real)))) (forall ((A_184 $$unsorted) (M_23 $$unsorted) (N_58 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_184))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_23) N_58)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int _let_1 M_23)) (hAPP_nat_int _let_1 N_58)))))) (forall ((B_36 $$unsorted) (A_45 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_36) A_45)) B_36) (hAPP_nat_nat (div_mod_nat A_45) B_36))) (forall ((K_2 $$unsorted)) (= zero_zero_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract zero_zero_int) K_2))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_n1865633855at_nat (hAPP_f837737749at_nat (hAPP_f999082675at_nat cOMBB_348438404at_nat P) Q) R) (hAPP_n1865633855at_nat P (hAPP_nat_nat Q R)))) (forall ((B_155 $$unsorted) (A_204 $$unsorted)) (=> (not (= A_204 zero_z891286103de_int)) (=> (not (= zero_z891286103de_int B_155)) (not (= zero_z891286103de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_204) B_155)))))) (forall ((Z_11 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_11) Z_11) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z_11) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((M_13 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral one_on1645066479umeral) (hAPP_n1108039445umeral semiri1619134803umeral M_13)) (hAPP_n1108039445umeral semiri1619134803umeral (hAPP_nat_nat suc M_13)))) (forall ((B_2 $$unsorted) (Q_8 $$unsorted) (R_5 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int B_2))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int B_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_2 Q_8)) R_5)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_2 Q_2)) R_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int R_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool _let_1 R_3)) (=> (hBOOL (hAPP_int_bool _let_1 R_5)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_2) Q_8))))))))) (forall ((Y_14 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex zero_zero_complex) Y_14) zero_zero_complex)) (forall ((F $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool (ord_gr788844697n_real A) B))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_1) _let_1)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real Y_2) _let_1)) (=> (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) (hAPP_r1134773055l_bool (ord_gr788844697n_real A) B))) (hBOOL (hAPP_real_bool (deriv_real F X_2) zero_zero_real)))) (= (hAPP_real_real F X_1) (hAPP_real_real F Y_2)))))))) (forall ((B_72 $$unsorted) (C_35 $$unsorted) (A_84 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int B_72))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_84)) (=> (hBOOL (hAPP_int_bool _let_1 C_35)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_84) C_35))))))) (forall ((Q_2 $$unsorted) (B_2 $$unsorted) (R_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int B_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_3) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int Q_2) C_1))) R_3)) (hAPP_int_int _let_1 C_1)))))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted)) (= (hAPP_complex_real re (rcis R_3 A_3)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real R_3) (hAPP_real_real cos A_3)))) (forall ((F $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B) X_1)) (=> (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) (hAPP_r1134773055l_bool (ord_gr788844697n_real B) X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real F X_2))))) (=> (hBOOL (hAPP_real_bool (isCont_real_real F) X_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real F X_1))))))) (forall ((Ta $$unsorted) (A_1 $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) D_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int X_2))) (let ((_let_2 (hAPP_i1948725293t_bool dvd_dvd_int D))) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa))))))))) (=> (not (hBOOL (hAPP_int_bool _let_2 (hAPP_int_int _let_1 Ta)))) (not (hBOOL (hAPP_int_bool _let_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 D_1)) Ta)))))))))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_2) K_2) (hAPP_int_int bit0 K_2))) (forall ((N_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 N_1)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int N_1) one_one_int) (hAPP_nat_int semiri1621563631at_int (hAPP_f957591787ol_nat finite_card_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) _let_1)) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) N_1))))))))) (forall ((M $$unsorted)) (= (hAPP_int_int abs_abs_int M) (hAPP_int_int (legacy_zgcd M) zero_zero_int))) (forall ((X_17 $$unsorted)) (= zero_zero_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_17) zero_zero_complex))) (exists ((K_4 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) K_4)) (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real norm_norm_real (hAPP_complex_real re X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4)))))) (forall ((A_229 $$unsorted) (C_95 $$unsorted) (D_20 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_229))) (let ((_let_2 (hAPP_C1594335432umeral plus_p1627245867umeral C_95))) (= (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral _let_2 D_20)) (hAPP_C498520661umeral _let_2 (hAPP_C498520661umeral _let_1 D_20)))))) (forall ((Nat_5 $$unsorted) (Nat_4 $$unsorted)) (= (= Nat_5 Nat_4) (= (hAPP_nat_nat suc Nat_5) (hAPP_nat_nat suc Nat_4)))) (forall ((A_3 $$unsorted) (N $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_2) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2)) N))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_nat_int semiri1621563631at_int X)) (hAPP_nat_int semiri1621563631at_int Y)) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X) Y)))) (forall ((W_12 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex one_one_complex) one_one_complex)) (hAPP_int_complex number528085621omplex W_12)) (hAPP_int_complex number528085621omplex (hAPP_int_int bit0 W_12)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X) Y)) (hAPP_nat_nat (nat_gcd X) Y)) (hAPP_nat_nat (nat_lcm X) Y))) (forall ((A $$unsorted)) (= (= zero_zero_real A) (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) A)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real sqrt X)) (hAPP_real_real sqrt Y)) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) Y)))) (forall ((A_55 $$unsorted) (C_25 $$unsorted) (B_46 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_55) B_46)) C_25) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_55) C_25)) B_46)) C_25))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int semiri1621563631at_int M)) (hAPP_nat_int semiri1621563631at_int N)))) (forall ((V_10 $$unsorted) (U_3 $$unsorted) (Y_26 $$unsorted) (X_32 $$unsorted) (A_209 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_32) A_209)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_26) A_209)) (=> (hBOOL (hAPP_int_bool _let_1 U_3)) (=> (hBOOL (hAPP_int_bool _let_1 V_10)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int U_3) V_10) one_one_int) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int U_3) X_32)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_10) Y_26))) A_209))))))))) (forall ((V_23 $$unsorted)) (= (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_23) (hAPP_int_int bit1 pls))) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int V_23)) one_one_int))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int A_3))) (let ((_let_2 (hAPP_int_int _let_1 R_3))) (=> (is_int C_1) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel B_2 C_1) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))) (=> (not (= C_1 zero_zero_int)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel (hAPP_int_int _let_1 B_2) C_1) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 Q_2)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int _let_2) C_1))) (hAPP_int_int (div_mod_int _let_2) C_1)))))))))) (= one_one_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat one_one_rat) _let_4)) (forall ((A_214 $$unsorted) (N_67 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_214) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_67))))) (forall ((B_155 $$unsorted) (A_204 $$unsorted)) (=> (not (= zero_z126310315umeral A_204)) (=> (not (= zero_z126310315umeral B_155)) (not (= zero_z126310315umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_204) B_155)))))) (forall ((X_35 $$unsorted) (Y_27 $$unsorted) (Q_11 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X_35) Y_27)) Q_11) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_35) Q_11)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_27) Q_11)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (hBOOL (fdisj P Q))) (hBOOL P) (hBOOL Q))) (forall ((K_1 $$unsorted) (P_1 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D)) (=> (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) D)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_1)) (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) D)))))))))) (forall ((M $$unsorted) (N $$unsorted) (R_5 $$unsorted) (S_3 $$unsorted) (S_1 $$unsorted) (T_2 $$unsorted) (T_1 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int R_5) R_3)))) (let ((_let_2 (xzgcda M N R_5 R_3 S_3 S_1 T_2 T_1))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int R_3) zero_zero_int)))) (and (=> _let_3 (= _let_2 (hAPP_P408881810nt_int (hAPP_i1730167831nt_int produc282740534nt_int R_5) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int S_3) T_2)))) (=> (not _let_3) (= _let_2 (xzgcda M N R_3 (hAPP_int_int (div_mod_int R_5) R_3) S_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int S_3) (hAPP_int_int _let_1 S_1)) T_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int T_2) (hAPP_int_int _let_1 T_1)))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f269654879t_real (hAPP_i1671359920t_real P R) Q) (hAPP_i627165055t_real (hAPP_f1323932638t_real (hAPP_f352226557t_real cOMBC_824100275t_real P) Q) R))) (not (= zero_zero_nat one_one_nat)) (forall ((Y_3 $$unsorted) (Y_2 $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (tendsto_nat_real X_3 X_1 sequentially)) (=> (hBOOL (tendsto_nat_real Y_3 Y_2 sequentially)) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_3) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real X_3 N_2)) (hAPP_nat_real Y_3 N_2)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)))))) (forall ((A_92 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_92) one_on1645066479umeral) A_92)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_rat (hAPP_P507092031nt_rat P R) (hAPP_P1175774780nt_int Q R)) (hAPP_P1853363688nt_rat (hAPP_f1065357839nt_rat (hAPP_f1120137083nt_rat cOMBS_549334880nt_rat P) Q) R))) (forall ((B $$unsorted) (A $$unsorted)) (= (= A zero_zero_rat) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B) A) B))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat V_2)) (hAPP_int_nat number_number_of_nat V_3)))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int V_2) pls)))) (and (=> (not _let_2) (= _let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_2) V_3)))) (=> _let_2 (= zero_zero_nat _let_1)))))) (forall ((V_11 $$unsorted) (W_9 $$unsorted)) (= (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_11) W_9)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int V_11)) (hAPP_int_int number_number_of_int W_9)))) (forall ((X_3 $$unsorted)) (=> (hBOOL (summable_complex X_3)) (hBOOL (summable_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat re) X_3))))) (forall ((A_237 $$unsorted)) (= A_237 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex (hAPP_int_int bit1 pls))) A_237))) (forall ((A_12 $$unsorted) (N_18 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_12))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat _let_1 N_18)) A_12) (hAPP_nat_rat _let_1 (hAPP_nat_nat suc N_18))))) (forall ((Y $$unsorted)) (exists ((X_2 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) _let_1)) (= (hAPP_real_real tan X_2) Y) (forall ((Y_1 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)) Y_1)) (= Y (hAPP_real_real tan Y_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_1) _let_1))) (= Y_1 X_2)))))))) (forall ((B_45 $$unsorted) (B_44 $$unsorted) (A_54 $$unsorted) (C_24 $$unsorted) (A_53 $$unsorted)) (=> (= (hAPP_nat_nat (div_mod_nat A_54) C_24) (hAPP_nat_nat (div_mod_nat A_53) C_24)) (=> (= (hAPP_nat_nat (div_mod_nat B_44) C_24) (hAPP_nat_nat (div_mod_nat B_45) C_24)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_54) B_45)) C_24) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_53) B_44)) C_24))))) (not (= zero_zero_real one_one_real)) (forall ((A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (hBOOL (hAPP_f215623910l_bool finite1395289673t_bool (setS A P_5))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (and (= zero_zero_rat Y_2) (= X_1 zero_zero_rat)) (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_1) X_1)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Y_2) Y_2))))) (forall ((X_1 $$unsorted)) (= (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_nat) X_1))) X_1)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) one_one_rat)) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) (hAPP_nat_nat suc zero_zero_nat))) N))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real Y)) one_one_real)) (= Y (hAPP_real_real cos (hAPP_real_real arccos Y))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)) (hBOOL (hAPP_f448129468l_bool nat_nat_set (hAPP_i1948725293t_bool (ord_at875362053st_int X_1) Y_2))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B) A)) E_2)) D))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) E_2)) C)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) E_2)) D))))) (forall ((X_31 $$unsorted) (Y_25 $$unsorted)) (=> (not (= X_31 Y_25)) (=> (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat X_31) Y_25))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat Y_25) X_31))))) (forall ((B_141 $$unsorted) (A_181 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (or (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_141) zero_zero_real)) (hBOOL (hAPP_real_bool _let_1 A_181))) (and (hBOOL (hAPP_real_bool _let_1 B_141)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_181) zero_zero_real)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_181) B_141)) zero_zero_real))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) (hAPP_int_int bit1 pls))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real X_1)) one_one_real)))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (isCont_real_real cos) X_1))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A_3) B_2)) (=> (not (= one_one_nat B_2)) (exists ((X_2 $$unsorted) (Y_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_2) Y_1)) one_one_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) X_2)))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (D_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z_1) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X) Z_1))) one_one_int)) D_3)))))) (forall ((N_29 $$unsorted) (K_6 $$unsorted) (M_16 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral K_6))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 M_16)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 N_29)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (div_mo1740067990umeral M_16) N_29))))))) (forall ((P_1 $$unsorted)) (= (collec50511176nt_int P_1) P_1)) (forall ((V_5 $$unsorted) (W_3 $$unsorted) (C_55 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_5) W_3))) C_55) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int V_5)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int number_number_of_int W_3)) C_55)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex cnj X)) (hAPP_complex_complex cnj Y)) (hAPP_complex_complex cnj (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X) Y)))) (forall ((N_27 $$unsorted) (Y_7 $$unsorted) (X_10 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Y_7) X_10)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X_10) Y_7)) N_27) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_10) N_27)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_7) N_27))))) (forall ((A $$unsorted)) (hBOOL (tendsto_complex_real re (hAPP_complex_real re A) (at_complex A)))) (forall ((V $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_rat number_number_of_rat W_1))) (let ((_let_2 (hAPP_int_rat number_number_of_rat V))) (= (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat _let_1) _let_2))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat _let_2) _let_1)))))) (hBOOL (hAPP_real_bool _let_21 pi)) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat X))) (= (hAPP_nat_nat (div_mod_nat X) (hAPP_nat_nat suc _let_1)) _let_1)))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_real_real inverse_inverse_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 (hAPP_real_real inverse_inverse_real X)))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)))))) (forall ((Z_14 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_14) Z_14) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_14))) (forall ((W_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) W_1)))) (=> (is_int W_1) (= (= Ma (hAPP_int_nat nat W_1)) (and (=> (not _let_1) (= Ma zero_zero_nat)) (=> _let_1 (= (hAPP_nat_int semiri1621563631at_int Ma) W_1))))))) (forall ((X $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (standardRes P_3) X)) P_3)))) (forall ((X $$unsorted)) (= (hAPP_real_real ln (hAPP_real_real exp_real X)) X)) (forall ((P_1 $$unsorted) (N_1 $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_2) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hBOOL (hAPP_nat_bool P_1 X_2)))) (forall ((M_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1)) (hBOOL (hAPP_nat_bool P_1 M_1)))))) (forall ((E_1 $$unsorted) (B_2 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat D_3) A_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat E_1) B_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A_3) B_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime D_3) E_1)))))) (forall ((X $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) X)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X) P_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime X) P_3)))))) (forall ((A_145 $$unsorted) (M_20 $$unsorted) (N_48 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_145))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat _let_1 M_20)) (hAPP_nat_rat _let_1 N_48)) (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_20) N_48))))) (forall ((B_120 $$unsorted) (A_159 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_120) A_159))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_159)) (hBOOL (hAPP_C24501650l_bool _let_1 B_120)))))) (forall ((A_89 $$unsorted)) (= A_89 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat one_one_rat) A_89))) (forall ((A $$unsorted) (B $$unsorted)) (= (and (= A zero_zero_real) (= zero_zero_real B)) (= (hAPP_real_complex (hAPP_r265291036omplex complex A) B) zero_zero_complex))) (forall ((X_1 $$unsorted)) (= (= one_one_complex X_1) (= X_1 one_one_complex))) (forall ((Y $$unsorted) (X $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong Y) zero_zero_int) P_3))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y)) zero_zero_int) P_3))))))) (forall ((A_149 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_149) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_149) one_one_nat)))) (forall ((C_37 $$unsorted) (A_95 $$unsorted) (B_77 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_95) B_77)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_95) C_37)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_77) C_37))))) (forall ((X_44 $$unsorted) (Y_32 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_44) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_32) _let_1))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) Y_32)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat X_44) Y_32)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (or (hBOOL (hAPP_nat_bool even_odd_even_nat Y_2)) (hBOOL (hAPP_nat_bool even_odd_even_nat X_1))) (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X_1) Y_2))))) (forall ((B_90 $$unsorted) (A_112 $$unsorted) (C_50 $$unsorted)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat C_50) A_112) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_90) A_112)) (= C_50 B_90))) (forall ((A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) P_5))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_5) A))) (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool X_2) (setS A P_5))) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))) (hAPP_f957591787ol_nat finite_card_int X_2))))))))) (forall ((A_198 $$unsorted)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex zero_zero_complex) A_198)) (= zero_zero_complex A_198))) (forall ((A_183 $$unsorted) (M_22 $$unsorted) (N_57 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_183))) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_nat_rat _let_1 M_22)) N_57) (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_22) N_57))))) (forall ((N $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat) P_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_3) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_3) (hAPP_nat_nat fact N)))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (= (or (= K_1 zero_zero_nat) (= Ma N_1)) (= (hAPP_nat_nat _let_1 N_1) (hAPP_nat_nat _let_1 Ma))))) (forall ((A_140 $$unsorted) (C_62 $$unsorted) (B_109 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_140) C_62)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_109) C_62))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_62)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_140) B_109))))) (forall ((X_1 $$unsorted)) (= (the_real (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool (hAPP_f1393328161l_bool (hAPP_f1900646853l_bool cOMBB_430461877l_real fequal_real) exp_real)) X_1)) (hAPP_real_real ln X_1))) (forall ((N_1 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real (hAPP_b646336293l_real if_real (hAPP_nat_bool even_odd_even_nat N_1)) zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) (hAPP_nat_nat suc zero_zero_nat))) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1))))) (hAPP_nat_real (hAPP_r474017924t_real power_power_real zero_zero_real) N_1)) zero_zero_real)) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N))))) (forall ((C_74 $$unsorted) (A_174 $$unsorted) (B_134 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_74))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_174) B_134)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_74)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 A_174)) (hAPP_nat_nat _let_1 B_134))))))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (= (hBOOL (hAPP_real_bool _let_1 A)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) A)))))) (forall ((X_40 $$unsorted) (N_69 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral X_40))) (let ((_let_2 (hAPP_n1108039445umeral _let_1 N_69))) (= (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_69)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral _let_2) _let_2))))) (forall ((Y $$unsorted) (X $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (log A_3))) (let ((_let_2 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_2 A_3)) (=> (not (= A_3 one_one_real)) (=> (hBOOL (hAPP_real_bool _let_2 X)) (=> (hBOOL (hAPP_real_bool _let_2 Y)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y)) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) Y)))))))))) (forall ((X_3 $$unsorted)) (=> (hBOOL (cauchy_complex X_3)) (hBOOL (cauchy_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat im) X_3))))) (forall ((M_25 $$unsorted) (A_185 $$unsorted) (N_60 $$unsorted) (B_142 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_185))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_nat_real _let_1 N_60)) B_142)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_25) N_60)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_nat_real _let_1 M_25)) B_142)))))) (forall ((K_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (hAPP_f782000547ol_nat big_co387207925at_nat F))) (=> (= zero_zero_nat (hAPP_nat_nat F zero_zero_nat)) (= (hAPP_f22106695ol_nat _let_1 (hAPP_n1699378549t_bool (ord_at238088361st_nat zero_zero_nat) K_1)) (hAPP_f22106695ol_nat _let_1 (hAPP_n1699378549t_bool (ord_at238088361st_nat (hAPP_nat_nat suc zero_zero_nat)) K_1)))))) (forall ((A_225 $$unsorted) (B_162 $$unsorted) (C_91 $$unsorted) (D_18 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_225))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 B_162)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int C_91) D_18)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 C_91)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_162) D_18))))) (= zero_z891286103de_int (hAPP_i1732201573de_int number1226105091de_int pls)) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat A))) (=> (hBOOL (hAPP_nat_bool _let_1 B)) (=> (hBOOL (hAPP_nat_bool _let_1 C)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B) A)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat C) A))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B) C))))))) (forall ((C_57 $$unsorted) (D_10 $$unsorted) (A_135 $$unsorted) (B_104 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_135) B_104)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C_57) D_10)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_104)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_57)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_135) C_57)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_104) D_10)))))))) (forall ((A_103 $$unsorted) (C_45 $$unsorted) (B_85 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_103) C_45)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_85) C_45))) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_103) B_85)))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_real_real _let_1 (hAPP_real_real uminus_uminus_real X)) (hAPP_real_real uminus_uminus_real (hAPP_real_real _let_1 X)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r265291036omplex complex A_3))) (= (hAPP_complex_complex cnj (hAPP_real_complex _let_1 B_2)) (hAPP_real_complex _let_1 (hAPP_real_real uminus_uminus_real B_2))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (= (hAPP_real_real exp_real Y) X) (= Y (hAPP_real_real ln X)))) (forall ((B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int min))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int _let_1) B_2) _let_1)))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) cos_coeff)) (hAPP_r474017924t_real power_power_real X_1))) (hAPP_real_real cos X_1)))) (forall ((L_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int pls) (hAPP_int_int bit1 L_2)) (hAPP_int_int bit1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int min) L_2)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3_1 $$unsorted)) (is_bool (tendst1507391555omplex B_1_1 B_2_1 B_3_1))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real ln X)) X)))) (forall ((A_69 $$unsorted) (B_57 $$unsorted)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (div_mod_int A_69) B_57)) B_57))) (forall ((A_134 $$unsorted) (N_47 $$unsorted) (B_103 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_134) N_47)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_103) N_47))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) B_103)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_134) B_103))))) (forall ((B_70 $$unsorted) (A_82 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_82) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B_70) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_82) B_70)) zero_zero_real))))) (forall ((W_6 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real W_6))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) _let_1)) _let_1) (hAPP_int_real number267125858f_real (hAPP_int_int bit1 W_6))))) (forall ((Y $$unsorted) (X $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (let ((_let_2 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool _let_2 X)) (=> (hBOOL (hAPP_real_bool _let_2 Y)) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r579619957l_real (hAPP_f823702159l_real (hAPP_f1040184293l_real cOMBB_557258983l_real P) Q) R) (hAPP_f1591894897l_real P (hAPP_r1250527377l_real Q R)))) (forall ((A_17 $$unsorted) (C_4 $$unsorted) (B_13 $$unsorted)) (=> (not (= zero_zero_nat B_13)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_17) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_13) C_4))) B_13) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat C_4) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_17) B_13))))) (forall ((R_3 $$unsorted)) (= (hAPP_real_real abs_abs_real R_3) (hAPP_real_real norm_norm_real R_3))) (= one_one_real (hAPP_real_real cos _let_54)) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real min)) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) one_one_real)) (hBOOL (hAPP_real_bool (deriv_real arcsin X_1) (hAPP_real_real inverse_inverse_real (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (hAPP_real_real _let_1 (hAPP_real_real inverse_inverse_real X)) (hAPP_real_real inverse_inverse_real (hAPP_real_real _let_1 X))))))) (hBOOL (hAPP_real_bool _let_21 one_one_real)) (= (hAPP_int_nat nat _let_91) _let_34) (forall ((Z_2 $$unsorted)) (=> (is_int Z_2) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int abs_abs_int Z_2)) one_one_int)) (= zero_zero_int Z_2)))) (forall ((U_1 $$unsorted) (V_2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (= X Y) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real U_1)) V_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) U_1)) Y))) V_2))))) (forall ((A_61 $$unsorted)) (= zero_zero_int (hAPP_int_int (div_mod_int zero_zero_int) A_61))) (forall ((J_2 $$unsorted) (A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (zcong J_2))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_3) A_3))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) (hAPP_int_int (multInv P_3) J_2))) P_3)))))))))) (forall ((X $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int zero_zero_int) X) (hAPP_int_int abs_abs_int X))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int W_1))) (=> (and (is_int W_1) (is_int Z_2)) (= (or (hBOOL (hAPP_int_bool _let_1 Z_2)) (= Z_2 W_1)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_2) one_one_int))))))) (forall ((A_124 $$unsorted) (N_34 $$unsorted) (B_102 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_124) N_34) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral B_102) N_34)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_124)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_102)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_34)) (= A_124 B_102))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat div_div_nat M))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) N)) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat suc N))))))) (forall ((A_21 $$unsorted) (B_17 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_21) B_17)) (= B_17 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral B_17) A_21)) A_21)))) (forall ((F $$unsorted) (A_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool (nat_tr160667106at_int F) A_1))) (= _let_37 (hAPP_nat_int semiri1621563631at_int _let_4)) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z1) W)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z2) W)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Z1) Z2)) W))) (forall ((P $$unsorted)) (=> (is_bool P) (or (= fFalse P) (= P fTrue)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (=> (= (hAPP_n546711566l_real Diff zero_zero_nat) F) (=> (forall ((M_1 $$unsorted) (T $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real T)) (hAPP_real_real abs_abs_real X_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) T) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) T))))) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_1))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real T)) (hAPP_real_real abs_abs_real X_1))) (= (hAPP_real_real F X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1)))))))))) (forall ((W $$unsorted)) (not (= ii (hAPP_int_complex number528085621omplex W)))) (forall ((W_5 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_5))) (let ((_let_2 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int zero_z891286103de_int) _let_1))) (let ((_let_3 (= _let_1 zero_zero_nat))) (and (=> (not _let_3) (= _let_2 zero_z891286103de_int)) (=> _let_3 (= _let_2 one_on1684967323de_int))))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X_1)) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real inverse_divide_real A)) (hAPP_r474017924t_real power_power_real X_1)) zero_zero_real sequentially)))) (forall ((A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real powr (hAPP_real_real ln X)) A_3)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real powr A_3) A_3)) X)))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (=> (is_int C) (= (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A) B)) (= C zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) C)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) C)))))) (forall ((X_41 $$unsorted) (Y_29 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_41) Y_29)) _let_2) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_41) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_29) _let_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) X_41)) Y_29)))))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int number_number_of_int Y_2))))) (forall ((A_109 $$unsorted) (B_87 $$unsorted) (C_47 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_109))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 B_87)) C_47) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_87) C_47))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) one_one_real)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (natceiling X_1)) one_one_nat)))) (forall ((A_23 $$unsorted)) (=> (not (= zero_z126310315umeral A_23)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_23) A_23) one_on1645066479umeral))) (forall ((A_183 $$unsorted) (M_22 $$unsorted) (N_57 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_183))) (= (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_22) N_57)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral (hAPP_n1108039445umeral _let_1 M_22)) N_57)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real Y_2))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_3 (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_2)))) (=> (hBOOL (hAPP_real_bool _let_3 Y_2)) (=> (hBOOL (hAPP_real_bool _let_1 _let_2)) (=> (hBOOL (hAPP_real_bool _let_3 X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) _let_2)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real tan Y_2)) (hAPP_real_real tan X_1))) (hBOOL (hAPP_real_bool _let_1 X_1))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex A))) (= (= B C) (= (hAPP_complex_complex _let_1 B) (hAPP_complex_complex _let_1 C))))) (forall ((V_7 $$unsorted) (B_101 $$unsorted) (C_56 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int V_7)))) (= (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B_101) C_56)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int _let_1 B_101)) (hAPP_int_int _let_1 C_56))))) (forall ((A_121 $$unsorted) (C_54 $$unsorted) (B_99 $$unsorted) (D_9 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_121) C_54)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_99) D_9)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A_121) B_99)) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex C_54) D_9)))) (forall ((A_182 $$unsorted)) (= A_182 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_182) one_one_nat))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) one_one_nat))) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat fact_fact_nat) _let_1))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1))) (hAPP_real_real sin X_1))))) (forall ((X $$unsorted)) (= (hAPP_int_int abs_abs_int X) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) zero_zero_int))) (forall ((A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong B) A) Ma)))) (forall ((A_230 $$unsorted) (C_96 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_230) C_96) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int C_96) A_230))) (not (hBOOL (hAPP_int_bool even_odd_even_int one_one_int))) (hBOOL (hAPP_real_bool _let_64 _let_99)) (forall ((M_13 $$unsorted)) (= (hAPP_n522471361de_int semiri1424489471de_int (hAPP_nat_nat suc M_13)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int one_on1684967323de_int) (hAPP_n522471361de_int semiri1424489471de_int M_13)))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat A) B))) (and (forall ((D_2 $$unsorted)) (=> (= A (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B) D_2)) (hBOOL (hAPP_nat_bool P_1 D_2)))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A) B)) (hBOOL (hAPP_nat_bool P_1 zero_zero_nat)))))) (forall ((C_39 $$unsorted) (D_7 $$unsorted) (A_97 $$unsorted) (B_79 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_97) B_79)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C_39) D_7)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_97) C_39)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_79) D_7)))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int Z1))) (= (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z2) Z3)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 Z2)) Z3)))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex invers1025623611omplex Z_1) (of_real_complex (hAPP_complex_real norm_norm_complex Z_1))) (hAPP_complex_complex sgn_sgn_complex Z_1))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_2) X_1))) (= X_1 Y_2))) (hBOOL (hAPP_int_bool zprime _let_18)) (forall ((A_62 $$unsorted)) (= A_62 (hAPP_C498520661umeral (div_mo1740067990umeral A_62) zero_z126310315umeral))) (forall ((N $$unsorted)) (=> (not (= N zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)))) (forall ((X_1 $$unsorted)) (=> (is_int X_1) (= (not (hBOOL (hAPP_int_bool even_odd_even_int X_1))) (exists ((Y_1 $$unsorted)) (and (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Y_1)) one_one_int) X_1) (is_int Y_1)))))) (hBOOL (hAPP_real_bool _let_64 _let_72)) (forall ((B_148 $$unsorted) (A_192 $$unsorted) (C_84 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool dvd_dvd_real A_192))) (=> (hBOOL (hAPP_real_bool _let_1 C_84)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_148) C_84)))))) (forall ((Z_8 $$unsorted) (X_23 $$unsorted) (Y_18 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool dvd_dvd_rat X_23))) (=> (hBOOL (hAPP_rat_bool _let_1 Y_18)) (=> (hBOOL (hAPP_rat_bool _let_1 Z_8)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat Y_18) Z_8))))))) (= (hAPP_real_real sin _let_52) _let_30) (forall ((A_198 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int zero_z891286103de_int) A_198)) (= A_198 zero_z891286103de_int))) (forall ((A_197 $$unsorted) (B_152 $$unsorted) (N_64 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_197) N_64)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral B_152) N_64)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_197) B_152)) N_64))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat X))) (let ((_let_2 (hAPP_nat_nat _let_1 Y))) (= _let_2 (hAPP_nat_nat _let_1 _let_2))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) X)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2)) X)))) (forall ((A_139 $$unsorted) (C_61 $$unsorted) (B_108 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_139) C_61)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_108) C_61))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_61)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_139) B_108))))) (forall ((A $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Ma)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd A) Ma)) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) X_2) Ma)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_2) (hAPP_i1948725293t_bool norRRset Ma))) (forall ((Y_1 $$unsorted)) (=> (is_int Y_1) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) Y_1) Ma)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_1) (hAPP_i1948725293t_bool norRRset Ma)))) (= X_2 Y_1)))) (is_int X_2)))))) (forall ((A_9 $$unsorted) (N_14 $$unsorted) (B_7 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_14))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_9) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_7) _let_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) B_7)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_9) B_7)))))) (= (hAPP_nat_nat fact_fact_nat one_one_nat) one_one_nat) (not (= zero_z126310315umeral one_on1645066479umeral)) (forall ((A_214 $$unsorted) (N_67 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_214) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_67))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int min))) (let ((_let_2 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int _let_1) N))) (or (= _let_2 _let_1) (= _let_2 one_one_int))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X)) (hAPP_real_real exp_real X)))) (forall ((A_90 $$unsorted)) (= A_90 (hAPP_real_real (hAPP_r1250527377l_real times_times_real one_one_real) A_90))) (forall ((B $$unsorted) (A $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool d22set A))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B)))) (forall ((A_70 $$unsorted) (B_58 $$unsorted)) (let ((_let_1 (hAPP_int_int (div_mod_int A_70) B_58))) (= _let_1 (hAPP_int_int (div_mod_int _let_1) B_58)))) (forall ((N_9 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat semiri151668891at_rat N_9)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_int_rat number_number_of_rat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_9)))) (forall ((A_158 $$unsorted) (B_119 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_158) B_119))) (=> (hBOOL (hAPP_real_bool _let_1 A_158)) (hBOOL (hAPP_real_bool _let_1 B_119)))))) (forall ((C_27 $$unsorted) (A_57 $$unsorted) (B_48 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_27))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat A_57) B_48)) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 A_57)) (hAPP_nat_nat _let_1 B_48))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int C))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B)))))) (forall ((N_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (let ((_let_2 (not (hBOOL (hAPP_int_bool nat_neg _let_1))))) (= (and _let_2 (=> _let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) (hAPP_int_nat nat _let_1))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc N_1)) (hAPP_int_nat number_number_of_nat V))))))) (forall ((A_69 $$unsorted) (B_57 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_69) B_57)) B_57) zero_z891286103de_int)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) Y)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (natfloor X)) (natfloor Y))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_nat_int semiri1621563631at_int X_1)) (image_nat_int semiri1621563631at_int A_1))) (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_1) A_1)))) (forall ((J_2 $$unsorted) (K_2 $$unsorted) (A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int (multInv P_3) J_2)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int J_2) K_2)) A_3) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 J_2)) K_2)) (hAPP_int_int _let_1 A_3)) P_3))))) (forall ((B_140 $$unsorted) (A_180 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (or (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_140) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_180) zero_zero_real))) (and (hBOOL (hAPP_real_bool _let_1 B_140)) (hBOOL (hAPP_real_bool _let_1 A_180)))) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_180) B_140)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_3) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B_2) C_1))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (div_mod_nat A_3) C_1)) (hAPP_nat_nat (div_mod_nat B_2) C_1))) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_3) B_2)) C_1))) (forall ((W_17 $$unsorted)) (= (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit1 pls)) W_17)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) (hAPP_int_int number_number_of_int W_17)))) (forall ((K_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) K_2)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) K_2)) M)))) (forall ((N $$unsorted) (A_3 $$unsorted)) (= (cis (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat (hAPP_nat_nat suc N))) A_3)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (cis A_3)) (cis (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) A_3))))) (forall ((A_124 $$unsorted) (N_34 $$unsorted) (B_102 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_124) N_34) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int B_102) N_34)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_124)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_102)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_34)) (= B_102 A_124))))))) (hBOOL (hAPP_int_bool _let_39 one_one_int)) (forall ((A_189 $$unsorted) (B_145 $$unsorted) (C_82 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_189) B_145)) C_82)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real A_189) C_82)))) (forall ((N_42 $$unsorted) (A_130 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_130)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_130) (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_130) N_42))))))) (forall ((X_24 $$unsorted) (N_32 $$unsorted)) (=> (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32)) (= X_24 one_on1684967323de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int X_24) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_24) N_32))))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 pls)) Y_2)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat one_one_rat) (hAPP_int_rat number_number_of_rat Y_2))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) (hAPP_real_real exp_real X_1))))) (forall ((A_230 $$unsorted) (C_96 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_230) C_96) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int C_96) A_230))) (forall ((C $$unsorted)) (= (hBOOL (vanishes (cOMBK_rat_nat C))) (= C zero_zero_rat))) (forall ((C_80 $$unsorted) (A_187 $$unsorted) (B_143 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int A_187))) (=> (hBOOL (hAPP_int_bool _let_1 B_143)) (=> (hBOOL (hAPP_int_bool _let_1 C_80)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_143) C_80))))))) (forall ((A_189 $$unsorted) (B_145 $$unsorted) (C_82 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_189) B_145)) C_82)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_189) C_82)))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat suc M)) N))) (forall ((A_48 $$unsorted) (B_39 $$unsorted) (C_20 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (div_mod_int A_48) C_20)) (hAPP_int_int (div_mod_int B_39) C_20))) C_20) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_48) B_39)) C_20))) (hBOOL (hAPP_int_bool _let_11 one_one_int)) (forall ((A_216 $$unsorted)) (= A_216 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat one_one_rat) A_216))) (forall ((A_3 $$unsorted) (N $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (cis A_3)) N) (cis (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) A_3)))) (forall ((N $$unsorted) (X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_int_real real_int N)) (hAPP_int_real real_int X))) (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int N) X)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (is_int X_1) (is_int Y_2)) (= (and (= X_1 zero_zero_int) (= Y_2 zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) X_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y_2) Y_2))) zero_zero_int))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (natfloor X))) (=> (= (hAPP_nat_real real_nat _let_1) X) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat _let_1) N) (natfloor (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) N)))))) (forall ((A_182 $$unsorted)) (= A_182 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_182) one_one_nat))) (forall ((A_148 $$unsorted) (N_51 $$unsorted) (N_50 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_148))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_51) N_50)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat one_one_rat) A_148)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat _let_1 N_51)) (hAPP_nat_rat _let_1 N_50))))))) (forall ((X_40 $$unsorted) (N_69 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat X_40))) (let ((_let_2 (hAPP_nat_rat _let_1 N_69))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat _let_2) _let_2) (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_69)))))) (forall ((M_12 $$unsorted)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) (hAPP_n1108039445umeral semiri1619134803umeral M_12)))) (= _let_76 _let_4) (= frac (produc93441119t_bool (hAPP_f428220345t_bool (hAPP_f654702867t_bool cOMBB_591320580ol_int (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool _let_96 _let_49))) (hAPP_i345030060t_bool (hAPP_f791698359t_bool cOMBC_241247961t_bool (hAPP_f791698359t_bool (hAPP_f847817363t_bool cOMBB_562416518ol_int cOMBC_int_int_bool) (hAPP_f725770969t_bool (hAPP_f983569339t_bool cOMBB_550562460ol_int (hAPP_f1399575567t_bool cOMBB_118231410ol_int fequal_int)) int_gcd))) one_one_int)))) (forall ((X_3 $$unsorted) (A $$unsorted)) (=> (hBOOL (tendsto_nat_complex X_3 A sequentially)) (hBOOL (tendsto_nat_complex (hAPP_f1646117269omplex (hAPP_f1457396693omplex cOMBB_117013006ex_nat cnj) X_3) (hAPP_complex_complex cnj A) sequentially)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int min))) (=> (and (is_int N_1) (is_int Ma)) (= (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Ma) N_1)) (or (and (= N_1 one_one_int) (= Ma one_one_int)) (and (= _let_1 N_1) (= Ma _let_1))))))) (forall ((V $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int V) pls)) (= zero_zero_nat (hAPP_int_nat number_number_of_nat V)))) (forall ((X_3 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (hBOOL (hAPP_f448129468l_bool (hAPP_f284875647l_bool ord_le951220754t_bool (image_int_int (standardRes Ma) X_3)) (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) Ma))))))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex Lx_2))) (= (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Ly) Rx_2)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex _let_1 Ly)) Rx_2)))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int N) one_one_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) N)) (= (hAPP_int_int fact_fact_int _let_1) (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_1) (hAPP_int_int fact_fact_int N)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_3)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2))) (hBOOL (hAPP_int_bool _let_1 B_2)))))) (= one_one_complex (expi (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex _let_98) (of_real_complex pi))) ii))) (forall ((X_8 $$unsorted) (Q_7 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X_8))) (= (hAPP_nat_int _let_1 (hAPP_nat_nat suc Q_7)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int _let_1 Q_7)) X_8)))) (forall ((B_120 $$unsorted) (A_159 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_120) A_159))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_159)) (hBOOL (hAPP_Q2096512830t_bool _let_1 B_120)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) Ma)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real real_nat N_1)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real real_nat Ma)) one_one_real))))) (forall ((B_131 $$unsorted) (A_171 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_171) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) B_131)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_171) B_131)) zero_zero_real))))) (forall ((B_2 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat D_3))) (=> (= one_one_nat (hAPP_nat_nat _let_1 A_3)) (=> (= (hAPP_nat_nat _let_1 B_2) one_one_nat) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2)) one_one_nat))))) (forall ((R_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) R_3)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) (hAPP_nat_real real_nat N_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_2) one_one_nat))) R_3)))))) (forall ((V_4 $$unsorted)) (let ((_let_1 (hAPP_nat_complex semiri2020571505omplex (hAPP_int_nat number_number_of_nat V_4)))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int number_number_of_int V_4))))) (and (=> _let_2 (= _let_1 (hAPP_int_complex number528085621omplex V_4))) (=> (not _let_2) (= zero_zero_complex _let_1)))))) (forall ((X_22 $$unsorted) (Y_17 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_22) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_17) _let_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) X_22)) Y_17)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_22) Y_17)) _let_2))))) (forall ((A_195 $$unsorted) (B_151 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat A_195) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_195) B_151)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real C) D) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C) D)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B))))) (= zero_zero_rat (hAPP_nat_rat semiri151668891at_rat zero_zero_nat)) (forall ((A_3 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real one_one_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_3)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3))))))) (= _let_2 (hAPP_int_int uminus_uminus_int min)) (not (hBOOL (hAPP_nat_bool prime one_one_nat))) (forall ((M_18 $$unsorted) (N_38 $$unsorted) (A_128 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_128))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A_128)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real _let_1 M_18)) (hAPP_nat_real _let_1 N_38))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_18) N_38)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real) cos)) (hAPP_int_nat number_number_of_nat _let_1)) X_1) (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) (hAPP_real_real cos X_1))) (hAPP_real_real sin X_1))))))) (forall ((A_211 $$unsorted) (M_26 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_211) one_one_nat)) M_26) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_211) M_26)) M_26))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd K_2) N)) (= (hAPP_int_int (legacy_zgcd M) N) (hAPP_int_int (legacy_zgcd (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) M)) N)))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) M)) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat suc M)))) N))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (hAPP_complex_real im (hAPP_real_complex (hAPP_r265291036omplex complex X) Y)))) (forall ((X_1 $$unsorted)) (= (= one_one_real X_1) (= X_1 one_one_real))) (= (hAPP_real_real sqrt one_one_real) one_one_real) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int Lx_2))) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int Ly) Rx_2)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int _let_1 Ly)) Rx_2)))) (forall ((A_3 $$unsorted) (C_1 $$unsorted) (B_2 $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_3) C_1)) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_2) D_3)) _let_1)))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_3) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_2) _let_1)))) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real C_1) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real D_3) _let_1)))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r632163725t_bool (hAPP_f1832844496t_bool (hAPP_f1990636069t_bool cOMBC_412863505t_bool P) Q) R) (hAPP_f1048215610t_bool (hAPP_r1623423338t_bool P R) Q))) (forall ((X $$unsorted) (N $$unsorted) (Y $$unsorted)) (=> (= (hAPP_nat_nat (div_mod_nat X) N) (hAPP_nat_nat (div_mod_nat Y) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Y) X)) (exists ((Q_4 $$unsorted)) (= X (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Y) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) Q_4))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_fun_nat_int power_power_int X))) (let ((_let_3 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int _let_2 _let_3)) _let_3) (hAPP_nat_int _let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_1)))))))) (forall ((N_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (let ((_let_2 (not (hBOOL (hAPP_int_bool nat_neg _let_1))))) (= (and _let_2 (=> _let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) (hAPP_int_nat nat _let_1))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc N_1)) (hAPP_int_nat number_number_of_nat V))))))) (forall ((B_129 $$unsorted) (A_169 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_169)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_129) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_169) B_129)) zero_zero_int))))) (forall ((X_4 $$unsorted) (Y_4 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X_4) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_4) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_4) _let_1)))))) (= (hAPP_real_real cos (hAPP_real_real arccos _let_2)) _let_2)))) (forall ((K_1 $$unsorted) (F $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (=> (is_int K_1) (=> (forall ((I_2 $$unsorted)) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) I_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_2) N_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int F (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_2) one_one_nat))) (hAPP_nat_int F I_2)))) one_one_int)))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int F Ma)) K_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) (hAPP_nat_int F N_1))) (exists ((I_2 $$unsorted)) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) I_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_2) N_1)) (= K_1 (hAPP_nat_int F I_2)))))))))) (forall ((B_43 $$unsorted) (B_42 $$unsorted) (A_52 $$unsorted) (C_23 $$unsorted) (A_51 $$unsorted)) (=> (= (hAPP_C498520661umeral (div_mo1740067990umeral A_52) C_23) (hAPP_C498520661umeral (div_mo1740067990umeral A_51) C_23)) (=> (= (hAPP_C498520661umeral (div_mo1740067990umeral B_42) C_23) (hAPP_C498520661umeral (div_mo1740067990umeral B_43) C_23)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_51) B_42)) C_23) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_52) B_43)) C_23))))) (forall ((X_24 $$unsorted) (N_32 $$unsorted)) (=> (or (= one_one_int X_24) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int X_24) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_24) N_32))))) (forall ((W $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real W) W))) (forall ((X_8 $$unsorted) (Q_7 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral X_8))) (= (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat suc Q_7)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral _let_1 Q_7)) X_8)))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex Rx))) (let ((_let_2 (hAPP_c172932010omplex times_times_complex Lx))) (= (hAPP_complex_complex _let_1 (hAPP_complex_complex _let_2 Ry)) (hAPP_complex_complex _let_2 (hAPP_complex_complex _let_1 Ry)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))))) (forall ((K_2 $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (div_mod_int M) K_2)) M)))) (= (hAPP_int_real real_int one_one_int) one_one_real) (forall ((X $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_3) X))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int)))) one_one_int) P_3))))) (is_int min) (forall ((A_226 $$unsorted) (B_163 $$unsorted) (C_92 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_226))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 C_92)) B_163) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 B_163)) C_92)))) (forall ((A_3 $$unsorted)) (= (cis (hAPP_real_real uminus_uminus_real A_3)) (hAPP_complex_complex invers1449016382omplex (cis A_3)))) (forall ((B_69 $$unsorted) (A_81 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_81)) (=> (hBOOL (hAPP_rat_bool _let_1 B_69)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_81) B_69))))))) (forall ((A_189 $$unsorted) (B_145 $$unsorted) (C_82 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_189) B_145)) C_82)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_189) C_82)))) (forall ((C_70 $$unsorted) (A_164 $$unsorted) (B_125 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_70))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_164) B_125)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_70)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 A_164)) (hAPP_nat_nat _let_1 B_125))))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real min)) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) one_one_real)) (hBOOL (hAPP_real_bool (deriv_real arccos X_1) (hAPP_real_real inverse_inverse_real (hAPP_real_real uminus_uminus_real (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (= Y X) (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool fequal_rat X) Y))))) (forall ((I_1 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_nat))) (let ((_let_2 (hAPP_f1080886329l_bool cOMBB_1015721476ol_nat fconj))) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat zero_zero_nat) M_2)) (= (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_f800510211t_bool (hAPP_f561022312t_bool cOMBS_nat_bool_bool (hAPP_f1146629647l_bool _let_2 (hAPP_f800510211t_bool (hAPP_f1722879237t_bool cOMBC_226598744l_bool member_nat) M_2))) (hAPP_n1699378549t_bool _let_1 (hAPP_nat_nat suc I_1))))) (hAPP_nat_nat suc (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_f800510211t_bool (hAPP_f561022312t_bool cOMBS_nat_bool_bool (hAPP_f1146629647l_bool _let_2 (hAPP_f800510211t_bool (hAPP_f1722879237t_bool cOMBC_226598744l_bool (hAPP_f66927821l_bool (hAPP_f2037783381l_bool cOMBB_1146692694ol_nat member_nat) suc)) M_2))) (hAPP_n1699378549t_bool _let_1 I_1)))))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int N_1) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (quickcheck_int_of N_1)) (quickcheck_int_of Ma))))) (forall ((C_43 $$unsorted) (A_101 $$unsorted) (B_83 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat C_43))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_101) B_83)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 A_101)) (hAPP_nat_nat _let_1 B_83)))))) (forall ((N_12 $$unsorted) (R_6 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) R_6)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real R_6) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real R_6) (hAPP_nat_nat suc N_12))) R_6))))) (forall ((U $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_1) J)) (= (= Ma (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J) I_1)) U)) N_1)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I_1) U)) Ma) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J) U)) N_1))))) (forall ((A_225 $$unsorted) (B_162 $$unsorted) (C_91 $$unsorted) (D_18 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex A_225))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 B_162)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex C_91) D_18)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 C_91)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_162) D_18))))) (forall ((R_3 $$unsorted) (X $$unsorted)) (= (hAPP_complex_real im (hAPP_complex_complex (scaleR1652505878omplex R_3) X)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real R_3) (hAPP_complex_real im X)))) (forall ((X $$unsorted) (Y $$unsorted) (L_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_real_real uminus_uminus_real M))) (let ((_let_2 (hAPP_real_real uminus_uminus_real L_2))) (let ((_let_3 (hAPP_r1250527377l_real plus_plus_real X))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_3 Y)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_2) _let_1)))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real abs_abs_real (hAPP_real_real _let_3 _let_2))) (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Y) _let_1))))))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int bit0 (hAPP_int_int uminus_uminus_int K_2)) (hAPP_int_int uminus_uminus_int (hAPP_int_int bit0 K_2)))) (forall ((Ta $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) D_1)) (forall ((X_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int D))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K) D_1))) Ta))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) Ta)))))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real exp_real X_1)) one_one_real)))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (hAPP_nat_int semiri1621563631at_int (hAPP_int_nat nat Z_1)))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_1)))) (=> (is_int Z_1) (and (=> _let_2 (= Z_1 _let_1)) (=> (not _let_2) (= zero_zero_int _let_1))))))) (= (ratreal one_one_rat) one_one_real) (forall ((V_23 $$unsorted)) (= (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_23) (hAPP_int_int bit1 pls))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real V_23)) one_one_real))) (not (= zero_z891286103de_int one_on1684967323de_int)) (forall ((K_1 $$unsorted)) (=> (is_int K_1) (= (= (hAPP_int_int bit1 K_1) min) (= min K_1)))) (forall ((A_23 $$unsorted)) (=> (is_int A_23) (=> (not (= zero_zero_int A_23)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_23) A_23) one_one_int)))) (forall ((X_3 $$unsorted) (A $$unsorted)) (=> (hBOOL (hAPP_complex_bool (sums_complex X_3) A)) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat re) X_3)) (hAPP_complex_real re A))))) (forall ((X_38 $$unsorted) (P_8 $$unsorted) (Q_12 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex X_38))) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_nat_complex _let_1 P_8)) Q_12) (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_8) Q_12))))) (forall ((B_1_1 $$unsorted)) (is_int (quickcheck_int_of B_1_1))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i157317923t_real (hAPP_f1613846310t_real (hAPP_f1720068861t_real cOMBC_295337211t_real P) Q) R) (hAPP_f1888375463t_real (hAPP_i447943416t_real P R) Q))) (forall ((M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) M)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong one_one_int) (hAPP_int_int number_number_of_int min)) M))))) (forall ((X_1 $$unsorted)) (= (= X_1 zero_z891286103de_int) (= zero_z891286103de_int X_1))) (forall ((V_12 $$unsorted) (W_10 $$unsorted)) (= (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_12) W_10)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat V_12)) (hAPP_int_rat number_number_of_rat W_10)))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (of_real_complex (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_complex_real re Z_1)) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_complex_real im Z_1)) _let_1))) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Z_1) (hAPP_complex_complex cnj Z_1))))) (forall ((W_5 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_5))) (let ((_let_2 (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex zero_zero_complex) _let_1))) (let ((_let_3 (= zero_zero_nat _let_1))) (and (=> _let_3 (= _let_2 one_one_complex)) (=> (not _let_3) (= _let_2 zero_zero_complex))))))) (forall ((X $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat fact_fact_nat X)) (hAPP_int_int fact_fact_int (hAPP_nat_int semiri1621563631at_int X)))) (forall ((N $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_3) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime P_3) N))))) (forall ((B_129 $$unsorted) (A_169 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_169)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_129) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_169) B_129)) zero_zero_real))))) (forall ((M $$unsorted) (D_3 $$unsorted) (R_3 $$unsorted)) (=> (= R_3 (hAPP_nat_nat (div_mod_nat M) D_3)) (exists ((Q_4 $$unsorted)) (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat R_3) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Q_4) D_3)))))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I) J_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int I) K_2)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int J_2) K_2))))) (forall ((Ma $$unsorted)) (= (= one_one_nat Ma) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Ma) one_one_nat)))) (forall ((N $$unsorted)) (=> (is_int N) (= (quickcheck_int_of (hAPP_i1732201573de_int quickcheck_of_int N)) N))) (forall ((A_13 $$unsorted) (B_9 $$unsorted)) (= A_13 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_13) B_9)) B_9)) (hAPP_Q1762011733de_int (div_mo231679042de_int A_13) B_9)))) (forall ((P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) _let_1))))))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (not (forall ((M_1 $$unsorted) (N_2 $$unsorted)) (not (= Z_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int semiri1621563631at_int M_1)) (hAPP_nat_int semiri1621563631at_int N_2)))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N))) (and (=> (= M zero_zero_nat) (= _let_1 zero_zero_nat)) (=> (not (= zero_zero_nat M)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) one_one_nat)) N)) _let_1))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C)) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int B) A)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int C) A))) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int B) C))))))) (forall ((C_37 $$unsorted) (A_95 $$unsorted) (B_77 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_95) B_77)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_95) C_37)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_77) C_37))))) (forall ((A_186 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int one_on1684967323de_int) A_186))) (forall ((M_13 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) (hAPP_nat_int semiri1621563631at_int M_13)) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc M_13)))) (= (hAPP_real_real _let_53 _let_84) pi) (forall ((C_88 $$unsorted) (A_206 $$unsorted) (B_157 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat A_206))) (=> (hBOOL (hAPP_nat_bool _let_1 B_157)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_157) C_88)) (hBOOL (hAPP_nat_bool _let_1 C_88)))))) (= (hAPP_nat_nat fact zero_zero_nat) one_one_nat) (forall ((N_52 $$unsorted) (A_150 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_150)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_150) N_52)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real cos X)) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sin X)) _let_1)) one_one_real))) (forall ((A $$unsorted) (B $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted) (C_3 $$unsorted)) (let ((_let_1 (hAPP_r2019696015l_real produc865579683l_real A_2))) (=> (and (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real _let_1 B_4))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_2) B_4)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_4) C_3)) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real B_4) C_3)))) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real _let_1 C_3)))))) (=> (not (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real A) B)))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (forall ((N_2 $$unsorted)) (let ((_let_1 (hAPP_n332733730l_real (bolzano_bisect P_1 A B) N_2))) (not (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real (hAPP_P731461727l_real produc1935615926l_real _let_1)) (hAPP_P731461727l_real produc556554744l_real _let_1))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B A) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B) zero_zero_real))) (forall ((C_88 $$unsorted) (A_206 $$unsorted) (B_157 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral A_206))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_157)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral B_157) C_88)) (hBOOL (hAPP_C24501650l_bool _let_1 C_88)))))) (forall ((C_64 $$unsorted) (A_142 $$unsorted) (B_111 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_64))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A_142)) (hAPP_int_int _let_1 B_111))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_64)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_142) B_111)))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int bit1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_2) L_2)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit0 K_2)) (hAPP_int_int bit1 L_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_2) X_1)))))) (= _let_1 _let_1))) (forall ((R1 $$unsorted) (A_3 $$unsorted) (R2 $$unsorted) (B_2 $$unsorted)) (= (rcis (hAPP_real_real (hAPP_r1250527377l_real times_times_real R1) R2) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_3) B_2)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (rcis R1 A_3)) (rcis R2 B_2)))) (forall ((C_43 $$unsorted) (A_101 $$unsorted) (B_83 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int C_43))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_101) B_83)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int _let_1 A_101)) (hAPP_Q1762011733de_int _let_1 B_83)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc Ma)) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) (hAPP_nat_rat semiri151668891at_rat N_1))))) (forall ((N $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int N))) zero_zero_int))) (forall ((F $$unsorted)) (=> (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat abs_abs_real) F))) (hBOOL (summable_real F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C))) (=> (not (= C zero_zero_real)) (= (= (hAPP_real_real _let_1 B) (hAPP_real_real _let_1 A)) (= B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C) zero_zero_int)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) A)))))) (forall ((C_64 $$unsorted) (A_142 $$unsorted) (B_111 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_64))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 A_142)) (hAPP_nat_nat _let_1 B_111))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_64)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_142) B_111)))))) (forall ((N_19 $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat zero_zero_nat) (hAPP_nat_nat suc N_19)))) (forall ((B_71 $$unsorted) (A_83 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_83)) (=> (hBOOL (hAPP_nat_bool _let_1 B_71)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_83) B_71))))))) (= real_nat semiri132038758t_real) (forall ((K_2 $$unsorted)) (=> (is_int K_2) (= K_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int pls) K_2)))) (forall ((Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_neg Z_1)) (= (hAPP_int_nat nat Z_1) zero_zero_nat))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex Lx_1))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex _let_1 Rx_1)) Ry_1) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Rx_1) Ry_1))))) (forall ((M_11 $$unsorted)) (not (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral semiri1619134803umeral M_11)) zero_z126310315umeral)))) (forall ((B_116 $$unsorted) (A_155 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_155)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_116)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_155) B_116))))))) (forall ((F $$unsorted) (Y_2 $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_real_bool (sums_real G) X_1)) (=> (hBOOL (hAPP_real_bool (sums_real F) Y_2)) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f335634176l_real cOMBS_337378985l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat F) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat div_div_nat) _let_1)))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat G) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat div_div_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat minus_minus_nat) one_one_nat))) _let_1)))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) Y_2))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Z_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y) Z_1)) Z_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) Z_1)) Y))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_nat_real sin_coeff X_2))) (let ((_let_2 (hBOOL (hAPP_nat_bool even_odd_even_nat X_2)))) (and (=> (not _let_2) (= _let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat X_2) (hAPP_nat_nat suc zero_zero_nat))) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat X_2))))) (=> _let_2 (= _let_1 zero_zero_real)))))) (forall ((M_10 $$unsorted) (N_24 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int M_10)) (hAPP_nat_int semiri1621563631at_int N_24))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_10) N_24)))) (forall ((B_1_1 $$unsorted)) (is_bool (vanishes B_1_1))) (forall ((N_41 $$unsorted)) (let ((_let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat zero_zero_rat) N_41))) (let ((_let_2 (= N_41 zero_zero_nat))) (and (=> (not _let_2) (= zero_zero_rat _let_1)) (=> _let_2 (= one_one_rat _let_1)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X)) (= (hAPP_nat_real real_nat (hAPP_int_nat nat X)) (hAPP_int_real real_int X)))) (forall ((N $$unsorted)) (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int N) one_one_int)) N))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted) (N $$unsorted)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2)) C_1) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int D_3) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) N)) (=> (= (hAPP_int_int (legacy_zgcd A_3) B_2) one_one_int) (=> (= (hAPP_int_int (legacy_zgcd B_2) C_1) one_one_int) (=> (= (hAPP_int_int (legacy_zgcd C_1) A_3) one_one_int) (exists ((K $$unsorted) (L_1 $$unsorted) (M_1 $$unsorted)) (and (is_int K) (is_int M_1) (= (hAPP_int_int abs_abs_int A_3) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int K) N)) (= (hAPP_int_int abs_abs_int B_2) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int L_1) N)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int M_1) N) (hAPP_int_int abs_abs_int C_1)) (is_int L_1))))))))) (forall ((I $$unsorted)) (= (quickcheck_nat_of I) (hAPP_int_nat nat (quickcheck_int_of I)))) (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) M))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) Z_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W_1) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Z_2) one_one_int))))) (forall ((A_211 $$unsorted) (M_26 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_211) one_one_complex)) M_26) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_211) M_26)) M_26))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real C) D) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C) D))))) (forall ((X_46 $$unsorted) (Y_34 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (let ((_let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int Y_34) _let_2) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_46) _let_2)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 X_46)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 Y_34)) (= Y_34 X_46))))))) (forall ((A_124 $$unsorted) (N_34 $$unsorted) (B_102 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (and (is_int A_124) (is_int B_102)) (=> (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_102) N_34) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_124) N_34)) (=> (hBOOL (hAPP_int_bool _let_1 A_124)) (=> (hBOOL (hAPP_int_bool _let_1 B_102)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_34)) (= B_102 A_124)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_real_real cos Y))) (let ((_let_2 (hAPP_real_real cos X))) (=> (not (= _let_2 zero_zero_real)) (=> (not (= _let_1 zero_zero_real)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real tan X)) (hAPP_real_real tan Y)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_2) _let_1)))))))) (forall ((N_25 $$unsorted)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) (hAPP_n1108039445umeral semiri1619134803umeral N_25)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r2019696015l_real (hAPP_f1591894897l_real (hAPP_f644105375l_real cOMBC_467724138l_real P) Q) R) (hAPP_f617735571l_real (hAPP_r712953929l_real P R) Q))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) one_one_int))) (forall ((V_7 $$unsorted) (B_101 $$unsorted) (C_56 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat V_7)))) (= (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat B_101) C_56)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_rat_rat _let_1 B_101)) (hAPP_rat_rat _let_1 C_56))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f289318786t_bool (hAPP_r653725362t_bool P R) Q) (hAPP_r373117745t_bool (hAPP_f1115375056t_bool (hAPP_f271976045t_bool cOMBC_1801450329t_bool P) Q) R))) (forall ((X_30 $$unsorted) (Y_24 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_30) Y_24)) (=> (not (= X_30 Y_24)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_30) Y_24))))) (forall ((X $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) (hAPP_real_real abs_abs_real X)) (hAPP_real_real sgn_sgn_real X))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A))) (= (= C B) (= (hAPP_rat_rat _let_1 B) (hAPP_rat_rat _let_1 C))))) (forall ((B_92 $$unsorted) (A_114 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_114) zero_zero_nat)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat B_92) zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_114) B_92)) zero_zero_nat))))) (forall ((D $$unsorted) (B $$unsorted) (C $$unsorted) (A $$unsorted)) (=> (not (= zero_z126310315umeral A)) (=> (not (= zero_z126310315umeral C)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A) B)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral C) D)) (= (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B) C) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A) D)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral B) A) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral D) C)))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat C))) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) B)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A)) (hAPP_rat_rat _let_1 B)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral B))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral) B)) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral _let_1 X_1)) (hAPP_n1108039445umeral _let_1 Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_1) Y_2)))))) (forall ((X_24 $$unsorted) (N_32 $$unsorted)) (=> (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32)) (= X_24 one_one_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat X_24) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_24) N_32))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X_1)) (=> (hBOOL (hAPP_real_bool _let_1 Y_2)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real ln X_1)) (hAPP_real_real ln Y_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted)) (= (forall ((M_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_1) N_1)) (hBOOL (hAPP_nat_bool P_1 M_1)))) (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_2) (hAPP_n1699378549t_bool (ord_at238088361st_nat zero_zero_nat) N_1))) (hBOOL (hAPP_nat_bool P_1 X_2)))))) (forall ((Y_21 $$unsorted) (X_27 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 X_27)) (=> (hBOOL (hAPP_rat_bool _let_1 Y_21)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat Y_21) one_one_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Y_21) X_27)) X_27))))))) (forall ((N_1 $$unsorted)) (= (= zero_zero_nat N_1) (= zero_zero_int (hAPP_nat_int semiri1621563631at_int N_1)))) (forall ((X $$unsorted)) (= (hAPP_i1732201573de_int quickcheck_of_int (quickcheck_int_of X)) X)) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (is_int A_3) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) B_2)) (= (hAPP_int_int (div_mod_int A_3) B_2) A_3))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (= (hAPP_int_int (div_mod_int A_3) B_2) (hAPP_P1175774780nt_int product_snd_int_int (negDivAlg A_3 B_2)))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) one_one_nat)) (forall ((B_1 $$unsorted) (K_1 $$unsorted) (Diff $$unsorted) (H $$unsorted) (N_1 $$unsorted)) (=> (forall ((M_1 $$unsorted) (T $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) H)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) T)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) T) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) T))))) (=> (= (hAPP_nat_nat suc K_1) N_1) (forall ((M_1 $$unsorted) (T $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc M_1))) (let ((_let_2 (hAPP_nat_fun_nat_nat minus_minus_nat N_1))) (let ((_let_3 (hAPP_nat_nat _let_2 _let_1))) (let ((_let_4 (hAPP_r474017924t_real power_power_real T))) (let ((_let_5 (hAPP_r1250527377l_real times_times_real B_1))) (let ((_let_6 (ord_at4362885an_nat zero_zero_nat))) (let ((_let_7 (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat))) (let ((_let_8 (hAPP_f224989205l_real cOMBB_1419615765al_nat Diff))) (let ((_let_9 (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real))) (let ((_let_10 (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real))) (let ((_let_11 (hAPP_nat_nat _let_2 M_1))) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) H)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) T))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real minus_minus_real) (hAPP_n546711566l_real Diff M_1))) (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real plus_plus_real) (hAPP_f2119584768l_real (hAPP_f59594445l_real cOMBC_2010481033l_real (hAPP_f1523861863l_real (hAPP_f1067681227l_real cOMBB_1934313333l_real big_co604158596t_real) (hAPP_f1993765077t_real (hAPP_f895854793t_real cOMBB_1948233853l_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_10 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_9 (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real (hAPP_f1904307534l_real _let_8 (hAPP_nat_fun_nat_nat plus_plus_nat M_1))) zero_zero_real))) _let_7)))) power_power_real))) (hAPP_n1699378549t_bool _let_6 _let_11)))) (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real _let_5) (hAPP_r1250527377l_real (hAPP_f203520653l_real cOMBC_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real inverse_divide_real) (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real power_power_real) _let_11))) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat _let_11)))))) T) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_n546711566l_real Diff _let_1) T)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_10 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_9 (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real (hAPP_f1904307534l_real _let_8 (hAPP_nat_fun_nat_nat plus_plus_nat _let_1))) zero_zero_real))) _let_7))) _let_4)) (hAPP_n1699378549t_bool _let_6 _let_3))) (hAPP_real_real _let_5 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real _let_4 _let_3)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat _let_3)))))))))))))))))))))))) (forall ((K_2 $$unsorted)) (= (ratreal (hAPP_int_rat number_number_of_rat K_2)) (hAPP_int_real number267125858f_real K_2))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f41603166t_bool P (hAPP_r373117745t_bool Q R)) (hAPP_r481142414t_bool (hAPP_f1341793266t_bool (hAPP_f571820015t_bool cOMBB_1159313332l_real P) Q) R))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int C))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) B))))) (= zero_zero_nat _let_97) (forall ((V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_real real_nat (hAPP_int_nat number_number_of_nat V_2)))) (let ((_let_2 (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int V_2))))) (and (=> (not _let_2) (= (hAPP_int_real number267125858f_real V_2) _let_1)) (=> _let_2 (= _let_1 zero_zero_real)))))) (forall ((N_59 $$unsorted) (M_24 $$unsorted) (X_28 $$unsorted) (Y_22 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_28) Y_22)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_59) M_24)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_28) N_59)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_22) M_24)))))) (forall ((M $$unsorted)) (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) zero_zero_nat))) (forall ((W_7 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W_7))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int zero_zero_int) _let_1)) _let_1) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 W_7))))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex Lx_6))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex _let_1 Ly_4)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Rx_6) Ry_4)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex _let_1 Rx_6)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Ly_4) Ry_4))))) (forall ((A $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_1))) (= (and (= zero_zero_real A) (not (= _let_1 zero_zero_nat))) (= zero_zero_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A) _let_1))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (=> (is_int A_3) (=> (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_3) B_2) C_1) (= A_3 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int C_1) B_2))))) (forall ((X_30 $$unsorted) (Y_24 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int X_30) Y_24)) (=> (not (= X_30 Y_24)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int X_30) Y_24))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X_1) _let_1)) Y_2) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) Y_2)) _let_1))))) (forall ((J_2 $$unsorted) (I $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) I)) I)))) (forall ((B_2 $$unsorted)) (=> (is_int B_2) (=> (not (= zero_zero_int B_2)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel zero_zero_int B_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) zero_zero_int)))))) (forall ((B_1_1 $$unsorted)) (is_int (archim791455193or_rat B_1_1))) (forall ((A_224 $$unsorted) (N_68 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_C471253896umeral power_2100829034umeral A_224))) (= (hAPP_n1108039445umeral _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_68)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral (hAPP_n1108039445umeral _let_2 N_68)) _let_1))))) (forall ((Ma $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcongm Ma) X_2) Xa)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X_2) Xa) Ma)))) (forall ((C_72 $$unsorted) (B_127 $$unsorted) (A_166 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_72))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B_127) A_166)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C_72) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_166)) (hAPP_real_real _let_1 B_127))))))) (forall ((Ta $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Ta) one_one_int)) B_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int Ta))) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa) X_2)))))))) (=> (hBOOL (hAPP_int_bool _let_1 X_2)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1))))))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) N) M))) (forall ((B_116 $$unsorted) (A_155 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_155)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_116)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_155) B_116))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat times_times_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) one_one_nat))) (let ((_let_2 (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X_1)) one_one_real)) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_2 (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_2 (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real inverse_divide_real one_one_real)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) _let_1)))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_int (hAPP_f1356864277nt_int (hAPP_f747162069nt_int cOMBB_int_int_int P) Q) R) (hAPP_int_int P (hAPP_int_int Q R)))) (forall ((P_1 $$unsorted) (N_1 $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_nat_bool P_1 X_2)) (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_2) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))))) (exists ((M_1 $$unsorted)) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1)) (hBOOL (hAPP_nat_bool P_1 M_1)))))) (forall ((X_9 $$unsorted)) (let ((_let_1 (hAPP_nat_real semiri132038758t_real (hAPP_int_nat nat X_9)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_9)) (= (hAPP_nat_real semiri132038758t_real (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_9))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) _let_1))))) (forall ((N_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) N_1)) (= (hAPP_int_int fact_fact_int N_1) (big_co1548731110nt_int cOMBI_int (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) N_1))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B A) (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_bool_bool (hAPP_i68813070l_bool P R) (hAPP_int_bool Q R)) (hAPP_int_bool (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool P) Q) R))) (forall ((A_77 $$unsorted)) (= zero_zero_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_77) zero_zero_complex))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X))))))) (forall ((A_3 $$unsorted)) (= (cis A_3) (rcis one_one_real A_3))) (forall ((P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_int number_number_of_int _let_1))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_2) P_3)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_int_nat nat P_3)) (hAPP_int_nat number_number_of_nat _let_1)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) _let_2))))))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real arccos Y)))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted)) (= (rcis (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) R_3) (hAPP_real_real uminus_uminus_real A_3)) (hAPP_complex_complex invers1449016382omplex (rcis R_3 A_3)))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int one_one_int) _let_1) (hAPP_P1175774780nt_int product_fst_int_int (hAPP_P1975530577nt_int negateSnd (negDivAlg (hAPP_int_int uminus_uminus_int one_one_int) (hAPP_int_int uminus_uminus_int _let_1)))))))) (forall ((N_13 $$unsorted) (A_8 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int one_one_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_8)) (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_8) (hAPP_nat_nat suc N_13))))))) (forall ((A_231 $$unsorted) (B_165 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_165) A_231) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_231) B_165))) (= (collect_real (hAPP_f101635158l_bool _let_87 (hAPP_f1625314454t_bool (hAPP_f340152631t_bool cOMBB_1453147152l_real _let_58) (hAPP_f1832844496t_bool (hAPP_f1990636069t_bool cOMBC_412863505t_bool (hAPP_f704188951t_bool (hAPP_f1456711209t_bool cOMBB_690122963l_real cOMBC_1683390479t_bool) (hAPP_f1063001928t_bool (hAPP_f2050994651t_bool cOMBB_2138578194l_real (hAPP_f85237525t_bool cOMBB_389152643ol_int cOMBS_int_bool_bool)) (hAPP_f381769257l_bool (hAPP_f512004221l_bool cOMBB_188663909l_real (hAPP_f1830214065l_bool cOMBB_793166024ol_int _let_96)) (hAPP_f956464319t_bool (hAPP_f422375781t_bool cOMBC_243356514t_bool (hAPP_f332806115t_bool (hAPP_f1177545951t_bool cOMBB_1459832681l_real cOMBB_95956018ol_int) (hAPP_f1920544743t_bool (hAPP_f866672739t_bool cOMBB_1247074793l_real cOMBB_real_bool_int) fequal_real))) (hAPP_f1323932638t_real (hAPP_f352226557t_real cOMBC_824100275t_real (hAPP_f74147283t_real (hAPP_f1169087445t_real cOMBB_2129825580al_int cOMBB_real_real_int) _let_86)) real_int)))))) (hAPP_f1805168059t_bool (hAPP_f627970963t_bool cOMBB_bool_bool_int fNot) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool fequal_int) zero_zero_int)))))) field_1210416355s_real) (forall ((K_1 $$unsorted)) (= (hAPP_n1699378549t_bool ord_lessThan_nat (hAPP_nat_nat suc K_1)) (hAPP_n1699378549t_bool ord_atMost_nat K_1))) (forall ((A_46 $$unsorted) (B_37 $$unsorted) (C_18 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_46))) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 B_37)) C_18) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat B_37) C_18))) C_18)))) (forall ((M_12 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real semiri132038758t_real M_12)))) (not (= zero_zero_real pi)) (forall ((N $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int D_3))) (=> (= one_one_int (hAPP_int_int _let_1 A_3)) (= (hAPP_int_int _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) N)) one_one_int)))) (forall ((B_117 $$unsorted) (A_156 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_156)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat B_117) zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_156) B_117)) zero_zero_nat))))) (forall ((C_34 $$unsorted) (D_6 $$unsorted) (A_80 $$unsorted) (B_68 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_80) B_68)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat C_34) D_6)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_80) C_34)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_68) D_6)))))) _let_95 (forall ((U $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (J $$unsorted) (I_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat J) I_1)) (= (= N_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat I_1) J)) U)) Ma)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J) U)) N_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I_1) U)) Ma))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_nat_real real_nat N))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) one_one_real))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) one_one_nat) (natceiling X)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat C) D) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C) D)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) B))))) (forall ((Z_2 $$unsorted) (X_3 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real Z_2) X_3)) (=> (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) X_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) Z_2)))) (= Z_2 (comple124823625p_real X_3))))) (forall ((K_2 $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat div_div_nat K_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) M)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 N)) (hAPP_nat_nat _let_1 M))))))) (forall ((X $$unsorted)) (= (ratreal (hAPP_rat_rat uminus_uminus_rat X)) (hAPP_real_real uminus_uminus_real (ratreal X)))) (forall ((C_70 $$unsorted) (A_164 $$unsorted) (B_125 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_70))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_164) B_125)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C_70)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_164)) (hAPP_real_real _let_1 B_125))))))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) zero_zero_int) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong zero_zero_int) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int)) _let_1)))) P_3))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_2) _let_1))) (and (= zero_zero_real X_1) (= zero_zero_real Y_2))))) (forall ((A_145 $$unsorted) (M_20 $$unsorted) (N_48 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_145))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 M_20)) (hAPP_nat_nat _let_1 N_48)) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_20) N_48))))) (exists ((K_4 $$unsorted)) (and (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real norm_norm_real (hAPP_complex_real im X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) K_4)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat (natfloor X))) X)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) C)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B) C))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)))) (forall ((A_107 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_107) zero_zero_real) A_107)) (forall ((A_24 $$unsorted) (B_19 $$unsorted) (C_8 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_8))) (let ((_let_2 (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int _let_1 A_24)) (hAPP_int_int _let_1 B_19)))) (=> (is_int C_8) (and (=> (not (= zero_zero_int C_8)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_24) B_19) _let_2)) (=> (= C_8 zero_zero_int) (= zero_zero_int _let_2))))))) (forall ((M $$unsorted) (N $$unsorted) (I $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat I))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) I)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int abs_abs_int X)) (hAPP_int_int abs_abs_int Y)) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y))) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_14) (hAPP_real_real arctan (hAPP_real_real _let_29 (hAPP_int_real number267125858f_real (hAPP_int_int bit1 _let_3)))))) (hAPP_real_real arctan (hAPP_real_real _let_29 (hAPP_int_real number267125858f_real (hAPP_int_int bit1 (hAPP_int_int bit1 (hAPP_int_int bit1 (hAPP_int_int bit1 (hAPP_int_int bit0 (hAPP_int_int bit1 _let_31)))))))))) _let_46) (forall ((A_203 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_203) zero_z891286103de_int) zero_z891286103de_int)) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)) zero_zero_int))))) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (=> (exists ((A_2 $$unsorted)) (and (forall ((N_2 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat abs_abs_rat (hAPP_nat_rat X_3 N_2))) A_2))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_2)))) (=> (hBOOL (vanishes Y_3)) (hBOOL (vanishes (hAPP_f2062659861at_rat (hAPP_f1131305186at_rat cOMBS_nat_rat_rat (hAPP_f1830834240at_rat (hAPP_f1073644437at_rat cOMBB_1926947at_nat times_times_rat) X_3)) Y_3)))))) (forall ((B_131 $$unsorted) (A_171 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_171) zero_z126310315umeral)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) B_131)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_171) B_131)) zero_z126310315umeral))))) (forall ((M $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_3))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N))) (or (hBOOL (hAPP_nat_bool _let_1 N)) (hBOOL (hAPP_nat_bool _let_1 M))))))) (forall ((V_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat V_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) _let_1)) (= _let_1 (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_1) one_one_nat)))))) (forall ((A $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) A)) zero_zero_int)))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_3) B_2)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_3)) (hAPP_real_real _let_1 B_2))))))) (forall ((Y_8 $$unsorted) (Z_6 $$unsorted) (X_11 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral Z_6))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 X_11)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 Y_8)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral X_11) Y_8)) Z_6) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral X_11) Z_6)) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral Y_8) Z_6))))))) (forall ((X_1 $$unsorted)) (= (hAPP_real_real sin X_1) (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) sin_coeff)) (hAPP_r474017924t_real power_power_real X_1))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) E_2)) C)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) E_2)) D))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B) A)) E_2)) D))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (is_int A_3) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2))) (hAPP_int_int (div_mod_int A_3) B_2)) A_3))) (forall ((A_217 $$unsorted) (M_29 $$unsorted) (B_160 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_217) M_29)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_160) M_29)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_217) B_160)) M_29))) (forall ((X_1 $$unsorted)) (let ((_let_1 (= X_1 zero_zero_rat))) (= _let_1 _let_1))) (hBOOL (hAPP_real_bool _let_40 _let_72)) (forall ((M_11 $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat semiri984289939at_nat M_11)) zero_zero_nat)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int fact_fact_int X))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (or (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real W) Z_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Z_1) W)))) (forall ((A_113 $$unsorted) (B_91 $$unsorted) (C_51 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex A_113))) (= (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_91) C_51)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex _let_1 B_91)) C_51)))) (forall ((X $$unsorted) (Y $$unsorted) (R_3 $$unsorted)) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) R_3)) Y) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_real_complex (hAPP_r265291036omplex complex X) Y)) (of_real_complex R_3)))) (= one_one_int (hAPP_int_int fact_fact_int one_one_int)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat P R) (hAPP_nat_nat Q R)) (hAPP_nat_nat (hAPP_f1914919701at_nat (hAPP_f1408247010at_nat cOMBS_nat_nat_nat P) Q) R))) (forall ((P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int bit1 pls))) (let ((_let_2 (hAPP_int_int bit0 _let_1))) (=> (is_int P_3) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (= P_3 (hAPP_int_int number_number_of_int _let_2))) (=> (not (= (hAPP_int_int number_number_of_int (hAPP_int_int bit1 _let_1)) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 _let_2))) P_3))))))))) (forall ((A_122 $$unsorted) (B_100 $$unsorted) (V_6 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real V_6))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_122) B_100)) _let_1) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_122) _let_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_100) _let_1))))) (forall ((W_7 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real W_7))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real zero_zero_real) _let_1)) _let_1) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 W_7))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= N_1 Ma) (= (hAPP_n522471361de_int semiri1424489471de_int Ma) (hAPP_n522471361de_int semiri1424489471de_int N_1)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (not (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int N_1)))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real N_1)) X_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_int_nat number_number_of_nat N_1)) (natfloor X_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (ratreal X)) (ratreal Y)) (ratreal (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat X) Y)))) (forall ((C_72 $$unsorted) (B_127 $$unsorted) (A_166 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_72))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_127) A_166)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C_72) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A_166)) (hAPP_int_int _let_1 B_127))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1836591008nt_int (hAPP_f400200275nt_int (hAPP_f1731308757nt_int cOMBB_735549356nt_int P) Q) R) (hAPP_f151095827nt_int P (hAPP_i1216375074nt_int Q R)))) (forall ((P_5 $$unsorted)) (= (hAPP_i1948725293t_bool sRStar P_5) (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) P_5))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_1))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat _let_1) Ma) (hAPP_nat_nat (nat_case_nat _let_1 (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat suc) (hAPP_nat_fun_nat_nat ord_max_nat N_1))) Ma)))) (forall ((C_38 $$unsorted) (A_96 $$unsorted) (B_78 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat C_38))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_96) B_78)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A_96)) (hAPP_rat_rat _let_1 B_78)))))) (forall ((I_1 $$unsorted) (K_1 $$unsorted)) (=> (is_int K_1) (= (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int I_1) K_1) zero_zero_int) (or (= K_1 zero_zero_int) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I_1) K_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) I_1))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I_1) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) I_1))))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (natceiling X)) one_one_nat) (natceiling (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) one_one_real))))) (forall ((P $$unsorted)) (= P (hAPP_nat_nat cOMBI_nat P))) (forall ((C_85 $$unsorted) (A_193 $$unsorted) (B_149 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int A_193))) (=> (hBOOL (hAPP_int_bool _let_1 B_149)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_149) C_85)))))) (forall ((X_8 $$unsorted) (Q_7 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex X_8))) (= (hAPP_nat_complex _let_1 (hAPP_nat_nat suc Q_7)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex _let_1 Q_7)) X_8)))) (forall ((A_12 $$unsorted) (N_18 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_12))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int _let_1 N_18)) A_12) (hAPP_nat_int _let_1 (hAPP_nat_nat suc N_18))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (norm_frac A B))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) zero_zero_int)))) (let ((_let_3 (hAPP_int_int (hAPP_int_fun_int_int int_gcd A) B))) (let ((_let_4 (= zero_zero_int B))) (=> (and (is_int B) (is_int A)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int norm_frac_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A) B))) (and (=> (not _let_2) (and (=> (or _let_4 (= zero_zero_int A)) (= _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) one_one_int))) (=> (not (or (= A zero_zero_int) _let_4)) (= _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A) _let_3)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B) _let_3)))))) (=> _let_2 (= _let_1 (norm_frac (hAPP_int_int uminus_uminus_int A) (hAPP_int_int uminus_uminus_int B)))))))))))) (forall ((A_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat zero_zero_nat) A_3)) (= zero_zero_nat A_3))) (forall ((D $$unsorted) (Ta $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) Ta)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int uminus_uminus_int D)) Ta)))) (forall ((M_18 $$unsorted) (N_38 $$unsorted) (A_128 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_128))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral) A_128)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral _let_1 M_18)) (hAPP_n1108039445umeral _let_1 N_38))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_18) N_38)))))) (forall ((B_96 $$unsorted) (A_118 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_118)) (=> (hBOOL (hAPP_int_bool _let_1 B_96)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_118) B_96))))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd K_2) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (legacy_zgcd (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) M)) N)) (hAPP_int_int (legacy_zgcd M) N))))) (forall ((C_72 $$unsorted) (B_127 $$unsorted) (A_166 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_72))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B_127) A_166)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C_72) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A_166)) (hAPP_rat_rat _let_1 B_127))))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (div_mod_int K_2))) (=> (not (= zero_zero_int (hAPP_int_int _let_1 (hAPP_int_int uminus_uminus_int L_2)))) (not (= (hAPP_int_int _let_1 L_2) zero_zero_int))))) (forall ((A_216 $$unsorted)) (=> (is_int A_216) (= A_216 (hAPP_int_int (hAPP_int_fun_int_int times_times_int one_one_int) A_216)))) (forall ((X_34 $$unsorted) (P_7 $$unsorted) (Q_10 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int X_34))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int _let_1 P_7)) (hAPP_n522471361de_int _let_1 Q_10)) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat P_7) Q_10))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool even_odd_even_int X)) (=> (hBOOL (hAPP_int_bool even_odd_even_int Y)) (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) Y)))))) (forall ((X_3 $$unsorted)) (=> (hBOOL (cauchy_complex X_3)) (hBOOL (cauchy_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat re) X_3))))) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (= X_1 (hAPP_int_complex number528085621omplex W_1)))) (= _let_1 _let_1))) (forall ((A $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_int_real real_int A)) one_one_real)) X_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) (archim856651990g_real X_1))))) (forall ((B_71 $$unsorted) (A_83 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_83)) (=> (hBOOL (hAPP_int_bool _let_1 B_71)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_83) B_71))))))) (forall ((N_1 $$unsorted) (Diff $$unsorted) (F $$unsorted) (H $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H)) (=> (= F (hAPP_n546711566l_real Diff zero_zero_nat)) (=> (forall ((M_1 $$unsorted) (T $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) T)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) H)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) T) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) T))))) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real H))) (and (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1))) (hAPP_real_real F H)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) H)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) T))))))))) (forall ((N $$unsorted) (M $$unsorted)) (= (quickc495462417de_int N M) (hAPP_Q1256397320de_int (hAPP_Q952608535de_int produc1318306967de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int N) M)) (hAPP_Q1762011733de_int (div_mo231679042de_int N) M)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int N_1)) one_one_real)) (hAPP_int_real real_int Ma))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int N_1) Ma)))) (forall ((N_54 $$unsorted) (A_151 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_151)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_151) N_54)))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) J_2)) I)))) (forall ((M $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (and (is_int Y) (is_int X)) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (=> (hBOOL (hAPP_int_bool _let_1 M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) Y) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y) M)) (= X Y)))))))))) (forall ((A_234 $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_234) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_234) A_234))) (forall ((X_17 $$unsorted)) (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_17) zero_zero_real))) (= (hAPP_int_real real_int zero_zero_int) zero_zero_real) (forall ((B_118 $$unsorted) (A_157 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_157)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat B_118) zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_118) A_157)) zero_zero_nat))))) (forall ((Ma $$unsorted)) (= (hAPP_i1948725293t_bool (bnorRset (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Ma) one_one_int)) Ma) (hAPP_i1948725293t_bool norRRset Ma))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_3))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))) (or (hBOOL (hAPP_nat_bool _let_1 A_3)) (hBOOL (hAPP_nat_bool _let_1 B_2))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_1) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int semiri1621563631at_int X_1)) (hAPP_nat_int semiri1621563631at_int Y_2))))) (forall ((A_3 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_3) one_one_int))) (let ((_let_2 (hAPP_i1948725293t_bool ord_less_int X))) (=> (is_int X) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) X)) (=> (hBOOL (hAPP_int_bool _let_2 A_3)) (=> (not (= X _let_1)) (hBOOL (hAPP_int_bool _let_2 _let_1))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Ma) (hAPP_int_int number_number_of_int N_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int Ma)) (hAPP_int_real number267125858f_real N_1))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int norm_frac_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A0) A1))) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (=> (and (is_int A_2) (is_int B_4)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int norm_frac_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A_2) B_4))) (=> (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_4) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 (hAPP_int_int uminus_uminus_int A_2)) (hAPP_int_int uminus_uminus_int B_4)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 A_2) B_4)))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int min))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int _let_1) (hAPP_int_nat nat X_1)) _let_1))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int abs_abs_int A_3)) _let_1) (hAPP_int_int abs_abs_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) _let_1))))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral Rx))) (let ((_let_2 (hAPP_C1594335432umeral times_1655362735umeral Lx))) (= (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral _let_2 Ry)) (hAPP_C498520661umeral _let_2 (hAPP_C498520661umeral _let_1 Ry)))))) (forall ((M $$unsorted) (N $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (=> (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel M N) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat Q_2) R_3))) (= Q_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)))) (forall ((A_122 $$unsorted) (B_100 $$unsorted) (V_6 $$unsorted)) (let ((_let_1 (hAPP_int_rat number_number_of_rat V_6))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_122) _let_1)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_100) _let_1)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A_122) B_100)) _let_1)))) (forall ((A_105 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat zero_zero_nat) A_105) A_105)) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) (hAPP_int_nat number_number_of_nat _let_1)))) (let ((_let_3 (hAPP_int_real number267125858f_real _let_1))) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real _let_2) _let_3))) (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) _let_3)))) _let_2)))))) (forall ((M $$unsorted)) (not (= (hAPP_nat_nat suc M) zero_zero_nat))) (forall ((X $$unsorted)) (= (hAPP_complex_complex uminus473333897omplex X) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real uminus_uminus_real (hAPP_complex_real re X))) (hAPP_real_real uminus_uminus_real (hAPP_complex_real im X))))) (forall ((C_69 $$unsorted) (A_163 $$unsorted) (B_124 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_69))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_163) B_124)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_69)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A_163)) (hAPP_int_int _let_1 B_124))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_1) X_1)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Y_2) Y_2)))) (or (not (= zero_zero_rat Y_2)) (not (= zero_zero_rat X_1))))) (forall ((A_237 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat (hAPP_int_int bit1 pls))) A_237) A_237)) (forall ((Q_2 $$unsorted)) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (=> (and (is_int A_2) (is_int B_4)) (=> (= Q_2 (hAPP_int_rat (hAPP_int_fun_int_rat fract A_2) B_4)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_4)) (=> (not (= zero_zero_int A_2)) (not (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_2) B_4)))))))) (= Q_2 zero_zero_rat))) (forall ((C_89 $$unsorted) (D_17 $$unsorted) (A_213 $$unsorted) (B_159 $$unsorted) (R_8 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real R_8))) (=> (not (= zero_zero_real R_8)) (=> (and (= A_213 B_159) (not (= C_89 D_17))) (not (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_213) (hAPP_real_real _let_1 C_89)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_159) (hAPP_real_real _let_1 D_17)))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_n546711566l_real root N_1) X_1)) zero_zero_real))))) (forall ((N $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I) J_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) I)) U_1)) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I) U_1)) M)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J_2) U_1)) N))))) (forall ((A_12 $$unsorted) (N_18 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_12))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat suc N_18)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 N_18)) A_12)))) (forall ((M $$unsorted) (N $$unsorted)) (= (xzgcd M N) (xzgcda M N M N one_one_int zero_zero_int zero_zero_int one_one_int))) (forall ((X_7 $$unsorted) (Q_6 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex X_7))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_7) (hAPP_nat_complex _let_1 Q_6)) (hAPP_nat_complex _let_1 (hAPP_nat_nat suc Q_6))))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit0 K_1)) pls)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)) zero_zero_int))))) (forall ((A_76 $$unsorted) (B_64 $$unsorted) (B_63 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex A_76))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 B_64)) (hAPP_complex_complex _let_1 B_63)) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_64) B_63))))) (forall ((V $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat V))) (let ((_let_2 (hAPP_int_nat number_number_of_nat W_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat _let_1) _let_2)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat _let_2) _let_1))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_fun_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat P) Q) R) (hAPP_nat_fun_nat_nat P (hAPP_nat_nat Q R)))) (forall ((N_59 $$unsorted) (M_24 $$unsorted) (X_28 $$unsorted) (Y_22 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat X_28) Y_22)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_59) M_24)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_28) N_59)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_22) M_24)))))) (forall ((X_22 $$unsorted) (Y_17 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_22) Y_17)) _let_2) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_22) _let_2)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex Y_17) _let_2))) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex _let_1)) X_22)) Y_17)))))) (forall ((A_221 $$unsorted)) (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_221) zero_zero_real))) (forall ((A $$unsorted) (B $$unsorted)) (= (forall ((D_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int D_2))) (=> (is_int D_2) (= (= one_one_int D_2) (and (hBOOL (hAPP_int_bool _let_1 A)) (hBOOL (hAPP_int_bool _let_1 B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) D_2))))))) (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) (= B A))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) A_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat B))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat _let_1 X_1)) (hAPP_nat_rat _let_1 Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (z3div K_2) L_2))) (let ((_let_2 (hAPP_int_fun_int_int div_div_int K_2))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) L_2)))) (and (=> (not _let_3) (= (hAPP_int_int uminus_uminus_int (hAPP_int_int _let_2 (hAPP_int_int uminus_uminus_int L_2))) _let_1)) (=> _let_3 (= (hAPP_int_int _let_2 L_2) _let_1))))))) (forall ((M $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat V_2))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat suc M)))) _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) M)) _let_1)))) (forall ((A_183 $$unsorted) (M_22 $$unsorted) (N_57 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex A_183))) (= (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_22) N_57)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_nat_complex _let_1 M_22)) N_57)))) (forall ((B_70 $$unsorted) (A_82 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_82) zero_zero_nat)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat B_70) zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_82) B_70)) zero_zero_nat))))) (forall ((A_224 $$unsorted) (N_68 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_rat_fun_nat_rat power_power_rat A_224))) (= (hAPP_nat_rat _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_68)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_nat_rat _let_2 N_68)) _let_1))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat M))) (= (hAPP_nat_nat _let_1 N) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat K_2) M)) N))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (int_lcm X) Y) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (nat_lcm (hAPP_int_nat nat (hAPP_int_int abs_abs_int X))) (hAPP_int_nat nat (hAPP_int_int abs_abs_int Y)))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_2) min) (hAPP_int_int pred K_2))) (forall ((A $$unsorted)) (= (not (= A zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real A) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N_1) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_1) Y_2))) (= (hAPP_int_int (div_mod_int X_1) N_1) (hAPP_int_int (div_mod_int Y_2) N_1)))) (exists ((K_4 $$unsorted)) (and (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_complex_real norm_norm_complex (hAPP_complex_complex cnj X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) K_4)))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) one_one_real)) (hBOOL (bseq_real (hAPP_r474017924t_real power_power_real X_1)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat B_2))) (let ((_let_2 (div_mod_nat A_3))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_3) B_2)) C_1))) (hAPP_nat_nat _let_2 B_2)) (hAPP_nat_nat _let_2 (hAPP_nat_nat _let_1 C_1)))))) (forall ((M_17 $$unsorted) (N_30 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat M_17))) (let ((_let_2 (hAPP_nat_nat _let_1 N_30))) (and (=> (not (= zero_zero_nat N_30)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_17) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_30) one_one_nat))) _let_2)) (=> (= N_30 zero_zero_nat) (= one_one_nat _let_2)))))) (= (hAPP_int_int succ pls) _let_2) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (not (= N zero_zero_nat)))) (forall ((V $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int V) pls)) (= zero_zero_nat (hAPP_int_nat number_number_of_nat V)))) (= (hAPP_nat_int semiri1621563631at_int _let_34) _let_91) (forall ((P_5 $$unsorted)) (= (hAPP_P1975530577nt_int (produc1518849193nt_int (hAPP_f1574055885nt_int (hAPP_f2054677283nt_int cOMBB_782625832nt_int product_Pair_int_int) uminus_uminus_int)) (quotient_of P_5)) (quotient_of (hAPP_rat_rat uminus_uminus_rat P_5)))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int pred (hAPP_int_int bit0 K_2)) (hAPP_int_int bit1 (hAPP_int_int pred K_2)))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int X_1)) zero_zero_int)))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (hAPP_int_int abs_abs_int K_2))) (let ((_let_2 (pdivmod K_2 L_2))) (let ((_let_3 (= L_2 zero_zero_int))) (=> (is_int L_2) (and (=> _let_3 (= _let_2 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) _let_1))) (=> (not _let_3) (= _let_2 (posDivAlg _let_1 (hAPP_int_int abs_abs_int L_2)))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real real_int Ma)) (hAPP_int_real number267125858f_real N_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Ma) (hAPP_int_int number_number_of_int N_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat B))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) B)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_1) Y_2)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat _let_1 X_1)) (hAPP_nat_rat _let_1 Y_2))))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (= (hAPP_n1699378549t_bool (ord_at4362885an_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_1) K_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J) K_1)) (image_nat_nat (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat plus_plus_nat) K_1) (hAPP_n1699378549t_bool (ord_at4362885an_nat I_1) J)))) (= one_one_real (hAPP_real_real tan _let_46)) (forall ((Q_2 $$unsorted)) (not (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (=> (and (is_int A_2) (is_int B_4)) (=> (= (hAPP_int_rat (hAPP_int_fun_int_rat fract A_2) B_4) Q_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_4)) (not (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_2) B_4))))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) N) (hAPP_nat_nat (div_mod_nat M) N)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat zero_zero_nat) _let_4) zero_zero_nat) (forall ((U $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_2) (hAPP_nat_nat F N_2)))) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool (hAPP_f618557131t_bool (hAPP_f1505651103t_bool cOMBB_800536526ol_nat ord_less_eq_nat) F)) U)))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_complex_real im X))) (hAPP_complex_real norm_norm_complex X)))) (forall ((X_39 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X_39) X_39) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_39) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_n546711566l_real root N_1) X_1)) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) one_one_real))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f465821005nt_int P (hAPP_i1778081398nt_int Q R)) (hAPP_i1778081398nt_int (hAPP_f2094497995nt_int (hAPP_f534361363nt_int cOMBB_1657320178nt_int P) Q) R))) (forall ((N $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real inverse_inverse_real (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_rat_rat P (hAPP_nat_rat Q R)) (hAPP_nat_rat (hAPP_f2062659861at_rat (hAPP_f1082758869at_rat cOMBB_rat_rat_nat P) Q) R))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int C) D)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C) D)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B))))) (forall ((C_27 $$unsorted) (A_57 $$unsorted) (B_48 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_27))) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral _let_1 A_57)) (hAPP_C498520661umeral _let_1 B_48)) (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (div_mo1740067990umeral A_57) B_48))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real sgn_sgn_real X) one_one_real))) (forall ((A $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) Ma)) (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool (hAPP_i1948725293t_bool (bnorRset A) Ma)) (rsetR Ma))))) (forall ((N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) one_one_nat)) N) one_one_nat)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int X))) (= (hAPP_int_int _let_1 Y) (hAPP_int_int _let_1 (hAPP_int_int abs_abs_int Y))))) (not (= _let_63 _let_17)) (forall ((C_76 $$unsorted) (B_136 $$unsorted) (A_176 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_136) A_176)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C_76) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_176) C_76)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_136) C_76)))))) (forall ((W_5 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_5))) (let ((_let_2 (hAPP_nat_real (hAPP_r474017924t_real power_power_real zero_zero_real) _let_1))) (and (=> (not (= zero_zero_nat _let_1)) (= _let_2 zero_zero_real)) (=> (= _let_1 zero_zero_nat) (= _let_2 one_one_real)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool twoSqu1770640450sum2sq X)) (=> (hBOOL (hAPP_int_bool twoSqu1770640450sum2sq Y)) (hBOOL (hAPP_int_bool twoSqu1770640450sum2sq (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y)))))) (forall ((A_215 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_215) one_on1645066479umeral) A_215)) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real min)) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X))) X)))) (forall ((A_186 $$unsorted)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex one_one_complex) A_186))) (forall ((X_36 $$unsorted) (Y_28 $$unsorted) (Z_9 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int X_36))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 Y_28)) (hAPP_int_int _let_1 Z_9)) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Y_28) Z_9))))) (forall ((P_1 $$unsorted) (K_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool P_1 K_1)) (=> (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat suc N_2))) (hBOOL (hAPP_nat_bool P_1 N_2)))) (hBOOL (hAPP_nat_bool P_1 zero_zero_nat))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_int zfact N))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int N) zero_zero_int)))) (and (=> (not _let_2) (= _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int N) (hAPP_int_int zfact (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int N) one_one_int))))) (=> _let_2 (= one_one_int _let_1)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_i2112223885l_bool member_int X_1))) (=> (not (hBOOL (hAPP_f448129468l_bool _let_1 zOdd))) (hBOOL (hAPP_f448129468l_bool _let_1 zEven))))) (forall ((Z_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) Z_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Z_2)))) (forall ((I $$unsorted) (J_2 $$unsorted) (K_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) J_2)) K_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) K_2)))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2))) (not (=> (hBOOL (hAPP_nat_bool _let_1 A_3)) (not (hBOOL (hAPP_nat_bool _let_1 B_2)))))))) (forall ((V_22 $$unsorted) (V_21 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_21)) (=> (hBOOL (hAPP_int_bool _let_1 V_22)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat V_21)) (hAPP_int_rat number_number_of_rat V_22)) (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_21) V_22))))))) (forall ((P_3 $$unsorted)) (= (normalize (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) zero_zero_int)) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) one_one_int))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) M)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat fact_fact_nat M)) (hAPP_nat_nat fact_fact_nat N)))))) (forall ((N $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat N))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (is_int X) (=> (hBOOL (hAPP_int_bool even_odd_even_int X)) (= X (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_1) (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (is_int A) (is_int B)) (= (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B) zero_zero_int) (= B A)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (hBOOL (hAPP_real_bool _let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sqrt X)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))))) (forall ((V_14 $$unsorted) (B_166 $$unsorted) (C_97 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int V_14)))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 B_166)) (hAPP_int_int _let_1 C_97)) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_166) C_97))))) (forall ((A_215 $$unsorted)) (=> (is_int A_215) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_215) one_one_int) A_215))) (forall ((X $$unsorted)) (let ((_let_1 (log (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 (hAPP_real_real exp_real one_one_real))) (hAPP_real_real ln X)) (hAPP_real_real _let_1 X))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 X_1)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 Y_2)) (= (and (= zero_z891286103de_int X_1) (= zero_z891286103de_int Y_2)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int X_1) Y_2) zero_z891286103de_int)))))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (hBOOL Q)) (hBOOL (fdisj P Q)))) (forall ((X $$unsorted) (K_2 $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (not (= zero_zero_nat N)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_3) K_2)) (exists ((I_2 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_3) I_2) X)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat M) N)) (or (= zero_zero_nat N) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N))))) (forall ((A_1 $$unsorted)) (= (hBOOL (hAPP_f448129468l_bool finite_finite_int (image_nat_int semiri1621563631at_int A_1))) (hBOOL (hAPP_f54304608l_bool finite_finite_nat A_1)))) (forall ((A_197 $$unsorted) (B_152 $$unsorted) (N_64 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_197) N_64)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int B_152) N_64)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_197) B_152)) N_64))) (forall ((P_1 $$unsorted)) (= (forall ((X_2 $$unsorted)) (hBOOL (hAPP_int_bool P_1 (hAPP_nat_int semiri1621563631at_int X_2)))) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2)) (hBOOL (hAPP_int_bool P_1 X_2))))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (div_mod_nat M) N) (hAPP_P1654798560at_nat product_snd_nat_nat (divmod_nat M N)))) (forall ((X $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_3)) (=> (not (= A_3 one_one_real)) (=> (hBOOL (hAPP_real_bool _let_1 B_2)) (=> (not (= one_one_real B_2)) (=> (hBOOL (hAPP_real_bool _let_1 X)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real ln B_2)) (hAPP_real_real ln A_3))) (hAPP_real_real (log B_2) X)) (hAPP_real_real (log A_3) X))))))))) (not (= _let_8 _let_10)) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X)) (=> (hBOOL (hAPP_int_bool nat_is_nat Y)) (hBOOL (hAPP_int_bool nat_is_nat (hAPP_int_int (div_mod_int X) Y)))))) (forall ((A_23 $$unsorted)) (=> (not (= zero_z891286103de_int A_23)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_23) A_23) one_on1684967323de_int))) (forall ((N_54 $$unsorted) (A_151 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_151)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_151) N_54)))))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real A N_2)))) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real A (hAPP_nat_nat suc N_2))) (hAPP_nat_real A N_2)))) (hBOOL (tendsto_nat_real (hAPP_f292751352t_real (hAPP_f1607377819t_real cOMBB_1533963633al_nat (hAPP_f1509287679l_real big_co604158596t_real _let_1)) (hAPP_f618557131t_bool (hAPP_f1505651103t_bool cOMBB_800536526ol_nat (ord_at4362885an_nat zero_zero_nat)) (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_f352196356l_real suminf_real _let_1) sequentially))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hAPP_nat_nat (nat_case_nat zero_zero_nat (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat suc) (hAPP_nat_fun_nat_nat ord_min_nat N_1))) Ma) (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat (hAPP_nat_nat suc N_1)) Ma))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Z_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y) Z_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) Z_1)) Y))))) (forall ((B_34 $$unsorted) (B_33 $$unsorted) (A_43 $$unsorted) (C_17 $$unsorted) (A_42 $$unsorted)) (=> (= (hAPP_int_int (div_mod_int A_42) C_17) (hAPP_int_int (div_mod_int A_43) C_17)) (=> (= (hAPP_int_int (div_mod_int B_34) C_17) (hAPP_int_int (div_mod_int B_33) C_17)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_43) B_34)) C_17) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_42) B_33)) C_17))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P621635040nt_int P (hAPP_i1524277240nt_int Q R)) (hAPP_i1153444985nt_int (hAPP_f1148171384nt_int (hAPP_f334321603nt_int cOMBB_1484610687nt_int P) Q) R))) (forall ((N_42 $$unsorted) (A_130 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_130)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_130) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_130) N_42))))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) (hAPP_n1108039445umeral semiri1619134803umeral N_1))))) (forall ((B_116 $$unsorted) (A_155 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_155)) (=> (hBOOL (hAPP_nat_bool _let_1 B_116)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_155) B_116))))))) (forall ((Z_7 $$unsorted) (W_2 $$unsorted) (Y_9 $$unsorted) (X_12 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral Y_9) X_12)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral Z_7) W_2)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral X_12) W_2)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral Y_9) Z_7)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral X_12) Y_9)) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral W_2) Z_7)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_n215258509l_bool (hAPP_f66927821l_bool (hAPP_f2037783381l_bool cOMBB_1146692694ol_nat P) Q) R) (hAPP_n215258509l_bool P (hAPP_nat_nat Q R)))) (forall ((A_87 $$unsorted) (B_75 $$unsorted)) (= A_87 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A_87) B_75)) B_75))) (forall ((B_97 $$unsorted) (A_119 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_119)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) B_97)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_119) B_97))))))) (forall ((A_149 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_149) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_149) one_one_rat)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (div_mod_nat M) N)) N)))) (forall ((C_46 $$unsorted) (A_104 $$unsorted) (B_86 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int C_46))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int _let_1 A_104)) (hAPP_Q1762011733de_int _let_1 B_86))) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_104) B_86))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (normalize (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A_3) B_2)) (quotient_of (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)))) (forall ((A_1 $$unsorted)) (= (hAPP_f957591787ol_nat finite_card_int (image_nat_int semiri1621563631at_int A_1)) (hAPP_f22106695ol_nat finite_card_nat A_1))) (forall ((X $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (= (hAPP_real_real _let_1 (hAPP_real_real uminus_uminus_real A_3)) (hAPP_real_real inverse_inverse_real (hAPP_real_real _let_1 A_3))))) (forall ((X $$unsorted)) (= X (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat zero_zero_nat) X))) (forall ((A_56 $$unsorted) (C_26 $$unsorted) (B_47 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_56) C_26)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_47) C_26)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_56) B_47)) C_26))) (exists ((K_4 $$unsorted)) (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real norm_norm_real (hAPP_complex_real re X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4))))) (not (hBOOL (hAPP_nat_bool prime zero_zero_nat))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C) zero_zero_rat)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B) A)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A)) (hAPP_rat_rat _let_1 B))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y))) (let ((_let_2 (hAPP_real_real tan Y))) (let ((_let_3 (hAPP_real_real tan X))) (=> (not (= (hAPP_real_real cos X) zero_zero_real)) (=> (not (= (hAPP_real_real cos Y) zero_zero_real)) (=> (not (= zero_zero_real (hAPP_real_real cos _let_1))) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_3) _let_2)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_3) _let_2))) (hAPP_real_real tan _let_1))))))))) (forall ((L_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat minus_minus_nat L_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 N)) (hAPP_nat_nat _let_1 M)))))) (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel M N) (divmod_nat M N)))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) E_2)) C)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) E_2)) D))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B) A)) E_2)) D))))) (forall ((U_1 $$unsorted) (X $$unsorted)) (=> (= X (hAPP_real_real exp_real U_1)) (= (hAPP_real_real ln X) U_1))) (forall ((A_220 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat zero_zero_rat) A_220) A_220)) (forall ((C_63 $$unsorted) (A_141 $$unsorted) (B_110 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_63))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral _let_1 A_141)) (hAPP_C498520661umeral _let_1 B_110))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_63)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_141) B_110)))))) (forall ((C_42 $$unsorted) (A_100 $$unsorted) (B_82 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_100) B_82)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_100) C_42)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_82) C_42))))) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) one_one_int) (quotient_of zero_zero_rat)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_P252494982t_bool P R) Q) (hAPP_P603027463t_bool (hAPP_i119638232t_bool (hAPP_f2018027565t_bool cOMBC_33652895t_bool P) Q) R))) (forall ((M $$unsorted) (N $$unsorted) (Qr_1 $$unsorted)) (=> (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel M N) Qr_1)) (= Qr_1 (divmod_nat M N)))) (forall ((C_33 $$unsorted) (D_5 $$unsorted) (A_79 $$unsorted) (B_67 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_79) B_67)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C_33) D_5)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_79) C_33)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_67) D_5)))))) (forall ((A_223 $$unsorted) (K_8 $$unsorted)) (=> (is_int A_223) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_223) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) K_8))) zero_zero_int)) (= A_223 zero_zero_int)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N))) (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))))) (forall ((Real1_2 $$unsorted) (Real2_2 $$unsorted) (Real1_1 $$unsorted) (Real2_1 $$unsorted)) (= (= (hAPP_real_complex (hAPP_r265291036omplex complex Real1_2) Real2_2) (hAPP_real_complex (hAPP_r265291036omplex complex Real1_1) Real2_1)) (and (= Real1_1 Real1_2) (= Real2_2 Real2_1)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real cos X))))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (legacy_zgcd K_2))) (= (hAPP_int_int _let_1 (hAPP_int_int (legacy_zgcd M) N)) (hAPP_int_int (legacy_zgcd (hAPP_int_int _let_1 M)) N)))) (forall ((A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (comple219730294t_bool (setS A P_5)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_48) zero_zero_real)) (forall ((X_18 $$unsorted) (Y_15 $$unsorted) (A_78 $$unsorted) (B_66 $$unsorted)) (let ((_let_1 (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex Y_15) B_66))) (let ((_let_2 (hAPP_c172932010omplex times_times_complex A_78))) (let ((_let_3 (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_18) A_78)))) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_18) Y_15)) (hAPP_complex_complex _let_2 B_66)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_3 _let_1)) (hAPP_complex_complex _let_3 B_66))) (hAPP_complex_complex _let_2 _let_1))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_n1006566506l_bool (hAPP_f1146629647l_bool (hAPP_f1080886329l_bool cOMBB_1015721476ol_nat P) Q) R) (hAPP_b589554111l_bool P (hAPP_nat_bool Q R)))) (forall ((A_50 $$unsorted) (C_22 $$unsorted) (B_41 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_50) B_41)) C_22) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_50) C_22)) B_41)) C_22))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int K_2))) (=> (is_int K_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int _let_1 M)) (hAPP_int_int _let_1 N))) (=> (not (= zero_zero_int K_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int M) N))))))) (not (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int one_on1684967323de_int) zero_z891286103de_int))) (forall ((N $$unsorted) (D_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) D_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat D_3) N)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real real_nat N)) (hAPP_nat_real real_nat D_3)) (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) D_3)))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat D) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_2) Sa)))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_2) Z)) (= _let_1 _let_1)))))) (forall ((N_19 $$unsorted)) (= zero_zero_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex zero_zero_complex) (hAPP_nat_nat suc N_19)))) (hBOOL (hAPP_int_bool _let_49 _let_18)) (forall ((A_75 $$unsorted) (A_74 $$unsorted) (B_62 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_75) B_62)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_74) B_62)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_75) A_74)) B_62))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int semiri1424489471de_int Ma)) (hAPP_n522471361de_int semiri1424489471de_int N_1))))) (forall ((B $$unsorted) (A $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool (bnorRset A) Ma))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (div_mod_int A_3) B_2)) B_2) zero_zero_int)) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real sqrt X_1)) one_one_real)))) (forall ((V_2 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V_2))) (let ((_let_2 (hAPP_nat_int semiri1621563631at_int (hAPP_int_nat number_number_of_nat V_2)))) (let ((_let_3 (hBOOL (hAPP_int_bool nat_neg _let_1)))) (and (=> _let_3 (= zero_zero_int _let_2)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X_1)) (=> (hBOOL (hAPP_int_bool _let_1 Y_2)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_int_nat nat X_1)) (hAPP_int_nat nat Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int X_1) Y_2))))))) (forall ((A_25 $$unsorted) (B_20 $$unsorted)) (=> (not (= zero_z126310315umeral B_20)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_25) B_20)) B_20) A_25))) (forall ((N $$unsorted)) (= N (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat one_one_nat) N))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (of_real_complex (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_complex_real im Z_1)))) ii) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex Z_1) (hAPP_complex_complex cnj Z_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_P1175774780nt_int product_snd_int_int X_1))) (let ((_let_2 (hAPP_P1175774780nt_int product_snd_int_int Y_2))) (= (and (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_P1175774780nt_int product_fst_int_int Y_2)) _let_1) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_P1175774780nt_int product_fst_int_int X_1)) _let_2)) (not (= zero_zero_int _let_2)) (not (= _let_1 zero_zero_int))) (hBOOL (hAPP_f526364711l_bool (hAPP_P1062890741l_bool member2143287562nt_int (hAPP_P230595783nt_int (hAPP_P941956607nt_int produc883642259nt_int X_1) Y_2)) ratrel)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_complex_real im X)) (hAPP_complex_real im Y)) (hAPP_complex_real im (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X) Y)))) (forall ((X_1 $$unsorted)) (=> (is_int X_1) (= (= zero_zero_int X_1) (= X_1 zero_zero_int)))) (forall ((V_10 $$unsorted) (U_3 $$unsorted) (Y_26 $$unsorted) (X_32 $$unsorted) (A_209 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat X_32) A_209)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat Y_26) A_209)) (=> (hBOOL (hAPP_rat_bool _let_1 U_3)) (=> (hBOOL (hAPP_rat_bool _let_1 V_10)) (=> (= one_one_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat U_3) V_10)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat U_3) X_32)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat V_10) Y_26))) A_209))))))))) (forall ((A_184 $$unsorted) (M_23 $$unsorted) (N_58 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_184))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_23) N_58)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_nat_rat _let_1 M_23)) (hAPP_nat_rat _let_1 N_58)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int B_2))) (=> (hBOOL (hAPP_int_bool _let_1 zero_zero_int)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (div_mod_int A_3) B_2)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_1) X_1)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Y_2) Y_2))) zero_zero_rat)) (and (= zero_zero_rat Y_2) (= X_1 zero_zero_rat)))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) (hAPP_nat_nat (div_mod_nat M) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)) N))) (forall ((A_225 $$unsorted) (B_162 $$unsorted) (C_91 $$unsorted) (D_18 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_225))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 C_91)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_162) D_18)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 B_162)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat C_91) D_18))))) (forall ((K_2 $$unsorted)) (=> (is_int K_2) (= K_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int K_2) pls)))) (forall ((Y $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real arctan Y)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_2))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N))) (hBOOL (hAPP_nat_bool _let_1 M))))) (forall ((N $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int P_3) N)))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_3) B_2))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2))) (hBOOL (hAPP_int_bool _let_1 A_3))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_int (div_mod_int A_3) (hAPP_int_int uminus_uminus_int B_2)) (hAPP_int_int uminus_uminus_int (hAPP_int_int (div_mod_int (hAPP_int_int uminus_uminus_int A_3)) B_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_1) Y_2)) zOdd))))) (forall ((A_36 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int zero_zero_int) A_36) zero_zero_int)) (forall ((A_63 $$unsorted)) (= (hAPP_int_int (div_mod_int A_63) A_63) zero_zero_int)) (forall ((M_28 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral M_28) M_28) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral one_on1645066479umeral) one_on1645066479umeral)) M_28))) (forall ((X_1 $$unsorted)) (= (= zero_zero_real X_1) (= (hAPP_real_real sqrt X_1) zero_zero_real))) (forall ((A_20 $$unsorted) (C_6 $$unsorted) (B_16 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral A_20))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral C_6) B_16)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral _let_1 B_16)) C_6) (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral B_16) C_6)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat C))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 A)) (hAPP_nat_nat _let_1 B))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A) B))))) (forall ((X_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= (or (= X_1 _let_1) (= Ma zero_zero_nat)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) Ma) _let_1)))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X)) one_one_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real Y)) one_one_real)) (= (hAPP_real_real arctan (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) Y)))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real arctan X)) (hAPP_real_real arctan Y)))))) (hBOOL (hAPP_C24501650l_bool _let_94 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral one_on1645066479umeral) one_on1645066479umeral))) (forall ((A_92 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_92) one_on1684967323de_int) A_92)) (hBOOL (hAPP_Q2096512830t_bool _let_75 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int one_on1684967323de_int) one_on1684967323de_int))) (forall ((C_79 $$unsorted) (D_15 $$unsorted) (A_179 $$unsorted) (B_139 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_179) B_139)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C_79) D_15)) (=> (hBOOL (hAPP_real_bool _let_1 B_139)) (=> (hBOOL (hAPP_real_bool _let_1 C_79)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_179) C_79)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_139) D_15))))))))) (= zero_zero_nat (hAPP_nat_nat size_size_nat zero_zero_nat)) (forall ((C_79 $$unsorted) (D_15 $$unsorted) (A_179 $$unsorted) (B_139 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_179) B_139)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral C_79) D_15)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_139)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C_79)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_179) C_79)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_139) D_15))))))))) (forall ((A_113 $$unsorted) (B_91 $$unsorted) (C_51 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int A_113))) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_91) C_51)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int _let_1 B_91)) C_51)))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 pls)) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) (hAPP_int_real number267125858f_real Y_2))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2)) B_2)))) (forall ((X_39 $$unsorted)) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_39) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_39) X_39))) (forall ((A_90 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat one_one_nat) A_90) A_90)) (forall ((A_55 $$unsorted) (C_25 $$unsorted) (B_46 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_55) B_46)) C_25) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (div_mod_int A_55) C_25)) B_46)) C_25))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (not (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int N_1)))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (natceiling X_1)) (hAPP_int_nat number_number_of_nat N_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) (hAPP_int_real number267125858f_real N_1))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1730463541l_real P (hAPP_r579619957l_real Q R)) (hAPP_r712953929l_real (hAPP_f1108539711l_real (hAPP_f1109256153l_real cOMBB_44084907l_real P) Q) R))) (forall ((V_2 $$unsorted)) (= (hAPP_int_nat nat (hAPP_int_int number_number_of_int V_2)) (hAPP_int_nat number_number_of_nat V_2))) (forall ((N_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_b992065680at_nat if_nat (hAPP_int_bool nat_neg _let_1)) zero_zero_nat) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat N_1) (hAPP_int_nat nat _let_1)))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat (hAPP_nat_nat suc N_1)) (hAPP_int_nat number_number_of_nat V))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (and (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong B_2) zero_zero_int) P_3))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) zero_zero_int) P_3)))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2)) zero_zero_int) P_3))))))) (forall ((B $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (deriv_real (log B) X_1) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real ln B)) X_1)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int A_3))) (= (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int B_2) C_1))) C_1) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 B_2)) C_1)))) (forall ((A $$unsorted) (N_1 $$unsorted)) (=> (is_int A) (= (and (= A zero_zero_int) (not (= zero_zero_nat N_1))) (= zero_zero_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) N_1))))) (= (produc1298267108nt_int (hAPP_f1760145644nt_int (hAPP_f808647893nt_int cOMBC_736024425nt_int (hAPP_f836602773nt_int (hAPP_f888249301nt_int cOMBB_1875755114nt_int cOMBB_int_int_int) (hAPP_f1760145644nt_int _let_56 _let_93))) _let_93)) twoSqu1907779896sum2sq) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat V_2))) (let ((_let_2 (hAPP_nat_nat (div_mod_nat _let_1) (hAPP_int_nat number_number_of_nat V_3)))) (let ((_let_3 (hAPP_int_int number_number_of_int V_3))) (let ((_let_4 (hBOOL (hAPP_int_bool nat_neg _let_3)))) (let ((_let_5 (hAPP_int_int number_number_of_int V_2))) (let ((_let_6 (hBOOL (hAPP_int_bool nat_neg _let_5)))) (and (=> _let_6 (= _let_2 zero_zero_nat)) (=> (not _let_6) (and (=> (not _let_4) (= _let_2 (hAPP_int_nat nat (hAPP_int_int (div_mod_int _let_5) _let_3)))) (=> _let_4 (= _let_2 _let_1)))))))))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real R_3))) (= (hAPP_complex_complex (scaleR1652505878omplex R_3) (hAPP_real_complex (hAPP_r265291036omplex complex A_3) B_2)) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real _let_1 A_3)) (hAPP_real_real _let_1 B_2))))) (= (hAPP_nat_rat semiri151668891at_rat one_one_nat) one_one_rat) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I) J_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) K_2))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I) J_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) L_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J_2) L_2)))))) (forall ((N_19 $$unsorted)) (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral zero_z126310315umeral) (hAPP_nat_nat suc N_19)) zero_z126310315umeral)) (forall ((X $$unsorted) (M $$unsorted) (Y $$unsorted)) (=> (= (hAPP_int_int (div_mod_int X) M) (hAPP_int_int (div_mod_int Y) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) Y) M)))) (forall ((N_37 $$unsorted) (A_126 $$unsorted)) (let ((_let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_126) N_37))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_126)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_126) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_126) _let_1)) _let_1)))))) (forall ((X $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real exp_real X)) zero_zero_real)))) (forall ((Z_1 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real one_one_real) Z_1) Z_1)) (forall ((A $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_int_int (rRset2norRR A_1 Ma) A))) (let ((_let_2 (and (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) A_1)) (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Ma))))) (and (=> (not _let_2) (= zero_zero_int _let_1)) (=> _let_2 (= (hilbert_Eps_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool (zcong A)) Ma))) (hAPP_f1805168059t_bool (hAPP_f202917053t_bool cOMBC_94739984l_bool member_int) (hAPP_i1948725293t_bool norRRset Ma)))) _let_1)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= (hAPP_nat_complex semiri2020571505omplex Ma) (hAPP_nat_complex semiri2020571505omplex N_1)) (= N_1 Ma))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= (= _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) N_1)) (or (and (= N_1 zero_zero_nat) (= _let_1 Ma)) (and (= Ma zero_zero_nat) (= _let_1 N_1)))))) (forall ((X $$unsorted) (N $$unsorted)) (= (hAPP_real_real tan X) (hAPP_real_real tan (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real N)) pi))))) (forall ((B_128 $$unsorted) (A_168 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_168)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_128)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_168) B_128))))))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int Lx_3))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 Ly_1)) Rx_3) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 Rx_3)) Ly_1)))) (not (hBOOL (hAPP_nat_bool prime _let_1))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_1))) (=> (hBOOL (hAPP_int_bool _let_1 N_1)) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (div_mod_int Ma) N_1))) (hBOOL (hAPP_int_bool _let_1 Ma)))))) (forall ((X_7 $$unsorted) (Q_6 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X_7))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_7) (hAPP_nat_int _let_1 Q_6)) (hAPP_nat_int _let_1 (hAPP_nat_nat suc Q_6))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_nat_real real_nat M)) N) (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M) N)))) (forall ((B_1_1 $$unsorted)) (is_bool (bseq_real B_1_1))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i418383825t_bool (hAPP_f1222178131t_bool (hAPP_f743790483t_bool cOMBB_1647910634ol_int P) Q) R) (hAPP_f737665877t_bool P (hAPP_i157317923t_real Q R)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (isCont_real_real (hAPP_n546711566l_real root N_1)) X_1))))) (forall ((N $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc N))))))) (forall ((V_13 $$unsorted) (W_11 $$unsorted) (Z_10 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int V_13)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int W_11)) Z_10)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_13) W_11))) Z_10))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (= Y (hAPP_real_real sin (hAPP_real_real arcsin Y)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f892584630t_bool (hAPP_P1400155668t_bool P R) (hAPP_P1668131738nt_int Q R)) (hAPP_P989584703t_bool (hAPP_f1187443546t_bool (hAPP_f11709033t_bool cOMBS_1676841879t_bool P) Q) R))) (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (not (= A zero_z891286103de_int)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A) B)) (= (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int C) A) B) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int B) A) C))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (= (or (= zero_zero_nat K_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Ma) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc M))) (let ((_let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_1) N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) _let_1)) (= (hAPP_nat_nat fact_fact_nat _let_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_2) (hAPP_nat_nat fact_fact_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (=> (and (is_int K_1) (is_int L)) (= (= L K_1) (= (hAPP_int_int bit0 L) (hAPP_int_int bit0 K_1))))) (forall ((A_219 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_219) zero_z126310315umeral) A_219)) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_int (hAPP_f1594865479ol_int B_1_1 B_2_1))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat Y_2))) (let ((_let_2 (hAPP_int_nat number_number_of_nat X_1))) (= (= zero_zero_nat (hAPP_nat_nat (div_mod_nat _let_1) _let_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_2) _let_1)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int A))) (=> (hBOOL (hAPP_int_bool _let_1 B)) (=> (hBOOL (hAPP_int_bool _let_1 C)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int B) A)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int C) A))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int B) C))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) B_2)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_3) B_2)) (= zero_zero_nat B_2)))) (forall ((A $$unsorted)) (= (= zero_zero_rat A) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) zero_zero_rat))) (forall ((N $$unsorted)) (= (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int N)) (archim1246769320r_real (hAPP_real_real uminus_uminus_real (hAPP_nat_real real_nat N))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool _let_1 X_2)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int F X_2))))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_f1594865479ol_int (hAPP_f1926459811ol_int big_co230513141nt_int F) A_1)))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) (hAPP_nat_nat fact N)) (hAPP_nat_nat fact _let_1)))) (forall ((A $$unsorted)) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real A N_2)))) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real A (hAPP_nat_nat suc N_2))) (hAPP_nat_real A N_2)))) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))))))) (forall ((Y_20 $$unsorted) (X_26 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X_26)) (=> (hBOOL (hAPP_real_bool _let_1 Y_20)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_20) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_26) Y_20)) X_26))))))) (forall ((N_59 $$unsorted) (M_24 $$unsorted) (X_28 $$unsorted) (Y_22 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real X_28) Y_22)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_59) M_24)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_28) N_59)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_22) M_24)))))) (hBOOL (hAPP_int_bool _let_81 _let_92)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) N_1) zero_zero_nat) (and (= zero_zero_nat Ma) (= N_1 zero_zero_nat)))) (forall ((A_139 $$unsorted) (C_61 $$unsorted) (B_108 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_139) C_61)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_108) C_61))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_61)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_139) B_108))))) (forall ((A_108 $$unsorted)) (= A_108 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_108) zero_z891286103de_int))) (forall ((A_109 $$unsorted) (B_87 $$unsorted) (C_47 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_109))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 B_87)) C_47) (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_87) C_47))))) (forall ((P $$unsorted)) (= (hAPP_real_real cOMBI_real P) P)) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) B)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B) C))))) (= zero_zero_real _let_77) (forall ((X_37 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_37) one_one_nat) X_37)) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N_1) K_1))) (and (=> (not (= K_1 zero_zero_nat)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat J_1) K_1)) (=> (= N_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat K_1) I_2)) J_1)) (hBOOL (hAPP_nat_bool P_1 I_2)))))) (=> (= zero_zero_nat K_1) (hBOOL (hAPP_nat_bool P_1 zero_zero_nat)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (=> (and (is_int R_3) (is_int B_2)) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))) (=> (not (= zero_zero_int B_2)) (= (hAPP_int_int (div_mod_int A_3) B_2) R_3))))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 pls)) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) (hAPP_int_int number_number_of_int Y_2))))) (forall ((X_30 $$unsorted) (Y_24 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral X_30) Y_24)) (=> (not (= Y_24 X_30)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral X_30) Y_24))))) (forall ((A_31 $$unsorted) (C_12 $$unsorted) (B_26 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_31) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat C_12) B_26))) B_26) (hAPP_nat_nat (div_mod_nat A_31) B_26))) (forall ((A_239 $$unsorted) (B_167 $$unsorted) (V_15 $$unsorted)) (let ((_let_1 (hAPP_i769753017umeral number1443263063umeral V_15))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_239) _let_1)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_167) _let_1)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_239) B_167)) _let_1)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) N)))))) (forall ((Z_13 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_13) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat Z_13) Z_13))) (forall ((A_69 $$unsorted) (B_57 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (div_mod_nat A_69) B_57)) B_57) zero_zero_nat)) (forall ((A_60 $$unsorted) (B_51 $$unsorted) (C_30 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int A_60))) (= (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 B_51)) C_30) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int B_51) C_30))) C_30)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_r1900510169t_bool (hAPP_f1480506641t_bool cOMBC_int_rat_bool P) Q) R) (hAPP_rat_bool (hAPP_i16292313t_bool P R) Q))) (forall ((A_202 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat zero_zero_nat) A_202) zero_zero_nat)) (forall ((X_38 $$unsorted) (P_8 $$unsorted) (Q_12 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X_38))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int _let_1 P_8)) Q_12) (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_8) Q_12))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc M)) (hAPP_nat_nat suc N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Y)) (exists ((R_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real R_1))) (and (= Y (hAPP_real_real _let_1 (hAPP_real_real sin A_2))) (= (hAPP_real_real _let_1 (hAPP_real_real cos A_2)) X)))))) (forall ((N_4 $$unsorted)) (= (hBOOL (hAPP_f54304608l_bool finite_finite_nat N_4)) (exists ((M_1 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_2) N_4)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_2) M_1))))))) (forall ((W_6 $$unsorted)) (let ((_let_1 (hAPP_int_complex number528085621omplex W_6))) (= (hAPP_int_complex number528085621omplex (hAPP_int_int bit1 W_6)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex one_one_complex) _let_1)) _let_1)))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))) (not (= (hAPP_int_int (inv P_3) A_3) A_3)))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_24 _let_17) _let_18)) (forall ((V $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_i769753017umeral number1443263063umeral V))) (let ((_let_2 (hAPP_i769753017umeral number1443263063umeral W_1))) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral _let_1) _let_2)) (not (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral _let_2) _let_1))))))) (forall ((V_14 $$unsorted) (B_166 $$unsorted) (C_97 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int (hAPP_i1732201573de_int number1226105091de_int V_14)))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 B_166)) (hAPP_Q1762011733de_int _let_1 C_97)) (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_166) C_97))))) (forall ((C_78 $$unsorted) (D_14 $$unsorted) (A_178 $$unsorted) (B_138 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_178) B_138)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C_78) D_14)) (=> (hBOOL (hAPP_int_bool _let_1 A_178)) (=> (hBOOL (hAPP_int_bool _let_1 C_78)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_178) C_78)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_138) D_14))))))))) (forall ((X_35 $$unsorted) (Y_27 $$unsorted) (Q_11 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_35) Q_11)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_27) Q_11)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_35) Y_27)) Q_11))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int semiri1621563631at_int M)) (hAPP_nat_int semiri1621563631at_int N)))) (forall ((C_2 $$unsorted)) (hBOOL (hAPP_f448129468l_bool nat_nat_set (image_nat_int semiri1621563631at_int C_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (nat_gcd X_1) Y_2))) (let ((_let_2 (= zero_zero_nat Y_2))) (=> (hBOOL (hAPP_P1555980039t_bool (accp_P490777396at_nat nat_gcd_rel) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat X_1) Y_2))) (and (=> _let_2 (= X_1 _let_1)) (=> (not _let_2) (= _let_1 (hAPP_nat_nat (nat_gcd Y_2) (hAPP_nat_nat (div_mod_nat X_1) Y_2))))))))) (hBOOL (hAPP_int_bool _let_16 zero_zero_int)) (forall ((R_3 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real R_3))) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (of_real_complex R_3)) (hAPP_real_complex (hAPP_r265291036omplex complex X) Y))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int X))) (let ((_let_2 (hAPP_int_fun_int_int plus_plus_int Y))) (= (hAPP_int_int _let_1 (hAPP_int_int _let_2 Z_1)) (hAPP_int_int _let_2 (hAPP_int_int _let_1 Z_1)))))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_3) A_3))) (exists ((X_2 $$unsorted) (Y_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) X_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_3) Y_1)) one_one_nat)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2) (hAPP_P1175774780nt_int product_fst_int_int (hAPP_P1975530577nt_int negateSnd (negDivAlg (hAPP_int_int uminus_uminus_int A_3) (hAPP_int_int uminus_uminus_int B_2)))))))) (forall ((C_58 $$unsorted) (D_11 $$unsorted) (A_136 $$unsorted) (B_105 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_136) B_105)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C_58) D_11)) (=> (hBOOL (hAPP_int_bool _let_1 A_136)) (=> (hBOOL (hAPP_int_bool _let_1 C_58)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_136) C_58)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_105) D_11))))))))) (forall ((Z_1 $$unsorted)) (= (hAPP_int_real ring_1_of_int_real Z_1) (hAPP_complex_real re (hAPP_int_complex ring_11397209091omplex Z_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real arctan X)) (hAPP_real_real arctan Y))))) (forall ((I $$unsorted) (K_2 $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) J_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) I)) K_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) K_2)) I)))) (forall ((M_17 $$unsorted) (N_30 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat M_17))) (let ((_let_2 (hAPP_nat_rat _let_1 N_30))) (let ((_let_3 (= N_30 zero_zero_nat))) (and (=> (not _let_3) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat M_17) (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_30) one_one_nat))) _let_2)) (=> _let_3 (= one_one_rat _let_2))))))) (forall ((A_218 $$unsorted) (B_161 $$unsorted) (C_90 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_218) C_90)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_161) C_90)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_218) B_161)) C_90))) (forall ((N_12 $$unsorted) (R_6 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) R_6)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat R_6) one_one_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat R_6) (hAPP_nat_nat suc N_12))) R_6))))) (forall ((A_228 $$unsorted) (C_94 $$unsorted) (D_19 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A_228))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 C_94)) D_19) (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat C_94) D_19))))) (forall ((N $$unsorted)) (= (natfloor (hAPP_int_real number267125858f_real N)) (hAPP_int_nat number_number_of_nat N))) (forall ((A_219 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_219) zero_zero_rat) A_219)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A) B) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex C) D)) (= (= A B) (= D C)))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_int_rat number_number_of_rat Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) Y_2)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= zero_z126310315umeral (hAPP_C498520661umeral (div_mo1740067990umeral B) A)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A) B)))) (forall ((B $$unsorted) (C $$unsorted) (A $$unsorted) (D $$unsorted)) (let ((_let_1 (hAPP_int_int abs_abs_int D))) (let ((_let_2 (hAPP_int_int abs_abs_int C))) (let ((_let_3 (hAPP_int_int abs_abs_int B))) (let ((_let_4 (hAPP_int_int abs_abs_int A))) (=> (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A) D)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int B) C) one_one_int) (= (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_4) _let_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_3) _let_1)) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A)) (hAPP_rat_rat _let_1 B))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A) B)))))) (forall ((A_154 $$unsorted)) (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_154) A_154)) zero_zero_rat)))) (forall ((X $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (zcong X))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 (hAPP_int_int number_number_of_int min)) P_3)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 one_one_int) P_3))))))) (not (hBOOL (hAPP_int_bool _let_41 min))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int semiri1621563631at_int X_1)) (hAPP_nat_int semiri1621563631at_int Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2)))) (forall ((N_43 $$unsorted) (A_131 $$unsorted)) (let ((_let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_131) N_43))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int) A_131)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int _let_1) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_131) _let_1)))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) L)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit0 K_1)) (hAPP_int_int bit0 L))))) (forall ((B_131 $$unsorted) (A_171 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_171) zero_zero_rat)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) B_131)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_171) B_131)) zero_zero_rat))))) (forall ((A_11 $$unsorted) (N_17 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_11))) (= (hAPP_nat_rat _let_1 (hAPP_nat_nat suc N_17)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_11) (hAPP_nat_rat _let_1 N_17))))) (forall ((I_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 K_1)) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int I_1) K_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) I_1)))))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit0 K_1)) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) pls)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1250527377l_real (hAPP_n682674106l_real P R) Q) (hAPP_n546711566l_real (hAPP_r195310020l_real (hAPP_f2126667875l_real cOMBC_746811033l_real P) Q) R))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sin X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (hAPP_complex_real re Y) (hAPP_complex_real re X)) (=> (= (hAPP_complex_real im Y) (hAPP_complex_real im X)) (= X Y)))) (forall ((Code_numeral_2 $$unsorted)) (not (= zero_z126310315umeral (code_S1047413653umeral Code_numeral_2)))) (forall ((V_17 $$unsorted) (V_16 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_16)) (=> (hBOOL (hAPP_int_bool _let_1 V_17)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat V_16)) (hAPP_int_rat number_number_of_rat V_17)) (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_16) V_17))))))) (forall ((A_113 $$unsorted) (B_91 $$unsorted) (C_51 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat A_113))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat _let_1 B_91)) C_51) (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_91) C_51))))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) Y)) (exists ((X_2 $$unsorted)) (and (= Y (hAPP_real_real exp_real X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Y) one_one_real))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_2)))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2)) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) Y_2)) (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) field_1210416355s_real))))))) (forall ((A $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_5)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) P_5))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_5) A))) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int)) _let_1) (hAPP_nat_int semiri1621563631at_int (hAPP_f521865025ol_nat finite1876863882t_bool (setS A P_5)))))))))) (forall ((A_111 $$unsorted) (B_89 $$unsorted) (C_49 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_111))) (=> (= (hAPP_C498520661umeral _let_1 C_49) (hAPP_C498520661umeral _let_1 B_89)) (= C_49 B_89)))) (forall ((B_70 $$unsorted) (A_82 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_82) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_70) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_82) B_70)) zero_zero_int))))) (forall ((N_41 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat zero_zero_nat) N_41))) (let ((_let_2 (= zero_zero_nat N_41))) (and (=> _let_2 (= one_one_nat _let_1)) (=> (not _let_2) (= _let_1 zero_zero_nat)))))) (forall ((A_91 $$unsorted)) (= A_91 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_91) one_one_rat))) (forall ((A_229 $$unsorted) (C_95 $$unsorted) (D_20 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_229))) (let ((_let_2 (hAPP_Q1729056540de_int plus_p1446045655de_int C_95))) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int _let_2 D_20)) (hAPP_Q1762011733de_int _let_2 (hAPP_Q1762011733de_int _let_1 D_20)))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat _let_1) N)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (hAPP_nat_nat suc X) (hAPP_nat_nat suc Y)) (= Y X))) (forall ((X_39 $$unsorted)) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_39) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int X_39) X_39))) (forall ((N_43 $$unsorted) (A_131 $$unsorted)) (let ((_let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_131) N_43))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral) A_131)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral _let_1) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_131) _let_1)))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_1) field_1210416355s_real)) (not (forall ((M_1 $$unsorted) (N_2 $$unsorted)) (=> (not (= N_2 zero_zero_nat)) (=> (= (hAPP_real_real abs_abs_real X_1) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real real_nat M_1)) (hAPP_nat_real real_nat N_2))) (not (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M_1) N_2) one_one_nat)))))))) (forall ((A_139 $$unsorted) (C_61 $$unsorted) (B_108 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_139) C_61)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_108) C_61))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_61)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_139) B_108))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat plus_plus_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (= (hAPP_real_real exp_real X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X_1)) (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat fact_fact_nat) _let_1))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc M)) N)))) (forall ((A_186 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real one_one_real) A_186))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_nat nat P_3))) (let ((_let_2 (hAPP_int_fun_nat_int power_power_int A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) P_3)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) (hAPP_nat_int _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_1) one_one_nat))) (hAPP_nat_int _let_2 _let_1)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1524277240nt_int (hAPP_f1735705551nt_int (hAPP_f151095827nt_int cOMBB_1389251822nt_int P) Q) R) (hAPP_P1975530577nt_int P (hAPP_i1524277240nt_int Q R)))) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real Rx_4) Ry_2))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real Lx_4))) (= (hAPP_real_real _let_2 (hAPP_real_real (hAPP_r1250527377l_real times_times_real Ly_2) _let_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_2 Ly_2)) _let_1))))) (forall ((M $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) M))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (hAPP_r1250527377l_real inverse_divide_real Y_2))) (= (= X_1 (hAPP_real_real _let_2 (hAPP_real_real _let_1 Z_2))) (= (hAPP_real_real _let_2 Z_2) (hAPP_real_real _let_1 X_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int M) N)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N) M)))))) (hBOOL (hAPP_int_bool _let_11 _let_91)) (forall ((A_107 $$unsorted)) (= A_107 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_107) zero_z126310315umeral))) (forall ((A_107 $$unsorted)) (= A_107 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_107) zero_zero_complex))) (forall ((A $$unsorted) (B $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (hAPP_b1463609396nt_int if_int (hAPP_int_bool (hAPP_i1948725293t_bool fequal_int R_2) zero_zero_int)))) (let ((_let_2 (hAPP_int_int uminus_uminus_int Q_1))) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A B) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_1) R_2))) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel (hAPP_int_int uminus_uminus_int A) B) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int _let_1 _let_2) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int _let_2) one_one_int))) (hAPP_int_int (hAPP_int_fun_int_int _let_1 zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B) R_2))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_i2112223885l_bool member_int X_1))) (= (hBOOL (hAPP_f448129468l_bool _let_1 zOdd)) (not (hBOOL (hAPP_f448129468l_bool _let_1 zEven)))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_1))) (= (and (hBOOL (hAPP_nat_bool _let_1 Ma)) (hBOOL (hAPP_nat_bool _let_1 N_1))) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Ma) N_1)))))) (= (frct _let_78) one_one_rat) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f617735571l_real (hAPP_r712953929l_real P R) (hAPP_r1250527377l_real Q R)) (hAPP_r2019696015l_real (hAPP_f320596107l_real (hAPP_f850851693l_real cOMBS_193881978l_real P) Q) R))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r794344869l_real (hAPP_f517738447l_real (hAPP_f1879982819l_real cOMBB_731595089l_real P) Q) R) (hAPP_f1607917947l_real P (hAPP_r1134773055l_bool Q R)))) (forall ((C_1 $$unsorted) (N $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A_3) B_2)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat C_1) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2)) (exists ((R_1 $$unsorted) (S_2 $$unsorted)) (and (= B_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat S_2) N)) (= A_3 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat R_1) N))))))) (forall ((A_200 $$unsorted) (B_153 $$unsorted) (C_86 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_200) B_153)) C_86) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_200) C_86)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_153) C_86)))) (forall ((A_200 $$unsorted) (B_153 $$unsorted) (C_86 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_200) B_153)) C_86) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_200) C_86)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_153) C_86)))) (forall ((A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int A_3)) X)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) (archim1246769320r_real X))))) (forall ((C_79 $$unsorted) (D_15 $$unsorted) (A_179 $$unsorted) (B_139 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_179) B_139)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int C_79) D_15)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_139)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C_79)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_179) C_79)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_139) D_15))))))))) (forall ((X_1 $$unsorted)) (= (= X_1 zero_zero_real) (= zero_zero_real X_1))) (forall ((N_13 $$unsorted) (A_8 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat one_one_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_8)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_8) (hAPP_nat_nat suc N_13))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int C) D) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C) D)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) B))))) (forall ((B_1_1 $$unsorted)) (is_int (hilbert_Eps_int B_1_1))) (= _let_44 (hAPP_P1175774780nt_int twoSqu1907779896sum2sq (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int s) one_one_int))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_1))) (=> (hBOOL (hAPP_nat_bool _let_1 N_1)) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (div_mod_nat Ma) N_1))) (hBOOL (hAPP_nat_bool _let_1 Ma)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool even_odd_even_int X)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) _let_1) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) one_one_int)) _let_1))))) (forall ((A_3 $$unsorted)) (= (cis A_3) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real cos A_3)) (hAPP_real_real sin A_3)))) (forall ((V_2 $$unsorted)) (= (hAPP_complex_real re (hAPP_int_complex number528085621omplex V_2)) (hAPP_int_real number267125858f_real V_2))) (forall ((M $$unsorted) (N $$unsorted)) (=> (is_int N) (=> (not (= zero_zero_int N)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract M) N)) one_one_rat) (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int M) N)) N))))) (forall ((N $$unsorted) (M $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_2)) (=> (= (hAPP_nat_nat _let_1 N) (hAPP_nat_nat _let_1 M)) (= M N))))) (forall ((Z_7 $$unsorted) (W_2 $$unsorted) (Y_9 $$unsorted) (X_12 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_9) X_12)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Z_7) W_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X_12) W_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Y_9) Z_7)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X_12) Y_9)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat W_2) Z_7)))))) (forall ((X_19 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_19) X_19)) one_one_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_19) one_one_real)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_19) one_one_real)))) (forall ((N $$unsorted)) (= (hAPP_nat_nat size_size_nat N) N)) (forall ((A_215 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_215) one_on1684967323de_int) A_215)) (forall ((V_3 $$unsorted) (K_2 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat V_3)) K_2))) (let ((_let_2 (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat V_2)))) (let ((_let_3 (hAPP_nat_nat _let_2 _let_1))) (let ((_let_4 (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int V_3))))) (let ((_let_5 (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int V_2))))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 (hAPP_nat_nat _let_2 K_2))) (=> (not _let_4) (= _let_3 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_2) V_3))) K_2)))))))))))) (forall ((M $$unsorted) (K_2 $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) J_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc J_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat K_2) M)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) K_2))) M)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (and (= one_one_nat N_1) (= Ma one_one_nat)) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) N_1)))) (forall ((P $$unsorted)) (or (hBOOL P) (hBOOL (hAPP_bool_bool fNot P)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_nat (nat_gcd X) Y) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y))) (forall ((X_2 $$unsorted)) (= (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) cos_coeff)) (hAPP_r474017924t_real power_power_real X_2))) (hAPP_real_real cos X_2))) (forall ((M $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) M)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) M)) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X))) X))) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))))) (forall ((N_27 $$unsorted) (Y_7 $$unsorted) (X_10 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral Y_7) X_10)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_10) N_27)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral Y_7) N_27)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral X_10) Y_7)) N_27)))) (forall ((C_46 $$unsorted) (A_104 $$unsorted) (B_86 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat C_46))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 A_104)) (hAPP_nat_nat _let_1 B_86))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_104) B_86))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (= (hAPP_P1175774780nt_int product_fst_int_int (negDivAlg A_3 B_2)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) K_2)) N)) (not (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) N))))))) (forall ((Z_1 $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_complex_real norm_norm_complex Z_1)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_complex_real norm_norm_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Z_1) (hAPP_complex_complex cnj Z_1))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat minus_minus_nat M))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 one_one_nat)) N) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc N))))) (is_bool fTrue) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (=> (is_int K_1) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N_1)) (= (exists ((S_2 $$unsorted) (T $$unsorted)) (and (is_int T) (= (hAPP_P408881810nt_int (hAPP_i1730167831nt_int produc282740534nt_int K_1) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int S_2) T)) (xzgcd Ma N_1)) (is_int S_2))) (= K_1 (hAPP_int_int (legacy_zgcd Ma) N_1)))))) (forall ((N_1 $$unsorted)) (= (exists ((M_1 $$unsorted)) (= N_1 (hAPP_nat_nat suc M_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)))) (forall ((A_124 $$unsorted) (N_34 $$unsorted) (B_102 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_124) N_34) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_102) N_34)) (=> (hBOOL (hAPP_nat_bool _let_1 A_124)) (=> (hBOOL (hAPP_nat_bool _let_1 B_102)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_34)) (= B_102 A_124))))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) one_one_nat)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (=> (is_int D) (= (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) E_2)) D) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) E_2)) C)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B)) E_2)) C) D)))) (forall ((X_1 $$unsorted)) (= (= (hAPP_int_int (div_mod_int X_1) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) zero_zero_int) (hBOOL (hAPP_int_bool even_odd_even_int X_1)))) (forall ((X $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (multInv P_3))) (let ((_let_2 (hAPP_int_int _let_1 X))) (let ((_let_3 (hAPP_int_int _let_1 _let_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong _let_3) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) _let_2)) _let_3)) P_3))))))))) (forall ((A $$unsorted) (D $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_f659380387ol_int (hAPP_f1599440987ol_int big_co1024481617at_int (hAPP_f1139079189at_int (hAPP_f1431025877at_int cOMBB_int_int_nat _let_1) (hAPP_int_fun_nat_int (hAPP_f1673103573at_int cOMBC_nat_int_int (hAPP_f1935805932nt_int (hAPP_f125788821nt_int cOMBB_859312247nt_nat times_times_int) semiri1621563631at_int)) D))) (hAPP_n1699378549t_bool ord_lessThan_nat N_1))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int semiri1621563631at_int N_1)) (hAPP_int_int _let_1 (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) one_one_nat))) D))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Qr_1 $$unsorted)) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel (hAPP_int_int uminus_uminus_int A_3) (hAPP_int_int uminus_uminus_int B_2)) Qr_1)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (hAPP_P1975530577nt_int negateSnd Qr_1))))) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (hBOOL (hAPP_C24501650l_bool P_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral L) X_2)))) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral L) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral X_2) zero_z126310315umeral))) (hBOOL (hAPP_C24501650l_bool P_1 X_2)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int semiri1424489471de_int Ma)) (hAPP_n522471361de_int semiri1424489471de_int N_1))))) (forall ((B_97 $$unsorted) (A_119 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_119)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) B_97)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_119) B_97))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B)) zero_zero_int)))) (forall ((A_3 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) zero_zero_int) (hAPP_int_rat (hAPP_int_fun_int_rat fract zero_zero_int) one_one_int))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2)) _let_2) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) _let_2)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_1)) A_3)) B_2))) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_2) _let_2)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_2) _let_1)))))) (forall ((D $$unsorted) (F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real F X_1) L)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D)) (=> (forall ((Y_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_1) Y_1))) D)) (= (hAPP_real_real F Y_1) (hAPP_real_real F X_1)))) (= L zero_zero_real))))) (forall ((M_28 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real M_28) M_28) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) one_one_real)) M_28))) (forall ((A_31 $$unsorted) (C_12 $$unsorted) (B_26 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_31) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int C_12) B_26))) B_26) (hAPP_Q1762011733de_int (div_mo231679042de_int A_31) B_26))) (forall ((K_5 $$unsorted) (M_15 $$unsorted) (N_28 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int K_5))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int M_15) N_28))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 N_28)) (hBOOL (hAPP_Q2096512830t_bool _let_1 M_15)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real cos X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos Y)) (hAPP_real_real cos X))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real sin Y)) (hAPP_real_real sin X))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (negDivAlg A_3 B_2)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r279757445t_bool (hAPP_f1840085295t_bool (hAPP_f1083049571t_bool cOMBB_2050079537l_real P) Q) R) (hAPP_f605995867t_bool P (hAPP_r1134773055l_bool Q R)))) (forall ((V_4 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V_4))) (let ((_let_2 (hAPP_nat_int semiri1621563631at_int (hAPP_int_nat number_number_of_nat V_4)))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_1)))) (and (=> (not _let_3) (= zero_zero_int _let_2)) (=> _let_3 (= _let_2 _let_1))))))) (forall ((A_61 $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat zero_zero_nat) A_61))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (is_int A) (is_int B)) (= (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B)) (= A B)))) (forall ((N $$unsorted) (K_2 $$unsorted) (M $$unsorted)) (=> (= (hAPP_int_int (legacy_zgcd K_2) M) one_one_int) (=> (= one_one_int (hAPP_int_int (legacy_zgcd N) M)) (= (hAPP_int_int (legacy_zgcd (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) N)) M) one_one_int)))) (forall ((A $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) A)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) zero_zero_int)))) (forall ((N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (not (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) one_one_nat)))) (hBOOL (hAPP_nat_bool even_odd_even_nat N_1))))) (forall ((A_146 $$unsorted)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_146) zero_zero_nat) one_one_int)) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_n546711566l_real root N_1) X_1)) one_one_real))))) (forall ((A_222 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral zero_z126310315umeral) A_222))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real sqrt X)) (hAPP_real_real sqrt Y))))) (forall ((N_25 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_nat_int semiri1621563631at_int N_25)))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int bit0 K_2)) (hAPP_int_int bit1 L_2)) (hAPP_int_int bit1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int pred K_2)) L_2)))) (forall ((M_7 $$unsorted) (N_21 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat semiri151668891at_rat M_7)) (hAPP_nat_rat semiri151668891at_rat N_21)) (hAPP_nat_rat semiri151668891at_rat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_7) N_21)))) (forall ((B_130 $$unsorted) (A_170 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_170)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral B_130) zero_z126310315umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_130) A_170)) zero_z126310315umeral))))) (forall ((M $$unsorted) (K_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int fact_fact_int M)) (hAPP_int_int fact_fact_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int M) one_one_int)) K_2))))))) (forall ((C_79 $$unsorted) (D_15 $$unsorted) (A_179 $$unsorted) (B_139 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_179) B_139)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C_79) D_15)) (=> (hBOOL (hAPP_rat_bool _let_1 B_139)) (=> (hBOOL (hAPP_rat_bool _let_1 C_79)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_179) C_79)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_139) D_15))))))))) (forall ((B_28 $$unsorted) (A_34 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_28) A_34)) B_28) zero_z891286103de_int)) (forall ((K_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (hAPP_n1699378549t_bool ord_atMost_nat K_1)))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_int_rat number_number_of_rat X_1)) one_one_rat)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) (hAPP_int_int bit1 pls))))) (forall ((A_184 $$unsorted) (M_23 $$unsorted) (N_58 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_184))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_23) N_58)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_nat_real _let_1 M_23)) (hAPP_nat_real _let_1 N_58)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_int (div_mod_int A_3) B_2) (hAPP_P1175774780nt_int product_snd_int_int (divmod_int A_3 B_2)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat fact_fact_nat M)) (hAPP_nat_nat fact_fact_nat N))))) (forall ((K_1 $$unsorted) (P_1 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D)) (=> (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_1)) (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) D)))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1406902706l_real (hAPP_r1409264866l_real P R) Q) (hAPP_real_real (hAPP_f2119584768l_real (hAPP_f59594445l_real cOMBC_2010481033l_real P) Q) R))) (forall ((Y $$unsorted)) (= (hAPP_real_real tan (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) Y)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) (hAPP_real_real tan Y)))) (forall ((V_18 $$unsorted) (W_14 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat V_18)) (hAPP_int_rat number_number_of_rat W_14)) (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_18) W_14)))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) (hAPP_real_real abs_abs_real X))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool X_1) A_1)) (hBOOL (hAPP_f448129468l_bool A_1 X_1)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2)) zero_zero_int) P_3)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong B_2) zero_zero_int) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) zero_zero_int) P_3))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_complex_real im X))) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real uminus_uminus_real _let_2)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_complex_real re X)) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_2) _let_1))) (hAPP_complex_real im (hAPP_complex_complex invers1449016382omplex X)))))) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (legacy_zgcd X) Y)))) (forall ((A_59 $$unsorted) (B_50 $$unsorted) (C_29 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (div_mod_int A_59) C_29)) B_50)) C_29) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_59) B_50)) C_29))) (forall ((I $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) (hAPP_nat_nat suc I))) N)))) (forall ((X_6 $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_6))) (= (hAPP_nat_real _let_1 (hAPP_nat_nat suc Q_5)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_6) (hAPP_nat_real _let_1 Q_5))))) (forall ((Q_2 $$unsorted) (R_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat B_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_1)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat R_3) B_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat Q_2) C_1))) R_3)) (hAPP_nat_nat _let_1 C_1))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) M)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) Y) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real uminus_uminus_real Y)))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W) Z_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int W) one_one_int)) Z_1)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_nat_real real_nat N))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) one_one_real))) (= (natfloor X) N))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y) N))))) (forall ((B_93 $$unsorted) (A_115 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_115) zero_zero_rat)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_93) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_115) B_93)) zero_zero_rat))))) (forall ((P_2 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))))) (=> (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2)) (= (hBOOL (hAPP_int_bool P_2 X_2)) (hBOOL (hAPP_int_bool P_1 X_2)))))) (= (collect_int (hAPP_f1805168059t_bool _let_1 P_1)) (collect_int (hAPP_f1805168059t_bool _let_1 P_2)))))) (forall ((B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted) (B_5 $$unsorted) (Q_8 $$unsorted) (R_5 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_5) Q_8)) R_5))) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) Q_2)) R_3) _let_2) (=> (hBOOL (hAPP_int_bool _let_1 _let_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_5) B_5)) (=> (hBOOL (hAPP_int_bool _let_1 R_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_5) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_2) Q_8))))))))))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int I))) (=> (= one_one_int (hAPP_int_int (legacy_zgcd I) J_2)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) J_2))) (hBOOL (hAPP_int_bool _let_1 K_2)))))) (forall ((A_134 $$unsorted) (N_47 $$unsorted) (B_103 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_134) N_47)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat B_103) N_47))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) B_103)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_134) B_103))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_1)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real sin Y)) (hAPP_real_real sin X)))))))) (forall ((A_17 $$unsorted) (C_4 $$unsorted) (B_13 $$unsorted)) (=> (not (= zero_z891286103de_int B_13)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int C_4) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_17) B_13)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_17) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_13) C_4))) B_13)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (= (hAPP_real_real _let_1 X_1) (hAPP_real_real _let_1 Y_2)) (= Y_2 X_1))))) (forall ((X_7 $$unsorted) (Q_6 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat X_7))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat suc Q_6)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X_7) (hAPP_nat_nat _let_1 Q_6))))) (forall ((A_13 $$unsorted) (B_9 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_13) B_9)) B_9)) (hAPP_C498520661umeral (div_mo1740067990umeral A_13) B_9)) A_13)) (forall ((P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool sRStar P_5))) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int)))) (forall ((A_106 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat zero_zero_rat) A_106) A_106)) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (= (not (= (hAPP_int_int (standardRes P_5) X_1) zero_zero_int)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X_1) zero_zero_int) P_5))))) (forall ((A_217 $$unsorted) (M_29 $$unsorted) (B_160 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_217) B_160)) M_29) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_217) M_29)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_160) M_29)))) (forall ((N $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_3) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime P_3) N)) (= N one_one_nat)))) (forall ((M $$unsorted) (K_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) K_2)) (= one_one_nat (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat K_2) M))) K_2)))) (forall ((X_45 $$unsorted) (Y_33 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_45) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_33) _let_1))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y_33)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_45) Y_33)))))) (forall ((A_201 $$unsorted) (E_3 $$unsorted) (B_154 $$unsorted) (C_87 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_201) E_3)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_154) E_3)) C_87)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_201) B_154)) E_3)) C_87))) (forall ((X_44 $$unsorted) (Y_32 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_44) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_32) _let_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) Y_32)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_44) Y_32)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_int_nat nat X)) (hAPP_int_nat nat Y)) (hAPP_int_nat nat (hAPP_int_int (nat_tsub X) Y))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) A_1)) (hBOOL (hAPP_int_bool nat_is_nat X_1))))) (= (hAPP_real_real cos pi) _let_90) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_int_rat number_number_of_rat X_1)) zero_zero_rat)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) pls)))) (forall ((M_19 $$unsorted) (N_44 $$unsorted) (A_132 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_132))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) A_132)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat _let_1 M_19)) (hAPP_nat_rat _let_1 N_44))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_19) N_44)))))) (forall ((A_133 $$unsorted) (N_46 $$unsorted) (N_45 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_133))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_46) N_45)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_133)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_133) one_on1645066479umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral _let_1 N_45)) (hAPP_n1108039445umeral _let_1 N_46)))))))) (forall ((C_89 $$unsorted) (D_17 $$unsorted) (A_213 $$unsorted) (B_159 $$unsorted) (R_8 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat R_8))) (=> (not (= zero_zero_nat R_8)) (=> (and (not (= C_89 D_17)) (= B_159 A_213)) (not (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_159) (hAPP_nat_nat _let_1 D_17)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_213) (hAPP_nat_nat _let_1 C_89)))))))) (forall ((J $$unsorted) (A $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int _let_1)) P_5)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) P_5))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_5) A))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong J) zero_zero_int) P_5))) (= (hAPP_int_nat number_number_of_nat _let_1) (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool (multInvPair A P_5) J)))))))))) (forall ((V_12 $$unsorted) (W_10 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex V_12)) (hAPP_int_complex number528085621omplex W_10)) (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_12) W_10)))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)) (= one_one_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int number_number_of_int min)) (hAPP_int_nat nat X_1)))))) (forall ((A_47 $$unsorted) (B_38 $$unsorted) (C_19 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_47) B_38)) C_19) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (div_mod_int A_47) C_19)) B_38)) C_19))) (forall ((A_3 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted) (B_2 $$unsorted)) (=> (and (is_int B_2) (is_int D_3)) (=> (not (= zero_zero_int B_2)) (=> (not (= D_3 zero_zero_int)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) D_3)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int C_1) B_2))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) D_3)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)) (hAPP_int_rat (hAPP_int_fun_int_rat fract C_1) D_3))))))) (forall ((N $$unsorted)) (not (= (hAPP_nat_nat suc N) N))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_1))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real T)) (hAPP_real_real abs_abs_real X_1))) (= (hAPP_real_real exp_real X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) _let_1)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat))) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real exp_real T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1)))))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (archim856651990g_real X)) A_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_int_real real_int A_3))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real pi)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real cos Y)) (hAPP_real_real cos X))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C))) (= (or (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B) A))) (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) B)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C)))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A)) (hAPP_rat_rat _let_1 B)))))) (forall ((R_3 $$unsorted) (X $$unsorted)) (let ((_let_1 (scaleR1652505878omplex R_3))) (= (hAPP_complex_complex cnj (hAPP_complex_complex _let_1 X)) (hAPP_complex_complex _let_1 (hAPP_complex_complex cnj X))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real Z_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_int P (hAPP_P1175774780nt_int Q R)) (hAPP_P1175774780nt_int (hAPP_f521271395nt_int (hAPP_f11151005nt_int cOMBB_47643171nt_int P) Q) R))) (forall ((C_44 $$unsorted) (D_8 $$unsorted) (A_102 $$unsorted) (B_84 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_102) B_84)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C_44) D_8)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_102) C_44)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_84) D_8)))))) (forall ((I $$unsorted) (K_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) K_2)) (=> (not (= (hAPP_nat_nat suc I) K_2)) (not (forall ((J_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) J_1)) (not (= K_2 (hAPP_nat_nat suc J_1))))))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A) (natfloor X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat A)) X_1))))) (forall ((A_48 $$unsorted) (B_39 $$unsorted) (C_20 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_48) B_39)) C_20) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_48) C_20)) (hAPP_C498520661umeral (div_mo1740067990umeral B_39) C_20))) C_20))) (forall ((P_3 $$unsorted) (Q_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Q_2) zero_zero_int)) (= (normalize (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int uminus_uminus_int P_3)) (hAPP_int_int uminus_uminus_int Q_2))) (normalize (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2))))) (forall ((C_44 $$unsorted) (D_8 $$unsorted) (A_102 $$unsorted) (B_84 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_102) B_84)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral C_44) D_8)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_102) C_44)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_84) D_8)))))) (= _let_37 _let_79) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (is_int B) (is_int A)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) zero_zero_int)) (= A B)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P752050971nt_int (hAPP_f301246617nt_int (hAPP_f1151807883nt_int cOMBB_563965291nt_int P) Q) R) (hAPP_f11151005nt_int P (hAPP_P2110489235nt_int Q R)))) (forall ((B_140 $$unsorted) (A_180 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (or (and (hBOOL (hAPP_int_bool _let_1 A_180)) (hBOOL (hAPP_int_bool _let_1 B_140))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_140) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_180) zero_zero_int)))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_180) B_140)))))) (forall ((X $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_3) X))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int)) _let_1)))) (hAPP_int_int number_number_of_int min)) P_3)))))))) (forall ((I $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int I))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int M) N))) (hBOOL (hAPP_int_bool _let_1 N))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))))) (forall ((A_28 $$unsorted) (B_23 $$unsorted) (C_10 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_10))) (=> (is_int C_10) (=> (not (= C_10 zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int _let_1 A_28)) (hAPP_int_int _let_1 B_23)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_28) B_23)))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral D) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral X_2) Sa)))))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral Z) X_2)) (= _let_1 _let_1)))))) (forall ((Ma $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes Ma) X_1)) (exists ((Y_1 $$unsorted)) (and (is_int Y_1) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X_1) Ma)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (hAPP_real_real (hAPP_r1250527377l_real (hAPP_b646336293l_real if_real fFalse) X) Y))) (forall ((V_2 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int number_number_of_int V_2)) (hAPP_int_int number_number_of_int W)) (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_2) (hAPP_int_int uminus_uminus_int W))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1325804733t_bool P (hAPP_P2053772734t_bool Q R)) (hAPP_P1400155668t_bool (hAPP_f223623489t_bool (hAPP_f1815301987t_bool cOMBB_650041899nt_int P) Q) R))) (forall ((B_97 $$unsorted) (A_119 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_119)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) B_97)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_119) B_97))))))) (forall ((A_108 $$unsorted)) (=> (is_int A_108) (= A_108 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_108) zero_zero_int)))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_real_real cos X_1))) (=> (not (= _let_1 zero_zero_real)) (hBOOL (hAPP_real_bool (deriv_real tan X_1) (hAPP_real_real inverse_inverse_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))))) (forall ((Ta $$unsorted) (A_1 $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) D_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int X_2))) (let ((_let_2 (hAPP_i1948725293t_bool dvd_dvd_int D))) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa) X_2)))))))) (=> (hBOOL (hAPP_int_bool _let_2 (hAPP_int_int _let_1 Ta))) (hBOOL (hAPP_int_bool _let_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 D_1)) Ta))))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_bool (hAPP_f737665877t_bool (hAPP_f605995867t_bool cOMBB_real_bool_nat P) Q) R) (hAPP_real_bool P (hAPP_nat_real Q R)))) (forall ((N $$unsorted) (A_3 $$unsorted)) (= (hAPP_complex_real im (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (cis A_3)) N)) (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) A_3)))) (forall ((C_46 $$unsorted) (A_104 $$unsorted) (B_86 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real C_46))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A_104)) (hAPP_real_real _let_1 B_86))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_104) B_86))))) (forall ((X $$unsorted)) (= (hAPP_real_real cos X) (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) pi))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat X))) (= X (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X) _let_1))))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W) Z_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_1) W)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (and (is_int X_1) (is_int Y_2)) (= (and (= Y_2 zero_zero_int) (= X_1 zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_1) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_2) _let_1))) zero_zero_int)))))) (forall ((V_22 $$unsorted) (V_21 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_21)) (=> (hBOOL (hAPP_int_bool _let_1 V_22)) (= (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_21) V_22)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real V_21)) (hAPP_int_real number267125858f_real V_22))))))) (forall ((N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (hBOOL (hAPP_real_bool (isCont_real_real (hAPP_n546711566l_real root N_1)) zero_zero_real)))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W))) (let ((_let_2 (negDivAlg one_one_int _let_1))) (let ((_let_3 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) _let_1))) (let ((_let_4 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_3)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) _let_1)) (and (=> _let_4 (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int number_number_of_int min)) _let_3) _let_2)) (=> (not _let_4) (= _let_2 (hAPP_P1975530577nt_int (adjust _let_1) (negDivAlg one_one_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) _let_1)))))))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) C_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) C_1)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) A_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) B_2)))))) (forall ((C_34 $$unsorted) (D_6 $$unsorted) (A_80 $$unsorted) (B_68 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_80) B_68)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral C_34) D_6)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_80) C_34)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_68) D_6)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1584592887nt_int (hAPP_f465821005nt_int (hAPP_f1081447804nt_int cOMBS_1470252563nt_int P) Q) R) (hAPP_f1735705551nt_int (hAPP_i1836591008nt_int P R) (hAPP_i1584592887nt_int Q R)))) (forall ((N $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_3) N))) (= (hAPP_int_int (legacy_zgcd N) P_3) one_one_int)))) (forall ((X_1 $$unsorted)) (= (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat uminus_uminus_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) sin_coeff)) (hAPP_r474017924t_real power_power_real X_1)))) (hAPP_real_real uminus_uminus_real (hAPP_real_real sin X_1)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) N)))))) (forall ((X $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_r1250527377l_real plus_plus_real X))) (= (hAPP_real_real sin (hAPP_real_real _let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat (hAPP_nat_nat suc M))) pi)) _let_1))) (hAPP_real_real cos (hAPP_real_real _let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat M)) pi)) _let_1))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r474017924t_real (hAPP_f1407095736t_real (hAPP_f1796904975t_real cOMBB_599996122l_real P) Q) R) (hAPP_r474017924t_real P (hAPP_real_real Q R)))) (forall ((Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_1)) (= (hAPP_nat_nat suc (hAPP_int_nat nat Z_1)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) Z_1))))) (forall ((A $$unsorted) (C $$unsorted) (D $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) D))) (=> (and (is_int D) (is_int B)) (=> (not (= B zero_zero_int)) (=> (not (= D zero_zero_int)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) D)) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int C) B)) _let_1))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B)) (hAPP_int_rat (hAPP_int_fun_int_rat fract C) D))))))))) (not (hBOOL (hAPP_int_bool nat_neg _let_63))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int Rx))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int Lx))) (= (hAPP_int_int _let_1 (hAPP_int_int _let_2 Ry)) (hAPP_int_int _let_2 (hAPP_int_int _let_1 Ry)))))) _let_89 (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real arcsin Y)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))))) (= field_1210416355s_real (collect_real (hAPP_f101635158l_bool _let_87 (hAPP_f1341793266t_bool (hAPP_f571820015t_bool cOMBB_1159313332l_real (hAPP_f389116883t_bool cOMBB_1593174431ol_int fEx_nat)) (hAPP_f1115375056t_bool (hAPP_f271976045t_bool cOMBC_1801450329t_bool (hAPP_f1927674023t_bool (hAPP_f1261108921t_bool cOMBB_172850899l_real cOMBC_678732631t_bool) (hAPP_f2084827628t_bool (hAPP_f1121609875t_bool cOMBB_2125215742l_real (hAPP_f1182713365t_bool cOMBB_2087181719ol_int cOMBS_nat_bool_bool)) (hAPP_f834119977l_bool (hAPP_f848516149l_bool cOMBB_270132509l_real (hAPP_f643658017l_bool cOMBB_2046938128ol_int (hAPP_f1080886329l_bool cOMBB_1015721476ol_nat fconj))) (hAPP_f1459420095t_bool (hAPP_f693283245t_bool cOMBC_1113900202t_bool (hAPP_f77155443t_bool (hAPP_f403082607t_bool cOMBB_984071017l_real cOMBB_1647910634ol_int) (hAPP_f1840085295t_bool (hAPP_f1083049571t_bool cOMBB_2050079537l_real cOMBB_real_bool_nat) fequal_real))) (hAPP_f1613846310t_real (hAPP_f1720068861t_real cOMBC_295337211t_real (hAPP_f1295083291t_real (hAPP_f212164053t_real cOMBB_929094628al_int cOMBB_real_real_nat) _let_86)) real_nat)))))) (hAPP_f800510211t_bool (hAPP_f894608603t_bool cOMBB_bool_bool_nat fNot) (hAPP_n1699378549t_bool _let_35 zero_zero_nat))))))) (forall ((M_27 $$unsorted) (A_212 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_212) one_one_complex)) M_27) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex M_27) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_212) M_27)))) (forall ((A_129 $$unsorted) (N_40 $$unsorted) (N_39 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_129))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_40) N_39)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) A_129)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat _let_1 N_40)) (hAPP_nat_rat _let_1 N_39))))))) (= (hAPP_int_int succ min) pls) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat N))) (=> (not (hBOOL (hAPP_nat_bool _let_1 M))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat suc M))) (= N M))))) (forall ((X_45 $$unsorted) (Y_33 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_45) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_33) _let_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) Y_33)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_45) Y_33)))))) (forall ((C_64 $$unsorted) (A_142 $$unsorted) (B_111 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_64))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int _let_1 A_142)) (hAPP_Q1762011733de_int _let_1 B_111))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_64)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_142) B_111)))))) (forall ((A_143 $$unsorted) (C_65 $$unsorted) (B_112 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_143) C_65)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_112) C_65))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C_65)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_143) B_112))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (not (= zero_zero_nat A_3)) (exists ((X_2 $$unsorted) (Y_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) X_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_2) Y_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2)))))) (forall ((X_9 $$unsorted)) (let ((_let_1 (hAPP_n1108039445umeral semiri1619134803umeral (hAPP_int_nat nat X_9)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_9)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral _let_1) _let_1) (hAPP_n1108039445umeral semiri1619134803umeral (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_9))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat C))) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A)) (hAPP_rat_rat _let_1 B))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A) B))))) (forall ((Y_3 $$unsorted) (B $$unsorted) (X_3 $$unsorted) (A $$unsorted)) (=> (hBOOL (tendsto_nat_real X_3 A sequentially)) (=> (hBOOL (tendsto_nat_real Y_3 B sequentially)) (hBOOL (tendsto_nat_complex (hAPP_f219720582omplex (hAPP_f1052840010omplex cOMBS_696648398omplex (hAPP_f23851874omplex (hAPP_f406530075omplex cOMBB_1714920583ex_nat complex) X_3)) Y_3) (hAPP_real_complex (hAPP_r265291036omplex complex A) B) sequentially))))) (forall ((K_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int K_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int _let_1 A_3)) (hAPP_int_int _let_1 B_2)) M))))) (forall ((X_44 $$unsorted) (Y_32 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_44) _let_1)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral Y_32) _let_1))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) Y_32)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral X_44) Y_32)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) A))))) (forall ((M_18 $$unsorted) (N_38 $$unsorted) (A_128 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_128))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) A_128)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat _let_1 M_18)) (hAPP_nat_rat _let_1 N_38))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_18) N_38)))))) (forall ((B_74 $$unsorted) (A_86 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_86) zero_zero_rat)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_74) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_86) B_74)) zero_zero_rat))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le382113706t_bool A_1) B_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_f284875647l_bool ord_le1912455174t_bool (image_nat_int semiri1621563631at_int A_1)) (image_nat_int semiri1621563631at_int B_1))))) (forall ((I_1 $$unsorted) (J $$unsorted)) (= (image_nat_nat suc (hAPP_n1699378549t_bool (ord_at238088361st_nat I_1) J)) (hAPP_n1699378549t_bool (ord_at238088361st_nat (hAPP_nat_nat suc I_1)) (hAPP_nat_nat suc J)))) (hBOOL (hAPP_nat_bool _let_7 one_one_nat)) (forall ((A $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_1))) (= (and (= zero_zero_complex A) (not (= zero_zero_nat _let_1))) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A) _let_1) zero_zero_complex)))) (forall ((B_93 $$unsorted) (A_115 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_115) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_93) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_115) B_93)) zero_zero_int))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) Ma)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat fact_fact_nat Ma)) (hAPP_nat_nat fact_fact_nat N_1)) (big_co1705425894at_nat cOMBI_nat (hAPP_n1699378549t_bool (ord_at238088361st_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N_1) one_one_nat)) Ma))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int uminus_uminus_int X)) Y))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (= (hBOOL (hAPP_real_bool _let_1 Y_2)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sqrt Y_2)))))) (forall ((A_207 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_207) A_207))) (forall ((X $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (hAPP_int_real real_int D_3))) (=> (is_int D_3) (=> (not (= D_3 zero_zero_int)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_int_real real_int X)) _let_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) D_3))) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_int_real real_int (hAPP_int_int (div_mod_int X) D_3))) _let_1))))))) (forall ((C_89 $$unsorted) (D_17 $$unsorted) (A_213 $$unsorted) (B_159 $$unsorted) (R_8 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat R_8))) (=> (not (= R_8 zero_zero_rat)) (=> (and (= A_213 B_159) (not (= D_17 C_89))) (not (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_213) (hAPP_rat_rat _let_1 C_89)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_159) (hAPP_rat_rat _let_1 D_17)))))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (and (is_int Y_2) (is_int X_1)) (=> (hBOOL (hAPP_int_bool _let_1 X_1)) (=> (hBOOL (hAPP_int_bool _let_1 Y_2)) (= (= (hAPP_int_nat nat Y_2) (hAPP_int_nat nat X_1)) (= Y_2 X_1))))))) (forall ((D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat D_3))) (=> (= one_one_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))) (= one_one_nat (hAPP_nat_nat _let_1 B_2))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int M) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int fact_fact_int M)) (hAPP_int_int fact_fact_int N))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) M) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_f2119767738t_bool (hAPP_f423804115t_bool cOMBB_1418110531ol_int P) Q) R) (hAPP_f448129468l_bool P (hAPP_i1948725293t_bool Q R)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_r1250527377l_real plus_plus_real one_one_real))) (= (hAPP_real_real arctan X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) (hAPP_real_real arctan (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) (hAPP_real_real _let_2 (hAPP_real_real sqrt (hAPP_real_real _let_2 (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat _let_1)))))))))))) (forall ((A_64 $$unsorted) (B_52 $$unsorted) (C_31 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_64) C_31) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_64) B_52)) B_52)) (hAPP_nat_nat (div_mod_nat A_64) B_52))) C_31))) (forall ((B_116 $$unsorted) (A_155 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_155)) (=> (hBOOL (hAPP_int_bool _let_1 B_116)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_155) B_116))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C))) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B))) (or (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B) A)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C) zero_zero_real))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) Ma)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N_1) Ma)) Ma)) (= N_1 one_one_nat)))) (forall ((A_184 $$unsorted) (M_23 $$unsorted) (N_58 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_184))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_23) N_58)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_n522471361de_int _let_1 M_23)) (hAPP_n522471361de_int _let_1 N_58)))))) (forall ((N $$unsorted)) (= (hAPP_nat_nat suc N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat one_one_nat) N))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) A))) (hBOOL (hAPP_int_bool _let_1 A))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= (or (and (= N_1 zero_zero_nat) (= _let_1 Ma)) (and (= N_1 _let_1) (= Ma zero_zero_nat))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) N_1) _let_1)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 X_1)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 Y_2)) (= (and (= zero_z126310315umeral Y_2) (= zero_z126310315umeral X_1)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral X_1) Y_2) zero_z126310315umeral)))))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_complex number528085621omplex W))) (= (hAPP_complex_complex cnj _let_1) _let_1))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat B_2) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat _let_1 B_2)) C_1)))) (forall ((A_88 $$unsorted) (B_76 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_88) B_76)) B_76) A_88)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int (hAPP_b1463609396nt_int if_int P_1) X_1) Y_2)))) (let ((_let_2 (hBOOL P_1))) (and (=> (not _let_2) (= (hAPP_int_nat nat Y_2) _let_1)) (=> _let_2 (= _let_1 (hAPP_int_nat nat X_1))))))) (forall ((C_7 $$unsorted) (A_22 $$unsorted) (B_18 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_22) B_18)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_18) C_7)) A_22) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int B_18) A_22)) C_7)))) (forall ((A_56 $$unsorted) (C_26 $$unsorted) (B_47 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_56) C_26)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_47) C_26)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (div_mod_nat A_56) B_47)) C_26))) (forall ((N_37 $$unsorted) (A_126 $$unsorted)) (let ((_let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_126) N_37))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) A_126)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_126) one_on1645066479umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_126) _let_1)) _let_1)))))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int fact_fact_int N))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) L)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 K_1)) (hAPP_int_int bit0 L))))) (forall ((A_235 $$unsorted)) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_235) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_235) A_235)) A_235))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int uminus_uminus_int A_3)) (hAPP_int_int uminus_uminus_int B_2)))) (forall ((X_46 $$unsorted) (Y_34 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (let ((_let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral Y_34) _let_2) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_46) _let_2)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 X_46)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 Y_34)) (= Y_34 X_46))))))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_3) B_2)) (hAPP_real_real (hAPP_r1250527377l_real powr (hAPP_real_real _let_1 A_3)) B_2)))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral Lx_2))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral _let_1 Ly)) Rx_2) (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral Ly) Rx_2))))) (forall ((F $$unsorted) (L $$unsorted) (C $$unsorted)) (=> (hBOOL (tendsto_real_real F L (at_real C))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) L)) (exists ((R_1 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) R_1)) (forall ((X_2 $$unsorted)) (=> (and (not (= C X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real C) X_2))) R_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real F X_2)))))))))) (forall ((N_66 $$unsorted) (A_210 $$unsorted) (B_158 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_210) B_158)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_210)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_66)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_210) N_66)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_158) N_66))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2) (hAPP_P1175774780nt_int product_fst_int_int (hAPP_P1975530577nt_int negateSnd (posDivAlg (hAPP_int_int uminus_uminus_int A_3) (hAPP_int_int uminus_uminus_int B_2)))))))) (hBOOL (hAPP_nat_bool prime _let_4)) (forall ((N_12 $$unsorted) (R_6 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) R_6)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int R_6) one_on1684967323de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int R_6) (hAPP_nat_nat suc N_12))) R_6))))) (= one_one_int _let_85) (= (hAPP_nat_int semiri1621563631at_int one_one_nat) one_one_int) (forall ((U $$unsorted)) (= (hAPP_f22106695ol_nat finite_card_nat (hAPP_n1699378549t_bool ord_lessThan_nat U)) U)) (= (hAPP_real_real sin pi) zero_zero_real) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_nat_real real_nat N))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (natfloor X)) N))))) (not (= one_one_int zero_zero_int)) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) K_2))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (= zero_zero_real (hAPP_real_real (hAPP_n546711566l_real root N_1) X_1)) (= X_1 zero_zero_real)))) (forall ((B_1 $$unsorted) (P_2 $$unsorted) (P_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) Z)) (= (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P_2 X_2))))))) (=> (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa))))))) (=> (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1))))))) (=> (forall ((X_2 $$unsorted) (K $$unsorted)) (=> (and (is_int X_2) (is_int K)) (= (hBOOL (hAPP_int_bool P_2 X_2)) (hBOOL (hAPP_int_bool P_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K) D_1))))))) (= (or (exists ((X_2 $$unsorted)) (and (is_int X_2) (hBOOL (hAPP_int_bool P_2 X_2)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_2) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))))) (exists ((X_2 $$unsorted)) (and (exists ((Xa $$unsorted)) (and (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) B_1)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xa) X_2))) (is_int Xa))) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_2) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (is_int X_2)))) (exists ((X1 $$unsorted)) (and (is_int X1) (hBOOL (hAPP_int_bool P_1 X1)))))))))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) J_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat J_2) K_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc I)) K_2))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real arctan X_1) (hAPP_real_real inverse_inverse_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int X))) (=> (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2) one_one_int) (=> (hBOOL (hAPP_int_bool _let_1 A_3)) (=> (hBOOL (hAPP_int_bool _let_1 B_2)) (= (hAPP_int_int abs_abs_int X) one_one_int)))))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real arccos Y))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) one_one_real)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) pi)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) _let_1))))))) (forall ((B_55 $$unsorted) (A_67 $$unsorted)) (= A_67 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_55) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_67) B_55))) (hAPP_nat_nat (div_mod_nat A_67) B_55)))) (forall ((A_220 $$unsorted)) (= A_220 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex zero_zero_complex) A_220))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int pred K_2) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int K_2) one_one_int))) (forall ((B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted) (B_5 $$unsorted) (Q_8 $$unsorted) (R_5 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_5) Q_8)) R_5))) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) Q_2)) R_3) _let_1) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_3) B_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_5) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_8) Q_2)))))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) Y) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) Z_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y) Z_1)) M)))) (forall ((B_155 $$unsorted) (A_204 $$unsorted)) (=> (not (= zero_zero_complex A_204)) (=> (not (= B_155 zero_zero_complex)) (not (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_204) B_155) zero_zero_complex))))) (forall ((A_194 $$unsorted) (B_150 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_194) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_150) A_194)))) (forall ((A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (= (hBOOL (hAPP_f448129468l_bool finite_finite_int A_1)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (image_int_nat nat A_1)))))) (forall ((N_1 $$unsorted) (K_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat K_1))) (=> (hBOOL (hAPP_nat_bool _let_1 Ma)) (=> (hBOOL (hAPP_nat_bool _let_1 N_1)) (= (= Ma N_1) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat Ma) K_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) K_1))))))) (forall ((W_8 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W_8))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_1) _let_1) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((R_3 $$unsorted) (P_3 $$unsorted) (Q_2 $$unsorted)) (=> (= (quotient_of R_3) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Q_2)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1409264866l_real (hAPP_f1523861863l_real (hAPP_f1067681227l_real cOMBB_1934313333l_real P) Q) R) (hAPP_f1509287679l_real P (hAPP_r474017924t_real Q R)))) (forall ((X $$unsorted) (M $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) (hAPP_int_int (standardRes M) X)) M))) (forall ((V_2 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int V_2)) (hAPP_int_int number_number_of_int W)) (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_2) W)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) B)) (or (= A zero_zero_rat) (= zero_zero_rat B)))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int Lx_1))) (= (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int Rx_1) Ry_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 Rx_1)) Ry_1)))) (forall ((P_1 $$unsorted)) (= P_1 (collec1979865426at_nat P_1))) (forall ((P_1 $$unsorted) (I_1 $$unsorted) (K_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I_1) K_1)) (=> (hBOOL (hAPP_int_bool P_1 K_1)) (=> (forall ((I_2 $$unsorted)) (=> (is_int I_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I_2) K_1)) (=> (hBOOL (hAPP_int_bool P_1 I_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int I_2) one_one_int))))))) (hBOOL (hAPP_int_bool P_1 I_1)))))) (forall ((N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat zero_zero_nat) N) zero_zero_nat)) (forall ((N_33 $$unsorted) (A_123 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int one_one_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_123)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_33)) (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_123) N_33))))))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_i1732201573de_int quickcheck_of_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (quickcheck_int_of N)) (quickcheck_int_of M))) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int N) M))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N))))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_int_nat nat X_1))) (hBOOL (hAPP_int_bool even_odd_even_int X_1))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_3) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) B_2)) (exists ((D_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D_2)) (forall ((Y_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) Y_1))) D_2)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_1) B_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_3) Y_1)))))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_1) X_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_2) Y_2))) (and (= Y_2 zero_zero_real) (= X_1 zero_zero_real)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (and (= Ma zero_zero_nat) (= zero_zero_nat N_1)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Ma) N_1)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (hBOOL (fdisj P Q)) (not (hBOOL P)))) (forall ((K_2 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat one_one_rat) (hAPP_int_rat number_number_of_rat K_2)) (frct (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int one_one_int) (hAPP_int_int number_number_of_int K_2))))) (forall ((L_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int minus_minus_int pls))) (= (hAPP_int_int bit0 (hAPP_int_int _let_1 L_2)) (hAPP_int_int _let_1 (hAPP_int_int bit0 L_2))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (div_mod_int A_3))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int B_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_1)) (= (hAPP_int_int _let_1 (hAPP_int_int _let_2 C_1)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_2 (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)) C_1))) (hAPP_int_int _let_1 B_2))))))) (forall ((N $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat zero_zero_nat) N))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit0 K_1)) (hAPP_int_int bit1 L))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) L)))) (forall ((N_12 $$unsorted) (R_6 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) R_6)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral R_6) one_on1645066479umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral R_6) (hAPP_nat_nat suc N_12))) R_6))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_i2112223885l_bool member_int X_1))) (not (and (hBOOL (hAPP_f448129468l_bool _let_1 zEven)) (hBOOL (hAPP_f448129468l_bool _let_1 zOdd)))))) (forall ((X $$unsorted) (N $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real real_int X)) N) (hAPP_int_real real_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) N)))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (= Z_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z_1) one_one_int)))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral Lx_3))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral _let_1 Ly_1)) Rx_3) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral _let_1 Rx_3)) Ly_1)))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A) B)) (= zero_z891286103de_int (hAPP_Q1762011733de_int (div_mo231679042de_int B) A)))) (forall ((R_3 $$unsorted) (S_1 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (ratreal (hAPP_int_rat number_number_of_rat R_3))) (ratreal (hAPP_int_rat number_number_of_rat S_1))) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_int_real number267125858f_real R_3)) (hAPP_int_real number267125858f_real S_1)))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((M_1 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool P_1 M_1) zero_zero_nat))) (=> (forall ((M_1 $$unsorted) (N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool P_1 N_2) (hAPP_nat_nat (div_mod_nat M_1) N_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool P_1 M_1) N_2))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool P_1 Ma) N_1))))) (= (code_c271388182l_size zero_z126310315umeral) zero_zero_nat) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_rat_rat uminus_uminus_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)) (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int uminus_uminus_int A_3)) B_2))) (forall ((X $$unsorted) (Y $$unsorted) (R_3 $$unsorted)) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) R_3)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y) R_3)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_real_complex (hAPP_r265291036omplex complex X) Y)) (of_real_complex R_3)))) (forall ((D_3 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D_3) (hAPP_int_int abs_abs_int D_3)))) (forall ((K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_1))) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N_1) K_1))) (hBOOL (hAPP_nat_bool _let_1 N_1))))) (forall ((V $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int V))) (= (=> (not (hBOOL (hAPP_int_bool _let_1 V_1))) (hBOOL (hAPP_int_bool _let_1 pls))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_int_nat number_number_of_nat V)) (hAPP_int_nat number_number_of_nat V_1)))))) (forall ((Y $$unsorted) (X $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (zcong X))) (let ((_let_2 (multInv P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong Y) zero_zero_int) P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int _let_2 X)) (hAPP_int_int _let_2 Y)) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 Y) P_3)))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat (div_mod_nat M) N)))) (let ((_let_2 (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc M)) N))) (and (=> (= _let_1 N) (= zero_zero_nat _let_2)) (=> (not (= N _let_1)) (= _let_2 _let_1)))))) (forall ((N_19 $$unsorted)) (= zero_zero_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int zero_zero_int) (hAPP_nat_nat suc N_19)))) (forall ((A_3 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N)) (=> (= (hAPP_int_int (legacy_zgcd A_3) N) one_one_int) (exists ((X_2 $$unsorted)) (and (is_int X_2) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) X_2)) one_one_int) N))))))) (forall ((A_224 $$unsorted) (N_68 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_int_fun_nat_int power_power_int A_224))) (= (hAPP_nat_int _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_68)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int _let_2 N_68)) _let_1))))) (forall ((A_66 $$unsorted) (B_54 $$unsorted)) (= A_66 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_66) B_54)) B_54)) (hAPP_Q1762011733de_int (div_mo231679042de_int A_66) B_54)))) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_i1732201573de_int number1226105091de_int W_1))) (= (= X_1 _let_1) (= _let_1 X_1)))) (forall ((N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_nat_nat suc (hAPP_nat_nat suc N)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int N_1)) Ma)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real N_1)) (hAPP_int_real real_int Ma))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real times_times_real) cos)) cos) X_1) (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_real_real cos X_1))) (hAPP_real_real sin X_1)))))) (forall ((A_188 $$unsorted) (B_144 $$unsorted) (C_81 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_188) B_144)) C_81)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real B_144) C_81)))) (forall ((I $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) I)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_int_nat nat I))) one_one_nat) (hAPP_list_int_nat size_size_list_int (quickc666637781d_zero I))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted)) (= (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat C) A) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B) A)) (= C B))) (forall ((B_117 $$unsorted) (A_156 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_156)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B_117) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_156) B_117)) zero_zero_rat))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set B_1)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_f284875647l_bool ord_le951220754t_bool A_1) B_1)) (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le1568362934t_bool (image_int_nat nat A_1)) (image_int_nat nat B_1))))))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (= (or (= K_1 zero_zero_nat) (= N_1 Ma)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N_1) K_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) K_1)))) (forall ((G $$unsorted) (X_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real G X_1) Ma)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real sin) G) X_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos (hAPP_real_real G X_1))) Ma))))) (forall ((X_1 $$unsorted) (X_3 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_1) X_3)) (=> (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) X_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) Z))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) (comple124823625p_real X_3)))))) (forall ((X_20 $$unsorted) (Y_16 $$unsorted) (A_120 $$unsorted) (B_98 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real X_20))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Y_16) B_98))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_20) A_120)) B_98)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real _let_1 Y_16)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_120) B_98))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int K_1)) (hAPP_int_int number_number_of_int L))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) L)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real exp_real (hAPP_real_real ln X)) X))) (forall ((A_17 $$unsorted) (C_4 $$unsorted) (B_13 $$unsorted)) (=> (is_int B_13) (=> (not (= B_13 zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int C_4) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_17) B_13)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_17) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_13) C_4))) B_13))))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real arccos Y))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) pi)) (= Y (hAPP_real_real cos _let_1))))))) (forall ((B_96 $$unsorted) (A_118 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_118)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_96)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_118) B_96))))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_nat_real real_nat A_3))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (natceiling X)) A_3)))) (forall ((R_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real R_3) one_one_real)) (hAPP_int_real real_int (archim1246769320r_real R_3))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_nat) X_1))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int succ K_2) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int K_2) min))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (= (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) A))) (hBOOL (hAPP_rat_bool _let_1 A))))) (forall ((C_42 $$unsorted) (A_100 $$unsorted) (B_82 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_100) B_82)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_100) C_42)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_82) C_42))))) (forall ((M_8 $$unsorted) (N_22 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int semiri1621563631at_int M_8)) (hAPP_nat_int semiri1621563631at_int N_22)) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_8) N_22)))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int D) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int X_2) Sa)))))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int X_2) Z)) (= _let_1 _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_P1860904029l_real (hAPP_P1982799375l_real (hAPP_b1482221219l_real if_Pro313124157l_real fFalse) X) Y) Y)) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_2) X_1)) (= (comple124823625p_real (hAPP_r1134773055l_bool (ord_at1496968948n_real Y_2) X_1)) X_1))) (forall ((A_68 $$unsorted) (B_56 $$unsorted)) (= A_68 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_68) B_56)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_68) B_56)) B_56)))) (forall ((C_77 $$unsorted) (B_137 $$unsorted) (A_177 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_77))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_137) A_177)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C_77) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A_177)) (hAPP_real_real _let_1 B_137))))))) (forall ((A_226 $$unsorted) (B_163 $$unsorted) (C_92 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A_226))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 B_163)) C_92) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 C_92)) B_163)))) (forall ((N_16 $$unsorted) (M_5 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_16) M_5)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_nat_real semiri132038758t_real M_5)) (hAPP_nat_real semiri132038758t_real N_16)) (hAPP_nat_real semiri132038758t_real (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M_5) N_16))))) (forall ((L $$unsorted) (U $$unsorted)) (= (image_int_int (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int plus_plus_int) L) (hAPP_i1948725293t_bool (ord_at641636577an_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int U) L))) (hAPP_i1948725293t_bool (ord_at641636577an_int L) U))) (forall ((B_90 $$unsorted) (A_112 $$unsorted) (C_50 $$unsorted)) (=> (and (is_int B_90) (is_int C_50)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int C_50) A_112) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_90) A_112)) (= B_90 C_50)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= X (hAPP_real_real (hAPP_n546711566l_real root _let_1) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)))))) (forall ((Sa $$unsorted) (Ta $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A) B)) (hBOOL (hAPP_f115998247l_bool (hAPP_P1876494581l_bool member180897546at_nat (hAPP_P369611207at_nat (hAPP_P402336767at_nat produc494345619at_nat (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat A) Sa)) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat B) Ta))) pair_leq)))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat) (hAPP_nat_nat fact_fact_nat N)))) (forall ((L $$unsorted) (U $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (hAPP_n1699378549t_bool (ord_gr660468384an_nat L) U)))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted) (L_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat K_2) L_2)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat K_2) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) L_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B))))))) (forall ((A_125 $$unsorted) (N_36 $$unsorted) (N_35 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_125))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_36) N_35)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_125)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_125) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real _let_1 N_35)) (hAPP_nat_real _let_1 N_36)))))))) (forall ((Ma $$unsorted) (X_3 $$unsorted)) (= (hBOOL (hAPP_f448129468l_bool (resSet Ma) X_3)) (forall ((Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (is_int Y2) (is_int Y1)) (=> (and (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y1) X_3)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y2) X_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong Y1) Y2) Ma))) (= Y2 Y1)))))) (forall ((A_158 $$unsorted) (B_119 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_158) B_119))) (=> (hBOOL (hAPP_nat_bool _let_1 A_158)) (hBOOL (hAPP_nat_bool _let_1 B_119)))))) (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (div_mod_nat M) N)) M))) (forall ((Y $$unsorted) (X $$unsorted) (N $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat N))) (=> (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) N) X) (= (hAPP_real_real (hAPP_n546711566l_real root N) X) Y)))) (forall ((K_1 $$unsorted)) (=> (is_int K_1) (= (= K_1 pls) (= (hAPP_int_int bit0 K_1) pls)))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int N_1) zero_zero_int)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real real_int N_1)) zero_zero_real)))) (forall ((A_18 $$unsorted) (C_5 $$unsorted) (B_14 $$unsorted)) (=> (not (= zero_z126310315umeral B_14)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_18) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral C_5) B_14))) B_14) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral C_5) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_18) B_14))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_1) one_one_int)) zEven)))) (forall ((C_58 $$unsorted) (D_11 $$unsorted) (A_136 $$unsorted) (B_105 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_136) B_105)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C_58) D_11)) (=> (hBOOL (hAPP_real_bool _let_1 A_136)) (=> (hBOOL (hAPP_real_bool _let_1 C_58)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_136) C_58)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_105) D_11))))))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_1))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (legacy_zgcd Ma) N_1))) (and (hBOOL (hAPP_int_bool _let_1 N_1)) (hBOOL (hAPP_int_bool _let_1 Ma)))))) (forall ((Xa_3 $$unsorted) (X_13 $$unsorted) (Y_10 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex Xa_3))) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex _let_1 X_13)) (hAPP_complex_complex _let_1 Y_10)) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_13) Y_10))))) (forall ((M $$unsorted)) (= (hAPP_nat_nat (div_mod_nat M) (hAPP_nat_nat suc zero_zero_nat)) zero_zero_nat)) (forall ((X_1 $$unsorted)) (=> (not (= (hAPP_real_real cos X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (isCont_real_real tan) X_1)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_f41603166t_bool (hAPP_f389116883t_bool cOMBB_1593174431ol_int P) Q) R) (hAPP_f54304608l_bool P (hAPP_i418383825t_bool Q R)))) (forall ((X_1 $$unsorted) (R_2 $$unsorted)) (= (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real R_2)) X_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) R_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X_1)) R_2)))) (= zero_z891286103de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int zero_z891286103de_int) _let_4)) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real sqrt X_1)) zero_zero_real)))) (forall ((V_14 $$unsorted) (B_166 $$unsorted) (C_97 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat V_14)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 B_166)) (hAPP_nat_nat _let_1 C_97)) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_166) C_97))))) (forall ((V_18 $$unsorted) (W_14 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real V_18)) (hAPP_int_real number267125858f_real W_14)) (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_18) W_14)))) (forall ((A_133 $$unsorted) (N_46 $$unsorted) (N_45 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_133))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_46) N_45)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_133)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_133) one_on1684967323de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int _let_1 N_45)) (hAPP_n522471361de_int _let_1 N_46)))))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3_1 $$unsorted)) (is_bool (tendsto_complex_real B_1_1 B_2_1 B_3_1))) (forall ((P_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_3))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A_3) B_2)) (not (and (hBOOL (hAPP_nat_bool prime P_3)) (hBOOL (hAPP_nat_bool _let_1 B_2)) (hBOOL (hAPP_nat_bool _let_1 A_3))))))) (forall ((X $$unsorted)) (= (hAPP_real_real inverse_inverse_real (hAPP_real_real sqrt X)) (hAPP_real_real sqrt (hAPP_real_real inverse_inverse_real X)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (and (= (hAPP_complex_real im X_1) (hAPP_complex_real im Y_2)) (= (hAPP_complex_real re Y_2) (hAPP_complex_real re X_1))) (= X_1 Y_2))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (=> (is_int N_1) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) K_1)) (= (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (and (is_int J_1) (is_int I_2)) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) J_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int J_1) K_1)) (= N_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) I_2)) J_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 I_2) J_1))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int N_1) K_1)) (hAPP_int_int (div_mod_int N_1) K_1))))))) (= _let_84 _let_10) (forall ((Xa_4 $$unsorted) (X_16 $$unsorted) (Y_13 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex Xa_4))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 X_16)) (hAPP_complex_complex _let_1 Y_13)) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X_16) Y_13))))) (forall ((F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real F N_2)))) (=> (hBOOL (summable_real F)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_f352196356l_real suminf_real F)))))) (forall ((A $$unsorted) (P_5 $$unsorted)) (= (image_275383677t_bool (multInvPair A P_5) (hAPP_i1948725293t_bool sRStar P_5)) (setS A P_5))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_1) X_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_2) Y_2))) (and (= Y_2 zero_zero_real) (= X_1 zero_zero_real)))) (forall ((Z_2 $$unsorted) (W_1 $$unsorted)) (=> (and (is_int W_1) (is_int Z_2)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z_2) W_1)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_2) W_1)) (not (= W_1 Z_2)))))) (= zero_z126310315umeral (hAPP_n1108039445umeral semiri1619134803umeral zero_zero_nat)) (= zero_zero_int _let_71) (forall ((A_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat suc A_3)) C_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_3) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat _let_1) C_1))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (div_mod_nat A_3) C_1)) (hAPP_nat_nat (div_mod_nat _let_1) C_1))) C_1))))) (forall ((B_1_1 $$unsorted)) (is_int (the_int B_1_1))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_n1699378549t_bool P (hAPP_nat_nat Q R)) (hAPP_n1699378549t_bool (hAPP_f618557131t_bool (hAPP_f1505651103t_bool cOMBB_800536526ol_nat P) Q) R))) (forall ((C_63 $$unsorted) (A_141 $$unsorted) (B_110 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_63))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int _let_1 A_141)) (hAPP_Q1762011733de_int _let_1 B_110))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_63)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_141) B_110)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (div_mod_int A_3) B_2))) (let ((_let_2 (hAPP_i1948725293t_bool ord_less_int B_2))) (=> (hBOOL (hAPP_int_bool _let_2 zero_zero_int)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int _let_1) zero_zero_int)) (hBOOL (hAPP_int_bool _let_2 _let_1))))))) (forall ((V_8 $$unsorted) (W_4 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_int_real number267125858f_real V_8)) (hAPP_int_real number267125858f_real W_4)) (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int V_8) W_4)))) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Rx_5))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real Lx_5) Ly_3)))) (= (hAPP_real_real _let_1 (hAPP_real_real _let_2 Ry_3)) (hAPP_real_real _let_2 (hAPP_real_real _let_1 Ry_3)))))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real A N_2)))) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real A (hAPP_nat_nat suc N_2))) (hAPP_nat_real A N_2)))) (hBOOL (tendsto_nat_real (hAPP_f292751352t_real (hAPP_f1607377819t_real cOMBB_1533963633al_nat (hAPP_f1509287679l_real big_co604158596t_real _let_1)) (hAPP_f618557131t_bool (hAPP_f1505651103t_bool cOMBB_800536526ol_nat (ord_at4362885an_nat zero_zero_nat)) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) one_one_nat))) (hAPP_f352196356l_real suminf_real _let_1) sequentially))))))) (= min (hAPP_int_int bit1 min)) (forall ((P_1 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (= (and (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Y_2) X_1)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int semiri1621563631at_int X_1)) (hAPP_nat_int semiri1621563631at_int Y_2))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)) (hBOOL (hAPP_int_bool P_1 zero_zero_int)))) (hBOOL (hAPP_int_bool P_1 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat X_1) Y_2)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_complex_real norm_norm_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_2) A_3))) (hAPP_complex_real norm_norm_complex B_2))) (hAPP_complex_real norm_norm_complex A_3)))) (forall ((Real1 $$unsorted) (Real2 $$unsorted)) (= zero_zero_nat (hAPP_complex_nat size_size_complex (hAPP_real_complex (hAPP_r265291036omplex complex Real1) Real2)))) (= zero_zero_complex _let_82) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_54)) pi)) (forall ((K_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_2) one_one_int) (hAPP_int_int succ K_2))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral D) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral X_2) Sa))))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral Z) X_2)) (= _let_1 _let_1)))))) (forall ((A_190 $$unsorted) (B_146 $$unsorted) (K_7 $$unsorted)) (=> (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_146) K_7) A_190) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int B_146) A_190)))) (forall ((M $$unsorted)) (= one_one_int (hAPP_int_int (legacy_zgcd M) one_one_int))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3_1 $$unsorted)) (is_bool (tendsto_real_real B_1_1 B_2_1 B_3_1))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A) B) zero_zero_complex) (or (= B zero_zero_complex) (= A zero_zero_complex)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_2) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_3) B_2))))) (forall ((N_11 $$unsorted) (A_7 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_7)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_7) one_one_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_7) (hAPP_nat_nat suc N_11))) one_one_rat))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (and (= N_1 one_one_nat) (= one_one_nat Ma)) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) N_1)))) (forall ((A_186 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int one_one_int) A_186))) (forall ((K_1 $$unsorted) (L $$unsorted)) (=> (and (is_int K_1) (is_int L)) (= (= K_1 L) (= (hAPP_int_int bit1 K_1) (hAPP_int_int bit1 L))))) (= (hAPP_real_real _let_29 _let_50) (hAPP_real_real tan _let_52)) (forall ((K_2 $$unsorted)) (=> (is_int K_2) (= (hAPP_int_int number_number_of_int K_2) K_2))) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real real_int N)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int X)) one_one_real))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int N) X)))) (forall ((B_5 $$unsorted) (Q_8 $$unsorted) (R_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_5) Q_8)) R_5)) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_5)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_8) zero_zero_int)))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) J_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat K_2) L_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) L_2)))))) (forall ((J_2 $$unsorted) (K_2 $$unsorted) (A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (zcong J_2))) (let ((_let_2 (multInv P_3))) (let ((_let_3 (hAPP_int_fun_int_int times_times_int A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong K_2) zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 zero_zero_int) P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int _let_3 (hAPP_int_int _let_2 J_2))) (hAPP_int_int _let_3 (hAPP_int_int _let_2 K_2))) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 K_2) P_3)))))))))))) (forall ((X_1 $$unsorted)) (= (= (hAPP_int_int abs_abs_int X_1) one_one_int) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int X_1) one_one_int)))) (= _let_80 one_one_real) (forall ((C_73 $$unsorted) (A_173 $$unsorted) (B_133 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_173) B_133)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_73)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_173) C_73)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_133) C_73)))))) (forall ((C_68 $$unsorted) (A_162 $$unsorted) (B_123 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_162) B_123)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C_68)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_162) C_68)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_123) C_68)))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A) B)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A) C)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B) C))))) (forall ((Ma $$unsorted) (W_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) W_1)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) (hAPP_nat_int semiri1621563631at_int Ma))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat nat W_1)) Ma))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool sRStar P_5))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) _let_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) _let_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (standardRes P_5) (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) Y_2))) _let_1)))))))) (forall ((P_3 $$unsorted)) (let ((_let_1 (normalize P_3))) (let ((_let_2 (hAPP_P1175774780nt_int product_snd_int_int P_3))) (let ((_let_3 (hAPP_P1175774780nt_int product_fst_int_int P_3))) (let ((_let_4 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int _let_3) _let_2))) (let ((_let_5 (hAPP_int_int uminus_uminus_int _let_4))) (let ((_let_6 (hAPP_int_fun_int_int div_div_int _let_2))) (let ((_let_7 (hAPP_int_fun_int_int div_div_int _let_3))) (let ((_let_8 (= _let_2 zero_zero_int))) (let ((_let_9 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) _let_2)))) (and (=> _let_9 (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int _let_7 _let_4)) (hAPP_int_int _let_6 _let_4)) _let_1)) (=> (not _let_9) (and (=> _let_8 (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) one_one_int) _let_1)) (=> (not _let_8) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int _let_7 _let_5)) (hAPP_int_int _let_6 _let_5)) _let_1))))))))))))))) (forall ((A_106 $$unsorted)) (= A_106 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex zero_zero_complex) A_106))) (forall ((B_148 $$unsorted) (A_192 $$unsorted) (C_84 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool dvd_dvd_rat A_192))) (=> (hBOOL (hAPP_rat_bool _let_1 C_84)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_148) C_84)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X_1))) (= (and (hBOOL (hAPP_nat_bool _let_1 Z_2)) (hBOOL (hAPP_nat_bool _let_1 Y_2))) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Y_2) Z_2)))))) (forall ((Y $$unsorted) (X $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_3)) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3)) (hAPP_real_real (hAPP_r1250527377l_real powr Y) A_3)))))))) (forall ((A_70 $$unsorted) (B_58 $$unsorted)) (let ((_let_1 (hAPP_C498520661umeral (div_mo1740067990umeral A_70) B_58))) (= (hAPP_C498520661umeral (div_mo1740067990umeral _let_1) B_58) _let_1))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_nat_int semiri1621563631at_int M))) (= _let_1 (hAPP_int_int abs_abs_int _let_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (= (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))) Y) (= zero_zero_real X)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real ln X))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (= X (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1)))) (= zero_zero_real Y)))) (forall ((C_77 $$unsorted) (B_137 $$unsorted) (A_177 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_77))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_137) A_177)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C_77) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A_177)) (hAPP_rat_rat _let_1 B_137))))))) (forall ((X_24 $$unsorted) (N_32 $$unsorted)) (=> (or (= one_one_real X_24) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real X_24) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_24) N_32))))) (forall ((S $$unsorted)) (= (hBOOL (hAPP_f54304608l_bool finite_finite_nat S)) (exists ((K $$unsorted)) (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le1568362934t_bool S) (hAPP_n1699378549t_bool ord_lessThan_nat K)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) Y_2))) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) Y_2)) (hBOOL (hAPP_nat_bool even_odd_even_nat X_1))))) (forall ((A_211 $$unsorted) (M_26 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_211) one_one_real)) M_26) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_211) M_26)) M_26))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Lx_1))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 Rx_1)) Ry_1) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real Rx_1) Ry_1))))) (= (natfloor one_one_real) one_one_nat) (forall ((M $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)))) (let ((_let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) K_2))) (=> (not (= M _let_2)) (=> (hBOOL (hAPP_nat_bool _let_1 _let_2)) (hBOOL (hAPP_nat_bool _let_1 K_2))))))) (forall ((R_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real R_3) (hAPP_int_real real_int (archim856651990g_real R_3))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) E_2)) C)) D)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) E_2)) C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B) E_2)) D))))) (forall ((W_8 $$unsorted)) (let ((_let_1 (hAPP_int_rat number_number_of_rat W_8))) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat _let_1) _let_1)))) (forall ((A_196 $$unsorted) (N_63 $$unsorted)) (let ((_let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_196) N_63))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_1) A_196) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_196) _let_1)))) (forall ((B_55 $$unsorted) (A_67 $$unsorted)) (= A_67 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_55) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_67) B_55))) (hAPP_Q1762011733de_int (div_mo231679042de_int A_67) B_55)))) (forall ((X_36 $$unsorted) (Y_28 $$unsorted) (Z_9 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat X_36))) (= (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat Y_28) Z_9)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 Y_28)) (hAPP_rat_rat _let_1 Z_9))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) (hAPP_nat_nat suc Ma))) (= Ma N_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_P1975530577nt_int (hAPP_P1145851913nt_int (hAPP_b40753821nt_int if_Pro1731782967nt_int fTrue) X) Y) X)) (not (= one_on1645066479umeral zero_z126310315umeral)) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (hBOOL (monoseq_real A)) (hBOOL (tendsto_nat_real (hAPP_f292751352t_real (hAPP_f1607377819t_real cOMBB_1533963633al_nat (hAPP_f1509287679l_real big_co604158596t_real _let_1)) (hAPP_f618557131t_bool (hAPP_f1505651103t_bool cOMBB_800536526ol_nat (ord_at4362885an_nat zero_zero_nat)) (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_f352196356l_real suminf_real _let_1) sequentially)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat M))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat suc N)))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat N))) (= (hAPP_real_real (hAPP_n546711566l_real root N) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) N)) X))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral semiri1619134803umeral Ma)) (hAPP_n1108039445umeral semiri1619134803umeral N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) E_2)) C)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) E_2)) D))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B) A)) E_2)) D))))) (forall ((C_80 $$unsorted) (A_187 $$unsorted) (B_143 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool dvd_dvd_real A_187))) (=> (hBOOL (hAPP_real_bool _let_1 B_143)) (=> (hBOOL (hAPP_real_bool _let_1 C_80)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_143) C_80))))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) (hAPP_real_real exp_real X_1))))) (forall ((A_94 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A_94) A_94) zero_zero_complex)) (forall ((A_194 $$unsorted) (B_150 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_194) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_150) A_194)))) (forall ((X $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_int_real real_int A_3))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (archim856651990g_real X)) A_3)))) (forall ((A_9 $$unsorted) (N_14 $$unsorted) (B_7 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_14))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_9) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat B_7) _let_1))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) B_7)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_9) B_7)))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int pred K_1)) L)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) L)))) (forall ((K_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int bit0 K_1))) (hBOOL (hAPP_int_bool _let_1 K_1))))) (forall ((A_218 $$unsorted) (B_161 $$unsorted) (C_90 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_218) B_161)) C_90) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_218) C_90)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_161) C_90)))) (forall ((A_203 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_203) zero_zero_complex) zero_zero_complex)) (hBOOL (hAPP_int_bool nat_is_nat one_one_int)) (forall ((X_37 $$unsorted)) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_37) one_one_nat) X_37)) (forall ((C_70 $$unsorted) (A_164 $$unsorted) (B_125 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_70))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_164) B_125)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_70)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A_164)) (hAPP_int_int _let_1 B_125))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P252494982t_bool (hAPP_f291087797t_bool (hAPP_f214467655t_bool cOMBB_182850971nt_int P) Q) R) (hAPP_i1948725293t_bool P (hAPP_P1175774780nt_int Q R)))) (forall ((B_2 $$unsorted) (Bq $$unsorted) (Br $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted) (Aq $$unsorted) (Ar $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Ar) Br))) (=> (is_int C_1) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 C_1) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Aq) Ar))) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel B_2 C_1) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Bq) Br))) (=> (not (= C_1 zero_zero_int)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2) C_1) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Aq) Bq)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int _let_1) C_1))) (hAPP_int_int (div_mod_int _let_1) C_1)))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_1))) (= (hAPP_nat_nat (nat_case_nat _let_1 (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat suc) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat ord_max_nat) N_1))) Ma) (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat Ma) _let_1)))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (div_mod_nat M) N)) K_2))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted) (W_13 $$unsorted) (W $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_13) W)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_4) Z_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int W_13) Z_4)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int W) Z_1)))))) (forall ((X_42 $$unsorted) (Y_30 $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_42) X_42)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_30) Y_30))) zero_zero_real)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X)) (= X Y)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_complex_real im X))) (let ((_let_3 (hAPP_complex_real re X))) (let ((_let_4 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_3) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_2) _let_1)))) (= (hAPP_complex_complex invers1449016382omplex X) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real _let_3) _let_4)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real uminus_uminus_real _let_2)) _let_4)))))))) (forall ((X_1 $$unsorted)) (=> (is_int X_1) (= (exists ((A_2 $$unsorted) (B_4 $$unsorted)) (and (= (hAPP_P1175774780nt_int twoSqu1907779896sum2sq (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A_2) B_4)) X_1) (is_int B_4) (is_int A_2))) (hBOOL (hAPP_int_bool twoSqu1770640450sum2sq X_1))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (= zero_zero_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A) B)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3_1 $$unsorted)) (is_bool (tendsto_nat_real B_1_1 B_2_1 B_3_1))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_int_bool even_odd_even_int Y)) (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y))))) (forall ((B_43 $$unsorted) (B_42 $$unsorted) (A_52 $$unsorted) (C_23 $$unsorted) (A_51 $$unsorted)) (=> (= (hAPP_Q1762011733de_int (div_mo231679042de_int A_52) C_23) (hAPP_Q1762011733de_int (div_mo231679042de_int A_51) C_23)) (=> (= (hAPP_Q1762011733de_int (div_mo231679042de_int B_42) C_23) (hAPP_Q1762011733de_int (div_mo231679042de_int B_43) C_23)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_51) B_42)) C_23) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_52) B_43)) C_23))))) (forall ((A_239 $$unsorted) (B_167 $$unsorted) (V_15 $$unsorted)) (let ((_let_1 (hAPP_int_rat number_number_of_rat V_15))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_239) B_167)) _let_1) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_239) _let_1)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_167) _let_1))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int W_1) one_one_int)) Z_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) Z_2)))) (forall ((B_130 $$unsorted) (A_170 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_170)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_130) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_130) A_170)) zero_zero_int))))) (= (hAPP_real_real sin _let_33) _let_51) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real tan X))))))) (forall ((C_71 $$unsorted) (B_126 $$unsorted) (A_165 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B_126) A_165)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C_71) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_165) C_71)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_126) C_71)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (or (= zero_zero_real A) (= B zero_zero_real)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) B) zero_zero_real))) (forall ((N_62 $$unsorted)) (= one_on1684967323de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int one_on1684967323de_int) N_62))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_n546711566l_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat P) Q) R) (hAPP_r1250527377l_real P (hAPP_nat_real Q R)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (hBOOL (hAPP_real_bool (isCont_real_real (hAPP_n546711566l_real root N_1)) X_1)))) (forall ((A_60 $$unsorted) (B_51 $$unsorted) (C_30 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral A_60))) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral _let_1 B_51)) C_30) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (div_mo1740067990umeral B_51) C_30))) C_30)))) (forall ((B_129 $$unsorted) (A_169 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_169)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_129) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_169) B_129)) zero_zero_rat))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (=> (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) one_one_real) (hAPP_real_real ln X)) (= X one_one_real)))) (not (= one_one_rat zero_zero_rat)) (forall ((B $$unsorted) (C $$unsorted) (A $$unsorted) (D $$unsorted)) (=> (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A) D)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat B) C) one_one_nat) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A) C) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B) D)) (and (= B A) (= D C)))))) (forall ((V_17 $$unsorted) (V_16 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_16)) (=> (hBOOL (hAPP_int_bool _let_1 V_17)) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_16) V_17)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat V_16)) (hAPP_int_nat number_number_of_nat V_17))))))) (forall ((N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat N) zero_zero_nat) N)) (forall ((B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int min))) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int _let_1) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B_2) one_one_int)) (negDivAlg _let_1 B_2)))) (forall ((P_1 $$unsorted)) (= (exists ((X1 $$unsorted)) (hBOOL (hAPP_nat_bool P_1 X1))) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_nat_bool P_1 (hAPP_int_nat nat X_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2)) (is_int X_2))))) (forall ((X $$unsorted)) (=> (is_int X) (= X (hAPP_int_int succ (hAPP_int_int pred X))))) (forall ((C_80 $$unsorted) (A_187 $$unsorted) (B_143 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat A_187))) (=> (hBOOL (hAPP_nat_bool _let_1 B_143)) (=> (hBOOL (hAPP_nat_bool _let_1 C_80)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_143) C_80))))))) (forall ((M_10 $$unsorted) (N_24 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat semiri984289939at_nat M_10)) (hAPP_nat_nat semiri984289939at_nat N_24))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_10) N_24)))) (forall ((B_141 $$unsorted) (A_181 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (or (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_141) zero_zero_int)) (hBOOL (hAPP_int_bool _let_1 A_181))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_181) zero_zero_int)) (hBOOL (hAPP_int_bool _let_1 B_141)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_181) B_141)) zero_zero_int))))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_2))) (=> (= one_one_int (hAPP_int_int (legacy_zgcd N) K_2)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N))) (hBOOL (hAPP_int_bool _let_1 M)))))) (= one_on1645066479umeral (hAPP_n1108039445umeral semiri1619134803umeral one_one_nat)) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real min)) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) one_one_real)) (hBOOL (hAPP_real_bool (isCont_real_real arcsin) X_1))))) (hBOOL (hAPP_nat_bool even_odd_even_nat zero_zero_nat)) (forall ((A $$unsorted) (B $$unsorted) (N_1 $$unsorted)) (=> (not (= zero_zero_nat N_1)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) N_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B) N_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A) B))))) (forall ((M_27 $$unsorted) (A_212 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_212) one_on1684967323de_int)) M_27) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int M_27) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_212) M_27)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc M))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (=> (not (= _let_1 N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat _let_1) N)))))) (forall ((L_2 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 K_2)) (=> (hBOOL (hAPP_int_bool _let_1 L_2)) (= (posDivAlg K_2 L_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int K_2) L_2)) (hAPP_int_int (div_mod_int K_2) L_2))))))) (forall ((X $$unsorted) (M $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) Y)) M) (hAPP_int_int (div_mod_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (div_mod_int X) M)) Y)) M))) (forall ((B_74 $$unsorted) (A_86 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_86) zero_zero_nat)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat B_74) zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_86) B_74)) zero_zero_nat))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (bezw X Y))) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_P1175774780nt_int product_fst_int_int _let_1)) (hAPP_nat_int semiri1621563631at_int X))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_P1175774780nt_int product_snd_int_int _let_1)) (hAPP_nat_int semiri1621563631at_int Y)))))) (forall ((M_17 $$unsorted) (N_30 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int M_17))) (let ((_let_2 (hAPP_n522471361de_int _let_1 N_30))) (and (=> (= zero_zero_nat N_30) (= _let_2 one_on1684967323de_int)) (=> (not (= N_30 zero_zero_nat)) (= _let_2 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int M_17) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_30) one_one_nat))))))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int bit0 (hAPP_int_int succ K_2)) (hAPP_int_int succ (hAPP_int_int bit1 K_2)))) (hBOOL (hAPP_int_bool _let_81 _let_66)) (forall ((P_5 $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool prime (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_5) N_1))) (and (= N_1 one_one_nat) (hBOOL (hAPP_nat_bool prime P_5))))) (forall ((N_61 $$unsorted) (X_29 $$unsorted) (Y_23 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_29) Y_23)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_29) N_61)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_23) N_61))))) (forall ((A_110 $$unsorted) (B_88 $$unsorted) (C_48 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_110))) (=> (and (is_int C_48) (is_int B_88)) (=> (= (hAPP_int_int _let_1 C_48) (hAPP_int_int _let_1 B_88)) (= B_88 C_48))))) (forall ((V_20 $$unsorted) (W_16 $$unsorted) (Z_15 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_20) W_16))) Z_15) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex V_20)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex W_16)) Z_15)))) (forall ((B_71 $$unsorted) (A_83 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_83)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_71)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_83) B_71))))))) (forall ((X $$unsorted) (Y $$unsorted) (C_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C_1) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real C_1) (hAPP_real_real abs_abs_real Y)))) (= zero_zero_real X)))) (forall ((A_146 $$unsorted)) (= one_one_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_146) zero_zero_nat))) (forall ((A_211 $$unsorted) (M_26 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_211) one_on1684967323de_int)) M_26) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_211) M_26)) M_26))) (forall ((Z_12 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Z_12) (hAPP_int_rat number_number_of_rat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat Z_12) Z_12))) (forall ((A_182 $$unsorted)) (=> (is_int A_182) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_182) one_one_nat) A_182))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat plus_plus_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat fact_fact_nat) _let_1))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (and (not (= N_1 zero_zero_nat)) (= Ma zero_zero_nat)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Ma) N_1)))) (forall ((X_38 $$unsorted) (P_8 $$unsorted) (Q_12 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int X_38))) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int (hAPP_n522471361de_int _let_1 P_8)) Q_12) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_8) Q_12))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_2))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N))) (hBOOL (hAPP_nat_bool _let_1 N))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int X))) (not (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) N)))))) (forall ((W_5 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_5))) (let ((_let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat zero_zero_nat) _let_1))) (let ((_let_3 (= _let_1 zero_zero_nat))) (and (=> (not _let_3) (= zero_zero_nat _let_2)) (=> _let_3 (= _let_2 one_one_nat))))))) (forall ((N_52 $$unsorted) (A_150 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_150)) (hBOOL (hAPP_real_bool _let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_150) N_52)))))) (forall ((N_56 $$unsorted)) (= one_one_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_56)))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real exp_real X)))) (forall ((C $$unsorted) (D $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat B))) (let ((_let_2 (hAPP_rat_fun_rat_rat times_times_rat A))) (= (not (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_2 D)) (hAPP_rat_rat _let_1 C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_2 C)) (hAPP_rat_rat _let_1 D)))) (and (not (= A B)) (not (= D C))))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) (archim1246769320r_real X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int A)) one_one_real)) X_1)))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1))))))) (forall ((F $$unsorted) (N_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (= (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat minus_minus_real) F)) R_2)) _let_1) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real F) _let_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_1)) R_2))))) (forall ((A_3 $$unsorted)) (not (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat zero_zero_nat) A_3)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) zero_zero_nat)))))) (forall ((N_56 $$unsorted)) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_int_rat number_number_of_rat min)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_56)) one_one_rat)) (forall ((Q_8 $$unsorted) (R_5 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (divmod_int_rel A_3 B_2))) (=> (and (is_int R_3) (is_int B_2) (is_int R_5)) (=> (hBOOL (hAPP_P603027463t_bool _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))) (=> (hBOOL (hAPP_P603027463t_bool _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_8) R_5))) (=> (not (= zero_zero_int B_2)) (= R_3 R_5))))))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_nat_nat fact_fact_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) (hAPP_nat_nat fact_fact_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) one_one_nat)))))) (forall ((A_183 $$unsorted) (M_22 $$unsorted) (N_57 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_183))) (= (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_22) N_57)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int _let_1 M_22)) N_57)))) (forall ((B_94 $$unsorted) (C_52 $$unsorted) (A_116 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int B_94))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_116)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C_52)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_116) C_52))))))) (forall ((M_8 $$unsorted) (N_22 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_nat_complex semiri2020571505omplex M_8)) (hAPP_nat_complex semiri2020571505omplex N_22)) (hAPP_nat_complex semiri2020571505omplex (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_8) N_22)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int fact_fact_int X)))))) (forall ((X_2 $$unsorted)) (= (hAPP_nat_real (diffs_real cos_coeff) X_2) (hAPP_real_real uminus_uminus_real (hAPP_nat_real sin_coeff X_2)))) (forall ((A_233 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex pls)) A_233) A_233)) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (= zero_zero_real (hAPP_real_real cos X)) (exists ((N_2 $$unsorted)) (and (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_2)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X) (not (hBOOL (hAPP_nat_bool even_odd_even_nat N_2)))))))) (forall ((A $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) A)) zero_zero_int)))) (forall ((X_40 $$unsorted) (N_69 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex X_40))) (let ((_let_2 (hAPP_nat_complex _let_1 N_69))) (= (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_69)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex _let_2) _let_2))))) (forall ((U $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (J $$unsorted) (I_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat J) I_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I_1) U)) Ma)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J) U)) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat I_1) J)) U)) Ma)) N_1))))) (forall ((A_189 $$unsorted) (B_145 $$unsorted) (C_82 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_189) B_145)) C_82)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_189) C_82)))) (forall ((Ma $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) W_1)))) (=> (is_int W_1) (= (= Ma (hAPP_int_nat nat W_1)) (and (=> _let_1 (= W_1 (hAPP_nat_int semiri1621563631at_int Ma))) (=> (not _let_1) (= Ma zero_zero_nat))))))) (forall ((C_74 $$unsorted) (A_174 $$unsorted) (B_134 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_74))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_174) B_134)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_74)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A_174)) (hAPP_rat_rat _let_1 B_134))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool even_odd_even_int X_1)))) (let ((_let_2 (hBOOL (hAPP_int_bool even_odd_even_int Y_2)))) (= (or (and _let_2 _let_1) (and (not _let_2) (not _let_1))) (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_1) Y_2))))))) (forall ((P_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat Ma) N_1))) (or (exists ((Q_4 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat N_1))) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 Q_4)) Ma)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc Q_4)))) (hBOOL (hAPP_nat_bool P_1 Q_4))))) (and (= zero_zero_nat N_1) (hBOOL (hAPP_nat_bool P_1 zero_zero_nat)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) one_one_real)) (= (hAPP_real_real cos (hAPP_real_real arcsin X)) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))))) (forall ((R_3 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (of_real_complex R_3)) ii) (hAPP_real_complex (hAPP_r265291036omplex complex zero_zero_real) R_3))) (forall ((A_19 $$unsorted) (B_15 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_19) B_15)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_19) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int B_15) A_19)) B_15))) (forall ((B_53 $$unsorted) (A_65 $$unsorted) (C_32 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_65) C_32) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_53) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_65) B_53))) (hAPP_C498520661umeral (div_mo1740067990umeral A_65) B_53))) C_32))) (forall ((Z_1 $$unsorted)) (exists ((A_2 $$unsorted) (R_1 $$unsorted)) (= Z_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (of_real_complex R_1)) (expi A_2))))) (= one_one_real _let_80) (forall ((A_37 $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_37) zero_zero_nat))) (forall ((N_49 $$unsorted) (A_147 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int one_on1684967323de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_147)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_147) N_49)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int X))) (= (hAPP_int_int _let_1 (hAPP_int_int uminus_uminus_int Y)) (hAPP_int_int _let_1 Y)))) (forall ((B_74 $$unsorted) (A_86 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_86) zero_z126310315umeral)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral B_74) zero_z126310315umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_86) B_74)) zero_z126310315umeral))))) (forall ((X $$unsorted)) (=> (not (= zero_zero_real X)) (= one_one_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real inverse_inverse_real X)) X)))) (forall ((A_219 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_219) zero_z891286103de_int) A_219)) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N) zero_zero_nat))) (exists ((K_4 $$unsorted)) (and (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real norm_norm_real (hAPP_complex_real re X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) K_4)))) (hBOOL (hAPP_f448129468l_bool (nat_tr876908586nt_nat nat) _let_11)) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= zero_zero_real (hAPP_real_real cos X_2)) (forall ((Y_1 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y_1)) (= zero_zero_real (hAPP_real_real cos Y_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_1) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (= X_2 Y_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_2)))) (forall ((D $$unsorted) (Ta $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int D))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int uminus_uminus_int Ta))) (hBOOL (hAPP_int_bool _let_1 Ta))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_int (hAPP_P2110489235nt_int P R) Q) (hAPP_P1175774780nt_int (hAPP_i61245889nt_int (hAPP_f578362681nt_int cOMBC_1417754532nt_int P) Q) R))) (forall ((B_92 $$unsorted) (A_114 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_114) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B_92) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_114) B_92)) zero_zero_real))))) (forall ((A_44 $$unsorted) (B_35 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_44) B_35)) B_35) (hAPP_int_int (div_mod_int A_44) B_35))) (forall ((A_49 $$unsorted) (B_40 $$unsorted) (C_21 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_49))) (= (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 B_40)) C_21) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int B_40) C_21))) C_21)))) (forall ((B_43 $$unsorted) (B_42 $$unsorted) (A_52 $$unsorted) (C_23 $$unsorted) (A_51 $$unsorted)) (=> (= (hAPP_int_int (div_mod_int A_51) C_23) (hAPP_int_int (div_mod_int A_52) C_23)) (=> (= (hAPP_int_int (div_mod_int B_42) C_23) (hAPP_int_int (div_mod_int B_43) C_23)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_51) B_42)) C_23) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_52) B_43)) C_23))))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (let ((_let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N)))) (and (=> (= zero_zero_nat K_2) (= _let_2 zero_zero_nat)) (=> (not (= K_2 zero_zero_nat)) (= _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N))))))) (forall ((N $$unsorted)) (=> (is_int N) (= (archim1246769320r_real (hAPP_int_real real_int N)) N))) (forall ((M_9 $$unsorted) (N_23 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_9) N_23)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat semiri151668891at_rat M_9)) (hAPP_nat_rat semiri151668891at_rat N_23))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_real (hAPP_f292751352t_real (hAPP_f1607377819t_real cOMBB_1533963633al_nat P) Q) R) (hAPP_f1406902706l_real P (hAPP_n1699378549t_bool Q R)))) (forall ((N $$unsorted) (F_3 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int F_3))) (=> (hBOOL (hAPP_int_bool _let_1 M)) (=> (hBOOL (hAPP_int_bool _let_1 N)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (div_mod_int M) N))))))) (forall ((C_59 $$unsorted) (D_12 $$unsorted) (A_137 $$unsorted) (B_106 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_137) B_106)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int C_59) D_12)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_137)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) C_59)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_137) C_59)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_106) D_12)))))))) (forall ((K_2 $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int K_2)) zero_zero_int)))) (= (hAPP_nat_nat semiri984289939at_nat zero_zero_nat) zero_zero_nat) (forall ((C_38 $$unsorted) (A_96 $$unsorted) (B_78 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat C_38))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_96) B_78)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 A_96)) (hAPP_nat_nat _let_1 B_78)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_i1732201573de_int number1226105091de_int X_1))) (let ((_let_2 (hAPP_i1732201573de_int number1226105091de_int Y_2))) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int _let_1) _let_2)) (= zero_z891286103de_int (hAPP_Q1762011733de_int (div_mo231679042de_int _let_2) _let_1)))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (= (archim856651990g_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_int_real real_int A_3))) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (archim856651990g_real X)) A_3))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 Z_1)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Y) Z_1)))))) (forall ((D $$unsorted) (F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real F X_1) L)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D)) (=> (forall ((Y_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_1) Y_1))) D)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real F X_1)) (hAPP_real_real F Y_1))))) (= zero_zero_real L))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat M))) (= (hAPP_nat_nat _let_1 N) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N))))) (forall ((X $$unsorted)) (= (hAPP_real_real uminus_uminus_real (hAPP_int_real real_int X)) (hAPP_int_real real_int (hAPP_int_int uminus_uminus_int X)))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (bolzano_bisect P_1 A B))) (let ((_let_2 (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)))) (=> _let_2 (=> _let_2 (=> _let_2 (=> (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat minus_minus_real) (hAPP_f73570213t_real (hAPP_f918606171t_real cOMBB_64450052al_nat produc1935615926l_real) _let_1))) (hAPP_f73570213t_real (hAPP_f918606171t_real cOMBB_64450052al_nat produc556554744l_real) _let_1)) zero_zero_real sequentially)) (exists ((L_1 $$unsorted)) (let ((_let_1 (bolzano_bisect P_1 A B))) (and (hBOOL (tendsto_nat_real (hAPP_f73570213t_real (hAPP_f918606171t_real cOMBB_64450052al_nat produc1935615926l_real) _let_1) L_1 sequentially)) (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real L_1) (hAPP_P731461727l_real produc556554744l_real (hAPP_n332733730l_real (bolzano_bisect P_1 A B) N_2))))) (hBOOL (tendsto_nat_real (hAPP_f73570213t_real (hAPP_f918606171t_real cOMBB_64450052al_nat produc556554744l_real) _let_1) L_1 sequentially)) (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_P731461727l_real produc1935615926l_real (hAPP_n332733730l_real (bolzano_bisect P_1 A B) N_2))) L_1))))))))))))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W))) (let ((_let_2 (posDivAlg one_one_int _let_1))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) _let_1)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) _let_1)) (and (=> (not _let_3) (= (hAPP_P1975530577nt_int (adjust _let_1) (posDivAlg one_one_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) _let_1))) _let_2)) (=> _let_3 (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) one_one_int) _let_2)))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r474017924t_real (hAPP_f1501741374t_real (hAPP_f1135648319t_real cOMBC_1329014627t_real P) Q) R) (hAPP_f1676298106t_real (hAPP_r50993370t_real P R) Q))) (= one_one_complex (hAPP_nat_complex semiri2020571505omplex one_one_nat)) (forall ((X_3 $$unsorted)) (= (forall ((J_1 $$unsorted)) (exists ((M_3 $$unsorted)) (forall ((M_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_3) M_1)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_3) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_nat_real X_3 M_1)) (hAPP_nat_real X_3 N_2)))) (hAPP_real_real inverse_inverse_real (hAPP_nat_real real_nat (hAPP_nat_nat suc J_1))))))))))) (hBOOL (cauchy_real X_3)))) (hBOOL (hAPP_int_bool _let_49 _let_79)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1250527377l_real P (hAPP_real_real Q R)) (hAPP_r1250527377l_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real P) Q) R))) (forall ((Z_8 $$unsorted) (X_23 $$unsorted) (Y_18 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int X_23))) (=> (hBOOL (hAPP_int_bool _let_1 Y_18)) (=> (hBOOL (hAPP_int_bool _let_1 Z_8)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Y_18) Z_8))))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X_1)) (=> (hBOOL (hAPP_real_bool _let_1 Y_2)) (= (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) Y_2) zero_zero_real) (and (= X_1 zero_zero_real) (= Y_2 zero_zero_real))))))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B))))))) (forall ((B_73 $$unsorted) (A_85 $$unsorted) (C_36 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral B_73))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_36)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_85)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_85) C_36))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3))) (let ((_let_2 (hAPP_nat_nat _let_1 B_2))) (= _let_2 (hAPP_nat_nat _let_1 _let_2))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int X) Y)) (= (hAPP_int_int abs_abs_int X) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y)))) (forall ((X $$unsorted) (N $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int abs_abs_int X)) N)))) (not (hBOOL (hAPP_int_bool _let_16 min))) (forall ((X $$unsorted)) (= (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_real_real uminus_uminus_real (hAPP_real_real sin X)))) (forall ((B_2 $$unsorted) (Q_8 $$unsorted) (R_5 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int B_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 Q_8)) R_5)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 Q_2)) R_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_5) B_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_3) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_8) Q_2)))))))) (= (hAPP_int_int pred pls) min) (forall ((M_14 $$unsorted) (D_4 $$unsorted)) (=> (= zero_zero_nat (hAPP_nat_nat (div_mod_nat M_14) D_4)) (exists ((Q_4 $$unsorted)) (= M_14 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat D_4) Q_4))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_2) _let_1)))) (or (not (= zero_zero_real X_1)) (not (= zero_zero_real Y_2)))))) (forall ((A_186 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat one_one_rat) A_186))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat M))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_1 M)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (Qr $$unsorted)) (let ((_let_1 (hAPP_P1654798560at_nat product_fst_nat_nat Qr))) (let ((_let_2 (= N_1 zero_zero_nat))) (let ((_let_3 (hAPP_P1654798560at_nat product_snd_nat_nat Qr))) (let ((_let_4 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)))) (= (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel Ma N_1) Qr)) (and (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_1)) _let_3) Ma) (=> (not _let_2) (and (=> _let_4 (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat _let_3) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) _let_3)))) (=> (not _let_4) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) _let_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat _let_3) zero_zero_nat)))))) (=> _let_2 (= zero_zero_nat _let_1))))))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_P1555980039t_bool B_1_1 B_2_1))) (forall ((D $$unsorted)) (= (collec1347809874nt_int (produc93441119t_bool (hAPP_f428220345t_bool (hAPP_f1878066172t_bool cOMBS_1720984575t_bool (hAPP_f1315737299t_bool (hAPP_f538565589t_bool cOMBB_1211207212ol_int cOMBB_bool_bool_int) (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int D)))) ord_less_int))) (int_ge_less_than D))) (forall ((A_33 $$unsorted) (B_27 $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_33) B_27)) B_27))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) zero_zero_real)) (= zero_zero_nat (natceiling X)))) (forall ((V $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (let ((_let_2 (not (hBOOL (hAPP_int_bool nat_neg _let_1))))) (= (and (=> _let_2 (= (hAPP_int_nat nat _let_1) N_1)) _let_2) (= (hAPP_nat_nat suc N_1) (hAPP_int_nat number_number_of_nat V)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))) (=> (hBOOL (hAPP_nat_bool even_odd_even_nat X)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X) _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat suc X)) _let_1))))) (forall ((A_226 $$unsorted) (B_163 $$unsorted) (C_92 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real A_226))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 B_163)) C_92) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 C_92)) B_163)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) zEven)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) B)) zOdd))))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Lx_3))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 Ly_1)) Rx_3) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 Rx_3)) Ly_1)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (hBOOL (monoseq_real A)) (=> (hBOOL (tendsto_nat_real A X_1 sequentially)) (or (and (forall ((M_1 $$unsorted) (N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_1) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real A M_1)) (hAPP_nat_real A N_2))))) (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real A N_2)) X_1)))) (and (forall ((M_1 $$unsorted) (N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_1) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real A N_2)) (hAPP_nat_real A M_1))))) (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) (hAPP_nat_real A N_2))))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_n332733730l_real (bolzano_bisect P_1 A B) N_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_P731461727l_real produc556554744l_real _let_1)) (hAPP_P731461727l_real produc1935615926l_real _let_1)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B) A)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_1)))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_2))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (hBOOL (hAPP_nat_bool _let_1 N))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2)))) (= (and (not (= X_1 Y_2)) _let_1) (and _let_1 (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_2) X_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos X)) (hAPP_real_real cos Y))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real sin X)) (hAPP_real_real sin Y))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A))) (=> (and (is_int C) (is_int B)) (= (= (hAPP_int_int _let_1 B) (hAPP_int_int _let_1 C)) (= B C))))) (forall ((Y_8 $$unsorted) (Z_6 $$unsorted) (X_11 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat Z_6))) (=> (hBOOL (hAPP_nat_bool _let_1 X_11)) (=> (hBOOL (hAPP_nat_bool _let_1 Y_8)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X_11) Z_6)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat Y_8) Z_6)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_11) Y_8)) Z_6)))))) (forall ((A_195 $$unsorted) (B_151 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real A_195) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_195) B_151)))) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (hBOOL (hAPP_complex_bool P_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex L) X_2)))) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex L) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X_2) zero_zero_complex))) (hBOOL (hAPP_complex_bool P_1 X_2)))))) (forall ((A_234 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_234) A_234) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_234) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real sin X_1)) (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_r195310020l_real (hAPP_f2126667875l_real cOMBC_746811033l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) zero_zero_real)) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min))) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat div_div_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat minus_minus_nat) (hAPP_nat_nat suc zero_zero_nat)))) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat))))) (hAPP_r474017924t_real power_power_real X_1))) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real inverse_inverse_real (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real abs_abs_real X_1)) N_1))))) (forall ((B_130 $$unsorted) (A_170 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_170)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_130) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_130) A_170)) zero_zero_rat))))) (forall ((B_116 $$unsorted) (A_155 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_155)) (=> (hBOOL (hAPP_rat_bool _let_1 B_116)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_155) B_116))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat A) B))) (not (or (and (not (hBOOL (hAPP_nat_bool P_1 zero_zero_nat))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A) B))) (exists ((D_2 $$unsorted)) (and (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B) D_2) A) (not (hBOOL (hAPP_nat_bool P_1 D_2))))))))) (forall ((Q_2 $$unsorted)) (let ((_let_1 (hAPP_rat_rat abs_abs_rat Q_2))) (let ((_let_2 (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat Q_2) zero_zero_rat)))) (and (=> _let_2 (= _let_1 (hAPP_rat_rat uminus_uminus_rat Q_2))) (=> (not _let_2) (= _let_1 Q_2)))))) (forall ((K_2 $$unsorted)) (= (ratreal (hAPP_int_rat number_number_of_rat K_2)) (hAPP_int_real number267125858f_real K_2))) (forall ((N_1 $$unsorted)) (= (= N_1 zero_zero_nat) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) (hAPP_nat_nat suc zero_zero_nat))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_1))) (let ((_let_2 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_r195310020l_real (hAPP_f2126667875l_real cOMBC_746811033l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) zero_zero_real)) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min))) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat div_div_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat minus_minus_nat) (hAPP_nat_nat suc zero_zero_nat)))) (hAPP_int_nat number_number_of_nat _let_2))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat))))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real T) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) (hAPP_int_real number267125858f_real _let_2))) (hAPP_nat_real real_nat N_1))) pi)))) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1))) (hAPP_real_real sin X_1)))))) (forall ((N_11 $$unsorted) (A_7 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) A_7)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_7) one_on1645066479umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_7) (hAPP_nat_nat suc N_11))) one_on1645066479umeral))))) (forall ((Z_5 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z_5) zero_zero_int)) (hBOOL (hAPP_int_bool nat_neg Z_5)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) zero_zero_int)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B)) zero_zero_rat))))) (forall ((P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int bit1 pls))) (let ((_let_2 (hAPP_int_fun_int_int minus_minus_int P_3))) (let ((_let_3 (hAPP_int_int bit0 _let_1))) (let ((_let_4 (hAPP_int_nat nat (hAPP_int_int _let_2 (hAPP_int_int number_number_of_int _let_3))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 _let_3))) P_3)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_4) _let_4) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat nat (hAPP_int_int _let_2 one_one_int))) (hAPP_int_nat nat (hAPP_int_int _let_2 (hAPP_int_int number_number_of_int (hAPP_int_int bit1 _let_1))))))))))))) (forall ((N $$unsorted)) (= (hAPP_nat_nat suc (hAPP_nat_nat suc N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N))) (forall ((C_68 $$unsorted) (A_162 $$unsorted) (B_123 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_162) B_123)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C_68)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_162) C_68)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_123) C_68)))))) (forall ((N $$unsorted) (X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real real_nat N)) (hAPP_nat_real real_nat X))) (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) X)))) one_one_real))) (forall ((X_47 $$unsorted) (Y_35 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_47) X_47)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y_35) Y_35))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) (hAPP_nat_nat suc N_1))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1173902867t_bool P (hAPP_r1134773055l_bool Q R)) (hAPP_r847664445t_bool (hAPP_f1920544743t_bool (hAPP_f866672739t_bool cOMBB_1247074793l_real P) Q) R))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool P (hAPP_P1175774780nt_int Q R)) (hAPP_P603027463t_bool (hAPP_f892584630t_bool (hAPP_f492612297t_bool cOMBB_798864284nt_int P) Q) R))) (forall ((A_237 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit1 pls))) A_237) A_237)) (forall ((B_141 $$unsorted) (A_181 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (or (and (hBOOL (hAPP_Q2096512830t_bool _let_1 B_141)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_181) zero_z891286103de_int))) (and (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int B_141) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool _let_1 A_181)))) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_181) B_141)) zero_z891286103de_int))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat suc M)) N) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N)))) (forall ((R_3 $$unsorted)) (= (of_real_complex R_3) (hAPP_real_complex (hAPP_r265291036omplex complex R_3) zero_zero_real))) (forall ((X_3 $$unsorted)) (=> (hBOOL (summable_complex X_3)) (= (hAPP_f352196356l_real suminf_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat re) X_3)) (hAPP_complex_real re (hAPP_f213450978omplex suminf_complex X_3))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 X_1)) (hAPP_real_real _let_1 Y_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)))))) (forall ((N_61 $$unsorted) (X_29 $$unsorted) (Y_23 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat X_29) Y_23)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_29) N_61)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_23) N_61))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int M) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int M) (hAPP_int_int fact_fact_int N)))))) (= ii (hAPP_real_complex _let_59 one_one_real)) (forall ((N_41 $$unsorted)) (let ((_let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int zero_z891286103de_int) N_41))) (let ((_let_2 (= zero_zero_nat N_41))) (and (=> (not _let_2) (= zero_z891286103de_int _let_1)) (=> _let_2 (= _let_1 one_on1684967323de_int)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (= (or (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A) zero_zero_rat)) (hBOOL (hAPP_rat_bool _let_1 B))) (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B) zero_zero_rat)) (hBOOL (hAPP_rat_bool _let_1 A)))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) B)) zero_zero_rat))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (=> (and (is_int B_4) (is_int A_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_4)) (hBOOL (hAPP_rat_bool P_1 (hAPP_int_rat (hAPP_int_fun_int_rat fract A_2) B_4)))))) (hBOOL (hAPP_rat_bool P_1 Q_1)))) (forall ((N $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_int_nat number_number_of_nat V_2)) N))) (let ((_let_2 (hAPP_int_int number_number_of_int V_2))) (let ((_let_3 (hBOOL (hAPP_int_bool nat_neg _let_2)))) (and (=> (not _let_3) (= (hAPP_int_nat nat (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int _let_2) N)) _let_1)) (=> _let_3 (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat zero_zero_nat) N) _let_1))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_1) N_1)) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract one_one_int) (hAPP_int_int number_number_of_int K_2)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat one_one_rat) (hAPP_int_rat number_number_of_rat K_2)))) (= (hAPP_nat_nat fact_fact_nat _let_1) _let_1) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real cos X))) (=> (not (= _let_2 zero_zero_real)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real tan X)) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real inverse_inverse_real _let_2)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_int_nat nat (hAPP_int_int abs_abs_int X))) (hAPP_int_nat nat (hAPP_int_int abs_abs_int Y)))) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y))) (forall ((A $$unsorted)) (hBOOL (hAPP_real_bool (isCont_real_real abs_abs_real) A))) (forall ((R_3 $$unsorted) (S_1 $$unsorted) (T_1 $$unsorted) (R_5 $$unsorted) (S_3 $$unsorted) (M $$unsorted) (T_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int R_5) R_3)))) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int S_3) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int T_2) N)) R_5) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int S_1) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int T_1) N)) R_3) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int S_3) (hAPP_int_int _let_1 S_1))) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int T_2) (hAPP_int_int _let_1 T_1))) N)) (hAPP_int_int (div_mod_int R_5) R_3)))))) (forall ((A_3 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime (hAPP_nat_nat suc zero_zero_nat)) A_3))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_int_rat number_number_of_rat X_1)) zero_zero_rat)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) pls)))) (forall ((R_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) R_3)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int N_2) one_one_int)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int N_2)) R_3)) (is_int N_2))))) (forall ((A_197 $$unsorted) (B_152 $$unsorted) (N_64 $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_197) B_152)) N_64) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A_197) N_64)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex B_152) N_64)))) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real F X_1) L)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real L) zero_zero_real)) (exists ((D_2 $$unsorted)) (and (forall ((H_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real H_1) D_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) H_1))) (hAPP_real_real F X_1)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D_2))))))) (forall ((X_1 $$unsorted)) (= (= (hAPP_int_real real_int (archim1246769320r_real X_1)) X_1) (exists ((N_2 $$unsorted)) (and (= (hAPP_int_real real_int N_2) X_1) (is_int N_2))))) (forall ((K_1 $$unsorted) (Xa_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real cos) (hAPP_r1250527377l_real (hAPP_f203520653l_real cOMBC_real_real_real plus_plus_real) K_1)) Xa_1) (hAPP_real_real uminus_uminus_real (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Xa_1) K_1)))))) (forall ((J_2 $$unsorted) (K_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int (hAPP_int_int number_number_of_int min)))) (let ((_let_2 (hAPP_nat_int _let_1 K_2))) (let ((_let_3 (hAPP_nat_int _let_1 J_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong _let_3) _let_2) M)) (= _let_3 _let_2))))))) (forall ((D_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real inverse_inverse_real (hAPP_real_real sqrt X_1)))) (=> (not (= zero_zero_real X_1)) (=> (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real _let_2) _let_1) D_1)) (=> (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) zero_zero_real)) (= D_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real uminus_uminus_real _let_2)) _let_1))) (hBOOL (hAPP_real_bool (deriv_real sqrt X_1) D_1)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C) zero_zero_int)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A)))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int D) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int X_2) Sa))))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int Z) X_2)) (= _let_1 _let_1)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1195171167l_real (hAPP_f1736103445l_real (hAPP_f1908301369l_real cOMBS_902912708l_real P) Q) R) (hAPP_P1860904029l_real (hAPP_r938550413l_real P R) (hAPP_r1195171167l_real Q R)))) (forall ((C_73 $$unsorted) (A_173 $$unsorted) (B_133 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_173) B_133)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_73)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_173) C_73)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_133) C_73)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sqrt X)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Y) (hAPP_nat_nat (div_mod_nat X) Y)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) B)) zOdd)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) zOdd))))) (forall ((B_2 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool coprime D_3))) (=> (hBOOL (hAPP_nat_bool _let_1 A_3)) (=> (hBOOL (hAPP_nat_bool _let_1 B_2)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))))))) (forall ((A_63 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral A_63) A_63) zero_z126310315umeral)) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_nat_real real_nat (natceiling X))))) (forall ((N $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int P_3) N)))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_3) A_3))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2))) (hBOOL (hAPP_int_bool _let_1 B_2))))))) (= zero_z126310315umeral (hAPP_i769753017umeral number1443263063umeral pls)) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_1) N_1)) zEven))))) (forall ((A_3 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (=> (and (is_int A_3) (is_int Q_2)) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 A_3) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))) (=> (not (= A_3 zero_zero_int)) (= Q_2 one_one_int))))) (forall ((A $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) A)) zero_zero_real)))) (forall ((K_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int pls))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int bit0 K_1))) (hBOOL (hAPP_int_bool _let_1 K_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat one_one_rat) (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool _let_1 Y)) (= (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real powr X) Y)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y) (hAPP_real_real ln X))))))) (forall ((I $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int I))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int M) N))) (hBOOL (hAPP_int_bool _let_1 M))))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real arcsin Y))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) _let_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_2)) _let_1)))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)))) (forall ((A_236 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_236) (hAPP_int_real number267125858f_real (hAPP_int_int bit1 pls))) A_236)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y))) (= _let_1 (hAPP_int_int abs_abs_int _let_1)))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real _let_1 A_3)) (hAPP_real_real _let_1 B_2)) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_3) B_2))))) (forall ((A_108 $$unsorted)) (= A_108 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_108) zero_zero_nat))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A) B)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B) C))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A)) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int A) B))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A)) (hBOOL (hAPP_int_bool _let_1 B))))))) (forall ((Z_11 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real Z_11) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Z_11) Z_11))) (forall ((A_12 $$unsorted) (N_18 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_12))) (= (hAPP_n522471361de_int _let_1 (hAPP_nat_nat suc N_18)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int _let_1 N_18)) A_12)))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (hAPP_f1485493409l_bool cOMBB_624415285l_real fconj))) (= (the_real (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_2 (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_1)))) (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_2 (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool ord_less_eq_real) _let_1))) (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool (hAPP_f1393328161l_bool (hAPP_f1900646853l_bool cOMBB_430461877l_real fequal_real) sin)) Y_2)))) (hAPP_real_real arcsin Y_2))))) (forall ((N $$unsorted)) (= N (hAPP_int_nat nat (hAPP_nat_int semiri1621563631at_int N)))) (forall ((M_6 $$unsorted) (N_20 $$unsorted)) (= (hAPP_nat_rat semiri151668891at_rat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M_6) N_20)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_nat_rat semiri151668891at_rat M_6)) N_20))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_rat_bool iszero_rat (hAPP_int_rat number_number_of_rat K_1))) (hBOOL (hAPP_int_bool iszero_int (hAPP_int_int number_number_of_int K_1))))) (forall ((I $$unsorted) (K_2 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat I))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) J_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 J_2)) K_2) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) K_2)))))) (forall ((X $$unsorted)) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) one_one_nat))) (forall ((A_224 $$unsorted) (N_68 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_nat_fun_nat_nat power_power_nat A_224))) (= (hAPP_nat_nat _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_68)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat _let_2 N_68)) _let_1))))) (forall ((F $$unsorted) (N_1 $$unsorted)) (= (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) F)) (hAPP_r474017924t_real power_power_real zero_zero_real))) (hAPP_n1699378549t_bool (ord_at4362885an_nat (hAPP_nat_nat suc zero_zero_nat)) N_1)) zero_zero_real)) (= number1226105091de_int quickcheck_of_int) (forall ((X_8 $$unsorted) (Q_7 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat X_8))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 Q_7)) X_8) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc Q_7))))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 K_1)) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) pls)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (A_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) A_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_5) B_2)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_1)))) (forall ((U $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (J $$unsorted) (I_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat J) I_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I_1) U)) Ma)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J) U)) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat I_1) J)) U)) Ma)) N_1))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2))) (=> (and (is_int B_2) (is_int A_3)) (=> (or (not (= zero_zero_int B_2)) (not (= zero_zero_int A_3))) (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_2) _let_1))))))) (forall ((X_21 $$unsorted) (N_31 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat X_21))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_31)) (= (hAPP_nat_nat _let_1 N_31) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_31) one_one_nat))) X_21))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N)) N))) (forall ((A_217 $$unsorted) (M_29 $$unsorted) (B_160 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_217) M_29)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_160) M_29)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_217) B_160)) M_29))) (forall ((C_80 $$unsorted) (A_187 $$unsorted) (B_143 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool dvd_dvd_rat A_187))) (=> (hBOOL (hAPP_rat_bool _let_1 B_143)) (=> (hBOOL (hAPP_rat_bool _let_1 C_80)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_143) C_80))))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int X_1)) zero_zero_int)))) (forall ((X $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) (natfloor X)))) (= (quotient_of one_one_rat) _let_78) (forall ((X $$unsorted)) (=> (is_int X) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (or (= zero_zero_int X) (= X one_one_int)))))) (forall ((M $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) X)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) M)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) M)))))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat) (hAPP_nat_nat fact N)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real exp_real X)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))))) (forall ((X $$unsorted) (I $$unsorted)) (= (hAPP_real_real tan (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real real_int I)) pi))) (hAPP_real_real tan X))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1293550189l_real (hAPP_r1043989325l_real P R) (hAPP_r2019696015l_real Q R)) (hAPP_r1230691443l_real (hAPP_f324002831l_real (hAPP_f677014621l_real cOMBS_107495110l_real P) Q) R))) (forall ((X_14 $$unsorted) (Y_11 $$unsorted) (Ya_1 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_14) Ya_1)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Y_11) Ya_1)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_14) Y_11)) Ya_1))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_complex_complex uminus473333897omplex (hAPP_real_complex (hAPP_r265291036omplex complex A_3) B_2)) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real uminus_uminus_real A_3)) (hAPP_real_real uminus_uminus_real B_2)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P1333854989l_bool P (hAPP_r1195171167l_real Q R)) (hAPP_real_bool (hAPP_f330985925l_bool (hAPP_f940061907l_bool cOMBB_1795223523l_real P) Q) R))) (forall ((N $$unsorted) (K_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_2))) (=> (hBOOL (hAPP_int_bool _let_1 M)) (=> (hBOOL (hAPP_int_bool _let_1 N)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int M) N))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1791153283t_bool P (hAPP_int_fun_int_int Q R)) (hAPP_i345030060t_bool (hAPP_f725770969t_bool (hAPP_f983569339t_bool cOMBB_550562460ol_int P) Q) R))) (forall ((B_118 $$unsorted) (A_157 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_157)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_118) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_118) A_157)) zero_zero_int))))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int W))) (= (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z1) Z2)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 Z1)) (hAPP_int_int _let_1 Z2))))) (forall ((C_71 $$unsorted) (B_126 $$unsorted) (A_165 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B_126) A_165)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C_71) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_165) C_71)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_126) C_71)))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X_1)) (=> (hBOOL (hAPP_real_bool _let_1 Y_2)) (= (= (hAPP_real_real ln Y_2) (hAPP_real_real ln X_1)) (= X_1 Y_2)))))) (forall ((M_18 $$unsorted) (N_38 $$unsorted) (A_128 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_128))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int) A_128)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int _let_1 M_18)) (hAPP_n522471361de_int _let_1 N_38))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_18) N_38)))))) (forall ((N_43 $$unsorted) (A_131 $$unsorted)) (let ((_let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_131) N_43))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) A_131)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat _let_1) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_131) _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) B)))) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral Lx_5) Ly_3)))) (let ((_let_2 (hAPP_C1594335432umeral times_1655362735umeral Rx_5))) (= (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral _let_2 Ry_3)) (hAPP_C498520661umeral _let_2 (hAPP_C498520661umeral _let_1 Ry_3)))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int number_number_of_int K_2)) one_one_int) (hAPP_int_rat number_number_of_rat K_2))) (forall ((M_8 $$unsorted) (N_22 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_n522471361de_int semiri1424489471de_int M_8)) (hAPP_n522471361de_int semiri1424489471de_int N_22)) (hAPP_n522471361de_int semiri1424489471de_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_8) N_22)))) (forall ((A_125 $$unsorted) (N_36 $$unsorted) (N_35 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_125))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_36) N_35)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) A_125)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_125) one_on1684967323de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int _let_1 N_35)) (hAPP_n522471361de_int _let_1 N_36)))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real) sin)) (hAPP_int_nat number_number_of_nat _let_1)) X_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) (hAPP_real_real cos X_1))) (hAPP_real_real sin X_1)))))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y)) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (= (hAPP_real_real tan X_2) Y))))) (forall ((B $$unsorted) (A $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool (wset A) P_5))) (let ((_let_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) _let_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) _let_2)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (inv P_5) B)) _let_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) _let_1))))))))))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_complex cnj (hAPP_complex_complex cnj Z_1)) Z_1)) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (hBOOL (hAPP_bool_bool (hAPP_b589554111l_bool fconj P) Q))) (hBOOL P))) (forall ((C_33 $$unsorted) (D_5 $$unsorted) (A_79 $$unsorted) (B_67 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_79) B_67)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral C_33) D_5)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_79) C_33)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_67) D_5)))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_2) (hAPP_n1699378549t_bool (ord_at238088361st_nat zero_zero_nat) N_1))) (hBOOL (hAPP_nat_bool P_1 X_2)))) (exists ((M_1 $$unsorted)) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_1) N_1)) (hBOOL (hAPP_nat_bool P_1 M_1)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C) zero_zero_real)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B) A)))))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) _let_1)))) (forall ((N_11 $$unsorted) (A_7 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_7)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_7) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_7) (hAPP_nat_nat suc N_11))) one_one_int))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1512942609t_bool P (hAPP_i1948725293t_bool Q R)) (hAPP_i872162435t_bool (hAPP_f1251097615t_bool (hAPP_f1475822739t_bool cOMBB_2027861294ol_int P) Q) R))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int A_3))) (let ((_let_2 (hAPP_int_fun_int_int gcd_gcd_int B_2))) (= (hAPP_int_int _let_1 (hAPP_int_int _let_2 C_1)) (hAPP_int_int _let_2 (hAPP_int_int _let_1 C_1)))))) (forall ((Y $$unsorted)) (=> (not (= Y zero_z126310315umeral)) (not (forall ((Code_numeral $$unsorted)) (not (= (code_S1047413653umeral Code_numeral) Y)))))) (forall ((A $$unsorted)) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (hBOOL (monoseq_real A)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real A zero_zero_nat)) zero_zero_real)) (forall ((N_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_2))) (let ((_let_2 (ord_at4362885an_nat zero_zero_nat))) (let ((_let_3 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))) (let ((_let_4 (hAPP_f1509287679l_real big_co604158596t_real _let_3))) (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real (hAPP_f352196356l_real suminf_real _let_3)) (hAPP_r1134773055l_bool (ord_at1589558736t_real (hAPP_f1406902706l_real _let_4 (hAPP_n1699378549t_bool _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat _let_1) one_one_nat)))) (hAPP_f1406902706l_real _let_4 (hAPP_n1699378549t_bool _let_2 _let_1)))))))))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (let ((_let_2 (hAPP_n1699378549t_bool dvd_dvd_nat Z_1))) (let ((_let_3 (hAPP_n1699378549t_bool dvd_dvd_nat Y))) (=> (and (not (hBOOL (hAPP_nat_bool _let_3 X))) (hBOOL (hAPP_nat_bool _let_1 Y))) (=> (and (not (hBOOL (hAPP_nat_bool _let_2 Y))) (hBOOL (hAPP_nat_bool _let_3 Z_1))) (and (not (hBOOL (hAPP_nat_bool _let_2 X))) (hBOOL (hAPP_nat_bool _let_1 Z_1))))))))) (forall ((B_92 $$unsorted) (A_114 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_114) zero_z891286103de_int)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int B_92) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_114) B_92)) zero_z891286103de_int))))) (forall ((K_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (= (hBOOL (hAPP_int_bool _let_1 K_1)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int bit1 K_1)))))) (forall ((A_9 $$unsorted) (N_14 $$unsorted) (B_7 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_14))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_9) _let_1)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int B_7) _let_1))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) B_7)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_9) B_7)))))) (forall ((X $$unsorted)) (= (hAPP_real_real cos X) (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X)))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat nat X_1))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int uminus_uminus_int A)) _let_1) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) _let_1)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X)) (= (hAPP_int_nat nat (hAPP_int_int fact_fact_int X)) (hAPP_nat_nat fact_fact_nat (hAPP_int_nat nat X))))) (forall ((A_230 $$unsorted) (C_96 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat C_96) A_230) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_230) C_96))) (forall ((X_35 $$unsorted) (Y_27 $$unsorted) (Q_11 $$unsorted)) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int X_35) Y_27)) Q_11) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_35) Q_11)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int Y_27) Q_11)))) (forall ((A_3 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (=> (and (is_int A_3) (is_int R_3)) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 A_3) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))) (=> (not (= zero_zero_int A_3)) (= R_3 zero_zero_int))))) (forall ((M_8 $$unsorted) (N_22 $$unsorted)) (= (hAPP_nat_nat semiri984289939at_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_8) N_22)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat semiri984289939at_nat M_8)) (hAPP_nat_nat semiri984289939at_nat N_22)))) (forall ((N_55 $$unsorted) (A_152 $$unsorted) (B_114 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_152) B_114)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_152)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_152) N_55)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral B_114) N_55)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= Y X)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool fequal_int X) Y)))) (forall ((M $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (=> (not (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) K_2))) (=> (not (= M _let_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat _let_1) M)))))) (forall ((N $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (= (hAPP_int_int (legacy_zgcd A_3) B_2) one_one_int) (= one_one_int (hAPP_int_int (legacy_zgcd (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) N)) B_2)))) (forall ((M $$unsorted)) (not (= (hAPP_nat_nat suc M) zero_zero_nat))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos X_1)) (hAPP_real_real sin X_1)))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real times_times_real) sin)) sin) X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) _let_1))))) (forall ((A $$unsorted) (P_5 $$unsorted) (X_2 $$unsorted)) (=> (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool X_2) (setS A P_5))) (hBOOL (hAPP_f448129468l_bool finite_finite_int X_2)))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int minus_minus_int M))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) M)) (= (hAPP_int_nat nat (hAPP_int_int _let_1 one_one_int)) (hAPP_nat_nat suc (hAPP_int_nat nat (hAPP_int_int _let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) (hAPP_real_real ln X)) (hAPP_real_real ln (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) N))))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_1)) (= (hAPP_P1175774780nt_int product_snd_int_int (posDivAlg one_one_int _let_1)) (hAPP_int_int (div_mod_int one_one_int) _let_1))))) (not (hBOOL (hAPP_int_bool _let_41 zero_zero_int))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit0 K_1)) min)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) min)))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int semiri1621563631at_int M)) (hAPP_nat_int semiri1621563631at_int N)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (=> (and (is_int N_1) (is_int Ma)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int Ma) N_1))) (or (not (= N_1 zero_zero_int)) (not (= Ma zero_zero_int)))))) (forall ((C_27 $$unsorted) (A_57 $$unsorted) (B_48 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_27))) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int A_57) B_48)) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int _let_1 A_57)) (hAPP_Q1762011733de_int _let_1 B_48))))) (forall ((K_1 $$unsorted) (F $$unsorted)) (=> (hBOOL (summable_real F)) (=> (forall ((D_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat))) D_2))) (let ((_let_2 (hAPP_nat_fun_nat_nat plus_plus_nat K_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real F (hAPP_nat_nat _let_2 _let_1))) (hAPP_nat_real F (hAPP_nat_nat _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat _let_1) one_one_nat))))))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real F) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) K_1))) (hAPP_f352196356l_real suminf_real F)))))) (forall ((V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_int_nat number_number_of_nat V_2)))) (let ((_let_2 (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int V_2))))) (and (=> (not _let_2) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int succ V_2)) _let_1)) (=> _let_2 (= one_one_nat _let_1)))))) (forall ((A_50 $$unsorted) (C_22 $$unsorted) (B_41 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_50) B_41)) C_22) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (div_mod_int A_50) C_22)) B_41)) C_22))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (hAPP_f1485493409l_bool cOMBB_624415285l_real fconj))) (= (hAPP_real_real arccos Y_2) (the_real (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_1 (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool ord_less_eq_real) pi))) (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool (hAPP_f1393328161l_bool (hAPP_f1900646853l_bool cOMBB_430461877l_real fequal_real) cos)) Y_2))))))) (forall ((A_26 $$unsorted) (B_21 $$unsorted)) (=> (not (= B_21 zero_z891286103de_int)) (= A_26 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_21) A_26)) B_21)))) (forall ((N_1 $$unsorted) (A $$unsorted) (B $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (hAPP_n332733730l_real (bolzano_bisect P_1 A B) N_1))) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted) (C_3 $$unsorted)) (let ((_let_1 (hAPP_r2019696015l_real produc865579683l_real A_2))) (=> (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real _let_1 B_4))) (=> (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real B_4) C_3))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_2) B_4)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_4) C_3)) (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real _let_1 C_3))))))))) (=> (not (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real A) B)))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)) (not (hBOOL (hAPP_P1333854989l_bool P_1 (hAPP_r1195171167l_real (hAPP_r2019696015l_real produc865579683l_real (hAPP_P731461727l_real produc1935615926l_real _let_1)) (hAPP_P731461727l_real produc556554744l_real _let_1)))))))))) (forall ((P_5 $$unsorted)) (= (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) P_5)) (forall ((M_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat M_1) P_5)) (or (= M_1 P_5) (= one_one_nat M_1))))) (hBOOL (hAPP_nat_bool prime P_5)))) (forall ((A_154 $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_154) A_154)) zero_zero_int)))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 Y)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Y) Z_1)))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat N))) (= X (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_n546711566l_real root N) X)) N)))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (=> (and (is_int A_2) (is_int B_4)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_4)) (=> (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_2) B_4)) (hBOOL (hAPP_rat_bool P_1 (hAPP_int_rat (hAPP_int_fun_int_rat fract A_2) B_4))))))) (hBOOL (hAPP_rat_bool P_1 Q_1)))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Y) X)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X) Y) (hAPP_int_int (nat_tsub X) Y)))) (forall ((C_85 $$unsorted) (A_193 $$unsorted) (B_149 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool dvd_dvd_real A_193))) (=> (hBOOL (hAPP_real_bool _let_1 B_149)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_149) C_85)))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) one_one_real)) (hAPP_nat_real real_nat (natfloor X))))) (forall ((N_52 $$unsorted) (A_150 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_150)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_150) N_52)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B)) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) B)))) (forall ((D_3 $$unsorted) (I $$unsorted)) (=> (is_int I) (=> (not (= zero_zero_int I)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D_3) I)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int abs_abs_int D_3)) (hAPP_int_int abs_abs_int I))))))) (forall ((V_2 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_int_int (div_mod_int (hAPP_int_int number_number_of_int V_2)) (hAPP_int_int number_number_of_int W))) (hAPP_int_int (div_mod_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 V_2))) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 W))))) (forall ((N_54 $$unsorted) (A_151 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_151)) (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_151) N_54)))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (= (archim1246769320r_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) (hAPP_int_real real_int A_3))) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (archim1246769320r_real X)) A_3))) (forall ((A_66 $$unsorted) (B_54 $$unsorted)) (= A_66 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_66) B_54)) B_54)) (hAPP_C498520661umeral (div_mo1740067990umeral A_66) B_54)))) (forall ((M $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) M)))) (forall ((X_9 $$unsorted)) (let ((_let_1 (hAPP_n522471361de_int semiri1424489471de_int (hAPP_int_nat nat X_9)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_9)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int _let_1) _let_1) (hAPP_n522471361de_int semiri1424489471de_int (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_9))))))) (forall ((A_208 $$unsorted)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_208) zero_z126310315umeral))) (= _let_77 zero_zero_real) (forall ((X $$unsorted) (N $$unsorted)) (= (hAPP_real_real tan X) (hAPP_real_real tan (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) pi))))) (not (hBOOL (hAPP_int_bool _let_27 t))) (forall ((P_3 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Q_2)) (=> (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int P_3) Q_2)) (= (normalize _let_1) _let_1))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B) C))) (or (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) B)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C))) (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B) A)))))) (forall ((V_23 $$unsorted)) (= (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_23) (hAPP_int_int bit1 pls))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat V_23)) one_one_rat))) (forall ((N_55 $$unsorted) (A_152 $$unsorted) (B_114 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_152) B_114)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_152)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_152) N_55)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_114) N_55)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A)) (= (= Ma N_1) (= (hAPP_nat_real _let_1 N_1) (hAPP_nat_real _let_1 Ma)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int uminus_uminus_int A_3)) (hAPP_int_int uminus_uminus_int B_2)) (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2))) (exists ((K_4 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) K_4)) (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real norm_norm_real (hAPP_complex_real im X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4)))))) (forall ((N_1 $$unsorted)) (= (hAPP_n1699378549t_bool (ord_at238088361st_nat zero_zero_nat) N_1) (hAPP_n1699378549t_bool ord_atMost_nat N_1))) (forall ((B_70 $$unsorted) (A_82 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_82) zero_z891286103de_int)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int B_70) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_82) B_70)) zero_z891286103de_int))))) (forall ((A_98 $$unsorted) (C_40 $$unsorted) (B_80 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_98) C_40)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_80) C_40))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_98) B_80)))) (forall ((A_38 $$unsorted) (C_13 $$unsorted) (B_29 $$unsorted)) (let ((_let_1 (div_mod_nat A_38))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat C_13) B_29)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 B_29)) C_13) (hAPP_nat_nat _let_1 C_13))))) (forall ((B_2 $$unsorted)) (= (hAPP_int_int (div_mod_int zero_zero_int) B_2) zero_zero_int)) (forall ((V_3 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat suc zero_zero_nat)) (hAPP_int_nat number_number_of_nat V_3)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int one_one_int) (hAPP_int_int number_number_of_int V_3))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B)) E_2)) C)) D)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) E_2)) C)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) E_2)) D))))) (forall ((X_1 $$unsorted) (K_1 $$unsorted)) (=> (= X_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) K_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)))) (forall ((A_121 $$unsorted) (C_54 $$unsorted) (B_99 $$unsorted) (D_9 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_121) C_54)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_99) D_9)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_121) B_99)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real C_54) D_9)))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_nat_int semiri1621563631at_int N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)))) (forall ((A_201 $$unsorted) (E_3 $$unsorted) (B_154 $$unsorted) (C_87 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_201) E_3)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_154) E_3)) C_87)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_201) B_154)) E_3)) C_87))) (forall ((A_214 $$unsorted) (N_67 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_214) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_67))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat nat W_1)) (hAPP_int_nat nat Z_2))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Z_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) Z_2))))) (forall ((I_1 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_nat))) (let ((_let_2 (hAPP_f1080886329l_bool cOMBB_1015721476ol_nat fconj))) (=> (not (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat zero_zero_nat) M_2))) (= (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_f800510211t_bool (hAPP_f561022312t_bool cOMBS_nat_bool_bool (hAPP_f1146629647l_bool _let_2 (hAPP_f800510211t_bool (hAPP_f1722879237t_bool cOMBC_226598744l_bool (hAPP_f66927821l_bool (hAPP_f2037783381l_bool cOMBB_1146692694ol_nat member_nat) suc)) M_2))) (hAPP_n1699378549t_bool _let_1 I_1)))) (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_f800510211t_bool (hAPP_f561022312t_bool cOMBS_nat_bool_bool (hAPP_f1146629647l_bool _let_2 (hAPP_f800510211t_bool (hAPP_f1722879237t_bool cOMBC_226598744l_bool member_nat) M_2))) (hAPP_n1699378549t_bool _let_1 (hAPP_nat_nat suc I_1)))))))))) (= (hAPP_int_int fact_fact_int zero_zero_int) one_one_int) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat fact M)) (hAPP_nat_nat fact N))))) (forall ((C_69 $$unsorted) (A_163 $$unsorted) (B_124 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_69))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_163) B_124)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C_69)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A_163)) (hAPP_rat_rat _let_1 B_124))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat M) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat N) M)) (= M N)))) (forall ((X_46 $$unsorted) (Y_34 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (let ((_let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_46) _let_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_34) _let_2)) (=> (hBOOL (hAPP_nat_bool _let_1 X_46)) (=> (hBOOL (hAPP_nat_bool _let_1 Y_34)) (= X_46 Y_34))))))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int one_one_int))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool _let_1 A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (inv P_3) A_3)))))))) (forall ((X $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) (natceiling X)))) (forall ((N_62 $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex one_one_complex) N_62) one_one_complex)) (forall ((Z_7 $$unsorted) (W_2 $$unsorted) (Y_9 $$unsorted) (X_12 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Y_9) X_12)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Z_7) W_2)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X_12) Y_9)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int W_2) Z_7)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_12) W_2)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y_9) Z_7)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= (hBOOL (hAPP_nat_bool even_odd_even_nat N_1)) (hBOOL (hAPP_nat_bool even_odd_even_nat Ma))) (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) N_1))))) (forall ((X_38 $$unsorted) (P_8 $$unsorted) (Q_12 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat X_38))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_8) Q_12)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat _let_1 P_8)) Q_12)))) (forall ((K_2 $$unsorted)) (= (quotient_of (hAPP_int_rat number_number_of_rat K_2)) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int number_number_of_int K_2)) one_one_int))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_1)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real cos X))))))) (forall ((A_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) one_one_nat)) (= one_one_nat A_3))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_real_complex (hAPP_r265291036omplex complex A_3) B_2)) (hAPP_real_complex (hAPP_r265291036omplex complex C_1) D_3)) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_3) C_1)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_2) D_3)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r2019696015l_real (hAPP_f1591894897l_real (hAPP_f2114902373l_real cOMBB_237479429l_real P) Q) R) (hAPP_r2019696015l_real P (hAPP_real_real Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_int (hAPP_nat_fun_int_int (hAPP_f2105620693nt_int cOMBC_int_nat_int P) Q) R) (hAPP_nat_int (hAPP_int_fun_nat_int P R) Q))) (= (hAPP_nat_real real_nat zero_zero_nat) zero_zero_real) (forall ((B_96 $$unsorted) (A_118 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_118)) (=> (hBOOL (hAPP_real_bool _let_1 B_96)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_118) B_96))))))) (forall ((M_9 $$unsorted) (N_23 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_9) N_23)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat semiri984289939at_nat M_9)) (hAPP_nat_nat semiri984289939at_nat N_23))))) (forall ((N_1 $$unsorted)) (= (hAPP_nat_nat suc N_1) (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_eq_nat) N_1))))) (forall ((A_3 $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int P_3))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) N))) (hBOOL (hAPP_int_bool _let_1 A_3)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (is_int X) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int X))) (= X (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_1) (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) _let_1))) one_one_int)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real real_int X)) (hAPP_int_real real_int Y)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) M)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd A_3) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M)) (= one_one_int (hAPP_int_int (legacy_zgcd B_2) M)))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int Z1))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 Z2)) Z3) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z2) Z3))))) (forall ((W $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V_2))) (let ((_let_2 (hAPP_int_int number_number_of_int W))) (let ((_let_3 (posDivAlg _let_2 _let_1))) (let ((_let_4 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_2) _let_1)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) _let_1)) (and (=> _let_4 (= _let_3 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) _let_2))) (=> (not _let_4) (= _let_3 (hAPP_P1975530577nt_int (adjust _let_1) (posDivAlg _let_2 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) _let_1)))))))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int semiri1621563631at_int X_1)) (hAPP_nat_int semiri1621563631at_int Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2)))) (forall ((A_9 $$unsorted) (N_14 $$unsorted) (B_7 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_14))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_9) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_7) _let_1))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) B_7)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_9) B_7)))))) (forall ((N $$unsorted) (M $$unsorted) (R_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int M)) R_3)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int N)) one_one_real))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int M) N))))) (forall ((A_50 $$unsorted) (C_22 $$unsorted) (B_41 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_50) B_41)) C_22) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (div_mod_nat A_50) C_22)) B_41)) C_22))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (and (is_int X_1) (is_int Y_2)) (=> (hBOOL (hAPP_int_bool _let_1 X_1)) (=> (hBOOL (hAPP_int_bool _let_1 Y_2)) (= (and (= Y_2 zero_zero_int) (= zero_zero_int X_1)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_1) Y_2)))))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_2))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (hBOOL (hAPP_nat_bool _let_1 M))))))) (forall ((A_196 $$unsorted) (N_63 $$unsorted)) (let ((_let_1 (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A_196) N_63))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex _let_1) A_196) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_196) _let_1)))) (forall ((D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int D_3))) (=> (= one_one_int (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2))) (= one_one_int (hAPP_int_int _let_1 A_3))))) (forall ((N_1 $$unsorted)) (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real (hAPP_nat_real real_nat N_1)) field_1210416355s_real))) (forall ((A_92 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_92) one_one_rat) A_92)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) pi)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real cos X)) (hAPP_real_real cos Y))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N_1))) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat N_1))) (=> (not (= zero_zero_real X_1)) (hBOOL (hAPP_real_bool (deriv_real _let_1 X_1) (hAPP_real_real inverse_inverse_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real _let_1 X_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) (hAPP_nat_nat suc zero_zero_nat))))))))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) pls)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real X_1)) zero_zero_real)))) (forall ((C_66 $$unsorted) (A_144 $$unsorted) (B_113 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_66))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A_144)) (hAPP_real_real _let_1 B_113))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C_66)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_144) B_113)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2)) zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2) (hAPP_int_int number_number_of_int min))))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_i1732201573de_int quickcheck_of_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int (quickcheck_int_of N)) (quickcheck_int_of M))) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int N) M))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_complex cnj (hAPP_complex_complex (hAPP_c172932010omplex invers1025623611omplex X) Y)) (hAPP_complex_complex (hAPP_c172932010omplex invers1025623611omplex (hAPP_complex_complex cnj X)) (hAPP_complex_complex cnj Y)))) (forall ((N $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_nat_int semiri1621563631at_int N)))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_real_real arcsin Y)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (not (= zero_zero_nat A_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2)) A_3)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (=> (not (= M N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int Ma)) (hAPP_nat_int semiri1621563631at_int N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y)))) (forall ((X $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) X)))) (not (and (not _let_1) _let_1)))) (forall ((X_20 $$unsorted) (Y_16 $$unsorted) (A_120 $$unsorted) (B_98 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat X_20))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_rat_rat _let_1 Y_16)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_120) B_98)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat Y_16) B_98))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat X_20) A_120)) B_98))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (is_int X_1) (is_int Y_2)) (= (= Y_2 X_1) (= (hAPP_int_real number267125858f_real Y_2) (hAPP_int_real number267125858f_real X_1))))) (forall ((B_118 $$unsorted) (A_157 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_157)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B_118) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_118) A_157)) zero_zero_real))))) (forall ((A_186 $$unsorted)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral one_on1645066479umeral) A_186))) (forall ((M $$unsorted) (N $$unsorted)) (=> (is_int M) (=> (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N)) (or (= M (hAPP_int_int number_number_of_int min)) (= one_one_int M))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_1))) (=> (is_int C_1) (=> (not (= C_1 zero_zero_int)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2) (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int _let_1 A_3)) (hAPP_int_int _let_1 B_2))))))) (forall ((B_73 $$unsorted) (A_85 $$unsorted) (C_36 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int B_73))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_36)) (=> (hBOOL (hAPP_int_bool _let_1 A_85)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_85) C_36))))))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc zero_zero_nat)) (hAPP_nat_nat fact_fact_nat N)))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int number_number_of_int Y_2))))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int K_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_2)) (= (hAPP_int_int _let_1 (hAPP_int_int (legacy_zgcd M) N)) (hAPP_int_int (legacy_zgcd (hAPP_int_int _let_1 M)) (hAPP_int_int _let_1 N)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X) Y) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X) (hAPP_complex_complex uminus473333897omplex Y)))) (forall ((M $$unsorted)) (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) zero_zero_nat))) (forall ((N $$unsorted) (M $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int N)) (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int M)))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_P62333565t_bool B_1_1 B_2_1))) (forall ((A_15 $$unsorted) (B_11 $$unsorted)) (=> (not (= B_11 zero_zero_nat)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_15) B_11)) one_one_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_15) B_11)) B_11)))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N) M)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int M) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int N) M))))) (forall ((N_13 $$unsorted) (A_8 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_8)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_8) (hAPP_nat_nat suc N_13))))))) (forall ((B_120 $$unsorted) (A_159 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_120) A_159))) (=> (hBOOL (hAPP_rat_bool _let_1 A_159)) (hBOOL (hAPP_rat_bool _let_1 B_120)))))) (forall ((F $$unsorted) (G $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_nat_real F N_2))) (hAPP_nat_real G N_2)))) (=> (hBOOL (summable_real G)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f352196356l_real suminf_real F)) (hAPP_f352196356l_real suminf_real G))) (hBOOL (summable_real F)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) (hAPP_nat_nat suc Ma))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_complex_real re X)) (hAPP_complex_real re Y)) (hAPP_complex_real re (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X) Y)))) (forall ((Sa $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Sa)) (hBOOL (tendsto_nat_real (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat powr) real_nat)) (hAPP_real_real uminus_uminus_real Sa)) zero_zero_real sequentially)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_2) X_1)) (= X_1 (comple124823625p_real (hAPP_r1134773055l_bool (ord_gr788844697n_real Y_2) X_1))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B))) (exists ((Y_1 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_1) zero_zero_real)) (hBOOL (hAPP_real_bool (deriv_real F X_2) Y_1)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F B)) (hAPP_real_real F A)))))) (forall ((N_4 $$unsorted)) (= (exists ((M_1 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_2) N_4)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_2) M_1))))) (hBOOL (hAPP_f54304608l_bool finite_finite_nat N_4)))) (forall ((B_95 $$unsorted) (C_53 $$unsorted) (A_117 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) A_117)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral B_95) C_53)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral B_95) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_117) C_53)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos X_1)) (hAPP_real_real sin X_1)))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real) sin)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) _let_1))))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_int_nat number_number_of_nat V_2)) (hAPP_int_nat number_number_of_nat V_3)))) (let ((_let_2 (hAPP_int_int number_number_of_int V_2))) (let ((_let_3 (hBOOL (hAPP_int_bool nat_neg _let_2)))) (and (=> _let_3 (= zero_zero_nat _let_1)) (=> (not _let_3) (= (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int _let_2) (hAPP_int_int number_number_of_int V_3))) _let_1))))))) (forall ((D $$unsorted) (B $$unsorted) (C $$unsorted) (A $$unsorted)) (=> (not (= zero_zero_nat A)) (=> (not (= zero_zero_nat C)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A) B)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat C) D)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat D) C) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B) A)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A) D) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B) C)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X)) (=> (hBOOL (hAPP_int_bool nat_is_nat Y)) (hBOOL (hAPP_int_bool nat_is_nat (hAPP_int_int (nat_tsub X) Y)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real X)) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) one_one_real)))) (forall ((A_89 $$unsorted)) (= A_89 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat one_one_nat) A_89))) (forall ((A_221 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_221) zero_z126310315umeral))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_1))) (=> (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int K_1) N_1) one_one_int) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int Ma) N_1))) (hBOOL (hAPP_int_bool _let_1 Ma)))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int K_2))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int abs_abs_int K_2)) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int M) N)) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int _let_1 M)) (hAPP_int_int _let_1 N))))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int U) L)) (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool (ord_at641636577an_int L) U)))) (forall ((A_139 $$unsorted) (C_61 $$unsorted) (B_108 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_139) C_61)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_108) C_61))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_61)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_139) B_108))))) (forall ((C_60 $$unsorted) (D_13 $$unsorted) (A_138 $$unsorted) (B_107 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_138) B_107)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C_60) D_13)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_138)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_60)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_138) C_60)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_107) D_13)))))))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (hAPP_real_real arctan Y))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)) _let_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_2) _let_1)))))) (forall ((A_30 $$unsorted) (B_25 $$unsorted) (C_11 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int A_30) B_25) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_30) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_25) C_11))) B_25))) (= (collect_int (hAPP_f2119767738t_bool _let_58 (hAPP_f1791153283t_bool _let_57 _let_55))) zEven) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int M))) (= (hAPP_int_int _let_1 N) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) M)) N))))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int W))) (= (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Z1) Z2)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int _let_1 Z1)) (hAPP_int_int _let_1 Z2))))) (hBOOL (hAPP_nat_bool _let_7 _let_76)) (forall ((B_53 $$unsorted) (A_65 $$unsorted) (C_32 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_65) C_32) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_53) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_65) B_53))) (hAPP_nat_nat (div_mod_nat A_65) B_53))) C_32))) (forall ((X $$unsorted)) (= (natfloor X) (hAPP_int_nat nat (archim1246769320r_real X)))) (forall ((V_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int V_2))) (= zero_zero_nat (hAPP_int_nat number_number_of_nat V_2)))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP_P62333565t_bool A_1 X_1)) (hBOOL (hAPP_f526364711l_bool (hAPP_P1062890741l_bool member2143287562nt_int X_1) A_1)))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) B)) zero_zero_int)))) (forall ((J $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J) K_1)) I_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat J) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_1) K_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Z_2)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_1) Z_2)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_2) Z_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2))))) (forall ((A_105 $$unsorted)) (= A_105 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real zero_zero_real) A_105))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (is_int A_3) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) A_3)) (= (hAPP_int_int (div_mod_int A_3) B_2) A_3))))) (forall ((V_14 $$unsorted) (B_166 $$unsorted) (C_97 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral (hAPP_i769753017umeral number1443263063umeral V_14)))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 B_166)) (hAPP_C498520661umeral _let_1 C_97)) (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_166) C_97))))) (forall ((A $$unsorted) (N_1 $$unsorted)) (= (and (= zero_z891286103de_int A) (not (= N_1 zero_zero_nat))) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A) N_1) zero_z891286103de_int))) (forall ((R_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int (archim1246769320r_real R_3))) one_one_real)))) (forall ((B_2 $$unsorted) (N $$unsorted) (X $$unsorted)) (let ((_let_1 (log B_2))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real _let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) N)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) (hAPP_real_real _let_1 X)))))) (= zero_zero_real (hAPP_real_real tan zero_zero_real)) (forall ((B_129 $$unsorted) (A_169 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_169)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int B_129) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_169) B_129)) zero_z891286103de_int))))) (hBOOL (hAPP_Q2096512830t_bool _let_75 one_on1684967323de_int)) (forall ((R_3 $$unsorted) (S_1 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real R_3) (hAPP_real_real uminus_uminus_real S_1)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real R_3) S_1))) (forall ((A $$unsorted) (B $$unsorted)) (= (= zero_zero_int (hAPP_int_int (div_mod_int B) A)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A) B)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (hBOOL Q) (not (hBOOL (hAPP_bool_bool (hAPP_b589554111l_bool fconj P) Q))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B) A) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat C) A)) (= C B))) (forall ((N_55 $$unsorted) (A_152 $$unsorted) (B_114 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_152) B_114)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_152)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_152) N_55)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_114) N_55)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (= X (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) _let_1)))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat M)) (hAPP_nat_real real_nat N)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int N_1) Ma)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real real_int N_1)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int Ma)) one_one_real))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (K_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) K_2) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)) B_2)) (hAPP_int_int (div_mod_int A_3) B_2))) K_2))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat C))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 A)) (hAPP_nat_nat _let_1 B))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A) B))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat semiri984289939at_nat N_1))) (hBOOL (hAPP_nat_bool _let_1 N_1))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_int_real real_int N_1))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int div_div_int A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_1)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int _let_1 B_2)) C_1) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) C_1)))))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_real_real (hAPP_n546711566l_real root N) one_one_real) one_one_real))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat times_times_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real))) (let ((_let_3 (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_2 (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))))) (let ((_let_4 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) _let_1)) one_one_nat))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real X_1)) one_one_real)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1122023986l_real (hAPP_f1786887945l_real cOMBB_1896127834l_real suminf_real) (hAPP_f1993765077t_real (hAPP_f895854793t_real cOMBB_1948233853l_real _let_3) (hAPP_f1993765077t_real (hAPP_f895854793t_real cOMBB_1948233853l_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_2 (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real inverse_divide_real one_one_real)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) _let_4))))) (hAPP_f1501741374t_real (hAPP_f1135648319t_real cOMBC_1329014627t_real (hAPP_f1163894827t_real (hAPP_f1998755145t_real cOMBB_421464275l_real cOMBB_nat_real_nat) power_power_real)) _let_4)))) X_1) (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real _let_3 (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1))))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_bool (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool P) Q) R) (hAPP_nat_bool (hAPP_n1699378549t_bool P R) Q))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real Y)) one_one_real)) (= (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_real_real sin (hAPP_real_real arccos Y))))) (forall ((N_49 $$unsorted) (A_147 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat one_one_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_147)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_147) N_49)))))) (forall ((A_106 $$unsorted)) (= A_106 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int zero_z891286103de_int) A_106))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) N_1))) (or (hBOOL (hAPP_nat_bool _let_1 N_1)) (hBOOL (hAPP_nat_bool _let_1 Ma)))))) (not (forall ((S_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) m)) one_one_int))) (=> (is_int S_2) (not (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong s1) S_2) _let_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int S_2) _let_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) S_2)))))))) (forall ((A_48 $$unsorted) (B_39 $$unsorted) (C_20 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_48) B_39)) C_20) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_48) C_20)) (hAPP_Q1762011733de_int (div_mo231679042de_int B_39) C_20))) C_20))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat X_1)) (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_nat_int semiri1621563631at_int X_1))))) (forall ((A_38 $$unsorted) (C_13 $$unsorted) (B_29 $$unsorted)) (let ((_let_1 (div_mod_int A_38))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int C_13) B_29)) (= (hAPP_int_int _let_1 C_13) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 B_29)) C_13))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real C))) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B))))) (forall ((X_19 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_19) one_one_int)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_19) one_one_int)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_19) X_19)) one_one_int))) (not (hBOOL (hAPP_nat_bool even_odd_even_nat one_one_nat))) (forall ((A_107 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_107) zero_zero_nat) A_107)) (forall ((C_46 $$unsorted) (A_104 $$unsorted) (B_86 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int C_46))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A_104)) (hAPP_int_int _let_1 B_86))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_104) B_86))))) (forall ((B_121 $$unsorted) (A_160 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_160) zero_zero_nat)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) B_121)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_160) B_121)) zero_zero_nat))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real B))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) B)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real _let_1 X_1)) (hAPP_nat_real _let_1 Y_2))))))) (forall ((A_198 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real zero_zero_real) A_198)) (= zero_zero_real A_198))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real exp_real X)) (hAPP_real_real exp_real Y))))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) (hAPP_int_rat number_number_of_rat Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) Y_2)))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (= (= zero_zero_real (hAPP_real_real ln X_1)) (= X_1 one_one_real)))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (and (is_int Z) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) Sa))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z) X_2)) (= _let_1 _let_1))))))) (forall ((P_1 $$unsorted)) (= (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) P_1)) (image_nat_int semiri1621563631at_int (collect_nat (hAPP_f1154658180t_bool (hAPP_f1361476881t_bool cOMBB_int_bool_nat P_1) semiri1621563631at_int))))) (forall ((F $$unsorted)) (let ((_let_1 (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat abs_abs_real) F))) (=> (hBOOL (summable_real _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_f352196356l_real suminf_real F))) (hAPP_f352196356l_real suminf_real _let_1)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 K1)) (hAPP_int_int bit0 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K1) K2)))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat K_2))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc M)) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)))) (forall ((B_132 $$unsorted) (A_172 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_172) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_132) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_172) B_132)))))) (forall ((Diff $$unsorted) (F $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real H) zero_zero_real)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (=> (= (hAPP_n546711566l_real Diff zero_zero_nat) F) (=> (forall ((M_1 $$unsorted) (T $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real H) T)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) T) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) T))))) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real H))) (and (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1))) (hAPP_real_real F H)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real T) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real H) T)))))))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted)) (= (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B) A) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral C) A)) (= B C))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A) B) zero_zero_complex) (= B A))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_nat_int semiri1621563631at_int K_2)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I) J_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 I)) (hAPP_int_int _let_1 J_2))))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) Y_2)) zOdd))))) (forall ((A_25 $$unsorted) (B_20 $$unsorted)) (=> (and (is_int A_25) (is_int B_20)) (=> (not (= B_20 zero_zero_int)) (= A_25 (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_25) B_20)) B_20))))) (forall ((X_1 $$unsorted)) (= (not (hBOOL (hAPP_nat_bool even_odd_even_nat X_1))) (exists ((Y_1 $$unsorted)) (= X_1 (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat))) Y_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex invers1025623611omplex X) Y) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X) (hAPP_complex_complex invers1449016382omplex Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1805168059t_bool (hAPP_i1529485324t_bool P R) (hAPP_i1948725293t_bool Q R)) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool (hAPP_f1878066172t_bool cOMBS_1720984575t_bool P) Q) R))) (forall ((B_90 $$unsorted) (A_112 $$unsorted) (C_50 $$unsorted)) (=> (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex C_50) A_112) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_90) A_112)) (= B_90 C_50))) (forall ((X_6 $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex X_6))) (= (hAPP_nat_complex _let_1 (hAPP_nat_nat suc Q_5)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_6) (hAPP_nat_complex _let_1 Q_5))))) (forall ((N $$unsorted)) (= (hAPP_nat_real real_nat N) (hAPP_int_real real_int (hAPP_nat_int semiri1621563631at_int N)))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit0 K_1)) (hAPP_int_int bit0 L))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) L)))) (forall ((A $$unsorted)) (= (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) zero_zero_complex) (= A zero_zero_complex))) (= _let_1 _let_74) (forall ((X_1 $$unsorted)) (=> (is_int X_1) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (not (forall ((K $$unsorted)) (=> (is_int K) (not (= X_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) K))))))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) sin_coeff)) (hAPP_r474017924t_real power_power_real X_1))) (hAPP_real_real sin X_1)))) (forall ((C_7 $$unsorted) (A_22 $$unsorted) (B_18 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_22) B_18)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_18) C_7)) A_22) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral B_18) A_22)) C_7)))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_i1948725293t_bool (ord_gr1297742076an_int L) U) (hAPP_i1948725293t_bool (ord_at641636577an_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int L) one_one_int)) U))) (forall ((A_3 $$unsorted) (N $$unsorted) (B_2 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2)) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_3) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_2) N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat M))) (= (hAPP_nat_nat suc (hAPP_nat_nat _let_1 N)) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc N))))) (forall ((Q_2 $$unsorted) (B_2 $$unsorted) (R_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_1)) (=> (hBOOL (hAPP_int_bool _let_1 R_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_3) B_2)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) (hAPP_int_int (div_mod_int Q_2) C_1))) R_3)))))))) (forall ((Qr_2 $$unsorted) (M $$unsorted) (N $$unsorted) (Qr_1 $$unsorted)) (let ((_let_1 (divmod_nat_rel M N))) (=> (hBOOL (hAPP_P1555980039t_bool _let_1 Qr_1)) (=> (hBOOL (hAPP_P1555980039t_bool _let_1 Qr_2)) (= Qr_2 Qr_1))))) (forall ((A_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool A_1) (rsetR Ma))) (hBOOL (hAPP_f448129468l_bool finite_finite_int A_1)))) (forall ((A_231 $$unsorted) (B_165 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_231) B_165) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_165) A_231))) (forall ((B_72 $$unsorted) (C_35 $$unsorted) (A_84 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat B_72))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_84)) (=> (hBOOL (hAPP_rat_bool _let_1 C_35)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_84) C_35))))))) (forall ((X_44 $$unsorted) (Y_32 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_44) _let_1)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int Y_32) _let_1))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) Y_32)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int X_44) Y_32)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i16292313t_bool (hAPP_f601898971t_bool (hAPP_f857296063t_bool cOMBB_214503962ol_int P) Q) R) (hAPP_r2115560837t_bool P (hAPP_int_rat Q R)))) (forall ((X_42 $$unsorted) (Y_30 $$unsorted)) (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_42) X_42)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Y_30) Y_30))) zero_zero_rat)))) (forall ((P_1 $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) I_1)) (=> (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_1) one_one_int))) (=> (forall ((I_2 $$unsorted)) (=> (is_int I_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) I_2)) (=> (hBOOL (hAPP_int_bool P_1 I_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int I_2) one_one_int))))))) (hBOOL (hAPP_int_bool P_1 I_1)))))) (forall ((C_64 $$unsorted) (A_142 $$unsorted) (B_111 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_64))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral _let_1 A_142)) (hAPP_C498520661umeral _let_1 B_111))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_64)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_142) B_111)))))) (forall ((A_231 $$unsorted) (B_165 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_165) A_231) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_231) B_165))) (forall ((A_66 $$unsorted) (B_54 $$unsorted)) (= A_66 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_66) B_54)) B_54)) (hAPP_nat_nat (div_mod_nat A_66) B_54)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f252743847l_bool P (hAPP_r373117745t_bool Q R)) (hAPP_r285062775l_bool (hAPP_f834119977l_bool (hAPP_f848516149l_bool cOMBB_270132509l_real P) Q) R))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP_int_bool A_1 X_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) A_1)))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (hAPP_f1485493409l_bool cOMBB_624415285l_real fconj))) (= (the_real (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_2 (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)))) (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_2 (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool ord_less_real) _let_1))) (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool (hAPP_f1393328161l_bool (hAPP_f1900646853l_bool cOMBB_430461877l_real fequal_real) tan)) Y_2)))) (hAPP_real_real arctan Y_2))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int X))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) _let_1)) one_one_int) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) one_one_int)) _let_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) (hAPP_real_real inverse_inverse_real Y)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) Y))) (= one_on1684967323de_int (hAPP_i1732201573de_int number1226105091de_int _let_2)) (= _let_73 (hAPP_real_real cos _let_46)) (forall ((B_95 $$unsorted) (C_53 $$unsorted) (A_117 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) A_117)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int B_95) C_53)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int B_95) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_117) C_53)))))) (forall ((N_1 $$unsorted)) (= N_1 (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_nat) N_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A))) (= (= C B) (= (hAPP_Q1762011733de_int _let_1 B) (hAPP_Q1762011733de_int _let_1 C))))) (forall ((Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_1) zero_zero_int)) (= zero_zero_nat (hAPP_int_nat nat Z_1)))) (forall ((A $$unsorted)) (=> (is_int A) (= (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) zero_zero_int) (= A zero_zero_int)))) (forall ((K_3 $$unsorted) (K_1 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (hAPP_nat_real F N_2))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) K_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real K_1) _let_1))))) (hBOOL (bseq_real F)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_real_real F A))) (let ((_let_2 (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real F B)))) (let ((_let_3 (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real _let_2 _let_1)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B) A))))) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real _let_1) (hAPP_real_real _let_3 A)) (hAPP_real_real _let_2 (hAPP_real_real _let_3 B))))))) (forall ((K_2 $$unsorted)) (let ((_let_1 (code_int_of K_2))) (let ((_let_2 (= zero_z126310315umeral K_2))) (let ((_let_3 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_4 (hAPP_i769753017umeral number1443263063umeral _let_3))) (let ((_let_5 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_3)) (code_int_of (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral K_2) _let_4))))) (let ((_let_6 (= zero_z126310315umeral (hAPP_C498520661umeral (div_mo1740067990umeral K_2) _let_4)))) (and (=> (not _let_2) (and (=> _let_6 (= _let_5 _let_1)) (=> (not _let_6) (= _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_5) one_one_int))))) (=> _let_2 (= zero_zero_int _let_1)))))))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat X_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_1)))) (forall ((A_105 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral zero_z126310315umeral) A_105) A_105)) (forall ((L_2 $$unsorted)) (not (= (hAPP_int_int bit1 L_2) pls))) (forall ((Z_2 $$unsorted) (W_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) W_1)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) Z_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat nat W_1)) (hAPP_int_nat nat Z_2)))))) (forall ((Y_21 $$unsorted) (X_27 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X_27)) (=> (hBOOL (hAPP_int_bool _let_1 Y_21)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Y_21) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y_21) X_27)) X_27))))))) (forall ((A_211 $$unsorted) (M_26 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_211) M_26)) M_26) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_211) one_one_int)) M_26))) (forall ((Code_numeral_3 $$unsorted)) (not (= (code_S1047413653umeral Code_numeral_3) zero_z126310315umeral))) (forall ((G $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D)) (=> (forall ((Z $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (= (hAPP_real_real G (hAPP_real_real F Z)) Z))) (=> (forall ((Z $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (hBOOL (hAPP_real_bool (isCont_real_real F) Z)))) (exists ((Z $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F X_1)) (hAPP_real_real F Z))))))))) (forall ((M_11 $$unsorted)) (not (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int semiri1424489471de_int M_11)) zero_z891286103de_int)))) (forall ((A_105 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex zero_zero_complex) A_105) A_105)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) (hAPP_nat_nat suc N_1))) (or (exists ((J_1 $$unsorted)) (and (= (hAPP_nat_nat suc J_1) Ma) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat J_1) N_1)))) (= Ma zero_zero_nat)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (P_3 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2))) (=> (= (quotient_of _let_1) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2)) (= _let_1 (hAPP_int_rat (hAPP_int_fun_int_rat fract P_3) Q_2))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (= (hAPP_real_real exp_real (hAPP_real_real ln X_1)) X_1))) (forall ((X_33 $$unsorted)) (= one_one_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_33) zero_zero_nat))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc N_1)) Ma)))) (forall ((A $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) (archim1246769320r_real X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int A)) X_1)))) (forall ((A_49 $$unsorted) (B_40 $$unsorted) (C_21 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_49))) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int _let_1 B_40)) C_21) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int B_40) C_21))) C_21)))) (forall ((B_45 $$unsorted) (B_44 $$unsorted) (A_54 $$unsorted) (C_24 $$unsorted) (A_53 $$unsorted)) (=> (= (hAPP_C498520661umeral (div_mo1740067990umeral A_54) C_24) (hAPP_C498520661umeral (div_mo1740067990umeral A_53) C_24)) (=> (= (hAPP_C498520661umeral (div_mo1740067990umeral B_45) C_24) (hAPP_C498520661umeral (div_mo1740067990umeral B_44) C_24)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_54) B_45)) C_24) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_53) B_44)) C_24))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= Ma N_1) (= (hAPP_nat_int semiri1621563631at_int N_1) (hAPP_nat_int semiri1621563631at_int Ma)))) (forall ((X_1 $$unsorted)) (= (= X_1 one_one_nat) (= one_one_nat X_1))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N))) (let ((_let_2 (hAPP_n1699378549t_bool ord_less_eq_nat M))) (=> (hBOOL (hAPP_nat_bool _let_2 _let_1)) (=> (not (hBOOL (hAPP_nat_bool _let_2 N))) (= _let_1 M)))))) (forall ((A_28 $$unsorted) (B_23 $$unsorted) (C_10 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_10))) (=> (not (= C_10 zero_z891286103de_int)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_28) B_23) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int _let_1 A_28)) (hAPP_Q1762011733de_int _let_1 B_23)))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int negDivAlg_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A0) A1))) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool P_1 A_2))) (=> (and (is_int A_2) (is_int B_4)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int negDivAlg_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A_2) B_4))) (=> (=> (not (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_2) B_4))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_4) zero_zero_int)))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) B_4)))) (hBOOL (hAPP_int_bool _let_1 B_4))))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((M_27 $$unsorted) (A_212 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat M_27) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_212) M_27)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_212) one_one_rat)) M_27))) (forall ((M $$unsorted) (N $$unsorted) (Z_1 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int semiri1621563631at_int M)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int semiri1621563631at_int N)) Z_1)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N))) Z_1))) (forall ((P_5 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_5)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int P_5) zOdd)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int)) _let_1))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Z_2))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Z_2)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 X_1)) (hAPP_real_real _let_1 Y_2))))))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) (hAPP_int_int number_number_of_int Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 pls)) Y_2)))) (forall ((Y_21 $$unsorted) (X_27 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X_27)) (=> (hBOOL (hAPP_real_bool _let_1 Y_21)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_21) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_21) X_27)) X_27))))))) (forall ((R_3 $$unsorted) (P_3 $$unsorted) (Q_2 $$unsorted)) (=> (= (quotient_of R_3) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int P_3) Q_2) one_one_int))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real sin X_1) (hAPP_real_real cos X_1)))) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_nat_real cos_coeff X_2))) (let ((_let_2 (hBOOL (hAPP_nat_bool even_odd_even_nat X_2)))) (and (=> _let_2 (= _let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X_2) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat X_2))))) (=> (not _let_2) (= zero_zero_real _let_1)))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (legacy_zgcd M))) (let ((_let_2 (legacy_zgcd K_2))) (= (hAPP_int_int _let_1 (hAPP_int_int _let_2 N)) (hAPP_int_int _let_2 (hAPP_int_int _let_1 N)))))) (forall ((N $$unsorted)) (= (hAPP_int_nat nat (hAPP_int_int uminus_uminus_int (hAPP_nat_int semiri1621563631at_int N))) zero_zero_nat)) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (is_int X_1) (= (or (= N_1 zero_zero_nat) (not (= zero_zero_int X_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int abs_abs_int X_1)) N_1)))))) (forall ((A_3 $$unsorted) (X $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real ln X)) (hAPP_real_real ln A_3)) (hAPP_real_real (log A_3) X))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1623423338t_bool (hAPP_f704188951t_bool (hAPP_f1456711209t_bool cOMBB_690122963l_real P) Q) R) (hAPP_f472159229t_bool P (hAPP_r1962736578t_bool Q R)))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real I))) (=> (hBOOL (hAPP_real_bool _let_1 J_2)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real J_2) K_2)) (hBOOL (hAPP_real_bool _let_1 K_2)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= N M)))) (forall ((B_92 $$unsorted) (A_114 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_114) zero_z126310315umeral)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral B_92) zero_z126310315umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_114) B_92)) zero_z126310315umeral))))) (not (hBOOL fFalse)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Xa_1 $$unsorted)) (= (= (of_real_complex Xa_1) (hAPP_real_complex (hAPP_r265291036omplex complex X_1) Y_2)) (and (= Y_2 zero_zero_real) (= X_1 Xa_1)))) (forall ((M_28 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat M_28) M_28) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat one_one_rat) one_one_rat)) M_28))) (forall ((X_7 $$unsorted) (Q_6 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_7))) (= (hAPP_nat_real _let_1 (hAPP_nat_nat suc Q_6)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_7) (hAPP_nat_real _let_1 Q_6))))) (forall ((N_1 $$unsorted)) (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real (hAPP_nat_real real_nat N_1)) ring_1_Ints_real))) (forall ((X $$unsorted)) (= (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) X)) (hAPP_real_real abs_abs_real X))) (forall ((Sa $$unsorted) (Ta $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A) B)) (hBOOL (hAPP_f115998247l_bool (hAPP_P1876494581l_bool member180897546at_nat (hAPP_P369611207at_nat (hAPP_P402336767at_nat produc494345619at_nat (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat A) Sa)) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat B) Ta))) pair_less)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_nat_bool even_odd_even_nat X)) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat X) (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))))) (forall ((A_98 $$unsorted) (C_40 $$unsorted) (B_80 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_98) C_40)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_80) C_40))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_98) B_80)))) (not (= pls min)) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_i2112223885l_bool member_int X_1))) (=> (hBOOL (hAPP_f448129468l_bool _let_1 (hAPP_i1948725293t_bool sRStar P_5))) (hBOOL (hAPP_f448129468l_bool _let_1 (hAPP_i1948725293t_bool sr P_5)))))) (forall ((V_20 $$unsorted) (W_16 $$unsorted) (Z_15 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_20) W_16))) Z_15) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real V_20)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real W_16)) Z_15)))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N)))) (hAPP_nat_real (hAPP_r474017924t_real power_power_real zero_zero_real) N)) zero_zero_real))) (forall ((X $$unsorted) (K_2 $$unsorted)) (= (hAPP_real_real sqrt (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) K_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sqrt X)) K_2))) (forall ((A_146 $$unsorted)) (= one_on1684967323de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_146) zero_zero_nat))) (forall ((A_195 $$unsorted) (B_151 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_195) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_195) B_151)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_nat P (hAPP_nat_nat Q R)) (hAPP_nat_nat (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat P) Q) R))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y_2) X_1)) (= (= Y_2 X_1) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X_1) Y_2))))) (forall ((C_7 $$unsorted) (A_22 $$unsorted) (B_18 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_22) B_18)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B_18) A_22)) C_7) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_18) C_7)) A_22)))) (forall ((A_227 $$unsorted) (B_164 $$unsorted) (C_93 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A_227))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat _let_1 B_164)) C_93) (hAPP_rat_rat _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_164) C_93))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_b992065680at_nat if_nat P_1) X_1) Y_2)))) (let ((_let_2 (hBOOL P_1))) (and (=> _let_2 (= (hAPP_nat_int semiri1621563631at_int X_1) _let_1)) (=> (not _let_2) (= _let_1 (hAPP_nat_int semiri1621563631at_int Y_2))))))) (forall ((A_216 $$unsorted)) (= A_216 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat one_one_nat) A_216))) (forall ((N $$unsorted)) (not (= (hAPP_nat_nat fact_fact_nat N) zero_zero_nat))) (forall ((K_2 $$unsorted) (N $$unsorted) (M $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat K_2) N)) M)) N) (hAPP_nat_nat (div_mod_nat M) N))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= N (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) one_one_nat))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_real (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real P) Q) R) (hAPP_real_real P (hAPP_real_real Q R)))) (forall ((C_39 $$unsorted) (D_7 $$unsorted) (A_97 $$unsorted) (B_79 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_97) B_79)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C_39) D_7)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_97) C_39)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_79) D_7)))))) (forall ((Y $$unsorted)) (=> (not (= Y zero_zero_nat)) (not (forall ((Nat_1 $$unsorted)) (not (= (hAPP_nat_nat suc Nat_1) Y)))))) (forall ((N $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) N)))) (forall ((M_8 $$unsorted) (N_22 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_nat_rat semiri151668891at_rat M_8)) (hAPP_nat_rat semiri151668891at_rat N_22)) (hAPP_nat_rat semiri151668891at_rat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_8) N_22)))) (= _let_71 zero_zero_int) (forall ((Q_2 $$unsorted) (B_2 $$unsorted) (R_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int B_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) R_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int R_3) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 C_1)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int Q_2) C_1))) R_3)))))))) (forall ((V_4 $$unsorted)) (let ((_let_1 (hAPP_nat_real semiri132038758t_real (hAPP_int_nat number_number_of_nat V_4)))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int number_number_of_int V_4))))) (and (=> _let_2 (= _let_1 (hAPP_int_real number267125858f_real V_4))) (=> (not _let_2) (= zero_zero_real _let_1)))))) (forall ((Z_1 $$unsorted)) (hBOOL (hAPP_int_bool nat_is_nat (hAPP_nat_int semiri1621563631at_int Z_1)))) (forall ((A_122 $$unsorted) (B_100 $$unsorted) (V_6 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V_6))) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_122) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_100) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_122) B_100)) _let_1)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) Ma)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) N_1)) Ma)) (= one_one_nat N_1)))) (= (hAPP_int_rat number_number_of_rat _let_3) _let_70) (forall ((W_5 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_5))) (let ((_let_2 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral zero_z126310315umeral) _let_1))) (let ((_let_3 (= _let_1 zero_zero_nat))) (and (=> (not _let_3) (= _let_2 zero_z126310315umeral)) (=> _let_3 (= one_on1645066479umeral _let_2))))))) (forall ((X_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_2 $$unsorted)) (=> (is_int A_2) (=> (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_2) one_one_int)))) (hBOOL (hAPP_int_bool P_1 A_2))))) (hBOOL (hAPP_int_bool P_1 X_1)))) (forall ((X_1 $$unsorted)) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) cos_coeff)) (hAPP_r474017924t_real power_power_real X_1))))) (forall ((A_105 $$unsorted)) (= A_105 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat zero_zero_rat) A_105))) (forall ((M_25 $$unsorted) (A_185 $$unsorted) (N_60 $$unsorted) (B_142 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex A_185))) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_nat_complex _let_1 N_60)) B_142)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_25) N_60)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_nat_complex _let_1 M_25)) B_142)))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat X)) A_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X) (natfloor A_3))))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I) J_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J_2) K_2))))) (forall ((A $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) A)) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A) zero_zero_rat)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_nat_bool B_1_1 B_2_1))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int Ma)) (hAPP_nat_int semiri1621563631at_int N_1))))) (= _let_65 (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex ii) _let_4)) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Rx_4) Ry_2))) (let ((_let_2 (hAPP_c172932010omplex times_times_complex Lx_4))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex _let_2 Ly_2)) _let_1) (hAPP_complex_complex _let_2 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Ly_2) _let_1)))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool _let_1 X)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_n546711566l_real root N) X))))))) (forall ((C_78 $$unsorted) (D_14 $$unsorted) (A_178 $$unsorted) (B_138 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_178) B_138)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat C_78) D_14)) (=> (hBOOL (hAPP_nat_bool _let_1 A_178)) (=> (hBOOL (hAPP_nat_bool _let_1 C_78)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_178) C_78)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_138) D_14))))))))) (forall ((M_28 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_28) M_28) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat one_one_nat) one_one_nat)) M_28))) (forall ((L $$unsorted) (U $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (hAPP_i1948725293t_bool (ord_at641636577an_int L) U)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) (hAPP_real_real exp_real X))))) (forall ((N_19 $$unsorted)) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat zero_zero_rat) (hAPP_nat_nat suc N_19)) zero_zero_rat)) (forall ((A_228 $$unsorted) (C_94 $$unsorted) (D_19 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_228))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 C_94)) D_19) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int C_94) D_19))))) (forall ((A_219 $$unsorted)) (=> (is_int A_219) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_219) zero_zero_int) A_219))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_3) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_2) _let_1)))) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real A_3) _let_2)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real uminus_uminus_real B_2)) _let_2)) (hAPP_complex_complex invers1449016382omplex (hAPP_real_complex (hAPP_r265291036omplex complex A_3) B_2)))))) (forall ((C_83 $$unsorted) (D_16 $$unsorted) (A_191 $$unsorted) (B_147 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real A_191) B_147)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real C_83) D_16)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_191) C_83)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_147) D_16)))))) (forall ((B_95 $$unsorted) (C_53 $$unsorted) (A_117 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_117)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_95) C_53)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_95) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_117) C_53)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (and (is_int B_2) (is_int A_3)) (=> (or (not (= B_2 zero_zero_int)) (not (= A_3 zero_zero_int))) (exists ((C_3 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int (legacy_zgcd A_3) B_2)))) (and (is_int D_2) (= A_3 (hAPP_int_int _let_1 C_3)) (= (hAPP_int_int _let_1 D_2) B_2) (= one_one_int (hAPP_int_int (legacy_zgcd C_3) D_2)) (is_int C_3))))))) (forall ((X_1 $$unsorted)) (= (= X_1 zero_zero_real) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_1) X_1)))))) (forall ((C_66 $$unsorted) (A_144 $$unsorted) (B_113 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_66))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral _let_1 A_144)) (hAPP_C498520661umeral _let_1 B_113))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) C_66)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_144) B_113)))))) (forall ((A_149 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_149) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_149) one_one_real)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real inverse_inverse_real X) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real inverse_inverse_real (hAPP_real_real sqrt X))) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (or (= (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))) P_3) (not (hBOOL (hAPP_nat_bool even_odd_even_nat P_3)))))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool (ord_at875362053st_int L) U)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int U) L)) one_one_int)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sin X)) _let_1) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real cos X)) _let_1))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) B_2)))) (=> _let_1 (=> (not (= A_3 B_2)) (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) A_3))) _let_1))))) (forall ((C_33 $$unsorted) (D_5 $$unsorted) (A_79 $$unsorted) (B_67 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_79) B_67)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int C_33) D_5)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_79) C_33)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_67) D_5)))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat suc K_1)))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1195171167l_real P (hAPP_real_real Q R)) (hAPP_r1195171167l_real (hAPP_f617735571l_real (hAPP_f800361423l_real cOMBB_2107848501l_real P) Q) R))) (forall ((B_128 $$unsorted) (A_168 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_168)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_128)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_168) B_128))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X)))) (let ((_let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)))) (=> (and (not _let_1) _let_2) (not (and (not _let_2) _let_1)))))) (= zero_zero_int _let_63) (forall ((A_103 $$unsorted) (C_45 $$unsorted) (B_85 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_103) C_45)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_85) C_45))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_103) B_85)))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) (hAPP_int_int fact_fact_int N))))) (forall ((I $$unsorted)) (let ((_let_1 (hAPP_int_int sgn_sgn_int I))) (let ((_let_2 (= zero_zero_int I))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) I)))) (=> (is_int I) (and (=> (not _let_2) (and (=> (not _let_3) (= (hAPP_int_int uminus_uminus_int one_one_int) _let_1)) (=> _let_3 (= one_one_int _let_1)))) (=> _let_2 (= zero_zero_int _let_1)))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real X_1)) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) Y_2))))) (forall ((A_236 $$unsorted)) (= A_236 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_236) (hAPP_int_complex number528085621omplex (hAPP_int_int bit1 pls))))) (forall ((A_111 $$unsorted) (B_89 $$unsorted) (C_49 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex A_111))) (=> (= (hAPP_complex_complex _let_1 C_49) (hAPP_complex_complex _let_1 B_89)) (= C_49 B_89)))) (forall ((B_96 $$unsorted) (A_118 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_118)) (=> (hBOOL (hAPP_rat_bool _let_1 B_96)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_118) B_96))))))) (forall ((P_1 $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) I_1)) (=> (hBOOL (hAPP_int_bool P_1 K_1)) (=> (forall ((I_2 $$unsorted)) (=> (is_int I_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) I_2)) (=> (hBOOL (hAPP_int_bool P_1 I_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int I_2) one_one_int))))))) (hBOOL (hAPP_int_bool P_1 I_1)))))) (not (hBOOL (hAPP_int_bool nat_neg zero_zero_int))) (forall ((A_221 $$unsorted)) (= zero_zero_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_221) zero_zero_complex))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real X_1)) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) Y_2))))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int Lx_1))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int _let_1 Rx_1)) Ry_1) (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int Rx_1) Ry_1))))) (forall ((A_35 $$unsorted)) (= A_35 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_35) one_one_nat))) (forall ((C_58 $$unsorted) (D_11 $$unsorted) (A_136 $$unsorted) (B_105 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_136) B_105)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int C_58) D_11)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_136)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C_58)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_136) C_58)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_105) D_11))))))))) (forall ((B_96 $$unsorted) (A_118 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_118)) (=> (hBOOL (hAPP_nat_bool _let_1 B_96)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_118) B_96))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int X_1)) (hAPP_nat_int semiri1621563631at_int Y_2))))) (forall ((X $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (multInv P_3) X)) zero_zero_int) P_3))))))) (forall ((A_226 $$unsorted) (B_163 $$unsorted) (C_92 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex A_226))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 C_92)) B_163) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 B_163)) C_92)))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (=> (is_int A_3) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) A_3)) one_one_int) P_3)) (or (= A_3 one_one_int) (= A_3 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))))))))) (forall ((Z_2 $$unsorted)) (let ((_let_1 (hAPP_f1485493409l_bool cOMBB_624415285l_real fconj))) (let ((_let_2 (hAPP_complex_complex sgn_sgn_complex Z_2))) (= (arg Z_2) (hilbert_Eps_real (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_1 (hAPP_f1402056515l_bool (hAPP_f824790735l_bool cOMBB_real_bool_real (hAPP_r1134773055l_bool fequal_real (hAPP_complex_real re _let_2))) cos))) (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_1 (hAPP_f1402056515l_bool (hAPP_f824790735l_bool cOMBB_real_bool_real (hAPP_r1134773055l_bool fequal_real (hAPP_complex_real im _let_2))) sin))) (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool (hAPP_f60716669l_bool _let_1 (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real pi)))) (hAPP_r1134773055l_bool (hAPP_f695504873l_bool cOMBC_real_real_bool ord_less_eq_real) pi))))))))) (forall ((X_38 $$unsorted) (P_8 $$unsorted) (Q_12 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral X_38))) (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral (hAPP_n1108039445umeral _let_1 P_8)) Q_12) (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_8) Q_12))))) (forall ((N_16 $$unsorted) (M_5 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_16) M_5)) (= (hAPP_nat_complex semiri2020571505omplex (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M_5) N_16)) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_nat_complex semiri2020571505omplex M_5)) (hAPP_nat_complex semiri2020571505omplex N_16))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (negDivAlg A_3 B_2))) (let ((_let_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2))) (let ((_let_3 (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_2))))) (and (=> (not _let_3) (= _let_1 (hAPP_P1975530577nt_int (adjust B_2) (negDivAlg A_3 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) B_2))))) (=> _let_3 (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int number_number_of_int min)) _let_2) _let_1))))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted) (N $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (rcis R_3 A_3)) N) (rcis (hAPP_nat_real (hAPP_r474017924t_real power_power_real R_3) N) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) A_3)))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat K_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1)))))) (forall ((X_1 $$unsorted)) (= (= X_1 one_one_real) (= one_one_real (hAPP_real_real sqrt X_1)))) (forall ((V_5 $$unsorted) (W_3 $$unsorted) (C_55 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_5) W_3))) C_55) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat V_5)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_int_rat number_number_of_rat W_3)) C_55)))) (forall ((A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) P_5))) (= (comple219730294t_bool (setS A P_5)) (hAPP_i1948725293t_bool sRStar P_5)))))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A)) (hAPP_real_real _let_1 B))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)))))) (forall ((C_58 $$unsorted) (D_11 $$unsorted) (A_136 $$unsorted) (B_105 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_136) B_105)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat C_58) D_11)) (=> (hBOOL (hAPP_nat_bool _let_1 A_136)) (=> (hBOOL (hAPP_nat_bool _let_1 C_58)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_136) C_58)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_105) D_11))))))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_int_rat number_number_of_rat X_1)) one_one_rat)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) (hAPP_int_int bit1 pls))))) (forall ((R_3 $$unsorted) (X $$unsorted)) (= (hAPP_complex_real re (hAPP_complex_complex (scaleR1652505878omplex R_3) X)) (hAPP_real_real (scaleR_scaleR_real R_3) (hAPP_complex_real re X)))) (forall ((Z_3 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (and (is_int Z_3) (is_int Z_2)) (=> (hBOOL (hAPP_int_bool _let_1 Z_2)) (=> (hBOOL (hAPP_int_bool _let_1 Z_3)) (= (= (hAPP_int_nat nat Z_2) (hAPP_int_nat nat Z_3)) (= Z_3 Z_2))))))) (forall ((V_9 $$unsorted) (U_2 $$unsorted) (Y_19 $$unsorted) (X_25 $$unsorted) (A_127 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_25) A_127)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_19) A_127)) (=> (hBOOL (hAPP_real_bool _let_1 U_2)) (=> (hBOOL (hAPP_real_bool _let_1 V_9)) (=> (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real U_2) V_9) one_one_real) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real U_2) X_25)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real V_9) Y_19))) A_127))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_bool P (hAPP_int_nat Q R)) (hAPP_int_bool (hAPP_f1448486952t_bool (hAPP_f696844121t_bool cOMBB_nat_bool_int P) Q) R))) (forall ((A_91 $$unsorted)) (=> (is_int A_91) (= A_91 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_91) one_one_int)))) (forall ((X_21 $$unsorted) (N_31 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X_21))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_31)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_31) one_one_nat))) X_21) (hAPP_nat_int _let_1 N_31))))) (forall ((A_234 $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A_234) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_234) A_234))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)) (not (= X_1 Y_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2)))) (= (hAPP_real_real cos _let_69) zero_zero_real) (forall ((A_194 $$unsorted) (B_150 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real A_194) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_150) A_194)))) (forall ((N_1 $$unsorted) (K_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat K_1))) (=> (hBOOL (hAPP_nat_bool _let_1 Ma)) (=> (hBOOL (hAPP_nat_bool _let_1 N_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat Ma) K_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) K_1)))))))) (forall ((V_5 $$unsorted) (W_3 $$unsorted) (C_55 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_5) W_3))) C_55) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex V_5)) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_int_complex number528085621omplex W_3)) C_55)))) (forall ((X_39 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_39) X_39) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_39) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((D $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool coprime D))) (= (and (hBOOL (hAPP_nat_bool _let_1 A)) (hBOOL (hAPP_nat_bool _let_1 B))) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A) B)))))) (forall ((Ta $$unsorted) (A_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int Ta))) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa))))))))) (=> (hBOOL (hAPP_int_bool _let_1 X_2)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) D_1)))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)))) (forall ((M_12 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_nat_int semiri1621563631at_int M_12)))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int one_one_int) Z_1) Z_1))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (= (hBOOL (hAPP_int_bool _let_1 A)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) A)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= Y_2 X_1) (= (hAPP_real_real exp_real X_1) (hAPP_real_real exp_real Y_2)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real sqrt X))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (hAPP_real_real inverse_inverse_real _let_1) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real _let_1) X))))) (forall ((B_2 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int D_3))) (=> (= one_one_int (hAPP_int_int _let_1 A_3)) (=> (= (hAPP_int_int _let_1 B_2) one_one_int) (= one_one_int (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (is_int Y_2) (is_int X_1)) (= (= X_1 Y_2) (= (hAPP_int_int number_number_of_int X_1) (hAPP_int_int number_number_of_int Y_2))))) (forall ((A_190 $$unsorted) (B_146 $$unsorted) (K_7 $$unsorted)) (=> (= A_190 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_146) K_7)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex B_146) A_190)))) (forall ((B_43 $$unsorted) (B_42 $$unsorted) (A_52 $$unsorted) (C_23 $$unsorted) (A_51 $$unsorted)) (=> (= (hAPP_nat_nat (div_mod_nat A_52) C_23) (hAPP_nat_nat (div_mod_nat A_51) C_23)) (=> (= (hAPP_nat_nat (div_mod_nat B_43) C_23) (hAPP_nat_nat (div_mod_nat B_42) C_23)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_52) B_43)) C_23) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_51) B_42)) C_23))))) (forall ((A $$unsorted)) (= (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) A) zero_zero_rat) (= A zero_zero_rat))) (forall ((A $$unsorted)) (hBOOL (tendst1507391555omplex cnj (hAPP_complex_complex cnj A) (at_complex A)))) (forall ((B_128 $$unsorted) (A_168 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_168)) (=> (hBOOL (hAPP_nat_bool _let_1 B_128)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_168) B_128))))))) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool P_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int L) X_2)))) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_Q2096512830t_bool P_1 X_2)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int L) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int X_2) zero_z891286103de_int))))))) (forall ((A_235 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_235) A_235)) A_235) (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_235) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))))) (forall ((K_2 $$unsorted) (M $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong K_2) K_2) M))) (= one_one_complex _let_25) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (is_int B_2) (=> (not (= B_2 zero_zero_int)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)) (hAPP_int_int (div_mod_int A_3) B_2))))))) (=> (not _let_19) (not _let_68)) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) X)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real cos X)) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sin X)) _let_2)))))) (forall ((A_3 $$unsorted) (X $$unsorted)) (= (hAPP_real_real (scaleR_scaleR_real A_3) X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_3) X))) (forall ((Y_6 $$unsorted) (P_6 $$unsorted) (N_10 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat Y_6))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_6) N_10)) (= (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc N_10)) P_6)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_10) P_6))) Y_6))))) (forall ((Y $$unsorted) (X $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (let ((_let_3 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (let ((_let_4 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real U_1) (hAPP_int_real number267125858f_real _let_1)))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) U_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) _let_4)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) _let_4)) (=> (hBOOL (hAPP_real_bool _let_3 X)) (=> (hBOOL (hAPP_real_bool _let_3 Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_2)))) U_1)))))))))))) (forall ((D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int D_3))) (=> (= (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2)) one_one_int) (= (hAPP_int_int _let_1 B_2) one_one_int)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) pi)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real cos X)) (hAPP_real_real cos Y))))))) (forall ((B_117 $$unsorted) (A_156 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) A_156)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral B_117) zero_z126310315umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_156) B_117)) zero_z126310315umeral))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f2119767738t_bool P (hAPP_r632163725t_bool Q R)) (hAPP_r481142414t_bool (hAPP_f1625314454t_bool (hAPP_f340152631t_bool cOMBB_1453147152l_real P) Q) R))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) B_2)))) (let ((_let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) A_3)))) (=> (and (not _let_2) _let_1) (not (and _let_2 (not _let_1))))))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_nat_nat fact_fact_nat N)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (is_int Y_2) (is_int X_1)) (= (or (not (= zero_zero_int X_1)) (not (= zero_zero_int Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) X_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y_2) Y_2))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (P_3 $$unsorted) (Q_2 $$unsorted)) (=> (= (normalize (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A_3) B_2)) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract P_3) Q_2) (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)))) (forall ((P_1 $$unsorted) (I_1 $$unsorted) (K_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I_1) K_1)) (=> (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int K_1) one_one_int))) (=> (forall ((I_2 $$unsorted)) (=> (is_int I_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I_2) K_1)) (=> (hBOOL (hAPP_int_bool P_1 I_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int I_2) one_one_int))))))) (hBOOL (hAPP_int_bool P_1 I_1)))))) (forall ((Y $$unsorted)) (= (hAPP_real_real tan (hAPP_real_real arctan Y)) Y)) (forall ((A_154 $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_154) A_154)) zero_zero_real)))) (forall ((K_2 $$unsorted)) (= (frct (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int number_number_of_int K_2)) one_one_int)) (hAPP_int_rat number_number_of_rat K_2))) (forall ((C_33 $$unsorted) (D_5 $$unsorted) (A_79 $$unsorted) (B_67 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_79) B_67)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C_33) D_5)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_79) C_33)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_67) D_5)))))) (forall ((N $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat V_2)) N)))) (let ((_let_2 (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int V_2))))) (and (=> (not _let_2) (= _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int succ V_2))) N))) (=> _let_2 (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat one_one_nat) N) _let_1)))))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real arcsin Y))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) one_one_real)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) _let_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_2)) _let_1)))))))) (forall ((B_1_1 $$unsorted)) (is_bool (cauchy_complex B_1_1))) (forall ((A_202 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int zero_zero_int) A_202) zero_zero_int)) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N))) (=> (not (= zero_zero_nat N)) (= (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_2) _let_1))) _let_2))))) (forall ((A_140 $$unsorted) (C_62 $$unsorted) (B_109 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_140) C_62)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_109) C_62))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_62)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_140) B_109))))) (forall ((X_42 $$unsorted) (Y_30 $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_42) X_42)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y_30) Y_30))) zero_zero_int)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (= (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) B))) (or (and (hBOOL (hAPP_rat_bool _let_1 B)) (hBOOL (hAPP_rat_bool _let_1 A))) (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A) zero_zero_rat))))))) (forall ((C_60 $$unsorted) (D_13 $$unsorted) (A_138 $$unsorted) (B_107 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_138) B_107)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int C_60) D_13)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) A_138)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_60)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_138) C_60)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_107) D_13)))))))) (forall ((B_45 $$unsorted) (B_44 $$unsorted) (A_54 $$unsorted) (C_24 $$unsorted) (A_53 $$unsorted)) (=> (= (hAPP_Q1762011733de_int (div_mo231679042de_int A_53) C_24) (hAPP_Q1762011733de_int (div_mo231679042de_int A_54) C_24)) (=> (= (hAPP_Q1762011733de_int (div_mo231679042de_int B_45) C_24) (hAPP_Q1762011733de_int (div_mo231679042de_int B_44) C_24)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_53) B_44)) C_24) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_54) B_45)) C_24))))) (forall ((P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_3) (hAPP_nat_nat suc zero_zero_nat)))))) (forall ((A_239 $$unsorted) (B_167 $$unsorted) (V_15 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real V_15))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_239) _let_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_167) _let_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_239) B_167)) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B)) zero_zero_real)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_complex_real norm_norm_complex X))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real _let_1)) _let_1)))) (not (= zero_zero_complex ii)) (forall ((C_73 $$unsorted) (A_173 $$unsorted) (B_133 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_173) B_133)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_73)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_173) C_73)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_133) C_73)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int N_1) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (quickcheck_int_of N_1)) (quickcheck_int_of Ma))))) (forall ((Z_2 $$unsorted) (W_1 $$unsorted)) (=> (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) W_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_int_nat nat W_1)) (hAPP_int_nat nat Z_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W_1) Z_2))))) (forall ((W_8 $$unsorted)) (let ((_let_1 (hAPP_int_complex number528085621omplex W_8))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex _let_1) _let_1) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((A $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) A_1)) (= one_one_int (hAPP_int_int (legacy_zgcd A) Ma))))) (forall ((A_140 $$unsorted) (C_62 $$unsorted) (B_109 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_140) C_62)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_109) C_62))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_62)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_140) B_109))))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (hAPP_P1975530577nt_int (hAPP_P1145851913nt_int (hAPP_b40753821nt_int if_Pro1731782967nt_int fFalse) X) Y))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (hAPP_int_int (legacy_zgcd A) B) one_one_int) (not (exists ((P_4 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int P_4))) (and (hBOOL (hAPP_int_bool zprime P_4)) (hBOOL (hAPP_int_bool _let_1 B)) (hBOOL (hAPP_int_bool _let_1 A)) (is_int P_4))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Y) X)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int abs_abs_int X)) (hAPP_int_int abs_abs_int Y)) (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) Y))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (is_int B_2_1) (is_bool (hAPP_int_bool B_1_1 B_2_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y)) X))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat Y))) (let ((_let_2 (hAPP_nat_fun_nat_nat plus_plus_nat X))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_2 Z_1)) (hAPP_nat_nat _let_2 (hAPP_nat_nat _let_1 Z_1)))))) (forall ((I $$unsorted) (K_2 $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) J_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat I) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) K_2)) J_2)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A) C)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B) C))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A) B)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (archim791455193or_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2))) (is_int m) (forall ((A_91 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_91) one_one_complex) A_91)) (= zero_zero_real (hAPP_complex_real im zero_zero_complex)) (forall ((Ma $$unsorted) (D $$unsorted)) (= (exists ((Q_4 $$unsorted)) (= Ma (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat D) Q_4))) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat Ma) D)))) (forall ((N_66 $$unsorted) (A_210 $$unsorted) (B_158 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_210) B_158)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_210)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_66)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_210) N_66)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_158) N_66))))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (= (archim856651990g_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) (hAPP_int_real real_int A_3))) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (archim856651990g_real X)) A_3))) (forall ((X_40 $$unsorted) (N_69 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X_40))) (let ((_let_2 (hAPP_nat_int _let_1 N_69))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_2) _let_2) (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_69)))))) (forall ((N_62 $$unsorted)) (= one_on1645066479umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral one_on1645066479umeral) N_62))) (forall ((A_216 $$unsorted)) (= A_216 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int one_on1684967323de_int) A_216))) (forall ((M_19 $$unsorted) (N_44 $$unsorted) (A_132 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_132))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int) A_132)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int _let_1 M_19)) (hAPP_n522471361de_int _let_1 N_44))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_19) N_44)))))) (forall ((Z_1 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (natfloor Z_1)) one_one_nat)) N)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Z_1) (hAPP_nat_real real_nat N))))) (forall ((M_27 $$unsorted) (A_212 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_212) one_on1645066479umeral)) M_27) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral M_27) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_212) M_27)))) (forall ((Sa $$unsorted) (Ta $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A) B)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Sa) Ta)) (hBOOL (hAPP_f115998247l_bool (hAPP_P1876494581l_bool member180897546at_nat (hAPP_P369611207at_nat (hAPP_P402336767at_nat produc494345619at_nat (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat A) Sa)) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat B) Ta))) pair_less))))) (forall ((X_8 $$unsorted) (Q_7 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_8))) (= (hAPP_nat_real _let_1 (hAPP_nat_nat suc Q_7)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real _let_1 Q_7)) X_8)))) (forall ((A_236 $$unsorted)) (=> (is_int A_236) (= A_236 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_236) (hAPP_int_int number_number_of_int (hAPP_int_int bit1 pls)))))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral minus_1690775515umeral zero_z126310315umeral) one_on1645066479umeral) zero_z126310315umeral) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (=> (= (hAPP_nat_nat (div_mod_nat N) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_1))) one_one_nat) (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) one_one_nat)) (hAPP_int_nat number_number_of_nat _let_1))))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N)) (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat M) N))))) (forall ((A_140 $$unsorted) (C_62 $$unsorted) (B_109 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_140) C_62)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_109) C_62))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) C_62)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_140) B_109))))) (forall ((C_75 $$unsorted) (A_175 $$unsorted) (B_135 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_75))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_175) B_135)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_75)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 A_175)) (hAPP_nat_nat _let_1 B_135))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (cis (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_3) B_2)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (cis A_3)) (cis B_2)))) (forall ((B_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B_2) one_one_int) (hAPP_int_int (div_mod_int (hAPP_int_int number_number_of_int min)) B_2)))) (forall ((N_29 $$unsorted) (K_6 $$unsorted) (M_16 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_6))) (=> (hBOOL (hAPP_nat_bool _let_1 M_16)) (=> (hBOOL (hAPP_nat_bool _let_1 N_29)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (div_mod_nat M_16) N_29))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f713949180nt_int P (hAPP_i1153444985nt_int Q R)) (hAPP_i1836591008nt_int (hAPP_f617310012nt_int (hAPP_f197974549nt_int cOMBB_638531587nt_int P) Q) R))) (forall ((C_79 $$unsorted) (D_15 $$unsorted) (A_179 $$unsorted) (B_139 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_179) B_139)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C_79) D_15)) (=> (hBOOL (hAPP_int_bool _let_1 B_139)) (=> (hBOOL (hAPP_int_bool _let_1 C_79)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_179) C_79)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_139) D_15))))))))) (forall ((R_2 $$unsorted)) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real plus_plus_real R_2)) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) suc))) R_2 sequentially))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (and (is_int Z) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) Sa)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) Z)) (= _let_1 _let_1))))))) (forall ((A_47 $$unsorted) (B_38 $$unsorted) (C_19 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_47) B_38)) C_19) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_47) C_19)) B_38)) C_19))) (forall ((N_53 $$unsorted) (M_21 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int one_one_int))) (=> (hBOOL (hAPP_int_bool _let_1 M_21)) (=> (hBOOL (hAPP_int_bool _let_1 N_53)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int M_21) N_53))))))) (forall ((A_230 $$unsorted) (C_96 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex C_96) A_230) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_230) C_96))) (forall ((A_218 $$unsorted) (B_161 $$unsorted) (C_90 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_218) C_90)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_161) C_90)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_218) B_161)) C_90))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (isCont_real_real arctan) X_1))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat I))) (=> (hBOOL (hAPP_nat_bool _let_1 J_2)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) M)))))) (forall ((X $$unsorted)) (= (hAPP_complex_real im (hAPP_complex_complex cnj X)) (hAPP_real_real uminus_uminus_real (hAPP_complex_real im X)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool even_odd_even_nat Y_2)))) (let ((_let_2 (hBOOL (hAPP_nat_bool even_odd_even_nat X_1)))) (= (or (and _let_2 _let_1) (and (not _let_2) (not _let_1))) (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_1) Y_2))))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set B_1)) (= (= B_1 A_1) (= (image_int_nat nat A_1) (image_int_nat nat B_1)))))) (forall ((B $$unsorted) (A $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool (bnorRset A) Ma))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A)))) (forall ((X_37 $$unsorted)) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_37) one_one_nat) X_37)) (forall ((X_41 $$unsorted) (Y_29 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_41) _let_2)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_29) _let_2))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_1)) X_41)) Y_29)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_41) Y_29)) _let_2))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N))) (let ((_let_2 (hAPP_nat_nat fact_fact_nat _let_1))) (and (=> (not (= M zero_zero_nat)) (= _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) (hAPP_nat_nat fact_fact_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) one_one_nat)) N))))) (=> (= zero_zero_nat M) (= (hAPP_nat_nat fact_fact_nat N) _let_2)))))) (forall ((X_9 $$unsorted)) (let ((_let_1 (hAPP_nat_int semiri1621563631at_int (hAPP_int_nat nat X_9)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_9)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_9))) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_1) _let_1))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 X_1)) (=> (hBOOL (hAPP_rat_bool _let_1 Y_2)) (= (and (= X_1 zero_zero_rat) (= zero_zero_rat Y_2)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_1) Y_2) zero_zero_rat)))))) (not (= ii one_one_complex)) (forall ((Z_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Z_1) Z_1))) (forall ((A_89 $$unsorted)) (= A_89 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int one_on1684967323de_int) A_89))) (forall ((N_49 $$unsorted) (A_147 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real one_one_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_147)) (hBOOL (hAPP_real_bool _let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_147) N_49)))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (not (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int N)))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (natfloor X)) (hAPP_int_nat number_number_of_nat N)) (natfloor (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_int_real number267125858f_real N))))))) _let_67 (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) one_one_nat)) N))) (= zero_zero_nat (hAPP_C2129356693al_nat size_s945831648umeral zero_z126310315umeral)) (forall ((B $$unsorted) (A $$unsorted)) (=> (and (is_int B) (is_int A)) (= (= zero_zero_int A) (= B (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B) A))))) (forall ((A_111 $$unsorted) (B_89 $$unsorted) (C_49 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real A_111))) (=> (= (hAPP_real_real _let_1 B_89) (hAPP_real_real _let_1 C_49)) (= C_49 B_89)))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real (hAPP_int_real real_int X_1)) ring_1_Ints_real))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_1) zero_zero_int)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat nat (hAPP_int_int uminus_uminus_int Z_1))) (hAPP_int_nat nat (hAPP_int_int uminus_uminus_int Z_4))) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z_1) Z_4))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex C))) (= (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_complex_complex _let_1 A)) (hAPP_complex_complex _let_1 B))) (or (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex A) B)) (= C zero_zero_complex))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i998473677nt_int (hAPP_f142232355nt_int (hAPP_f1377453843nt_int cOMBB_320287386nt_int P) Q) R) (hAPP_f2002277285nt_int P (hAPP_i1584592887nt_int Q R)))) (forall ((A_129 $$unsorted) (N_40 $$unsorted) (N_39 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_129))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_40) N_39)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_129)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int _let_1 N_40)) (hAPP_nat_int _let_1 N_39))))))) (forall ((V_7 $$unsorted) (B_101 $$unsorted) (C_56 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex V_7)))) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex _let_1 B_101)) (hAPP_complex_complex _let_1 C_56)) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex B_101) C_56))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (= A_1 B_1) (= (image_nat_int semiri1621563631at_int A_1) (image_nat_int semiri1621563631at_int B_1)))) (forall ((N $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X)) (hBOOL (hAPP_int_bool nat_is_nat (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) N))))) (forall ((X $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) M)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd X) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) (hAPP_int_nat phi M))) one_one_int) M))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_2)) Y)) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat (hAPP_nat_nat suc N_2))) Y)))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_2 $$unsorted)) (= (= (hAPP_nat_nat (div_mod_nat X_1) N_1) (hAPP_nat_nat (div_mod_nat Y_2) N_1)) (exists ((Q1 $$unsorted) (Q2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat N_1))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Y_2) (hAPP_nat_nat _let_1 Q2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_1) (hAPP_nat_nat _let_1 Q1))))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (=> (is_int Z_2) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W_1) Z_2)) (exists ((N_2 $$unsorted)) (= Z_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int W_1) (hAPP_nat_int semiri1621563631at_int N_2))))))) (= (hAPP_real_real sin zero_zero_real) zero_zero_real) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (inv P_3))) (=> (is_int A_3) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) P_3)) (= A_3 (hAPP_int_int _let_1 (hAPP_int_int _let_1 A_3)))))))))) (forall ((V_2 $$unsorted)) (= (hAPP_int_real real_int (hAPP_int_int number_number_of_int V_2)) (hAPP_int_real number267125858f_real V_2))) (forall ((B_1_1 $$unsorted)) (is_bool (monoseq_real B_1_1))) (forall ((N $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int N) (archim856651990g_real (hAPP_nat_real real_nat N)))) (forall ((M $$unsorted) (N $$unsorted) (S_3 $$unsorted) (S_1 $$unsorted) (T_2 $$unsorted) (T_1 $$unsorted) (R_5 $$unsorted) (R_3 $$unsorted) (K_2 $$unsorted)) (=> (= (hAPP_int_int (legacy_zgcd R_5) R_3) K_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) R_3)) (exists ((Sn $$unsorted) (Tn $$unsorted)) (and (is_int Tn) (= (hAPP_P408881810nt_int (hAPP_i1730167831nt_int produc282740534nt_int K_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Sn) Tn)) (xzgcda M N R_5 R_3 S_3 S_1 T_2 T_1)) (is_int Sn)))))) (forall ((A_145 $$unsorted) (M_20 $$unsorted) (N_48 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_145))) (= (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_20) N_48)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int _let_1 M_20)) (hAPP_nat_int _let_1 N_48))))) (hBOOL (hAPP_int_bool nat_is_nat _let_37)) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) (or (= M zero_zero_nat) (= N one_one_nat)))) (forall ((Y $$unsorted) (X $$unsorted)) (exists ((R_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real R_1))) (and (= X (hAPP_real_real _let_1 (hAPP_real_real cos A_2))) (= Y (hAPP_real_real _let_1 (hAPP_real_real sin A_2))))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (deriv_real ln X_1) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) X_1))))) (hBOOL (hAPP_real_bool _let_64 one_one_real)) (forall ((A_9 $$unsorted) (N_14 $$unsorted) (B_7 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_14))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_9) _let_1)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral B_7) _let_1))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) B_7)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_9) B_7)))))) (forall ((V_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat one_one_nat) (hAPP_int_nat number_number_of_nat V_2)))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int V_2) pls)))) (and (=> _let_2 (= _let_1 one_one_nat)) (=> (not _let_2) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int succ V_2)) _let_1)))))) (forall ((A_33 $$unsorted) (B_27 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_33) B_27)) B_27) zero_zero_int)) (forall ((A_203 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_203) zero_zero_nat) zero_zero_nat)) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Z1))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 Z2)) Z3) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real Z2) Z3))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_i769753017umeral number1443263063umeral Y_2))) (let ((_let_2 (hAPP_i769753017umeral number1443263063umeral X_1))) (= (= (hAPP_C498520661umeral (div_mo1740067990umeral _let_1) _let_2) zero_z126310315umeral) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral _let_2) _let_1)))))) (forall ((V_19 $$unsorted) (W_15 $$unsorted)) (= (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_19) W_15)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real V_19)) (hAPP_int_real number267125858f_real W_15)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1356864277nt_int (hAPP_i744251628nt_int P R) Q) (hAPP_int_fun_int_int (hAPP_f1760145644nt_int (hAPP_f808647893nt_int cOMBC_736024425nt_int P) Q) R))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X_1)) (=> (hBOOL (hAPP_int_bool _let_1 Y_2)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) Y_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_int_nat nat X_1)) (hAPP_int_nat nat Y_2)))))))) (= _let_5 _let_65) (forall ((M_19 $$unsorted) (N_44 $$unsorted) (A_132 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_132))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral) A_132)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral _let_1 M_19)) (hAPP_n1108039445umeral _let_1 N_44))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_19) N_44)))))) (forall ((A_3 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime one_one_nat) A_3))) (forall ((X_1 $$unsorted)) (= (= X_1 zero_zero_real) (= one_one_real (hAPP_real_real exp_real X_1)))) (forall ((A_113 $$unsorted) (B_91 $$unsorted) (C_51 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral A_113))) (= (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_91) C_51)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral _let_1 B_91)) C_51)))) (forall ((A_188 $$unsorted) (B_144 $$unsorted) (C_81 $$unsorted)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_188) B_144)) C_81)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex B_144) C_81)))) (forall ((Z_8 $$unsorted) (X_23 $$unsorted) (Y_18 $$unsorted)) (let ((_let_1 (hAPP_c1403687985x_bool dvd_dvd_complex X_23))) (=> (hBOOL (hAPP_complex_bool _let_1 Y_18)) (=> (hBOOL (hAPP_complex_bool _let_1 Z_8)) (hBOOL (hAPP_complex_bool _let_1 (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex Y_18) Z_8))))))) (forall ((Y_20 $$unsorted) (X_26 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X_26)) (=> (hBOOL (hAPP_int_bool _let_1 Y_20)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Y_20) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_26) Y_20)) X_26))))))) (forall ((X_1 $$unsorted)) (=> (is_int X_1) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (not (forall ((K $$unsorted)) (=> (is_int K) (not (= X_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) K)) one_one_int))))))))) (hBOOL (hAPP_int_bool twoSqu1770640450sum2sq _let_44)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat nat X)) (hAPP_int_nat nat Y)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) Y))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_1) X))) (let ((_let_3 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) _let_1))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_3)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) _let_3)) (= (hAPP_real_real tan X) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real sin _let_2)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real cos _let_2)) one_one_real))))))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) X_1)) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_r474017924t_real power_power_real X_1)) zero_zero_real sequentially)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_real real_int N))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) one_one_real))) (= (archim856651990g_real X) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int N) one_one_int)))))) (forall ((A_228 $$unsorted) (C_94 $$unsorted) (D_19 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real A_228))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 C_94)) D_19) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real C_94) D_19))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) pi)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sin X))))))) (forall ((A_10 $$unsorted) (N_15 $$unsorted) (B_8 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (let ((_let_2 (hAPP_nat_nat suc N_15))) (=> (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int B_8) _let_2) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_10) _let_2)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_10)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (hBOOL (monoseq_real A)) (hBOOL (tendsto_nat_real (hAPP_f292751352t_real (hAPP_f1607377819t_real cOMBB_1533963633al_nat (hAPP_f1509287679l_real big_co604158596t_real _let_1)) (hAPP_f618557131t_bool (hAPP_f1505651103t_bool cOMBB_800536526ol_nat (ord_at4362885an_nat zero_zero_nat)) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) one_one_nat))) (hAPP_f352196356l_real suminf_real _let_1) sequentially)))))) (forall ((M_27 $$unsorted) (A_212 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_212) one_one_real)) M_27) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real M_27) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_212) M_27)))) (forall ((B_2 $$unsorted) (B_5 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int div_div_int A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_5) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 B_2)) (hAPP_int_int _let_1 B_5)))))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) J_2)) (exists ((K $$unsorted)) (and (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I) K) J_2) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K)))))) (forall ((A_183 $$unsorted) (M_22 $$unsorted) (N_57 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_183))) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int (hAPP_n522471361de_int _let_1 M_22)) N_57) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_22) N_57))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z_1) W) (hAPP_int_int (hAPP_int_fun_int_int times_times_int W) Z_1))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_2))) (=> (= one_one_int (hAPP_int_int (legacy_zgcd N) K_2)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) M)) (hBOOL (hAPP_int_bool _let_1 M))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int X_1)) (hAPP_int_int number_number_of_int Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) Y_2)))) (forall ((X_35 $$unsorted) (Y_27 $$unsorted) (Q_11 $$unsorted)) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_35) Y_27)) Q_11) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_35) Q_11)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_27) Q_11)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A) C)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B) C))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A) B)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) zero_zero_int)) (= (hAPP_P1175774780nt_int product_snd_int_int (hAPP_P1975530577nt_int negateSnd (negDivAlg (hAPP_int_int uminus_uminus_int A_3) (hAPP_int_int uminus_uminus_int B_2)))) (hAPP_int_int (div_mod_int A_3) B_2))))) (forall ((R_3 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) R_3)) (not (forall ((S_2 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) S_2)) (forall ((T $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) T)) (not (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat S_2) T) R_3))))))))) (forall ((Ta $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= X_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa))))))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) Ta)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1)) Ta)))))))) (forall ((Ta $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real D) D_1)) (forall ((X_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool dvd_dvd_real D))) (= (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_2) Ta))) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_2) (hAPP_real_real (hAPP_r1250527377l_real times_times_real K) D_1))) Ta)))))))) (forall ((C_34 $$unsorted) (D_6 $$unsorted) (A_80 $$unsorted) (B_68 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_80) B_68)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C_34) D_6)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_80) C_34)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_68) D_6)))))) (forall ((A_229 $$unsorted) (C_95 $$unsorted) (D_20 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real C_95))) (let ((_let_2 (hAPP_r1250527377l_real plus_plus_real A_229))) (= (hAPP_real_real _let_1 (hAPP_real_real _let_2 D_20)) (hAPP_real_real _let_2 (hAPP_real_real _let_1 D_20)))))) (forall ((N $$unsorted)) (not (hBOOL (hAPP_int_bool nat_neg (hAPP_nat_int semiri1621563631at_int N))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (= (hAPP_int_nat nat (hAPP_int_int (div_mod_int X) Y)) (hAPP_nat_nat (div_mod_nat (hAPP_int_nat nat X)) (hAPP_int_nat nat Y))))))) (forall ((N_1 $$unsorted) (F $$unsorted)) (=> (hBOOL (summable_real F)) (=> (forall ((M_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) M_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real F M_1))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real F) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_f352196356l_real suminf_real F)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= (hAPP_nat_real semiri132038758t_real N_1) (hAPP_nat_real semiri132038758t_real Ma)) (= N_1 Ma))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (deriv_real sqrt X_1) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real inverse_inverse_real (hAPP_real_real sqrt X_1))) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))) (forall ((N_61 $$unsorted) (X_29 $$unsorted) (Y_23 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real X_29) Y_23)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_29) N_61)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_23) N_61))))) (forall ((A_146 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_146) zero_zero_nat) one_one_nat)) (forall ((A_87 $$unsorted) (B_75 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_87) B_75)) B_75) A_87)) (forall ((V_19 $$unsorted) (W_15 $$unsorted)) (= (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_19) W_15)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex V_19)) (hAPP_int_complex number528085621omplex W_15)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (is_int Y_2) (is_int X_1)) (= (= (hAPP_int_real real_int Y_2) (hAPP_int_real real_int X_1)) (= X_1 Y_2)))) (forall ((B_36 $$unsorted) (A_45 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral A_45) B_36) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_36) A_45)) B_36))) (forall ((A_220 $$unsorted)) (=> (is_int A_220) (= A_220 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int zero_zero_int) A_220)))) (forall ((A_77 $$unsorted)) (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_77) zero_zero_real))) (forall ((B_74 $$unsorted) (A_86 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_86) zero_z891286103de_int)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int B_74) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_86) B_74)) zero_z891286103de_int))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_2) _let_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_1) Y_2))))) (forall ((N $$unsorted)) (= (hAPP_real_real (hAPP_n546711566l_real root N) zero_zero_real) zero_zero_real)) (forall ((A_227 $$unsorted) (B_164 $$unsorted) (C_93 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_227))) (= (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_164) C_93)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 B_164)) C_93)))) (forall ((Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) Z_1))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_f115998247l_bool B_1_1 B_2_1))) (forall ((P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) P_3)))) (forall ((A_182 $$unsorted)) (= A_182 (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A_182) one_one_nat))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_complex_real re X))) (= (hAPP_complex_real re (hAPP_complex_complex invers1449016382omplex X)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real _let_2) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_2) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_complex_real im X)) _let_1))))))) (forall ((R_3 $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real R_3) X)) Y) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (of_real_complex R_3)) (hAPP_real_complex (hAPP_r265291036omplex complex X) Y)))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_1)) (= (= (hAPP_nat_nat _let_1 Ma) (hAPP_nat_nat _let_1 N_1)) (= N_1 Ma))))) (forall ((K_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (hAPP_n1699378549t_bool ord_lessThan_nat K_1)))) (forall ((I $$unsorted) (J_2 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat minus_minus_nat I))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 J_2)) K_2) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) K_2))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f448129468l_bool (hAPP_i2112223885l_bool P R) Q) (hAPP_int_bool (hAPP_f1805168059t_bool (hAPP_f202917053t_bool cOMBC_94739984l_bool P) Q) R))) (forall ((X $$unsorted)) (= (hAPP_int_real number267125858f_real X) (hAPP_int_real ring_1_of_int_real X))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N) (hAPP_P1654798560at_nat product_fst_nat_nat (divmod_nat M N)))) (forall ((M $$unsorted)) (= (hAPP_int_int abs_abs_int M) (hAPP_int_int (legacy_zgcd zero_zero_int) M))) (forall ((A_205 $$unsorted) (B_156 $$unsorted)) (=> (and (is_int B_156) (is_int A_205)) (=> (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_205) B_156)) (or (= zero_zero_int B_156) (= zero_zero_int A_205))))) (forall ((A_216 $$unsorted)) (= A_216 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral one_on1645066479umeral) A_216))) (forall ((V_8 $$unsorted) (W_4 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int number_number_of_int V_8)) (hAPP_int_int number_number_of_int W_4)) (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int V_8) W_4)))) (forall ((C_73 $$unsorted) (A_173 $$unsorted) (B_133 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_173) B_133)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_73)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_173) C_73)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_133) C_73)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_nat_nat (nat_gcd X) Y))) (and (=> (not (= zero_zero_nat Y)) (= (hAPP_nat_nat (nat_gcd Y) (hAPP_nat_nat (div_mod_nat X) Y)) _let_1)) (=> (= Y zero_zero_nat) (= X _let_1))))) (forall ((A_55 $$unsorted) (C_25 $$unsorted) (B_46 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (div_mod_nat A_55) C_25)) B_46)) C_25) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_55) B_46)) C_25))) (forall ((Q $$unsorted) (P $$unsorted)) (or (hBOOL P) (hBOOL (hAPP_bool_bool (fimplies P) Q)))) (forall ((A_90 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int one_on1684967323de_int) A_90) A_90)) (forall ((B_117 $$unsorted) (A_156 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_156)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B_117) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_156) B_117)) zero_zero_real))))) (forall ((A_20 $$unsorted) (C_6 $$unsorted) (B_16 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat A_20))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat C_6) B_16)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat _let_1 B_16)) C_6) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B_16) C_6)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1948725293t_bool (hAPP_f1791153283t_bool (hAPP_f735247205t_bool cOMBC_983868720t_bool P) Q) R) (hAPP_f429935748t_bool (hAPP_i872162435t_bool P R) Q))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) one_one_nat))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) (hAPP_nat_nat fact_fact_nat N)) (hAPP_nat_nat fact_fact_nat _let_1)))) (forall ((A_202 $$unsorted)) (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat zero_zero_rat) A_202))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (= (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sqrt Y_2))) (hBOOL (hAPP_real_bool _let_1 Y_2))))) (forall ((R_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real R_3) one_one_real)) (hAPP_int_real real_int (archim1246769320r_real R_3))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (= (or (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) zero_zero_int)) (hBOOL (hAPP_int_bool _let_1 B))) (and (hBOOL (hAPP_int_bool _let_1 A)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) zero_zero_int)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) B)) zero_zero_int))))) (forall ((A_91 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_91) one_on1645066479umeral) A_91)) (forall ((A_29 $$unsorted) (B_24 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_29) B_24)) (= zero_zero_nat (hAPP_nat_nat (div_mod_nat B_24) A_29)))) (forall ((Xa_4 $$unsorted) (X_16 $$unsorted) (Y_13 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Xa_4))) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_16) Y_13)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 X_16)) (hAPP_real_real _let_1 Y_13))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 N_1)) (= (hAPP_int_nat nat N_1) (hAPP_f957591787ol_nat finite_card_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) _let_1)) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) N_1)))))))) (forall ((C_88 $$unsorted) (A_206 $$unsorted) (B_157 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_206))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_157)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int B_157) C_88)) (hBOOL (hAPP_Q2096512830t_bool _let_1 C_88)))))) (forall ((A_36 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat zero_zero_nat) A_36) zero_zero_nat)) (forall ((N $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A_3) B_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_3) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_2) N))))) (forall ((M_6 $$unsorted) (N_20 $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_nat_real semiri132038758t_real M_6)) N_20) (hAPP_nat_real semiri132038758t_real (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M_6) N_20)))) (forall ((B_128 $$unsorted) (A_168 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_168)) (=> (hBOOL (hAPP_real_bool _let_1 B_128)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_168) B_128))))))) (forall ((N_53 $$unsorted) (M_21 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat one_one_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 M_21)) (=> (hBOOL (hAPP_nat_bool _let_1 N_53)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_21) N_53))))))) (forall ((V_11 $$unsorted) (W_9 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex V_11)) (hAPP_int_complex number528085621omplex W_9)) (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_11) W_9)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)))) (=> (and _let_1 (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X)))) _let_1))) (forall ((B $$unsorted) (A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool (wset A) P_5)))))))) (forall ((Z_1 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_complex_real im Z_1)) (hAPP_complex_real norm_norm_complex Z_1)) (hAPP_complex_real im (hAPP_complex_complex sgn_sgn_complex Z_1)))) (forall ((C_37 $$unsorted) (A_95 $$unsorted) (B_77 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_95) B_77)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_95) C_37)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_77) C_37))))) (forall ((A $$unsorted) (B $$unsorted)) (= (forall ((P_4 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_4))) (not (and (hBOOL (hAPP_nat_bool prime P_4)) (hBOOL (hAPP_nat_bool _let_1 B)) (hBOOL (hAPP_nat_bool _let_1 A)))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A) B)))) (forall ((A_73 $$unsorted) (A_72 $$unsorted) (B_61 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A_73) A_72)) B_61) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_73) B_61)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_72) B_61)))) (forall ((N $$unsorted) (X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) X))) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real real_nat N)) (hAPP_nat_real real_nat X))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1948725293t_bool (hAPP_f428220345t_bool (hAPP_f654702867t_bool cOMBB_591320580ol_int P) Q) R) (hAPP_f1805168059t_bool P (hAPP_i1948725293t_bool Q R)))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat Lx_3))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 Ly_1)) Rx_3) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 Rx_3)) Ly_1)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_real_real cos Y))) (let ((_let_2 (hAPP_real_real cos X))) (=> (not (= _let_2 zero_zero_real)) (=> (not (= _let_1 zero_zero_real)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_2) _let_1)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real tan X)) (hAPP_real_real tan Y))))))))) (forall ((C_42 $$unsorted) (A_100 $$unsorted) (B_82 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_100) B_82)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_100) C_42)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_82) C_42))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_2) zero_zero_int)) (= (hAPP_P1175774780nt_int product_snd_int_int (hAPP_P1975530577nt_int negateSnd (posDivAlg (hAPP_int_int uminus_uminus_int A_3) (hAPP_int_int uminus_uminus_int B_2)))) (hAPP_int_int (div_mod_int A_3) B_2))))) (forall ((A_3 $$unsorted) (N $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_2) N))) (=> (not (= zero_zero_nat N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_3) B_2))))) (forall ((W_8 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real W_8))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_1) _let_1) (hAPP_nat_real (hAPP_r474017924t_real power_power_real _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((A_91 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_91) one_on1684967323de_int) A_91)) (forall ((X_3 $$unsorted) (A $$unsorted)) (=> (hBOOL (tendsto_nat_complex X_3 A sequentially)) (hBOOL (tendsto_nat_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat im) X_3) (hAPP_complex_real im A) sequentially)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real sin Y))) (let ((_let_3 (hAPP_r1250527377l_real times_times_real (hAPP_real_real sin X)))) (let ((_let_4 (hAPP_real_real cos Y))) (let ((_let_5 (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos X)))) (let ((_let_6 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y))) (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real sin _let_6)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_3 _let_4)) (hAPP_real_real _let_5 _let_2)))) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real cos _let_6)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real _let_5 _let_4)) (hAPP_real_real _let_3 _let_2)))) _let_1)))))))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int D) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int X_2) Sa))))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int X_2) Z)) (= _let_1 _let_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) M)) M) (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat N) M))) (forall ((M $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat V_2))) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat suc M)))) _let_1) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) M)) _let_1)))) (is_int t) (forall ((A_24 $$unsorted) (B_19 $$unsorted) (C_8 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_8))) (let ((_let_2 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int _let_1 A_24)) (hAPP_Q1762011733de_int _let_1 B_19)))) (let ((_let_3 (= zero_z891286103de_int C_8))) (and (=> (not _let_3) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_24) B_19) _let_2)) (=> _let_3 (= _let_2 zero_z891286103de_int))))))) (forall ((C_69 $$unsorted) (A_163 $$unsorted) (B_124 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_69))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_163) B_124)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_69)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 A_163)) (hAPP_nat_nat _let_1 B_124))))))) (forall ((N_16 $$unsorted) (M_5 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_16) M_5)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int semiri1621563631at_int M_5)) (hAPP_nat_int semiri1621563631at_int N_16)) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M_5) N_16))))) (forall ((X_36 $$unsorted) (Y_28 $$unsorted) (Z_9 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int X_36))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 Y_28)) (hAPP_Q1762011733de_int _let_1 Z_9)) (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int Y_28) Z_9))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int N_1) zero_zero_int)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int N_1)) zero_zero_real)))) (forall ((Y $$unsorted) (U_1 $$unsorted) (X1_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool _let_1 X1_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X1_1) Y)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) U_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y) (hAPP_real_real inverse_inverse_real X))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real U_1) (hAPP_real_real inverse_inverse_real X1_1))))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) M)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N) M) (= (hAPP_nat_nat suc zero_zero_nat) N)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real X_1)) (hAPP_int_real number267125858f_real Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) Y_2)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y)) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) Y)))) (forall ((C_70 $$unsorted) (A_164 $$unsorted) (B_125 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int C_70))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_164) B_125)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) C_70)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int _let_1 A_164)) (hAPP_Q1762011733de_int _let_1 B_125))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int B))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat X_1) Y_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int _let_1 X_1)) (hAPP_nat_int _let_1 Y_2))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1778081398nt_int (hAPP_f2004554147nt_int (hAPP_f1228585167nt_int cOMBB_1102189010nt_int P) Q) R) (hAPP_f1574055885nt_int P (hAPP_int_fun_int_int Q R)))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat I))) (=> (hBOOL (hAPP_nat_bool _let_1 J_2)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) M)))))) (not (hBOOL (trivial_limit_nat sequentially))) (forall ((A $$unsorted)) (hBOOL (hAPP_complex_bool (isCont_complex_real im) A))) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real _let_30)) suc)) one_one_real)) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A) B)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A) C)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B) C))))) (forall ((K_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_nat) K_1))))) (forall ((A_10 $$unsorted) (N_15 $$unsorted) (B_8 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (let ((_let_2 (hAPP_nat_nat suc N_15))) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_10) _let_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_8) _let_2)) (=> (hBOOL (hAPP_nat_bool _let_1 A_10)) (=> (hBOOL (hAPP_nat_bool _let_1 B_8)) (= B_8 A_10))))))) (forall ((V_17 $$unsorted) (V_16 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_16)) (=> (hBOOL (hAPP_int_bool _let_1 V_17)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_int_complex number528085621omplex V_16)) (hAPP_int_complex number528085621omplex V_17)) (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_16) V_17))))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int K_1)) (hAPP_int_int number_number_of_int L))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) L)))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) M)) K_2))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_b992065680at_nat if_nat fTrue) X) Y) X)) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (= A_3 B_2) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) C_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) C_1))))) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_3) B_2)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 A_3)) (hAPP_real_real _let_1 B_2))))))) (forall ((Q_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat N_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat Ma) N_1) Q_1) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc Q_1)))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 Q_1)) Ma))))))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (legacy_zgcd M) N)) (hAPP_int_int (legacy_zgcd (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) M)) N)))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) E_2)) C)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) E_2)) D))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B)) E_2)) C)) D)))) (forall ((A_89 $$unsorted)) (=> (is_int A_89) (= A_89 (hAPP_int_int (hAPP_int_fun_int_int times_times_int one_one_int) A_89)))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 Z_1)) (=> (hBOOL (hAPP_int_bool _let_1 Z_4)) (= (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_1) Z_4)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat nat Z_1)) (hAPP_int_nat nat Z_4))))))) (forall ((A_184 $$unsorted) (M_23 $$unsorted) (N_58 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex A_184))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_23) N_58)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_nat_complex _let_1 M_23)) (hAPP_nat_complex _let_1 N_58)))))) (forall ((A_64 $$unsorted) (B_52 $$unsorted) (C_31 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_64) B_52)) B_52)) (hAPP_int_int (div_mod_int A_64) B_52))) C_31) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_64) C_31))) (forall ((B_90 $$unsorted) (A_112 $$unsorted) (C_50 $$unsorted)) (=> (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat C_50) A_112) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_90) A_112)) (= C_50 B_90))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_real_complex (hAPP_r265291036omplex complex A_3) B_2)) (hAPP_real_complex (hAPP_r265291036omplex complex C_1) D_3)) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_3) C_1)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B_2) D_3)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_1))) (let ((_let_2 (hAPP_n1699378549t_bool ord_less_eq_nat Ma))) (= (or (= _let_1 Ma) (hBOOL (hAPP_nat_bool _let_2 N_1))) (hBOOL (hAPP_nat_bool _let_2 _let_1)))))) (forall ((N $$unsorted)) (= N (natfloor (hAPP_nat_real real_nat N)))) (forall ((B_122 $$unsorted) (A_161 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_161) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_122) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_161) B_122)))))) (forall ((C_83 $$unsorted) (D_16 $$unsorted) (A_191 $$unsorted) (B_147 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_191) B_147)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat C_83) D_16)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_191) C_83)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_147) D_16)))))) (forall ((A_227 $$unsorted) (B_164 $$unsorted) (C_93 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real A_227))) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_164) C_93)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 B_164)) C_93)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real ln X))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int bit0 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_2) (hAPP_int_int succ L_2))) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit1 K_2)) (hAPP_int_int bit1 L_2)))) (forall ((A_24 $$unsorted) (B_19 $$unsorted) (C_8 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_8))) (let ((_let_2 (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral _let_1 A_24)) (hAPP_C498520661umeral _let_1 B_19)))) (let ((_let_3 (= zero_z126310315umeral C_8))) (and (=> _let_3 (= _let_2 zero_z126310315umeral)) (=> (not _let_3) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_24) B_19) _let_2))))))) (forall ((X_33 $$unsorted)) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_33) zero_zero_nat) one_one_rat)) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_nat_real real_nat M)) N) (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M) N)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_2) X_1)) (= (comple124823625p_real (hAPP_r1134773055l_bool (ord_at1589558736t_real Y_2) X_1)) X_1))) (forall ((M_10 $$unsorted) (N_24 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat semiri151668891at_rat M_10)) (hAPP_nat_rat semiri151668891at_rat N_24))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_10) N_24)))) (= (hAPP_complex_real im ii) one_one_real) (forall ((A_229 $$unsorted) (C_95 $$unsorted) (D_20 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int C_95))) (let ((_let_2 (hAPP_int_fun_int_int plus_plus_int A_229))) (= (hAPP_int_int _let_1 (hAPP_int_int _let_2 D_20)) (hAPP_int_int _let_2 (hAPP_int_int _let_1 D_20)))))) (forall ((B_97 $$unsorted) (A_119 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_119)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) B_97)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_119) B_97))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat M))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat suc N)))))) (forall ((P $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP_nat_bool P X))) (hBOOL (hAPP_f54304608l_bool fEx_nat P)))) (forall ((P_5 $$unsorted)) (= (quotient_of (hAPP_rat_rat inverse_inverse_rat P_5)) (hAPP_P1975530577nt_int (produc1518849193nt_int (hAPP_f465821005nt_int (hAPP_f1081447804nt_int cOMBS_1470252563nt_int (hAPP_f400200275nt_int (hAPP_f1731308757nt_int cOMBB_735549356nt_int cOMBB_1389251822nt_int) (hAPP_P621635040nt_int (hAPP_f1582586579nt_int cOMBC_707974837nt_int (hAPP_f251264923nt_int (hAPP_f279307923nt_int cOMBB_662120866nt_int if_Pro1731782967nt_int) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool fequal_int) zero_zero_int))) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) one_one_int)))) (hAPP_f1574055885nt_int (hAPP_f434654626nt_int cOMBS_2011279539nt_int (hAPP_f2094497995nt_int (hAPP_f534361363nt_int cOMBB_1657320178nt_int cOMBC_1964283556nt_int) (hAPP_f2004554147nt_int (hAPP_f1228585167nt_int cOMBB_1102189010nt_int (hAPP_f2054677283nt_int cOMBB_782625832nt_int product_Pair_int_int)) (hAPP_f1760145644nt_int (hAPP_f1629352853nt_int cOMBB_1496585939nt_int times_times_int) sgn_sgn_int)))) abs_abs_int))) (quotient_of P_5)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_int (nat_tsub X) Y))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Y) X)))) (and (=> _let_2 (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X) Y) _let_1)) (=> (not _let_2) (= zero_zero_int _let_1)))))) (forall ((D_3 $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (zcong A_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 B_2) M)) (=> (= C_1 B_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong C_1) D_3) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 D_3) M))))))) (forall ((B_118 $$unsorted) (A_157 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_157)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B_118) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_118) A_157)) zero_zero_rat))))) (forall ((C_41 $$unsorted) (A_99 $$unsorted) (B_81 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral C_41))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral _let_1 A_99)) (hAPP_C498520661umeral _let_1 B_81))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_99) B_81))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_2))) (=> (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int K_2) N)) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N))) (hBOOL (hAPP_int_bool _let_1 M)))))) (forall ((X_14 $$unsorted) (Y_11 $$unsorted) (Ya_1 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_14) Y_11)) Ya_1) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_14) Ya_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_11) Ya_1)))) (forall ((V_20 $$unsorted) (W_16 $$unsorted) (Z_15 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int V_20)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int W_16)) Z_15)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_20) W_16))) Z_15))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int semiri1621563631at_int Ma)) (hAPP_nat_int semiri1621563631at_int N_1))))) (forall ((M_10 $$unsorted) (N_24 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral semiri1619134803umeral M_10)) (hAPP_n1108039445umeral semiri1619134803umeral N_24))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_10) N_24)))) (forall ((B_115 $$unsorted) (C_67 $$unsorted) (A_153 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real B_115))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_153)) (=> (hBOOL (hAPP_real_bool _let_1 C_67)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_153) C_67))))))) (forall ((A_145 $$unsorted) (M_20 $$unsorted) (N_48 $$unsorted)) (let ((_let_1 (hAPP_c1088319240omplex power_power_complex A_145))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex _let_1 M_20)) (hAPP_nat_complex _let_1 N_48)) (hAPP_nat_complex _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_20) N_48))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= (hAPP_complex_complex cnj Y_2) (hAPP_complex_complex cnj X_1)) (= X_1 Y_2))) (forall ((N $$unsorted) (K_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat minus_minus_nat M))) (let ((_let_2 (hAPP_n1699378549t_bool ord_less_eq_nat K_2))) (=> (hBOOL (hAPP_nat_bool _let_2 M)) (=> (hBOOL (hAPP_nat_bool _let_2 N)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) K_2)) (hAPP_nat_nat _let_1 N))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_bool (hAPP_f800510211t_bool (hAPP_f894608603t_bool cOMBB_bool_bool_nat P) Q) R) (hAPP_bool_bool P (hAPP_nat_bool Q R)))) (forall ((X $$unsorted)) (= (hAPP_real_real tan (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) pi)) (hAPP_real_real tan X))) (forall ((A_216 $$unsorted)) (= A_216 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex one_one_complex) A_216))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_rat_rat (hAPP_nat_fun_rat_rat P R) (hAPP_nat_rat Q R)) (hAPP_nat_rat (hAPP_f2062659861at_rat (hAPP_f1131305186at_rat cOMBS_nat_rat_rat P) Q) R))) (forall ((M $$unsorted)) (= (divmod_nat M zero_zero_nat) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat zero_zero_nat) M))) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (=> (hBOOL (vanishes X_3)) (=> (hBOOL (vanishes Y_3)) (hBOOL (vanishes (hAPP_f2062659861at_rat (hAPP_f1131305186at_rat cOMBS_nat_rat_rat (hAPP_f1830834240at_rat (hAPP_f1073644437at_rat cOMBB_1926947at_nat plus_plus_rat) X_3)) Y_3)))))) (forall ((A_93 $$unsorted)) (= A_93 (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A_93) zero_zero_rat))) (forall ((A_129 $$unsorted) (N_40 $$unsorted) (N_39 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_129))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_40) N_39)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) A_129)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real _let_1 N_40)) (hAPP_nat_real _let_1 N_39))))))) (forall ((N $$unsorted)) (exists ((P_4 $$unsorted)) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) P_4)) (hBOOL (hAPP_nat_bool prime P_4))))) (forall ((N $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)) N) (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real times_times_real pi) (hAPP_nat_real real_nat N))))) (forall ((A_190 $$unsorted) (B_146 $$unsorted) (K_7 $$unsorted)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_146) K_7) A_190) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_146) A_190)))) (not (forall ((S1 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (=> (is_int S1) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int S1) (hAPP_int_nat number_number_of_nat _let_1))) (hAPP_int_int number_number_of_int min)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 _let_1))) m)) one_one_int)))))))) (forall ((V $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat (hAPP_int_nat number_number_of_nat V)) (hAPP_nat_nat suc N_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_b992065680at_nat if_nat (hAPP_int_bool nat_neg _let_1)) zero_zero_nat) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat (hAPP_int_nat nat _let_1)) N_1)))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real times_times_real) cos)) cos) X_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 min))) (hAPP_real_real cos X_1))) (hAPP_real_real sin X_1))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat N_1)) zero_zero_real)) (= N_1 zero_zero_nat))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex ii))) (let ((_let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_3 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_2)))) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (of_real_complex (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) _let_3))) (hAPP_complex_complex _let_1 (of_real_complex (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real Y) _let_3)))) (hAPP_complex_complex invers1449016382omplex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (of_real_complex X)) (hAPP_complex_complex _let_1 (of_real_complex Y))))))))) (= _let_1 (hAPP_nat_nat fact_fact_nat zero_zero_nat)) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (div_mod_int A_3) B_2)) zero_zero_int)))) (= (hAPP_nat_complex semiri2020571505omplex zero_zero_nat) zero_zero_complex) (forall ((A_15 $$unsorted) (B_11 $$unsorted)) (=> (not (= zero_z891286103de_int B_11)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_15) B_11)) one_on1684967323de_int) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_15) B_11)) B_11)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (the_Pr588456374at_nat (divmod_nat_rel Ma N_1)) (divmod_nat Ma N_1))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real sqrt X_1)) (hAPP_real_real sqrt Y_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)))) (forall ((X_5 $$unsorted) (Y_5 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_5) Y_5)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_5) Y_5)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_5) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_5) _let_1))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real ln (hAPP_real_real inverse_inverse_real X)) (hAPP_real_real uminus_uminus_real (hAPP_real_real ln X))))) (is_int pls) (forall ((X $$unsorted)) (= X (hAPP_real_real (hAPP_n546711566l_real root (hAPP_nat_nat suc zero_zero_nat)) X))) (forall ((V $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int V) V_1)))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat number_number_of_nat V)) (hAPP_int_nat number_number_of_nat V_1))) (and (=> _let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) V_1))) _let_1)))) (forall ((X_43 $$unsorted) (Y_31 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_43) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_31) _let_1)))))) (forall ((A_14 $$unsorted) (B_10 $$unsorted) (Q_9 $$unsorted) (Y $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_10)))) (=> (and (is_int Y) (is_int B_10)) (=> (= A_14 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_10) Q_9)) Y)) (=> (and (=> (not _let_1) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Y) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_10) Y)))) (=> _let_1 (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y) B_10))))) (=> (not (= zero_zero_int B_10)) (= Y (hAPP_int_int (div_mod_int A_14) B_10)))))))) (forall ((Ma $$unsorted) (V $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V))) (= (= (hAPP_nat_int semiri1621563631at_int Ma) _let_1) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_1)) (= (hAPP_int_nat nat _let_1) Ma))))) (not (= zero_zero_real _let_48)) (forall ((N_1 $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) N_1)))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) C_1)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_2) C_1)) M)))) (hBOOL (hAPP_real_bool _let_64 pi)) (forall ((M $$unsorted) (X $$unsorted)) (=> (is_int X) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) M)) (= X zero_zero_int)))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong _let_22) _let_17) _let_18)) (forall ((M $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) one_one_nat) one_one_nat)) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat M))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 N)) K_2) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) K_2))))) (forall ((S $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_2) S)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2))))) (hBOOL (hAPP_f448129468l_bool nat_nat_set S)))) (forall ((A_208 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real A_208) zero_zero_real))) (forall ((A_47 $$unsorted) (B_38 $$unsorted) (C_19 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_47) C_19)) B_38)) C_19) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_47) B_38)) C_19))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) (hAPP_int_real real_int A))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (archim856651990g_real X_1)) A)))) (forall ((A_217 $$unsorted) (M_29 $$unsorted) (B_160 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_217) M_29)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_160) M_29)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_217) B_160)) M_29))) (exists ((X_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) m)) one_one_int))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) _let_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong s1) X_2) _let_1)) (forall ((Y_1 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) m)) one_one_int))) (=> (is_int Y_1) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong s1) Y_1) _let_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_1) _let_1))) (= X_2 Y_1))))) (is_int X_2)))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int Lx_3))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int _let_1 Rx_3)) Ly_1) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int _let_1 Ly_1)) Rx_3)))) (forall ((Z_1 $$unsorted)) (not (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) Z_1)) Z_1)))) (forall ((Y $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_3)) (=> (not (= A_3 one_one_real)) (= (hAPP_real_real (log A_3) (hAPP_real_real (hAPP_r1250527377l_real powr A_3) Y)) Y)))) (forall ((B_71 $$unsorted) (A_83 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_83)) (=> (hBOOL (hAPP_real_bool _let_1 B_71)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_83) B_71))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (ratreal X)) (ratreal Y)) (ratreal (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X) Y)))) (forall ((P $$unsorted)) (=> (is_bool P) (or (= P fFalse) (= fTrue P)))) (forall ((C_75 $$unsorted) (A_175 $$unsorted) (B_135 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_75))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_175) B_135)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_75)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat _let_1 A_175)) (hAPP_rat_rat _let_1 B_135))))))) (forall ((A_106 $$unsorted)) (= A_106 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real zero_zero_real) A_106))) (forall ((G $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (sums_real G) X_1)) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_r195310020l_real (hAPP_f2126667875l_real cOMBC_746811033l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) zero_zero_real)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat G) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat div_div_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat minus_minus_nat) one_one_nat))) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) X_1)))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))) (not (= zero_zero_int (hAPP_int_int (inv P_3) A_3))))))) (forall ((B_94 $$unsorted) (C_52 $$unsorted) (A_116 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat B_94))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_116)) (=> (hBOOL (hAPP_rat_bool _let_1 C_52)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_116) C_52))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_real (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real P) Q) R) (hAPP_nat_real (hAPP_r474017924t_real P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_b589554111l_bool P (hAPP_int_bool Q R)) (hAPP_i68813070l_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int P) Q) R))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) Y)) (= (natfloor (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) (hAPP_nat_real real_nat Y))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (natfloor X)) Y))))) (= zero_z891286103de_int (hAPP_n522471361de_int semiri1424489471de_int zero_zero_nat)) (forall ((A_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool (ord_at4362885an_nat K_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat K_1) (hAPP_f22106695ol_nat finite_card_nat A_1))))) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le1568362934t_bool A_1) _let_1)) (= _let_1 A_1)))) (forall ((W_7 $$unsorted)) (let ((_let_1 (hAPP_int_rat number_number_of_rat W_7))) (= (hAPP_int_rat number_number_of_rat (hAPP_int_int bit0 W_7)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat zero_zero_rat) _let_1)) _let_1)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (div_mod_nat M))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) N)) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat suc N))))))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) J_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 I)) (hAPP_nat_nat _let_1 J_2))))))) (forall ((X_30 $$unsorted) (Y_24 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat X_30) Y_24)) (=> (not (= X_30 Y_24)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat X_30) Y_24))))) (forall ((N_53 $$unsorted) (M_21 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 M_21)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 N_53)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral M_21) N_53))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat P R) Q) (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat P) Q) R))) (forall ((A_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_3)) (=> (not (= A_3 one_one_real)) (= one_one_real (hAPP_real_real (log A_3) A_3))))) (forall ((A_31 $$unsorted) (C_12 $$unsorted) (B_26 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral A_31) B_26) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_31) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral C_12) B_26))) B_26))) (= one_one_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract one_one_int) one_one_int)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1908301369l_real P (hAPP_r1230691443l_real Q R)) (hAPP_r224952523l_real (hAPP_f1663701695l_real (hAPP_f774948957l_real cOMBB_3698607l_real P) Q) R))) (forall ((C_88 $$unsorted) (A_206 $$unsorted) (B_157 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool dvd_dvd_real A_206))) (=> (hBOOL (hAPP_real_bool _let_1 B_157)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real B_157) C_88)) (hBOOL (hAPP_real_bool _let_1 C_88)))))) (forall ((I $$unsorted) (J_2 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat minus_minus_nat I))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 J_2)) K_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 K_2)) J_2)))) (forall ((B_5 $$unsorted) (Q_8 $$unsorted) (R_5 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_5) Q_8)) R_5))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_5) B_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_5)) (hBOOL (hAPP_int_bool _let_1 Q_8))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos X)) (hAPP_real_real cos Y))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real sin X)) (hAPP_real_real sin Y))) (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) Y)))) (forall ((N_66 $$unsorted) (A_210 $$unsorted) (B_158 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_210) B_158)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_210)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_66)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_210) N_66)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat B_158) N_66))))))) (hBOOL (hAPP_int_bool _let_11 _let_63)) (= _let_12 _let_62) (forall ((A_3 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat one_one_nat) A_3))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) X_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Y_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int N_2) X_1))))) X_1)) (is_int N_2)))))) (forall ((N_1 $$unsorted) (F $$unsorted)) (=> (hBOOL (summable_real F)) (=> (forall ((M_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) M_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real F M_1))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real F) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_f352196356l_real suminf_real F)))))) (forall ((X_5 $$unsorted) (Y_5 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_5) Y_5)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X_5) Y_5)) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_5) _let_1)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex Y_5) _let_1))))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (= (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Ma) N_1)) (= K_1 zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) K_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N_1) K_1))))) (forall ((N_1 $$unsorted)) (= (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1) (hAPP_n1699378549t_bool ord_lessThan_nat N_1))) (forall ((A_129 $$unsorted) (N_40 $$unsorted) (N_39 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_129))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_40) N_39)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int) A_129)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int _let_1 N_40)) (hAPP_n522471361de_int _let_1 N_39))))))) (forall ((C_41 $$unsorted) (A_99 $$unsorted) (B_81 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int C_41))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int _let_1 A_99)) (hAPP_Q1762011733de_int _let_1 B_81))) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_99) B_81))))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 K_1)) min)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) min)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_3) B_2)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_nat_int semiri1621563631at_int A_3)) (hAPP_nat_int semiri1621563631at_int B_2)))) (forall ((N_37 $$unsorted) (A_126 $$unsorted)) (let ((_let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_126) N_37))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_126)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_126) one_one_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_126) _let_1)) _let_1)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) Ma))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A_3) B_2)) A_3)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real number267125858f_real X_1)) (hAPP_int_real number267125858f_real Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) Y_2)))) (forall ((A_38 $$unsorted) (C_13 $$unsorted) (B_29 $$unsorted)) (let ((_let_1 (div_mo1740067990umeral A_38))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral C_13) B_29)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral _let_1 B_29)) C_13) (hAPP_C498520661umeral _let_1 C_13))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) E_2)) C) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B) E_2)) D)) (= D (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) E_2)) C)))) (forall ((Z_1 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Z_1) N)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_1) N))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_b589554111l_bool P (hAPP_real_bool Q R)) (hAPP_r1938957037l_bool (hAPP_f60716669l_bool (hAPP_f1485493409l_bool cOMBB_624415285l_real P) Q) R))) (forall ((Y_8 $$unsorted) (Z_6 $$unsorted) (X_11 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int Z_6))) (=> (hBOOL (hAPP_int_bool _let_1 X_11)) (=> (hBOOL (hAPP_int_bool _let_1 Y_8)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_11) Y_8)) Z_6) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X_11) Z_6)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int Y_8) Z_6))))))) (forall ((L_2 $$unsorted)) (not (= min (hAPP_int_int bit0 L_2)))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int I))) (=> (hBOOL (hAPP_int_bool _let_1 J_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int J_2) K_2)) (hBOOL (hAPP_int_bool _let_1 K_2)))))) (forall ((P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_int number_number_of_int _let_1))) (let ((_let_3 (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int)) _let_2))) (= (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_2) _let_3)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat _let_1)) (hAPP_int_nat nat _let_3))))))) (forall ((X $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (multInv P_3) X)) X)) one_one_int) P_3)))))) (forall ((A_89 $$unsorted)) (= A_89 (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex one_one_complex) A_89))) (forall ((X $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_r1250527377l_real plus_plus_real X))) (= (hAPP_real_real uminus_uminus_real (hAPP_real_real sin (hAPP_real_real _let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat M)) pi)) _let_1)))) (hAPP_real_real cos (hAPP_real_real _let_2 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat (hAPP_nat_nat suc M))) pi)) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (M $$unsorted)) (=> (= one_one_nat (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X) Y)) M)) (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) M)))) (forall ((X_1 $$unsorted)) (= (= X_1 one_on1645066479umeral) (= one_on1645066479umeral X_1))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat)))) (=> (hBOOL (hAPP_nat_bool even_odd_even_nat X)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X) _let_1)) X)))) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set B_1)) (= (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le382113706t_bool (image_int_nat nat A_1)) (image_int_nat nat B_1))) (hBOOL (hAPP_f448129468l_bool (hAPP_f284875647l_bool ord_le1912455174t_bool A_1) B_1)))))) _let_61 (= zero_zero_real (hAPP_complex_real re ii)) (forall ((A_24 $$unsorted) (B_19 $$unsorted) (C_8 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_8))) (let ((_let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat _let_1 A_24)) (hAPP_nat_nat _let_1 B_19)))) (let ((_let_3 (= C_8 zero_zero_nat))) (and (=> (not _let_3) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_24) B_19) _let_2)) (=> _let_3 (= zero_zero_nat _let_2))))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) B_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat _let_1 A_3)) (hAPP_nat_nat _let_1 B_2)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int B))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int) B)) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int _let_1 X_1)) (hAPP_n522471361de_int _let_1 Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)))))) (forall ((A_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (= A_1 (image_nat_int semiri1621563631at_int (image_int_nat nat A_1))))) (forall ((D2 $$unsorted) (D1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 D1)) (=> (hBOOL (hAPP_real_bool _let_1 D2)) (exists ((E $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real E))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) E)) (hBOOL (hAPP_real_bool _let_1 D1)) (hBOOL (hAPP_real_bool _let_1 D2))))))))) (forall ((A_207 $$unsorted)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex A_207) A_207))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (isCont_real_real ln) X_1)))) (forall ((L $$unsorted) (U $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (hAPP_i1948725293t_bool (ord_gr1297742076an_int L) U)))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool A_1 X_1)) (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_1) A_1)))) (forall ((B_155 $$unsorted) (A_204 $$unsorted)) (=> (not (= zero_zero_real A_204)) (=> (not (= B_155 zero_zero_real)) (not (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_204) B_155) zero_zero_real))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C) zero_zero_rat)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A)) (hAPP_rat_rat _let_1 B))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B) A)))))) (forall ((C_1 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong C_1) D_3) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) C_1)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_2) D_3)) M))))) (forall ((B_116 $$unsorted) (A_155 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_155)) (=> (hBOOL (hAPP_real_bool _let_1 B_116)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_155) B_116))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real ln (hAPP_real_real exp_real one_one_real))) (hAPP_real_real ln _let_1))) (hAPP_real_real ln X)) (hAPP_real_real (log _let_1) X))))) (forall ((A_134 $$unsorted) (N_47 $$unsorted) (B_103 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_134) N_47)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real B_103) N_47))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) B_103)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_134) B_103))))) (forall ((A_217 $$unsorted) (M_29 $$unsorted) (B_160 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_217) M_29)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_160) M_29)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_217) B_160)) M_29))) (forall ((N $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_3) N)))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_3) B_2))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))) (hBOOL (hAPP_nat_bool _let_1 A_3))))))) (forall ((K_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int K_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) K_2)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_nat_int _let_1 M)) K_2) (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) (hAPP_nat_nat suc zero_zero_nat)))))))) (forall ((N_27 $$unsorted) (Y_7 $$unsorted) (X_10 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int Y_7) X_10)) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int X_10) Y_7)) N_27) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_10) N_27)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int Y_7) N_27))))) (forall ((N $$unsorted) (K_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_2))) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N))))))) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Rx_4) Ry_2))) (let ((_let_2 (hAPP_rat_fun_rat_rat times_times_rat Lx_4))) (= (hAPP_rat_rat _let_2 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Ly_2) _let_1)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat _let_2 Ly_2)) _let_1))))) (forall ((N $$unsorted)) (not (= (hAPP_nat_nat suc N) N))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C))) (= (or (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat A) B)) (= C zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_rat_rat _let_1 A)) (hAPP_rat_rat _let_1 B)))))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool even_odd_even_nat N)) (exists ((X_2 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat N) (hAPP_int_nat number_number_of_nat _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_1))) X_2)))))) (forall ((Code_numeral_5 $$unsorted) (Code_numeral_4 $$unsorted)) (= (= Code_numeral_4 Code_numeral_5) (= (code_S1047413653umeral Code_numeral_4) (code_S1047413653umeral Code_numeral_5)))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat Lx_1))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Rx_1) Ry_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 Rx_1)) Ry_1)))) (forall ((Z_13 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_13) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex Z_13) Z_13))) (forall ((N_33 $$unsorted) (A_123 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_123)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_33)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_123) N_33))))))) (forall ((M_11 $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int M_11)) zero_zero_int)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (is_bool P) (= (hAPP_nat_bool (cOMBK_bool_nat P) Q) P))) (forall ((A_32 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int A_32) one_on1684967323de_int) zero_z891286103de_int)) (forall ((C_70 $$unsorted) (A_164 $$unsorted) (B_125 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_70))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_164) B_125)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) C_70)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A_164)) (hAPP_rat_rat _let_1 B_125))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int X))) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int Y))) (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) Y)))))) (forall ((X $$unsorted) (Y $$unsorted) (M $$unsorted)) (=> (= one_one_int (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y)) M)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) M) one_one_int))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int abs_abs_int X))) (= (hAPP_nat_int semiri1621563631at_int (hAPP_int_nat nat _let_1)) _let_1))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) N)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat fact_fact_nat) _let_1))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1))) (hAPP_real_real cos X_1))))) (forall ((A_148 $$unsorted) (N_51 $$unsorted) (N_50 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_148))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_51) N_50)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat) A_148)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 N_51)) (hAPP_nat_nat _let_1 N_50))))))) (forall ((N $$unsorted) (M $$unsorted) (R_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat M) R_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat N) R_3)) (=> (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) R_3)))))) (forall ((A_226 $$unsorted) (B_163 $$unsorted) (C_92 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_226))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 C_92)) B_163) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 B_163)) C_92)))) (forall ((P $$unsorted) (Q $$unsorted)) (= P (hAPP_nat_rat (cOMBK_rat_nat P) Q))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc Ma)) N_1)) (hBOOL (hAPP_nat_bool (nat_case_bool fFalse (hAPP_n1699378549t_bool ord_less_eq_nat Ma)) N_1)))) (forall ((P_1 $$unsorted)) (= (collect_int P_1) P_1)) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_3) B_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat C_1) A_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat A_3) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat B_2) C_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) M)))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int Z_1))) (let ((_let_2 (hAPP_nat_int _let_1 (hAPP_int_nat number_number_of_nat W)))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_2) _let_2) (hAPP_nat_int _let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 W))))))) (forall ((I $$unsorted) (K_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc I)) K_2)) (not (forall ((J_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) J_1)) (not (= (hAPP_nat_nat suc J_1) K_2))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)))) (=> _let_1 (or (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X))) _let_1) (= Y X))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_1))) (let ((_let_2 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (and (= (hAPP_real_real sin X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_r195310020l_real (hAPP_f2126667875l_real cOMBC_746811033l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) zero_zero_real)) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min))) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat div_div_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat minus_minus_nat) (hAPP_nat_nat suc zero_zero_nat)))) (hAPP_int_nat number_number_of_nat _let_2))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat))))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real T) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) (hAPP_int_real number267125858f_real _let_2))) (hAPP_nat_real real_nat N_1))) pi)))) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real T)) (hAPP_real_real abs_abs_real X_1)))))))) (hBOOL (hAPP_int_bool _let_60 pls)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) N_1) _let_1) (and (= Ma _let_1) (= _let_1 N_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_1) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_2) _let_1)))) (or (not (= X_1 zero_zero_rat)) (not (= Y_2 zero_zero_rat)))))) (forall ((N $$unsorted) (K_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat K_2))) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))))))) (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (not (= zero_zero_nat A)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A) B)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat C) A) B) (= C (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B) A)))))) (forall ((A $$unsorted) (N_1 $$unsorted)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A) N_1) zero_zero_nat) (and (= zero_zero_nat A) (not (= N_1 zero_zero_nat))))) (forall ((R_3 $$unsorted) (S_1 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_int_real number267125858f_real R_3)) (hAPP_int_real number267125858f_real S_1)) (ratreal (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat (hAPP_int_rat number_number_of_rat R_3)) (hAPP_int_rat number_number_of_rat S_1))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real P R) Q) (hAPP_real_real (hAPP_r1250527377l_real (hAPP_f203520653l_real cOMBC_real_real_real P) Q) R))) (forall ((B_93 $$unsorted) (A_115 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_115) zero_z126310315umeral)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral B_93) zero_z126310315umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_115) B_93)) zero_z126310315umeral))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Y) X)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y) (hAPP_int_int abs_abs_int Y)))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat) M)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat M) (hAPP_nat_nat fact_fact_nat N)))))) (forall ((C_85 $$unsorted) (A_193 $$unsorted) (B_149 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_193))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_149)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_149) C_85)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P507092031nt_rat (hAPP_f1547007718nt_rat (hAPP_f382317021nt_rat cOMBB_170828966nt_int P) Q) R) (hAPP_int_fun_int_rat P (hAPP_P1175774780nt_int Q R)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex cnj X)) (hAPP_complex_complex cnj Y)) (hAPP_complex_complex cnj (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X) Y)))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_1))) (=> (not (= one_one_real X_1)) (= (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real _let_1) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_nat_real _let_1 N_1)) one_one_real)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_1) one_one_real)))))) (forall ((A_28 $$unsorted) (B_23 $$unsorted) (C_10 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat C_10))) (=> (not (= zero_zero_nat C_10)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat _let_1 A_28)) (hAPP_nat_nat _let_1 B_23)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_28) B_23))))) (forall ((Z_1 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Z_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Z_1) Z_1))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex B) A)) E_2)) D) C) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A) E_2)) C) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B) E_2)) D)))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat D) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_2) Sa))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_2) Z)) (= _let_1 _let_1)))))) (forall ((I_1 $$unsorted) (K_1 $$unsorted) (J $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_1) J)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J) K_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_1) K_1)) J))))) (forall ((K_2 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) X)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) K_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) K_2)) X))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_real_bool B_1_1 B_2_1))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat C) D) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A) B)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C) D))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_f54304608l_bool B_1_1 B_2_1))) (forall ((C_39 $$unsorted) (D_7 $$unsorted) (A_97 $$unsorted) (B_79 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_97) B_79)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat C_39) D_7)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_97) C_39)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_79) D_7)))))) (forall ((J_2 $$unsorted) (A_3 $$unsorted) (P_3 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) (hAPP_int_int (multInv P_3) K_2)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong J_2) _let_1) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int J_2) K_2)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_1) K_2)) P_3))))) (forall ((A_64 $$unsorted) (B_52 $$unsorted) (C_31 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_64) B_52)) B_52)) (hAPP_Q1762011733de_int (div_mo231679042de_int A_64) B_52))) C_31) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_64) C_31))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (= (or (and (hBOOL (hAPP_real_bool _let_1 B)) (hBOOL (hAPP_real_bool _let_1 A))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) zero_zero_real)))) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) B)))))) (forall ((U $$unsorted)) (= (hAPP_f22106695ol_nat finite_card_nat (hAPP_n1699378549t_bool ord_atMost_nat U)) (hAPP_nat_nat suc U))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_real im (of_real_complex Z_1)) zero_zero_real)) (forall ((W $$unsorted)) (= (hAPP_int_complex number528085621omplex W) (hAPP_int_complex ring_11397209091omplex W))) (forall ((A_197 $$unsorted) (B_152 $$unsorted) (N_64 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_197) N_64)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_152) N_64)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_197) B_152)) N_64))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_i1732201573de_int quickcheck_of_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (quickcheck_int_of N)) (quickcheck_int_of M))) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int minus_534354567de_int N) M))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat Rx))) (let ((_let_2 (hAPP_rat_fun_rat_rat times_times_rat Lx))) (= (hAPP_rat_rat _let_1 (hAPP_rat_rat _let_2 Ry)) (hAPP_rat_rat _let_2 (hAPP_rat_rat _let_1 Ry)))))) (forall ((G $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D)) (=> (forall ((Z $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (= (hAPP_real_real G (hAPP_real_real F Z)) Z))) (=> (forall ((Z $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (hBOOL (hAPP_real_bool (isCont_real_real F) Z)))) (exists ((Z $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F Z)) (hAPP_real_real F X_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X) (hAPP_nat_nat suc _let_1))) (or (= X zero_zero_nat) (= _let_1 X))))) (forall ((Code_numeral_1 $$unsorted)) (= (code_c271388182l_size (code_S1047413653umeral Code_numeral_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (code_c271388182l_size Code_numeral_1)) (hAPP_nat_nat suc zero_zero_nat)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_1) Y_2)) zOdd))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Z_1) W) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_1) (hAPP_int_int uminus_uminus_int W)))) (forall ((B_130 $$unsorted) (A_170 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_170)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_130) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_130) A_170)) zero_zero_real))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (= X_1 (hAPP_real_real (hAPP_r1250527377l_real powr X_1) one_one_real)))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int number_number_of_int N))) (and (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit1 N)))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 N)))))))) (forall ((N $$unsorted) (D_3 $$unsorted)) (=> (is_int D_3) (=> (not (= D_3 zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D_3) N)) (= (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int N) D_3)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_int_real real_int N)) (hAPP_int_real real_int D_3))))))) (forall ((A_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime A_3)) (hBOOL (hAPP_int_bool zprime (hAPP_nat_int semiri1621563631at_int A_3))))) (forall ((N_13 $$unsorted) (A_8 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_8)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_8) (hAPP_nat_nat suc N_13))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2))) (let ((_let_2 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) X)) (not (hBOOL (hAPP_nat_bool _let_2 B_2)))) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_1) X)) (not (hBOOL (hAPP_nat_bool _let_2 _let_1)))))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat A_3))) (=> (hBOOL (hAPP_nat_bool _let_1 B_2)) (=> (= B_2 C_1) (hBOOL (hAPP_nat_bool _let_1 C_1)))))) (forall ((X_7 $$unsorted) (Q_6 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat X_7))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_7) (hAPP_nat_rat _let_1 Q_6)) (hAPP_nat_rat _let_1 (hAPP_nat_nat suc Q_6))))) (forall ((X_38 $$unsorted) (P_8 $$unsorted) (Q_12 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat X_38))) (= (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_8) Q_12)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_nat_rat _let_1 P_8)) Q_12)))) (forall ((N_16 $$unsorted) (M_5 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_16) M_5)) (= (hAPP_nat_rat semiri151668891at_rat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M_5) N_16)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_nat_rat semiri151668891at_rat M_5)) (hAPP_nat_rat semiri151668891at_rat N_16))))) (forall ((B_55 $$unsorted) (A_67 $$unsorted)) (=> (is_int A_67) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_55) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_67) B_55))) (hAPP_int_int (div_mod_int A_67) B_55)) A_67))) (forall ((C_42 $$unsorted) (A_100 $$unsorted) (B_82 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_100) B_82)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_100) C_42)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_82) C_42))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_P603027463t_bool B_1_1 B_2_1))) (forall ((C_64 $$unsorted) (A_142 $$unsorted) (B_111 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_64))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_142)) (hAPP_real_real _let_1 B_111))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_64)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_142) B_111)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (forall ((D_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat D_2))) (= (and (hBOOL (hAPP_nat_bool _let_1 A)) (hBOOL (hAPP_nat_bool _let_1 B))) (= D_2 one_one_nat)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A) B) one_one_nat))) (= (hAPP_real_complex _let_59 zero_zero_real) zero_zero_complex) (forall ((A $$unsorted) (D $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N_1) (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) one_one_nat)) D)))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat))) (hAPP_f22106695ol_nat (hAPP_f782000547ol_nat big_co387207925at_nat (hAPP_f1914919701at_nat (hAPP_f1585078997at_nat cOMBB_nat_nat_nat _let_1) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat times_times_nat) D))) (hAPP_n1699378549t_bool ord_lessThan_nat N_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) N) M))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real sqrt X_1)) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) one_one_real)))) (forall ((N_26 $$unsorted)) (= (hAPP_nat_nat semiri984289939at_nat N_26) (hAPP_int_nat number_number_of_nat (hAPP_nat_int semiri1621563631at_int N_26)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc M)) (hAPP_nat_nat suc N))))) (forall ((A_107 $$unsorted)) (=> (is_int A_107) (= A_107 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_107) zero_zero_int)))) (forall ((L_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int minus_minus_int min))) (= (hAPP_int_int bit1 (hAPP_int_int _let_1 L_2)) (hAPP_int_int _let_1 (hAPP_int_int bit0 L_2))))) (forall ((C_70 $$unsorted) (A_164 $$unsorted) (B_125 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_70))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_164) B_125)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) C_70)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral _let_1 A_164)) (hAPP_C498520661umeral _let_1 B_125))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_3)) (=> (hBOOL (hAPP_real_bool _let_1 B_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (natfloor A_3)) (natfloor B_2))) (natfloor (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_3) B_2)))))))) (forall ((C_83 $$unsorted) (D_16 $$unsorted) (A_191 $$unsorted) (B_147 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_191) B_147)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int C_83) D_16)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_191) C_83)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_147) D_16)))))) (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel M N) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)) (hAPP_nat_nat (div_mod_nat M) N))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool P (hAPP_int_int Q R)) (hAPP_int_bool (hAPP_f429935748t_bool (hAPP_f1512942609t_bool cOMBB_int_bool_int P) Q) R))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real arccos Y))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) pi))))))) (forall ((A_111 $$unsorted) (B_89 $$unsorted) (C_49 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_111))) (=> (= (hAPP_nat_nat _let_1 B_89) (hAPP_nat_nat _let_1 C_49)) (= B_89 C_49)))) (forall ((N $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real real_nat (hAPP_nat_nat suc N))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real ln X_1)) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) one_one_real))))) (forall ((A_92 $$unsorted)) (=> (is_int A_92) (= A_92 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_92) one_one_int)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (= (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Y_2) Z_2) X_1) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) Z_2) Y_2))) (forall ((B_120 $$unsorted) (A_159 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_120) A_159))) (=> (hBOOL (hAPP_nat_bool _let_1 A_159)) (hBOOL (hAPP_nat_bool _let_1 B_120)))))) (forall ((A_107 $$unsorted)) (= A_107 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_107) zero_zero_rat))) (forall ((X_19 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_19) X_19)) one_one_rat) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_19) one_one_rat)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat X_19) one_one_rat)))) (forall ((X_2 $$unsorted)) (= (hAPP_real_real inverse_inverse_real (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat X_2))) (hAPP_nat_real (diffs_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat))) X_2))) (forall ((N_37 $$unsorted) (A_126 $$unsorted)) (let ((_let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_126) N_37))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) A_126)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_126) one_on1684967323de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_126) _let_1)) _let_1)))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted)) (= (rcis R_3 A_3) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (of_real_complex R_3)) (cis A_3)))) (forall ((M $$unsorted) (N $$unsorted) (K_2 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) K_2) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc M)) N)) (hAPP_nat_nat suc K_2)))) (forall ((X $$unsorted)) (= (hAPP_real_real abs_abs_real (hAPP_int_real real_int X)) (hAPP_int_real real_int (hAPP_int_int abs_abs_int X)))) (forall ((A_3 $$unsorted)) (= (hAPP_real_real sin A_3) (hAPP_complex_real im (cis A_3)))) (forall ((P_1 $$unsorted) (P_2 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D)) (=> (forall ((X_2 $$unsorted) (K $$unsorted)) (=> (and (is_int X_2) (is_int K)) (= (hBOOL (hAPP_int_bool P_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K) D)))) (hBOOL (hAPP_int_bool P_2 X_2))))) (=> (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z) X_2)) (= (hBOOL (hAPP_int_bool P_2 X_2)) (hBOOL (hAPP_int_bool P_1 X_2))))))) (=> (exists ((X1 $$unsorted)) (hBOOL (hAPP_int_bool P_2 X1))) (exists ((X1 $$unsorted)) (and (hBOOL (hAPP_int_bool P_1 X1)) (is_int X1)))))))) (forall ((N_1 $$unsorted) (Q_3 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_lessThan_nat N_1))) (=> (forall ((X_2 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat Q_3 X_2)) (hAPP_nat_nat P_1 X_2)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_f22106695ol_nat (hAPP_f782000547ol_nat big_co387207925at_nat P_1) _let_1)) (hAPP_f22106695ol_nat (hAPP_f782000547ol_nat big_co387207925at_nat Q_3) _let_1)) (hAPP_f22106695ol_nat (hAPP_f782000547ol_nat big_co387207925at_nat (hAPP_f1914919701at_nat (hAPP_f1408247010at_nat cOMBS_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat minus_minus_nat) P_1)) Q_3)) _let_1))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat suc K_1)))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1)))))) (forall ((N_9 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int N_9)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_9)))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real exp_real X_1)) one_one_real)))) (forall ((P_1 $$unsorted) (I_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (collect_nat (hAPP_f800510211t_bool (hAPP_f561022312t_bool cOMBS_nat_bool_bool (hAPP_f1146629647l_bool (hAPP_f1080886329l_bool cOMBB_1015721476ol_nat fconj) P_1)) (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_nat) I_1)))))) (forall ((I_1 $$unsorted) (P_1 $$unsorted) (P_5 $$unsorted)) (=> (forall ((I_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_2) P_5)) (=> (hBOOL (hAPP_nat_bool P_1 I_2)) (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc I_2)) P_5)))))) (=> (hBOOL (hAPP_nat_bool P_1 I_1)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_1) P_5)) (hBOOL (hAPP_nat_bool P_1 zero_zero_nat)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (hAPP_int_fun_int_int plus_plus_int one_one_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_3)) (= (hAPP_int_int _let_2 (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int B_2) A_3))) (hAPP_int_int (div_mod_int (hAPP_int_int _let_2 (hAPP_int_int _let_1 B_2))) (hAPP_int_int _let_1 A_3))))))) (forall ((B $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (hAPP_f2054677283nt_int cOMBB_782625832nt_int product_Pair_int_int))) (let ((_let_3 (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int minus_minus_int) B))) (= (produc1518849193nt_int (hAPP_f465821005nt_int (hAPP_f1081447804nt_int cOMBS_1470252563nt_int (hAPP_f617310012nt_int (hAPP_f197974549nt_int cOMBB_638531587nt_int cOMBS_1891347093nt_int) (hAPP_f55007289nt_int (hAPP_f747475781nt_int cOMBB_222539774nt_int (hAPP_f1311564564nt_int cOMBS_1640193733nt_int (hAPP_f251264923nt_int (hAPP_f279307923nt_int cOMBB_662120866nt_int if_Pro1731782967nt_int) (hAPP_f429935748t_bool (hAPP_f1512942609t_bool cOMBB_int_bool_int (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int)) _let_3)))) (hAPP_f1574055885nt_int (hAPP_f960630521nt_int cOMBC_1805044090nt_int (hAPP_f142232355nt_int (hAPP_f1377453843nt_int cOMBB_320287386nt_int cOMBB_1846624359nt_int) (hAPP_f1574055885nt_int _let_2 (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int (hAPP_f1760145644nt_int (hAPP_f1629352853nt_int cOMBB_1496585939nt_int plus_plus_int) _let_1)) one_one_int)))) _let_3)))) (hAPP_f1574055885nt_int _let_2 _let_1))) (adjust B)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1529485324t_bool (hAPP_f1315737299t_bool (hAPP_f538565589t_bool cOMBB_1211207212ol_int P) Q) R) (hAPP_f627970963t_bool P (hAPP_i68813070l_bool Q R)))) (forall ((A_235 $$unsorted)) (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_235) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_235) A_235)) A_235))) (= real_int ring_1_of_int_real) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r265291036omplex P (hAPP_nat_real Q R)) (hAPP_n1983812447omplex (hAPP_f23851874omplex (hAPP_f406530075omplex cOMBB_1714920583ex_nat P) Q) R))) (forall ((Ma $$unsorted)) (= (= (hAPP_int_int abs_abs_int Ma) one_one_int) (= (hAPP_int_int (legacy_zgcd zero_zero_int) Ma) one_one_int))) (forall ((A_90 $$unsorted)) (= A_90 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat one_one_rat) A_90))) (forall ((P_3 $$unsorted) (X $$unsorted)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hAPP_int_int (multInv P_3) X))) (forall ((X_1 $$unsorted) (F $$unsorted)) (=> (hBOOL (summable_real F)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real F) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_2))) X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f352196356l_real suminf_real F)) X_1))))) (forall ((V_18 $$unsorted) (W_14 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex V_18)) (hAPP_int_complex number528085621omplex W_14)) (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_18) W_14)))) (forall ((C_74 $$unsorted) (A_174 $$unsorted) (B_134 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_74))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_174) B_134)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_74)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral _let_1 A_174)) (hAPP_C498520661umeral _let_1 B_134))))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 X_1)) (=> (hBOOL (hAPP_nat_bool _let_1 Y_2)) (= (and (= zero_zero_nat Y_2) (= X_1 zero_zero_nat)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_1) Y_2))))))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int Lx))) (let ((_let_2 (hAPP_Q1729056540de_int times_123202395de_int Rx))) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int _let_2 Ry)) (hAPP_Q1762011733de_int _let_2 (hAPP_Q1762011733de_int _let_1 Ry)))))) (forall ((B_69 $$unsorted) (A_81 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_81)) (=> (hBOOL (hAPP_int_bool _let_1 B_69)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_81) B_69))))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N))))) (forall ((B_95 $$unsorted) (C_53 $$unsorted) (A_117 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_117)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat B_95) C_53)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat B_95) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_117) C_53)))))) (forall ((K_2 $$unsorted) (N $$unsorted) (M $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc M)) N) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat K_2) N)) M))) N))) (forall ((A_109 $$unsorted) (B_87 $$unsorted) (C_47 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex A_109))) (= (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_87) C_47)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 B_87)) C_47)))) (forall ((X $$unsorted)) (not (= (hAPP_real_real cos (hAPP_real_real arctan X)) zero_zero_real))) (forall ((A_240 $$unsorted)) (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_240) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) zero_zero_rat)))) (forall ((C_60 $$unsorted) (D_13 $$unsorted) (A_138 $$unsorted) (B_107 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_138) B_107)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C_60) D_13)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_138)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_60)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_138) C_60)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_107) D_13)))))))) (forall ((N_62 $$unsorted)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int one_one_int) N_62) one_one_int)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real sqrt X)) (hAPP_real_real sqrt Y))))) (= zero_z126310315umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral zero_z126310315umeral) _let_4)) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_int (hAPP_P1175774780nt_int B_1_1 B_2_1))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int X_1)) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) (hAPP_int_int bit1 pls))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat suc K_1)))) (= (= N_1 Ma) (= (hAPP_nat_nat _let_1 Ma) (hAPP_nat_nat _let_1 N_1))))) (forall ((R_3 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex ii) (of_real_complex R_3)) (hAPP_real_complex (hAPP_r265291036omplex complex zero_zero_real) R_3))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) _let_2)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int _let_1)) A_3)) B_2))) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_2) _let_2)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_3) B_2)) _let_2))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_real number267125858f_real _let_1))) (let ((_let_3 (hAPP_int_nat number_number_of_nat _let_1))) (let ((_let_4 (hAPP_r474017924t_real power_power_real X))) (let ((_let_5 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) _let_3))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real inverse_inverse_real (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat _let_5)))) (hAPP_nat_real _let_4 _let_5))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real _let_4 _let_3)) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) _let_2)) N)))))))))))) (is_int s1) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 K1)) (hAPP_int_int bit1 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K1) K2)))) (forall ((A_219 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_219) zero_zero_nat) A_219)) (forall ((X $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) one_one_real)) (hBOOL (monoseq_real (hAPP_r474017924t_real power_power_real X_1)))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real real_int A)) X_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) (archim856651990g_real X_1))))) (forall ((L $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (divmod_int K_1 L))) (let ((_let_2 (pdivmod K_1 L))) (let ((_let_3 (hAPP_f2054677283nt_int cOMBB_782625832nt_int product_Pair_int_int))) (let ((_let_4 (hAPP_int_int sgn_sgn_int L))) (let ((_let_5 (= L zero_zero_int))) (let ((_let_6 (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int))) (=> (and (is_int L) (is_int K_1)) (and (=> (= K_1 zero_zero_int) (= _let_1 (hAPP_i1524277240nt_int _let_6 zero_zero_int))) (=> (not (= zero_zero_int K_1)) (and (=> _let_5 (= (hAPP_i1524277240nt_int _let_6 K_1) _let_1)) (=> (not _let_5) (= (hAPP_P1975530577nt_int (produc713050258nt_int (hAPP_int_fun_int_int times_times_int _let_4)) (hAPP_P1975530577nt_int (hAPP_P1145851913nt_int (hAPP_b40753821nt_int if_Pro1731782967nt_int (hAPP_int_bool (hAPP_i1948725293t_bool fequal_int (hAPP_int_int sgn_sgn_int K_1)) _let_4)) _let_2) (hAPP_P1975530577nt_int (produc1518849193nt_int (hAPP_f465821005nt_int (hAPP_f1081447804nt_int cOMBS_1470252563nt_int (hAPP_f617310012nt_int (hAPP_f197974549nt_int cOMBB_638531587nt_int cOMBS_1891347093nt_int) (hAPP_f1148171384nt_int (hAPP_f334321603nt_int cOMBB_1484610687nt_int (hAPP_f1582586579nt_int cOMBC_707974837nt_int (hAPP_f251264923nt_int (hAPP_f279307923nt_int cOMBB_662120866nt_int if_Pro1731782967nt_int) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool fequal_int) zero_zero_int)))) (hAPP_i1584592887nt_int (hAPP_f465821005nt_int cOMBC_1964283556nt_int (hAPP_f1574055885nt_int _let_3 uminus_uminus_int)) zero_zero_int)))) (hAPP_f1574055885nt_int (hAPP_f960630521nt_int cOMBC_1805044090nt_int (hAPP_f142232355nt_int (hAPP_f1377453843nt_int cOMBB_320287386nt_int cOMBB_1846624359nt_int) (hAPP_f1574055885nt_int _let_3 (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int (hAPP_f1760145644nt_int (hAPP_f1629352853nt_int cOMBB_1496585939nt_int minus_minus_int) uminus_uminus_int)) one_one_int)))) (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int abs_abs_int L))))) _let_2))) _let_1))))))))))))) (forall ((N $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) zero_zero_nat)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real sqrt X_1)) (hAPP_real_real sqrt Y_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2)))) (forall ((X $$unsorted)) (= (hAPP_real_real uminus_uminus_real (hAPP_real_real sqrt X)) (hAPP_real_real sqrt (hAPP_real_real uminus_uminus_real X)))) (forall ((C_69 $$unsorted) (A_163 $$unsorted) (B_124 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_69))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_163) B_124)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) C_69)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral _let_1 A_163)) (hAPP_C498520661umeral _let_1 B_124))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (N $$unsorted)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) B_2) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int C_1) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) N)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd A_3) B_2)) (exists ((K $$unsorted)) (and (is_int K) (= (hAPP_int_int abs_abs_int A_3) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int K) N)))))))) (forall ((A_221 $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_221) zero_zero_nat))) (forall ((P_3 $$unsorted) (A_3 $$unsorted)) (= (hAPP_int_int (inv P_3) A_3) (hAPP_int_int (div_mod_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) P_3))) (hBOOL (hAPP_f54304608l_bool (nat_tr160667106at_int semiri1621563631at_int) (cOMBK_bool_nat fTrue))) (forall ((X_39 $$unsorted)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_39) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_39) X_39))) (forall ((W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int pls) W) pls)) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_real re (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X) Y)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real re X)) (hAPP_complex_real re Y))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real im X)) (hAPP_complex_real im Y))))) (forall ((V_8 $$unsorted) (W_4 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_int_complex number528085621omplex V_8)) (hAPP_int_complex number528085621omplex W_4)) (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int V_8) W_4)))) (forall ((A_218 $$unsorted) (B_161 $$unsorted) (C_90 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_218) B_161)) C_90) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_218) C_90)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_161) C_90)))) (forall ((M_25 $$unsorted) (A_185 $$unsorted) (N_60 $$unsorted) (B_142 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_185))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_n522471361de_int _let_1 N_60)) B_142)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_25) N_60)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_n522471361de_int _let_1 M_25)) B_142)))))) (forall ((C_63 $$unsorted) (A_141 $$unsorted) (B_110 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat C_63))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A_141)) (hAPP_rat_rat _let_1 B_110))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_63)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_141) B_110)))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_int bit1 pls))) (let ((_let_2 (hAPP_int_int bit0 _let_1))) (=> (= (hAPP_nat_nat (div_mod_nat N) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_2))) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 _let_1))) (not (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) one_one_nat)) (hAPP_int_nat number_number_of_nat _let_2))))))))) (forall ((A_103 $$unsorted) (C_45 $$unsorted) (B_85 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_103) C_45)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_85) C_45))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_103) B_85)))) (forall ((X $$unsorted) (Y $$unsorted) (Xa_2 $$unsorted) (Ya $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real Xa_2) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Ya) _let_1))))) (= _let_2 (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sqrt _let_2)) _let_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 X_1)) (hAPP_real_real _let_1 Y_2))))))) (forall ((A_29 $$unsorted) (B_24 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_29) B_24)) (= (hAPP_int_int (div_mod_int B_24) A_29) zero_zero_int))) (forall ((X_34 $$unsorted) (P_7 $$unsorted) (Q_10 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X_34))) (= (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat P_7) Q_10)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int _let_1 P_7)) (hAPP_nat_int _let_1 Q_10))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat N_1)) (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (div_mod_nat N_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))))) (forall ((B_141 $$unsorted) (A_181 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (or (and (hBOOL (hAPP_C24501650l_bool _let_1 B_141)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_181) zero_z126310315umeral))) (and (hBOOL (hAPP_C24501650l_bool _let_1 A_181)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral B_141) zero_z126310315umeral)))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_181) B_141)) zero_z126310315umeral))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime X) Y))) (exists ((P_4 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_4))) (and (hBOOL (hAPP_nat_bool prime P_4)) (hBOOL (hAPP_nat_bool _let_1 X)) (hBOOL (hAPP_nat_bool _let_1 Y))))))) (forall ((W_6 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W_6))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) _let_1)) _let_1) (hAPP_int_int number_number_of_int (hAPP_int_int bit1 W_6))))) (= zOdd (collect_int (hAPP_f2119767738t_bool _let_58 (hAPP_f1791153283t_bool _let_57 (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int (hAPP_f1760145644nt_int _let_56 _let_55)) one_one_int))))) (forall ((B_118 $$unsorted) (A_157 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) A_157)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int B_118) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_118) A_157)) zero_z891286103de_int))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_real im (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X) Y)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_complex_real im X)) (hAPP_complex_real im Y)))) (forall ((B_148 $$unsorted) (A_192 $$unsorted) (C_84 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral A_192))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C_84)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_148) C_84)))))) (forall ((P_1 $$unsorted)) (= (collect_nat P_1) (image_int_nat nat (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (hAPP_f1448486952t_bool (hAPP_f696844121t_bool cOMBB_nat_bool_int P_1) nat)))))) (forall ((A_13 $$unsorted) (B_9 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_13) B_9)) B_9)) (hAPP_nat_nat (div_mod_nat A_13) B_9)) A_13)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X) Y)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat X) Y)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y) _let_1))))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (=> (not (hBOOL (hAPP_int_bool nat_neg Z_1))) (= (hAPP_nat_int semiri1621563631at_int (hAPP_int_nat nat Z_1)) Z_1)))) (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (and (is_int B) (is_int A) (is_int C)) (=> (not (= zero_zero_int A)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A) B)) (= (= B (hAPP_int_int (hAPP_int_fun_int_int times_times_int C) A)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int B) A) C)))))) (forall ((K_2 $$unsorted) (A_3 $$unsorted) (J_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (multInv P_3) J_2))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int _let_1))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong J_2) zero_zero_int) P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_2 J_2)) K_2)) (hAPP_int_int _let_2 A_3)) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong K_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) _let_1)) P_3))))))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted)) (= (= C B) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex C) A) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B) A)))) (forall ((N_62 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat one_one_nat) N_62) one_one_nat)) (forall ((I_1 $$unsorted) (P_1 $$unsorted) (K_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool P_1 K_1)) (=> (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat suc N_2))) (hBOOL (hAPP_nat_bool P_1 N_2)))) (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat K_1) I_1)))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit0 K_2)) (hAPP_int_int bit0 L_2)) (hAPP_int_int bit0 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_2) L_2)))) (forall ((C_58 $$unsorted) (D_11 $$unsorted) (A_136 $$unsorted) (B_105 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_136) B_105)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral C_58) D_11)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_136)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C_58)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_136) C_58)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_105) D_11))))))))) (forall ((C_44 $$unsorted) (D_8 $$unsorted) (A_102 $$unsorted) (B_84 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_102) B_84)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat C_44) D_8)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_102) C_44)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_84) D_8)))))) (forall ((A_222 $$unsorted)) (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat zero_zero_rat) A_222))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_int (big_co1548731110nt_int B_1_1 B_2_1))) (= (hAPP_real_real cos zero_zero_real) one_one_real) (forall ((Q $$unsorted) (P $$unsorted)) (or (hBOOL (hAPP_bool_bool (hAPP_b589554111l_bool fconj P) Q)) (not (hBOOL Q)) (not (hBOOL P)))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 Y)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) Z_1)) (hBOOL (hAPP_nat_bool _let_1 Z_1)))))) (forall ((A_208 $$unsorted)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex A_208) zero_zero_complex))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat D) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_2) Sa)))))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat Z) X_2)) (= _let_1 _let_1)))))) (forall ((X_36 $$unsorted) (Y_28 $$unsorted) (Z_9 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat X_36))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Y_28) Z_9)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 Y_28)) (hAPP_nat_nat _let_1 Z_9))))) (forall ((A_205 $$unsorted) (B_156 $$unsorted)) (=> (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_205) B_156) zero_z126310315umeral) (or (= zero_z126310315umeral B_156) (= A_205 zero_z126310315umeral)))) (forall ((A_223 $$unsorted) (K_8 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_223) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) K_8))) zero_zero_rat)) (= A_223 zero_zero_rat))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat div_div_nat A_3))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_2) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat _let_1 B_2)) C_1)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r653725362t_bool (hAPP_f1927674023t_bool (hAPP_f1261108921t_bool cOMBB_172850899l_real P) Q) R) (hAPP_f729588221t_bool P (hAPP_r1562208522t_bool Q R)))) (forall ((B $$unsorted) (A $$unsorted) (D $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int D))) (=> (is_int D) (= (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int A) B) D) (and (forall ((E $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int E))) (=> (is_int E) (=> (and (hBOOL (hAPP_int_bool _let_1 B)) (hBOOL (hAPP_int_bool _let_1 A))) (hBOOL (hAPP_int_bool _let_1 D)))))) (hBOOL (hAPP_int_bool _let_1 B)) (hBOOL (hAPP_int_bool _let_1 A)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) D))))))) (= zero_zero_real (hAPP_real_real sin _let_54)) (forall ((W_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit0 W_1)) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) zero_zero_int)))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat X))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Y) Z_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat _let_1 Y)) Z_1)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= (hAPP_n1108039445umeral semiri1619134803umeral Ma) (hAPP_n1108039445umeral semiri1619134803umeral N_1)) (= N_1 Ma))) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int Lx_5) Ly_3)))) (let ((_let_2 (hAPP_Q1729056540de_int times_123202395de_int Rx_5))) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int _let_2 Ry_3)) (hAPP_Q1762011733de_int _let_2 (hAPP_Q1762011733de_int _let_1 Ry_3)))))) (= (hAPP_real_real cos _let_52) _let_51) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real W) Z_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Z_1) W))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Y) X))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= X_1 Y_2) (= (quickcheck_int_of X_1) (quickcheck_int_of Y_2)))) (forall ((A $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime B) A)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A) B)))) (hBOOL (hAPP_int_bool nat_neg _let_17)) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Lx_5) Ly_3)))) (let ((_let_2 (hAPP_rat_fun_rat_rat times_times_rat Rx_5))) (= (hAPP_rat_rat _let_1 (hAPP_rat_rat _let_2 Ry_3)) (hAPP_rat_rat _let_2 (hAPP_rat_rat _let_1 Ry_3)))))) (forall ((M $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int M) one_one_int) one_one_int)) (forall ((M_25 $$unsorted) (A_185 $$unsorted) (N_60 $$unsorted) (B_142 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_185))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_nat_rat _let_1 N_60)) B_142)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_25) N_60)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_nat_rat _let_1 M_25)) B_142)))))) (forall ((X_1 $$unsorted)) (= (the_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_r481142414t_bool (hAPP_f1845081853t_bool cOMBC_int_real_bool (hAPP_f801032407l_bool (hAPP_f499530369l_bool cOMBB_1317819104ol_int ord_less_eq_real) ring_1_of_int_real)) X_1))) (hAPP_f429384717t_bool (hAPP_f1173902867t_bool cOMBB_real_bool_int (hAPP_r1134773055l_bool ord_less_real X_1)) (hAPP_f563293398t_real (hAPP_f134192053t_real cOMBB_int_real_int ring_1_of_int_real) (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int plus_plus_int) one_one_int))))) (archim1246769320r_real X_1))) (forall ((X_24 $$unsorted) (N_32 $$unsorted)) (=> (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32)) (= one_one_complex X_24)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex X_24) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_24) N_32))))) (forall ((Ta $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa) X_2)))))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_2) Ta)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1)) Ta)))))))) (forall ((B_121 $$unsorted) (A_160 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_160) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_121)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_160) B_121)) zero_zero_int))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_fun_int_int (hAPP_f1935805932nt_int (hAPP_f125788821nt_int cOMBB_859312247nt_nat P) Q) R) (hAPP_int_fun_int_int P (hAPP_nat_int Q R)))) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= (hAPP_real_real (hAPP_n546711566l_real root (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) X) (hAPP_real_real (hAPP_n546711566l_real root M) (hAPP_real_real (hAPP_n546711566l_real root N) X)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool sRStar P_5))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) P_5))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) _let_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (standardRes P_5) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) (hAPP_int_int (multInv P_5) X_1)))) _let_1)))))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (forall ((Y_1 $$unsorted)) (exists ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_2)) X))))))) (forall ((V_2 $$unsorted)) (= zero_zero_real (hAPP_complex_real im (hAPP_int_complex number528085621omplex V_2)))) (hBOOL (hAPP_int_bool _let_49 one_one_int)) (forall ((C_60 $$unsorted) (D_13 $$unsorted) (A_138 $$unsorted) (B_107 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_138) B_107)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C_60) D_13)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_138)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_60)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_138) C_60)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_107) D_13)))))))) (forall ((A_12 $$unsorted) (N_18 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_12))) (= (hAPP_nat_real _let_1 (hAPP_nat_nat suc N_18)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real _let_1 N_18)) A_12)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_48) zero_zero_real)) (= (hAPP_int_nat nat zero_zero_int) zero_zero_nat) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (rsetR Ma))) (=> (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool A_1) _let_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd X_1) Ma)) (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool (image_int_int (hAPP_int_fun_int_int (hAPP_f2135977429nt_int cOMBC_int_int_int times_times_int) X_1) A_1)) _let_1))))))) (forall ((C $$unsorted) (D $$unsorted) (A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int D))) (let ((_let_2 (zcong C))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_2 (hAPP_int_int _let_1 B)) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_2 (hAPP_int_int _let_1 A)) Ma))))))) (forall ((V_17 $$unsorted) (V_16 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_16)) (=> (hBOOL (hAPP_int_bool _let_1 V_17)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int V_16)) (hAPP_int_int number_number_of_int V_17)) (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_16) V_17))))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (= X (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_n546711566l_real root N) X)) N))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X)) (=> (hBOOL (hAPP_int_bool nat_is_nat Y)) (hBOOL (hAPP_int_bool nat_is_nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) Y)))))) (= sqrt (hAPP_n546711566l_real root _let_4)) (forall ((X_33 $$unsorted)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_33) zero_zero_nat) one_one_real)) (forall ((Z_2 $$unsorted) (X_1 $$unsorted) (X_3 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_1) X_3)) (=> (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) X_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) Z_2)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) (comple124823625p_real X_3)))))) (forall ((X_34 $$unsorted) (P_7 $$unsorted) (Q_10 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_34))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real _let_1 P_7)) (hAPP_nat_real _let_1 Q_10)) (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat P_7) Q_10))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1584592887nt_int (hAPP_f1574055885nt_int (hAPP_f434654626nt_int cOMBS_2011279539nt_int P) Q) R) (hAPP_i1584592887nt_int (hAPP_i1778081398nt_int P R) (hAPP_int_int Q R)))) (forall ((P $$unsorted)) (=> (is_bool P) (or (= fTrue P) (= P fFalse)))) (forall ((I $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat minus_minus_nat N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I) N)) (= I (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_1 I)))))) (forall ((K_5 $$unsorted) (M_15 $$unsorted) (N_28 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_5))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (div_mod_int M_15) N_28))) (=> (hBOOL (hAPP_int_bool _let_1 N_28)) (hBOOL (hAPP_int_bool _let_1 M_15)))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) Y_2)) zEven)))) (= (hAPP_i769753017umeral number1443263063umeral _let_2) one_on1645066479umeral) (forall ((A_94 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A_94) A_94) zero_zero_real)) (forall ((N_49 $$unsorted) (A_147 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat one_one_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_147)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_147) N_49)))))) (forall ((C_59 $$unsorted) (D_12 $$unsorted) (A_137 $$unsorted) (B_106 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_137) B_106)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat C_59) D_12)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_137)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) C_59)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_137) C_59)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_106) D_12)))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int X))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int _let_1 Y)) one_one_int) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Y) Z_1))) one_one_int) P_3))))) (forall ((F $$unsorted) (K_3 $$unsorted) (N_1 $$unsorted)) (=> (forall ((P_4 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat P_4) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real F P_4)) K_3)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real F) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_1)) K_3))))) (forall ((N $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real real_nat N)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N)))) (forall ((A_229 $$unsorted) (C_95 $$unsorted) (D_20 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A_229))) (let ((_let_2 (hAPP_rat_fun_rat_rat plus_plus_rat C_95))) (= (hAPP_rat_rat _let_1 (hAPP_rat_rat _let_2 D_20)) (hAPP_rat_rat _let_2 (hAPP_rat_rat _let_1 D_20)))))) (forall ((B_71 $$unsorted) (A_83 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_83)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_71)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_83) B_71))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (= X_1 one_one_real) (= one_one_real (hAPP_real_real (hAPP_n546711566l_real root N_1) X_1))))) (forall ((A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_3)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real ln X)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3)) A_3)))))) (forall ((A_70 $$unsorted) (B_58 $$unsorted)) (let ((_let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int A_70) B_58))) (= _let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int _let_1) B_58)))) (forall ((K_1 $$unsorted) (F $$unsorted) (N_1 $$unsorted)) (=> (is_int K_1) (=> (forall ((I_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_2) N_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int F (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_2) one_one_nat))) (hAPP_nat_int F I_2)))) one_one_int)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int F zero_zero_nat)) K_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) (hAPP_nat_int F N_1))) (exists ((I_2 $$unsorted)) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_2) N_1)) (= (hAPP_nat_int F I_2) K_1)))))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_f448129468l_bool B_1_1 B_2_1))) (forall ((N_66 $$unsorted) (A_210 $$unsorted) (B_158 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_210) B_158)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_210)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_66)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_210) N_66)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int B_158) N_66))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_f1241350704t_bool (hAPP_f1131424617t_bool cOMBB_rat_bool_int P) Q) R) (hAPP_rat_bool P (hAPP_int_rat Q R)))) (forall ((A $$unsorted)) (hBOOL (tendsto_complex_real im (hAPP_complex_real im A) (at_complex A)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (=> (and (is_int Ma) (is_int N_1)) (= (and (= Ma zero_zero_int) (= zero_zero_int N_1)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int Ma) N_1))))) (forall ((A_211 $$unsorted) (M_26 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_211) one_on1645066479umeral)) M_26) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_211) M_26)) M_26))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_complex_bool B_1_1 B_2_1))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (div_mod_int A_3))) (let ((_let_2 (hAPP_int_int _let_1 (hAPP_int_int uminus_uminus_int B_2)))) (let ((_let_3 (hAPP_int_int _let_1 B_2))) (and (=> (not (= zero_zero_int _let_3)) (= _let_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int _let_3) B_2))) (=> (= _let_3 zero_zero_int) (= zero_zero_int _let_2))))))) (forall ((C $$unsorted) (D $$unsorted) (A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (let ((_let_1 (zcong C))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) D)) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) D)) Ma)))))) (forall ((B_90 $$unsorted) (A_112 $$unsorted) (C_50 $$unsorted)) (=> (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_90) A_112) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real C_50) A_112)) (= B_90 C_50))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (not (= (hAPP_real_real sqrt X) zero_zero_real)))) (forall ((A_217 $$unsorted) (M_29 $$unsorted) (B_160 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_217) M_29)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_160) M_29)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_217) B_160)) M_29))) (forall ((X $$unsorted) (Y $$unsorted)) (= (ratreal (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat X) Y)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (ratreal X)) (ratreal Y)))) (forall ((A $$unsorted) (N_1 $$unsorted)) (= (and (= A zero_zero_real) (not (= N_1 zero_zero_nat))) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real A) N_1) zero_zero_real))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) _let_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (inv P_3) A_3)) _let_1))))))) (forall ((A_201 $$unsorted) (E_3 $$unsorted) (B_154 $$unsorted) (C_87 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_201) E_3)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_154) E_3)) C_87)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_201) B_154)) E_3)) C_87))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r938550413l_real (hAPP_f1293550189l_real (hAPP_f183342685l_real cOMBS_794971624l_real P) Q) R) (hAPP_P1982799375l_real (hAPP_r931665397l_real P R) (hAPP_r1195171167l_real Q R)))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_1)) (not (forall ((M_1 $$unsorted)) (not (= Z_1 (hAPP_nat_int semiri1621563631at_int M_1)))))))) (forall ((A $$unsorted) (N_1 $$unsorted)) (= (and (= A zero_zero_complex) (not (= zero_zero_nat N_1))) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A) N_1) zero_zero_complex))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (is_int Y) (is_int X)) (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y) X)) (= Y X) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X) Y))))) (hBOOL (hAPP_rat_bool _let_47 one_one_rat)) (forall ((B_131 $$unsorted) (A_171 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_171) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) B_131)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_171) B_131)) zero_zero_int))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sin X)) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real cos X)) _let_1)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_bool_bool (hAPP_r1938957037l_bool P R) (hAPP_real_bool Q R)) (hAPP_real_bool (hAPP_f1861673493l_bool (hAPP_f1010710745l_bool cOMBS_real_bool_bool P) Q) R))) (forall ((A_70 $$unsorted) (B_58 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (div_mod_nat A_70) B_58))) (= (hAPP_nat_nat (div_mod_nat _let_1) B_58) _let_1))) (forall ((M $$unsorted) (V_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) V_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc M)) (hAPP_int_nat number_number_of_nat V_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) (hAPP_int_nat number_number_of_nat (hAPP_int_int pred V_2)))))) (forall ((R_3 $$unsorted) (X $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real R_3) (hAPP_complex_real re X)) (hAPP_complex_real re (hAPP_complex_complex (scaleR1652505878omplex R_3) X)))) (= pls (hAPP_int_int bit0 pls)) (forall ((D $$unsorted) (K_1 $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_5)) (= (exists ((I_2 $$unsorted)) (and (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_5) I_2) D) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_2) K_1)))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat D) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_5) K_1)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_rat_bool P (hAPP_P1853363688nt_rat Q R)) (hAPP_P603027463t_bool (hAPP_f1084724746t_bool (hAPP_f374502857t_bool cOMBB_569260360nt_int P) Q) R))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (=> (hBOOL (hAPP_P1555980039t_bool (accp_P490777396at_nat nat_gcd_rel) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat A0) A1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (hBOOL (hAPP_P1555980039t_bool (accp_P490777396at_nat nat_gcd_rel) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat X_2) Y_1))) (=> (=> (not (= Y_1 zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool P_1 Y_1) (hAPP_nat_nat (div_mod_nat X_2) Y_1)))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool P_1 X_2) Y_1))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool P_1 A0) A1))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1250527377l_real (hAPP_n682674106l_real P R) (hAPP_nat_real Q R)) (hAPP_n546711566l_real (hAPP_f451358433l_real (hAPP_f335634176l_real cOMBS_337378985l_real P) Q) R))) (forall ((Q_8 $$unsorted) (R_5 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (divmod_int_rel A_3 B_2))) (=> (and (is_int Q_8) (is_int B_2) (is_int Q_2)) (=> (hBOOL (hAPP_P603027463t_bool _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))) (=> (hBOOL (hAPP_P603027463t_bool _let_1 (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_8) R_5))) (=> (not (= zero_zero_int B_2)) (= Q_8 Q_2))))))) (forall ((A $$unsorted)) (= (= A one_one_nat) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A) one_one_nat)))) (forall ((X_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (let ((_let_2 (hAPP_int_nat number_number_of_nat W_1))) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) _let_2))) (or (= zero_zero_nat _let_2) (hBOOL (hAPP_nat_bool _let_1 X_1))))))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I) J_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 I)) (hAPP_nat_nat _let_1 J_2)))))) (= (hAPP_real_real arctan one_one_real) _let_46) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (=> (hBOOL (hAPP_nat_bool _let_1 M)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) M))))))) (forall ((V_17 $$unsorted) (V_16 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int pls))) (=> (hBOOL (hAPP_int_bool _let_1 V_16)) (=> (hBOOL (hAPP_int_bool _let_1 V_17)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real V_16)) (hAPP_int_real number267125858f_real V_17)) (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_16) V_17))))))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Lx_6))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 Ly_4)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Rx_6) Ry_4)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 Rx_6)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Ly_4) Ry_4))))) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract zero_zero_int) one_one_int) zero_zero_rat) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= (divmod_nat M N) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat _let_1) N))) (hAPP_nat_nat (div_mod_nat _let_1) N))))))) (forall ((A_110 $$unsorted) (B_88 $$unsorted) (C_48 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_110))) (=> (= (hAPP_nat_nat _let_1 B_88) (hAPP_nat_nat _let_1 C_48)) (= C_48 B_88)))) (forall ((B_97 $$unsorted) (A_119 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_119)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) B_97)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_119) B_97))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= one_one_int (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N))) (= (hAPP_int_int abs_abs_int M) one_one_int))) (forall ((N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) one_one_nat) N)) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sqrt X)))))) (forall ((X_9 $$unsorted)) (let ((_let_1 (hAPP_nat_rat semiri151668891at_rat (hAPP_int_nat nat X_9)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_9)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat _let_1) _let_1) (hAPP_nat_rat semiri151668891at_rat (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_9))))))) (forall ((X $$unsorted)) (= (natceiling X) (hAPP_int_nat nat (archim856651990g_real X)))) (forall ((P_2 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hBOOL P_2))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_1)))) (let ((_let_3 (hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) _let_45 (forall ((A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (=> (= (hAPP_int_int (legacy_zgcd B) Ma) one_one_int) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool (bnorRset A) Ma))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_real (hAPP_f269654879t_real (hAPP_f766218899t_real cOMBB_real_real_int P) Q) R) (hAPP_real_real P (hAPP_int_real Q R)))) (forall ((C_39 $$unsorted) (D_7 $$unsorted) (A_97 $$unsorted) (B_79 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_97) B_79)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real C_39) D_7)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_97) C_39)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_79) D_7)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int C))) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A) B)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int _let_1 A)) (hAPP_Q1762011733de_int _let_1 B)))))) (forall ((B_94 $$unsorted) (C_52 $$unsorted) (A_116 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int B_94))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_116)) (=> (hBOOL (hAPP_int_bool _let_1 C_52)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_116) C_52))))))) (forall ((A_16 $$unsorted) (B_12 $$unsorted)) (=> (is_int B_12) (=> (not (= B_12 zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_16) B_12)) one_one_int) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_12) A_16)) B_12))))) (forall ((A $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) A)) zero_zero_rat)))) (forall ((X $$unsorted)) (exists ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_nat_real real_nat N_2))))) (forall ((B_115 $$unsorted) (C_67 $$unsorted) (A_153 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral B_115))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) A_153)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C_67)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_153) C_67))))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int uminus_uminus_int Z_1)) (hAPP_int_int uminus_uminus_int W)) (hAPP_int_int uminus_uminus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_1) W)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (natfloor X)) one_one_nat) (natfloor (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) one_one_real))))) (not (hBOOL (hAPP_int_bool nat_neg one_one_int))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int K_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I) J_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 I)) (hAPP_int_int _let_1 J_2)))))) (forall ((N_59 $$unsorted) (M_24 $$unsorted) (X_28 $$unsorted) (Y_22 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int X_28) Y_22)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_59) M_24)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_28) N_59)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int Y_22) M_24)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool fequal_rat X) Y)) (not (= Y X)))) (forall ((W_1 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat X_1))) (let ((_let_2 (hAPP_nat_fun_nat_nat times_times_nat W_1))) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_2 Z_2)) (hAPP_nat_nat _let_1 Y_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_2 Y_2)) (hAPP_nat_nat _let_1 Z_2))) (or (= Y_2 Z_2) (= W_1 X_1)))))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat Lx_6))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 Rx_6)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ly_4) Ry_4)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 Ly_4)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Rx_6) Ry_4))))) (forall ((B_69 $$unsorted) (A_81 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_81)) (=> (hBOOL (hAPP_nat_bool _let_1 B_69)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_81) B_69))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) M)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_2) M)))) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (div_mod_int A_3) M)) (hAPP_int_int (div_mod_int B_2) M))) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_3) B_2))) (forall ((F $$unsorted) (A_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool (nat_tr160667106at_int F) A_1))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Z_1) W)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real W) Z_1)) (= Z_1 W)))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (=> (not (= X_1 zero_zero_real)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_real_real abs_abs_real T))) (let ((_let_2 (hAPP_r474017924t_real power_power_real X_1))) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) _let_1)) (= (hAPP_real_real exp_real X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) _let_2)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat))) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real exp_real T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_2 N_1)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) (hAPP_real_real abs_abs_real X_1)))))))))) (forall ((Y_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_n546711566l_real root N_1) Y_2))) (hBOOL (hAPP_real_bool _let_1 Y_2)))))) (= (natfloor zero_zero_real) zero_zero_nat) (forall ((C_42 $$unsorted) (A_100 $$unsorted) (B_82 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_100) B_82)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_100) C_42)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_82) C_42))))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit0 K_1)) min)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) min)))) (forall ((M $$unsorted) (N $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (=> (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel M N) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat Q_2) R_3))) (= (hAPP_nat_nat (div_mod_nat M) N) R_3))) (forall ((X_41 $$unsorted) (Y_29 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_41) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat Y_29) _let_1))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) X_41)) Y_29)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_41) Y_29)) _let_1)))) (forall ((A_109 $$unsorted) (B_87 $$unsorted) (C_47 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_109))) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_87) C_47)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int _let_1 B_87)) C_47)))) (forall ((X $$unsorted) (A_3 $$unsorted)) (not (= zero_zero_real (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3)))) (forall ((X $$unsorted)) (= (hAPP_real_real uminus_uminus_real (hAPP_real_real sin X)) (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real pi) X)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) Y_2)) zEven)) (or (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zEven))))) (forall ((F $$unsorted)) (=> (hBOOL (summable_real F)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real F N_2)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_f352196356l_real suminf_real F)))))) (forall ((A_90 $$unsorted)) (=> (is_int A_90) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int one_one_int) A_90) A_90))) (forall ((A $$unsorted) (N_1 $$unsorted)) (= (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A) N_1) zero_z126310315umeral) (and (not (= zero_zero_nat N_1)) (= zero_z126310315umeral A)))) (forall ((C $$unsorted) (D $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex B))) (let ((_let_2 (hAPP_c172932010omplex times_times_complex A))) (= (not (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_2 C)) (hAPP_complex_complex _let_1 D)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_2 D)) (hAPP_complex_complex _let_1 C)))) (and (not (= C D)) (not (= A B))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real sin X)) (hAPP_real_real cos Y))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real cos X)) (hAPP_real_real sin Y))) (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) Y)))) (forall ((B_95 $$unsorted) (C_53 $$unsorted) (A_117 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_117)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_95) C_53)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real B_95) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_117) C_53)))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (hBOOL (hAPP_f448129468l_bool (nat_tr876908586nt_nat F) A_1))) (exists ((K_4 $$unsorted)) (and (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_complex_real norm_norm_complex (hAPP_complex_complex cnj X_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_complex_real norm_norm_complex X_2)) K_4)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) K_4)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) N_1) one_one_nat) (or (= one_one_nat X_1) (= N_1 zero_zero_nat)))) (not (hBOOL (hAPP_int_bool _let_41 pls))) (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (not (= zero_z126310315umeral A)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A) B)) (= (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral B) A) C) (= B (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral C) A)))))) (forall ((Z_12 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex Z_12) Z_12) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Z_12) (hAPP_int_complex number528085621omplex (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((A_235 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_235) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_235) A_235)) A_235))) (forall ((X $$unsorted) (Y $$unsorted)) (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool fequal_nat X) Y)) (not (= X Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1150855451l_bool (hAPP_f381769257l_bool (hAPP_f512004221l_bool cOMBB_188663909l_real P) Q) R) (hAPP_f1344929775l_bool P (hAPP_r632163725t_bool Q R)))) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) X)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y) Y)))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int X_1)) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) (hAPP_int_int bit1 pls))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) Y))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (div_mod_int A_3) B_2))))) (forall ((A_194 $$unsorted) (B_150 $$unsorted)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_194) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_150) A_194)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat B_2))) (let ((_let_2 (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_2 C_1)) (hAPP_nat_nat _let_2 (hAPP_nat_nat _let_1 C_1)))))) (forall ((A_3 $$unsorted) (J_2 $$unsorted) (K_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (multInv P_3))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int A_3))) (let ((_let_3 (zcong K_2))) (let ((_let_4 (zcong J_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_3 zero_zero_int) P_3))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_4 zero_zero_int) P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_4 (hAPP_int_int _let_2 (hAPP_int_int _let_1 K_2))) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_3 (hAPP_int_int _let_2 (hAPP_int_int _let_1 J_2))) P_3)))))))))))) (forall ((A $$unsorted) (C $$unsorted) (D $$unsorted) (B $$unsorted)) (=> (and (is_int B) (is_int D)) (=> (not (= zero_zero_int B)) (=> (not (= D zero_zero_int)) (= (= (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B) (hAPP_int_rat (hAPP_int_fun_int_rat fract C) D)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) D) (hAPP_int_int (hAPP_int_fun_int_int times_times_int C) B))))))) (forall ((A_201 $$unsorted) (E_3 $$unsorted) (B_154 $$unsorted) (C_87 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_201) B_154)) E_3)) C_87) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_201) E_3)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_154) E_3)) C_87)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) zero_zero_int)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int div_div_int A) B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) zero_zero_int))))) (not (hBOOL (hAPP_real_bool _let_40 zero_zero_real))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A) C)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B) C))) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A) B)))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) (hAPP_int_int bit1 K_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) K_1)))) (forall ((A_37 $$unsorted)) (= zero_z891286103de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_37) zero_z891286103de_int))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)) zero_zero_int))))) (forall ((Ma $$unsorted)) (= (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool norRRset Ma)) (hAPP_int_nat phi Ma))) (forall ((Y_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real one_one_real))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool _let_1 Y_2)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_n546711566l_real root N_1) Y_2))))))) (forall ((C_68 $$unsorted) (A_162 $$unsorted) (B_123 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_162) B_123)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_68)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_162) C_68)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_123) C_68)))))) (forall ((X_3 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (=> (hBOOL (hAPP_f448129468l_bool (resSet Ma) X_3)) (hBOOL (hAPP_f448129468l_bool finite_finite_int X_3))))) (forall ((P_1 $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (is_int X_2) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2)) (hBOOL (hAPP_int_bool P_1 X_2)))) (exists ((X_2 $$unsorted)) (hBOOL (hAPP_int_bool P_1 (hAPP_nat_int semiri1621563631at_int X_2)))))) (hBOOL (hAPP_int_bool _let_39 _let_18)) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X_1)) (=> (hBOOL (hAPP_int_bool _let_1 Y_2)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat nat X_1)) (hAPP_int_nat nat Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) Y_2))))))) (forall ((I_1 $$unsorted) (P_1 $$unsorted) (K_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool P_1 K_1)) (=> (forall ((I_2 $$unsorted)) (=> (is_int I_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) I_2)) (=> (hBOOL (hAPP_int_bool P_1 I_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int I_2) one_one_int))))))) (=> (forall ((I_2 $$unsorted)) (=> (is_int I_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I_2) K_1)) (=> (hBOOL (hAPP_int_bool P_1 I_2)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int I_2) one_one_int))))))) (hBOOL (hAPP_int_bool P_1 I_1)))))) (forall ((A_26 $$unsorted) (B_21 $$unsorted)) (=> (not (= B_21 zero_z126310315umeral)) (= A_26 (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_21) A_26)) B_21)))) (forall ((C_42 $$unsorted) (A_100 $$unsorted) (B_82 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_100) B_82)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_100) C_42)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_82) C_42))))) (forall ((C_77 $$unsorted) (B_137 $$unsorted) (A_177 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_77))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_137) A_177)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C_77) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A_177)) (hAPP_int_int _let_1 B_137))))))) (forall ((M_8 $$unsorted) (N_22 $$unsorted)) (= (hAPP_n1108039445umeral semiri1619134803umeral (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_8) N_22)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_n1108039445umeral semiri1619134803umeral M_8)) (hAPP_n1108039445umeral semiri1619134803umeral N_22)))) (forall ((B_92 $$unsorted) (A_114 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_114) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_92) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_114) B_92)) zero_zero_int))))) (forall ((C_60 $$unsorted) (D_13 $$unsorted) (A_138 $$unsorted) (B_107 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_138) B_107)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral C_60) D_13)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) A_138)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) C_60)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_138) C_60)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_107) D_13)))))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real uminus_uminus_real pi)) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real sin X)) zero_zero_real))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) N)))) (forall ((N_1 $$unsorted) (X_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (=> (and (= (hAPP_n546711566l_real Diff zero_zero_nat) F) (forall ((M_1 $$unsorted) (X_2 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) X_2) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) X_2))))) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real X_1))) (and (= (hAPP_real_real F X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real T)) (hAPP_real_real abs_abs_real X_1)))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (negDivAlg A_3 B_2))) (let ((_let_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_3) B_2))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_2)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (and (=> (not _let_3) (= _let_1 (hAPP_P1975530577nt_int (adjust B_2) (negDivAlg A_3 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) B_2))))) (=> _let_3 (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int number_number_of_int min)) _let_2) _let_1)))))))) (forall ((A_197 $$unsorted) (B_152 $$unsorted) (N_64 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_197) N_64)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat B_152) N_64)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_197) B_152)) N_64))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) C)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B) C))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)))) (forall ((P_3 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat P_3))) (let ((_let_2 (hAPP_nat_nat _let_1 M))) (and (=> (not (= M zero_zero_nat)) (= _let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_3) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) one_one_nat))))) (=> (= zero_zero_nat M) (= _let_2 one_one_nat)))))) (forall ((V_13 $$unsorted) (W_11 $$unsorted) (Z_10 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_13) W_11))) Z_10) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real V_13)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real W_11)) Z_10)))) (forall ((X_33 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_33) zero_zero_nat) one_one_nat)) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Y)) (exists ((X_2 $$unsorted)) (= Y (hAPP_real_real exp_real X_2))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat K_1))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 Ma)) (hAPP_nat_nat _let_1 N_1)))))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Y)) (= zero_zero_real (hAPP_real_real cos (arg (hAPP_real_complex (hAPP_r265291036omplex complex zero_zero_real) Y)))))) (forall ((D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool coprime D_3))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))) (hBOOL (hAPP_nat_bool _let_1 B_2))))) (forall ((A_106 $$unsorted)) (=> (is_int A_106) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int zero_zero_int) A_106) A_106))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2))) (let ((_let_2 (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2))) (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_int_rat ring_1_of_int_rat _let_1)) _let_2)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat _let_2) (hAPP_int_rat ring_1_of_int_rat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_1) one_one_int)))))))) (forall ((B_122 $$unsorted) (A_161 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_161) zero_zero_rat)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B_122) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_161) B_122)))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (frct (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int number_number_of_int K_2)) (hAPP_int_int number_number_of_int L_2))) (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat (hAPP_int_rat number_number_of_rat K_2)) (hAPP_int_rat number_number_of_rat L_2)))) (forall ((D $$unsorted) (B $$unsorted) (C $$unsorted) (A $$unsorted)) (=> (and (is_int A) (is_int C)) (=> (not (= A zero_zero_int)) (=> (not (= C zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A) B)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int C) D)) (= (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int B) A) (hAPP_int_int (hAPP_int_fun_int_int div_div_int D) C)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) D) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) C))))))))) (forall ((Z_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z_2) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) Z_2)) Z_2)) zero_zero_int)))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) L_2)) (exists ((N_2 $$unsorted)) (= L_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat K_2) N_2))))) (forall ((Ma $$unsorted) (No $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real F N_2)) (hAPP_nat_real F (hAPP_nat_nat suc N_2))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real F Ma)) (hAPP_nat_real F (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) No)))))) (forall ((B $$unsorted) (A $$unsorted)) (= (= zero_zero_real A) (= B (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B) A)))) (forall ((C_83 $$unsorted) (D_16 $$unsorted) (A_191 $$unsorted) (B_147 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_191) B_147)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int C_83) D_16)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_191) C_83)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_147) D_16)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat semiri984289939at_nat Ma)) (hAPP_nat_nat semiri984289939at_nat N_1))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_rat ring_1_of_int_rat K_2) (hAPP_int_rat (hAPP_int_fun_int_rat fract K_2) one_one_int))) (forall ((A_148 $$unsorted) (N_51 $$unsorted) (N_50 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int A_148))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_51) N_50)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int one_on1684967323de_int) A_148)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int _let_1 N_51)) (hAPP_n522471361de_int _let_1 N_50))))))) (= _let_6 (of_real_complex _let_38)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1962736578t_bool (hAPP_f1063001928t_bool (hAPP_f2050994651t_bool cOMBB_2138578194l_real P) Q) R) (hAPP_f1545556668t_bool P (hAPP_r1150855451l_bool Q R)))) (forall ((Y_6 $$unsorted) (P_6 $$unsorted) (N_10 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat Y_6))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_6) N_10)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_10) P_6))) Y_6) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc N_10)) P_6)))))) (forall ((Y $$unsorted)) (=> (not (= zero_zero_real Y)) (= zero_zero_real (hAPP_real_real cos (arg (hAPP_real_complex (hAPP_r265291036omplex complex zero_zero_real) Y)))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real real_nat (natfloor X))) one_one_real)))) (forall ((Q_2 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool prime Q_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_3) Q_2)) (= P_3 Q_2))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (archim1246769320r_real X))) (=> (= (hAPP_int_real real_int _let_1) X) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int _let_1) N) (archim1246769320r_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) N)))))) (forall ((Z_2 $$unsorted) (Z_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Z_2) Z_3))) (let ((_let_2 (hAPP_int_nat nat Z_2))) (let ((_let_3 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_2) (hAPP_int_nat nat Z_3)))) (let ((_let_4 (hBOOL (hAPP_int_bool nat_neg Z_3)))) (and (=> _let_4 (= _let_2 _let_3)) (=> (not _let_4) (= _let_3 (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_b992065680at_nat if_nat (hAPP_int_bool nat_neg _let_1)) zero_zero_nat) (hAPP_int_nat nat _let_1)))))))))) (forall ((X_1 $$unsorted)) (= (exists ((Y_1 $$unsorted)) (= X_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat))) Y_1))) (hBOOL (hAPP_nat_bool even_odd_even_nat X_1)))) (forall ((A_14 $$unsorted) (B_10 $$unsorted) (Y $$unsorted) (R_7 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_10)))) (=> (and (is_int B_10) (is_int Y)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_10) Y)) R_7) A_14) (=> (and (=> (not _let_1) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_10) R_7)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int R_7) zero_zero_int)))) (=> _let_1 (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_7)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_7) B_10))))) (=> (not (= zero_zero_int B_10)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_14) B_10) Y))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int X))) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int Y))) (not (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_b992065680at_nat if_nat fFalse) X) Y) Y)) (forall ((X $$unsorted) (N $$unsorted)) (= (hAPP_int_real real_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) N)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_int_real real_int X)) N))) (forall ((A $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_1))) (=> (is_int A) (= (= zero_zero_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) _let_1)) (and (= A zero_zero_int) (not (= _let_1 zero_zero_nat))))))) (forall ((M_27 $$unsorted) (A_212 $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_212) one_one_nat)) M_27) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_27) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_212) M_27)))) (forall ((C_76 $$unsorted) (B_136 $$unsorted) (A_176 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_136) A_176)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C_76) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_176) C_76)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_136) C_76)))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y))))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_3)) (=> (not (= A_3 one_one_real)) (=> (hBOOL (hAPP_real_bool _let_1 X)) (= (hAPP_real_real (hAPP_r1250527377l_real powr A_3) (hAPP_real_real (log A_3) X)) X)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A))))) (forall ((A_27 $$unsorted) (B_22 $$unsorted) (C_9 $$unsorted)) (=> (not (= zero_zero_nat C_9)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_27) C_9)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_22) C_9)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat A_27) B_22)))) (forall ((N $$unsorted)) (=> (is_int N) (= N (archim856651990g_real (hAPP_int_real real_int N))))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int pls) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_int_real number267125858f_real Y_2))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls))))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int abs_abs_int X)) _let_1) (hAPP_int_int abs_abs_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X) _let_1))))) (forall ((N $$unsorted) (Z_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_1)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_int_nat nat Z_1)) N) (hAPP_int_nat nat (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Z_1) N))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A) C)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B) C))) (or (= C zero_zero_rat) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat A) B))))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I) J_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J_2) K_2)))))) (forall ((C_41 $$unsorted) (A_99 $$unsorted) (B_81 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int C_41))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A_99)) (hAPP_int_int _let_1 B_81))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_99) B_81))))) (forall ((B_70 $$unsorted) (A_82 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_82) zero_zero_rat)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat B_70) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_82) B_70)) zero_zero_rat))))) (forall ((Ta $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex D) D_1)) (forall ((X_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_c1403687985x_bool dvd_dvd_complex D))) (= (not (hBOOL (hAPP_complex_bool _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_2) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex K) D_1))) Ta)))) (not (hBOOL (hAPP_complex_bool _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X_2) Ta))))))))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) M)) zero_zero_nat)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_complex_real re Y))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real (hAPP_complex_real im X)))) (let ((_let_3 (hAPP_complex_real im Y))) (let ((_let_4 (hAPP_r1250527377l_real times_times_real (hAPP_complex_real re X)))) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real _let_4 _let_1)) (hAPP_real_real _let_2 _let_3))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_4 _let_3)) (hAPP_real_real _let_2 _let_1))) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X) Y))))))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) (hAPP_nat_nat (div_mod_nat M) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)))) (forall ((B_28 $$unsorted) (A_34 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_28) A_34)) B_28) zero_zero_int)) (forall ((A_59 $$unsorted) (B_50 $$unsorted) (C_29 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_59) B_50)) C_29) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (div_mod_nat A_59) C_29)) B_50)) C_29))) (forall ((A $$unsorted) (P_5 $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (hAPP_i1948725293t_bool (wset A) P_5)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool even_odd_even_int X_1)))) (let ((_let_2 (hBOOL (hAPP_int_bool even_odd_even_int Y_2)))) (= (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_1) Y_2))) (or (and (not _let_1) (not _let_2)) (and _let_2 _let_1)))))) (forall ((A_188 $$unsorted) (B_144 $$unsorted) (C_81 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_188) B_144)) C_81)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int B_144) C_81)))) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (= (hAPP_int_int number_number_of_int W_1) X_1))) (=> (is_int X_1) (= _let_1 _let_1)))) (forall ((N_66 $$unsorted) (A_210 $$unsorted) (B_158 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_210) B_158)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_210)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_66)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_210) N_66)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_158) N_66))))))) (forall ((P $$unsorted)) (or (not (hBOOL (hAPP_bool_bool fNot P))) (not (hBOOL P)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_1) Y_2)) zEven))))) (forall ((V_14 $$unsorted) (B_166 $$unsorted) (C_97 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex V_14)))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 B_166)) (hAPP_complex_complex _let_1 C_97)) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_166) C_97))))) (forall ((N_59 $$unsorted) (M_24 $$unsorted) (X_28 $$unsorted) (Y_22 $$unsorted)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex X_28) Y_22)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_59) M_24)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_28) N_59)) (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex Y_22) M_24)))))) (forall ((R_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real R_3) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int (archim1246769320r_real R_3))) one_one_real)))) (forall ((A_167 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_167) A_167)))) (forall ((X $$unsorted)) (= X (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) zero_zero_nat))) (forall ((M $$unsorted) (I $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat M) N)) I) (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) I)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) I)))) (forall ((X_3 $$unsorted)) (=> (hBOOL (summable_complex X_3)) (= (hAPP_f352196356l_real suminf_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat im) X_3)) (hAPP_complex_real im (hAPP_f213450978omplex suminf_complex X_3))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat M))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) (hAPP_nat_nat _let_1 N)) (hAPP_nat_nat _let_1 (hAPP_nat_nat suc N))))) (forall ((Ta $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat D) D_1)) (forall ((X_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool dvd_dvd_rat D))) (= (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_2) Ta))) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat X_2) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat K) D_1))) Ta)))))))) (forall ((A_93 $$unsorted)) (=> (is_int A_93) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_93) zero_zero_int) A_93))) (forall ((A_40 $$unsorted) (B_31 $$unsorted) (C_15 $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (div_mod_int A_40) C_15)) B_31)) C_15) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_40) B_31)) C_15))) (forall ((X_18 $$unsorted) (Y_15 $$unsorted) (A_78 $$unsorted) (B_66 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real A_78))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Y_15) B_66))) (let ((_let_3 (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_18) A_78)))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_3 _let_2)) (hAPP_real_real _let_3 B_66))) (hAPP_real_real _let_1 _let_2)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_18) Y_15)) (hAPP_real_real _let_1 B_66))))))) (forall ((I_1 $$unsorted) (J $$unsorted) (F $$unsorted)) (=> (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_2) J_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat F I_2)) (hAPP_nat_nat F J_1))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_1) J)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat F I_1)) (hAPP_nat_nat F J)))))) (forall ((X_2 $$unsorted)) (= (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) sin_coeff)) (hAPP_r474017924t_real power_power_real X_2))) (hAPP_real_real sin X_2))) (forall ((C_33 $$unsorted) (D_5 $$unsorted) (A_79 $$unsorted) (B_67 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_79) B_67)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real C_33) D_5)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_79) C_33)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_67) D_5)))))) (forall ((A_3 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A_3) (hAPP_nat_nat suc zero_zero_nat)))) (= one_one_rat _let_36) (forall ((B_1_1 $$unsorted)) (is_bool (summable_real B_1_1))) (forall ((N_42 $$unsorted) (A_130 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat one_one_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_130)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_130) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_130) N_42))))))) (forall ((B_121 $$unsorted) (A_160 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_160) zero_zero_rat)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) B_121)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_160) B_121)) zero_zero_rat))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) K_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat M) N)))))) (forall ((Y $$unsorted) (X $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (log A_3))) (let ((_let_2 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_2 A_3)) (=> (not (= one_one_real A_3)) (=> (hBOOL (hAPP_real_bool _let_2 X)) (=> (hBOOL (hAPP_real_bool _let_2 Y)) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 Y)))))))))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int Lx_2))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 Ly)) Rx_2) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int Ly) Rx_2))))) (forall ((N_1 $$unsorted) (N_7 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat F N_2)) (hAPP_nat_nat F (hAPP_nat_nat suc N_2))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) N_7)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat F N_1)) (hAPP_nat_nat F N_7)))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Z_1) W) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_1) (hAPP_int_int uminus_uminus_int W)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_n546711566l_real root N_1) X_1)) zero_zero_real))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real))) (let ((_let_3 (hAPP_f1960414057l_real cOMBB_882763271l_real plus_plus_real))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real _let_3 (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real _let_2 (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real _let_3 (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real sin) uminus_uminus_real))) sin))) _let_1))) (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real _let_2 (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real minus_minus_real) (hAPP_f1950183573l_real (hAPP_f1992866895l_real cOMBB_real_real_real cos) uminus_uminus_real))) cos))) _let_1)) X_2) zero_zero_real)))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N $$unsorted) (J_2 $$unsorted) (I $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat J_2) I)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat I) J_2)) U_1)) M)) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I) U_1)) M)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J_2) U_1)) N))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_real (hAPP_n546711566l_real P R) (hAPP_nat_real Q R)) (hAPP_nat_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real P) Q) R))) (forall ((B_155 $$unsorted) (A_204 $$unsorted)) (=> (not (= A_204 zero_zero_nat)) (=> (not (= B_155 zero_zero_nat)) (not (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_204) B_155)))))) (hBOOL (hAPP_int_bool _let_11 _let_37)) (forall ((A $$unsorted)) (=> (is_int A) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (not (= zero_zero_int A))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (= X_1 zero_zero_nat))) (= _let_1 _let_1))) (= _let_36 one_one_rat) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (= (hAPP_int_int (legacy_zgcd I) J_2) (hAPP_int_int (legacy_zgcd J_2) I))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (= (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real pi) (hAPP_nat_real real_nat (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat _let_1)) M))))) (hAPP_int_real number267125858f_real _let_1))) zero_zero_real))) (forall ((A_11 $$unsorted) (N_17 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_11))) (= (hAPP_nat_int _let_1 (hAPP_nat_nat suc N_17)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_11) (hAPP_nat_int _let_1 N_17))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_1 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_1 (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real inverse_divide_real one_one_real)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat plus_plus_nat) one_one_nat)))))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_1) one_one_real))) suc))) (hAPP_real_real ln X_1)))))) (forall ((N $$unsorted) (M $$unsorted) (R_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat M) R_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat N) R_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N)) R_3)))))) (forall ((G $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D)) (=> (forall ((Z $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (= Z (hAPP_real_real G (hAPP_real_real F Z))))) (=> (forall ((Z $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Z) X_1))) D)) (hBOOL (hAPP_real_bool (isCont_real_real F) Z)))) (exists ((E $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) E)) (forall ((Y_1 $$unsorted)) (let ((_let_1 (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real Y_1) (hAPP_real_real F X_1))))) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) E))) (= Y_1 (hAPP_real_real F (hAPP_real_real G Y_1)))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_int_int (legacy_zgcd M) N) (hAPP_int_int (legacy_zgcd N) (hAPP_int_int (div_mod_int M) N)))) (forall ((A_3 $$unsorted)) (= zero_zero_real (hAPP_real_real (log A_3) one_one_real))) (forall ((I $$unsorted) (K_2 $$unsorted) (J_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) J_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) K_2)) I) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J_2) I)) K_2)))) (forall ((N $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool (zcong A_3) B_2))) (=> (hBOOL (hAPP_int_bool _let_1 M)) (=> (hBOOL (hAPP_int_bool _let_1 N)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd M) N)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int M) N)))))))) (forall ((P_5 $$unsorted)) (= (hAPP_i1948725293t_bool sr P_5) (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) P_5))))) (forall ((B_2 $$unsorted) (M $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) M)) (=> (hBOOL (hAPP_int_bool _let_1 B_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) A_3)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M))))))))) (forall ((B_132 $$unsorted) (A_172 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_172) zero_zero_rat)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_132) zero_zero_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_172) B_132)))))) (forall ((B_148 $$unsorted) (A_192 $$unsorted) (C_84 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_192))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C_84)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_148) C_84)))))) (forall ((L_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) L_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) L_2))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc M)) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex ii))) (= (hAPP_complex_complex uminus473333897omplex X) (hAPP_complex_complex _let_1 (hAPP_complex_complex _let_1 X))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int bit0 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int K_2) L_2)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int bit1 K_2)) (hAPP_int_int bit1 L_2)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (N $$unsorted)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (legacy_zgcd A_3) B_2)) N) (hAPP_int_int (legacy_zgcd (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_2) N)))) (forall ((V_19 $$unsorted) (W_15 $$unsorted)) (= (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_19) W_15)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int V_19)) (hAPP_int_int number_number_of_int W_15)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) zero_zero_real)) (= (natfloor X) zero_zero_nat))) (forall ((C_46 $$unsorted) (A_104 $$unsorted) (B_86 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral C_46))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral _let_1 A_104)) (hAPP_C498520661umeral _let_1 B_86))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A_104) B_86))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Z_2)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_int_nat nat W_1)) (hAPP_int_nat nat Z_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) Z_2))))) (forall ((P_3 $$unsorted)) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int sgn_sgn_int (hAPP_P1175774780nt_int product_fst_int_int (quotient_of P_3)))) one_one_int) (quotient_of (hAPP_rat_rat sgn_sgn_rat P_3)))) (forall ((M_7 $$unsorted) (N_21 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_nat_complex semiri2020571505omplex M_7)) (hAPP_nat_complex semiri2020571505omplex N_21)) (hAPP_nat_complex semiri2020571505omplex (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_7) N_21)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_nat_int semiri1621563631at_int X)) (hAPP_nat_int semiri1621563631at_int Y)) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y)))) (forall ((C_41 $$unsorted) (A_99 $$unsorted) (B_81 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat C_41))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat _let_1 A_99)) (hAPP_rat_rat _let_1 B_81))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_99) B_81))))) (forall ((P $$unsorted)) (=> (is_bool P) (or (= fFalse P) (= P fTrue)))) (forall ((X $$unsorted) (N $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (hAPP_complex_complex cnj X)) N) (hAPP_complex_complex cnj (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X) N)))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (legendre A_3) P_3)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int)) _let_1)))) P_3)))))) (forall ((A_3 $$unsorted)) (= (hAPP_complex_real re (cis A_3)) (hAPP_real_real cos A_3))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)) (hAPP_int_rat (hAPP_int_fun_int_rat fract C_1) D_3)) (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) D_3)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) C_1)))) (forall ((C_60 $$unsorted) (D_13 $$unsorted) (A_138 $$unsorted) (B_107 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_138) B_107)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat C_60) D_13)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) A_138)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_60)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_138) C_60)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_107) D_13)))))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) (hAPP_n522471361de_int semiri1424489471de_int N_1))))) (forall ((Y_6 $$unsorted) (P_6 $$unsorted) (N_10 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral Y_6))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_6) N_10)) (= (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc N_10)) P_6)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_10) P_6))) Y_6))))) (forall ((D $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int D))) (= (= one_one_int (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) B))) (and (= (hAPP_int_int _let_1 A) one_one_int) (= one_one_int (hAPP_int_int _let_1 B)))))) (forall ((B_97 $$unsorted) (A_119 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_119)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) B_97)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_119) B_97))))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (hBOOL (hAPP_real_bool (deriv_real ln X_1) (hAPP_real_real inverse_inverse_real X_1))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (= (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int div_div_int X) Y)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_int_nat nat X)) (hAPP_int_nat nat Y))))))) (forall ((A_37 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_37) zero_z126310315umeral))) (forall ((N_42 $$unsorted) (A_130 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int one_one_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_130)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_130) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_130) N_42))))))) (forall ((Z_1 $$unsorted) (Z_4 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_4)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Z_4) Z_1)) (= (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Z_1) Z_4)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_int_nat nat Z_1)) (hAPP_int_nat nat Z_4)))))) (forall ((Ta $$unsorted) (B_1 $$unsorted) (D $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) D_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int D))) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) B_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Xb) Xa) X_2)))))))) (=> (not (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) Ta)))) (not (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) D_1)) Ta))))))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted) (F $$unsorted)) (let ((_let_1 (hAPP_nat_nat F Ma))) (let ((_let_2 (hAPP_nat_nat F N_1))) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat F N_2))) (let ((_let_2 (hAPP_nat_nat F (hAPP_nat_nat suc N_2)))) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_1) _let_2)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_2) _let_1))))))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) Ma)) (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_1) _let_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_2) _let_1)))))))) (forall ((A_36 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int zero_z891286103de_int) A_36) zero_z891286103de_int)) (forall ((U $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_1) J)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J) I_1)) U)) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I_1) U)) Ma)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J) U)) N_1)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real uminus_uminus_real (hAPP_real_real sin X_1))) (hAPP_real_real cos X_1)))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real) cos)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) _let_1))))) (forall ((V_3 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V_3))) (let ((_let_2 (hAPP_nat_nat suc zero_zero_nat))) (let ((_let_3 (hAPP_nat_nat (div_mod_nat _let_2) (hAPP_int_nat number_number_of_nat V_3)))) (let ((_let_4 (hBOOL (hAPP_int_bool nat_neg _let_1)))) (and (=> _let_4 (= _let_2 _let_3)) (=> (not _let_4) (= _let_3 (hAPP_int_nat nat (hAPP_int_int (div_mod_int one_one_int) _let_1)))))))))) (forall ((X $$unsorted)) (= (hAPP_real_real sin X) (hAPP_real_real sin (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) pi))))) (forall ((R_3 $$unsorted)) (exists ((X_2 $$unsorted)) (let ((_let_1 (hAPP_P1175774780nt_int product_snd_int_int X_2))) (let ((_let_2 (hAPP_P1175774780nt_int product_fst_int_int X_2))) (and (forall ((Y_1 $$unsorted)) (let ((_let_1 (hAPP_P1175774780nt_int product_snd_int_int Y_1))) (let ((_let_2 (hAPP_P1175774780nt_int product_fst_int_int Y_1))) (=> (and (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int _let_2) _let_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) _let_1)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract _let_2) _let_1) R_3)) (= Y_1 X_2))))) (= one_one_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int _let_2) _let_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) _let_1)) (= R_3 (hAPP_int_rat (hAPP_int_fun_int_rat fract _let_2) _let_1))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (=> (is_int N_1) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) zero_zero_int)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int N_1) K_1)) (hAPP_int_int (div_mod_int N_1) K_1))) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (and (is_int I_2) (is_int J_1)) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) J_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int J_1) zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) I_2)) J_1) N_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 I_2) J_1))))))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) pi)) (= X (hAPP_real_real arccos (hAPP_real_real cos X)))))) (forall ((Lx_6 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int Lx_6))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 Ly_4)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Rx_6) Ry_4)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 Rx_6)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Ly_4) Ry_4))))) (forall ((A_195 $$unsorted) (B_151 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_195) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_195) B_151)))) (forall ((X $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (hAPP_nat_real real_nat D_3))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) D_3)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real real_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X) D_3))) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real real_nat (hAPP_nat_nat (div_mod_nat X) D_3))) _let_1)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_nat_real real_nat X)) _let_1))))) (= one_one_real (hAPP_nat_real real_nat one_one_nat)) (forall ((K_2 $$unsorted)) (= zero_zero_rat (frct (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int zero_zero_int) K_2)))) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) zero_zero_nat))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (div_mod_nat X) Y)) (hAPP_int_int (div_mod_int (hAPP_nat_int semiri1621563631at_int X)) (hAPP_nat_int semiri1621563631at_int Y)))) (forall ((A_58 $$unsorted) (B_49 $$unsorted) (C_28 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (div_mod_nat A_58) C_28)) (hAPP_nat_nat (div_mod_nat B_49) C_28))) C_28) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_58) B_49)) C_28))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X_1) N_1))) (or (= zero_zero_nat N_1) (hBOOL (hAPP_nat_bool _let_1 X_1)))))) (forall ((A_195 $$unsorted) (B_151 $$unsorted)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_195) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_195) B_151)))) (forall ((A_203 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_203) zero_z126310315umeral) zero_z126310315umeral)) (forall ((F $$unsorted) (F_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2))) (hBOOL (hAPP_real_bool (deriv_real F X_2) (hAPP_real_real F_1 X_2))))) (exists ((Z $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) Z)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Z) B)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real F B)) (hAPP_real_real F A)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B) A)) (hAPP_real_real F_1 Z)))))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_n546711566l_real root N) X)) N) X)))) (forall ((C_69 $$unsorted) (A_163 $$unsorted) (B_124 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_69))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_163) B_124)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) C_69)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_163)) (hAPP_real_real _let_1 B_124))))))) (forall ((A_3 $$unsorted) (R_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int R_3))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_3) (hAPP_int_int _let_1 B_2))) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int C_1) (hAPP_int_int _let_1 D_3))) N)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int C_1) N))) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int D_3) N))))))) (forall ((C_74 $$unsorted) (A_174 $$unsorted) (B_134 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_74))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_174) B_134)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_74)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int _let_1 A_174)) (hAPP_int_int _let_1 B_134))))))) (forall ((Y $$unsorted)) (exists ((X_2 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (and (= Y (hAPP_real_real tan X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)) X_2)))))) (forall ((A_88 $$unsorted) (B_76 $$unsorted)) (=> (is_int A_88) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_88) B_76)) B_76) A_88))) (forall ((Lx_5 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat Rx_5))) (let ((_let_2 (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Lx_5) Ly_3)))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_2 Ry_3)) (hAPP_nat_nat _let_2 (hAPP_nat_nat _let_1 Ry_3)))))) (forall ((A_238 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_238) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex cnj X)) (hAPP_complex_complex cnj Y)) (hAPP_complex_complex cnj (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X) Y)))) (forall ((A_125 $$unsorted) (N_36 $$unsorted) (N_35 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_125))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_36) N_35)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) A_125)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat A_125) one_one_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_nat_rat _let_1 N_35)) (hAPP_nat_rat _let_1 N_36)))))))) (forall ((R_3 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int (archim1246769320r_real R_3))) R_3))) (forall ((M $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_3))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hBOOL (hAPP_nat_bool _let_1 M)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat one_one_rat) A)) (= (= (hAPP_nat_rat _let_1 Ma) (hAPP_nat_rat _let_1 N_1)) (= Ma N_1))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int (hAPP_int_int number_number_of_int min)))) (let ((_let_2 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_2 X_1)) (=> (hBOOL (hAPP_int_bool _let_2 Y_2)) (=> (= (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zEven))) (= (hAPP_nat_int _let_1 (hAPP_int_nat nat Y_2)) (hAPP_nat_int _let_1 (hAPP_int_nat nat X_1))))))))) (forall ((N_1 $$unsorted) (N_4 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat X_2) N_4)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_2) N_1)))) (hBOOL (hAPP_f54304608l_bool finite_finite_nat N_4)))) (forall ((A_232 $$unsorted)) (= A_232 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_232) (hAPP_int_real number267125858f_real pls)))) (forall ((B_28 $$unsorted) (A_34 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_28) A_34)) B_28))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted)) (=> (and (is_int B) (is_int C)) (= (= C B) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int C) A) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B) A))))) (forall ((X $$unsorted) (N_5 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) N_5)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_n546711566l_real root N) X)) (hAPP_real_real (hAPP_n546711566l_real root N_5) X)))))))) (forall ((B_128 $$unsorted) (A_168 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 A_168)) (=> (hBOOL (hAPP_int_bool _let_1 B_128)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_168) B_128))))))) (forall ((A_218 $$unsorted) (B_161 $$unsorted) (C_90 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_218) C_90)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_161) C_90)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_218) B_161)) C_90))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_f22106695ol_nat finite_card_nat (hAPP_n1699378549t_bool (ord_at238088361st_nat L) U)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc U)) L))) (forall ((C_63 $$unsorted) (A_141 $$unsorted) (B_110 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real C_63))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real _let_1 A_141)) (hAPP_real_real _let_1 B_110))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_63)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_141) B_110)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i345030060t_bool (hAPP_f791698359t_bool (hAPP_f847817363t_bool cOMBB_562416518ol_int P) Q) R) (hAPP_f428220345t_bool P (hAPP_i345030060t_bool Q R)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_2) (hAPP_real_real uminus_uminus_real X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) Y_2)) zero_zero_real)))) (= (hAPP_real_complex (hAPP_r265291036omplex complex one_one_real) zero_zero_real) one_one_complex) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1529485324t_bool (hAPP_f1545556668t_bool (hAPP_f85237525t_bool cOMBB_389152643ol_int P) Q) R) (hAPP_f727283836t_bool P (hAPP_i1823918693l_bool Q R)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A) C)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B) C))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A) B)))) (and (hBOOL (hAPP_int_bool _let_11 s)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int s) _let_18)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong s1) s) _let_18))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real exp_real X))) (= (hAPP_real_real abs_abs_real _let_1) _let_1))) (forall ((A $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (natceiling X_1)) A)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) (hAPP_nat_real real_nat A)))))) (forall ((J_2 $$unsorted) (A_3 $$unsorted) (K_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int J_2) K_2)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong K_2) zero_zero_int) P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) (hAPP_int_int (multInv P_3) K_2))) K_2)) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_1 A_3) P_3)))))))) (forall ((R_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) R_3)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) (hAPP_nat_real real_nat (hAPP_nat_nat suc N_2)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real real_nat N_2)) R_3)))))) (= pred_nat (collec1979865426at_nat (produc1922581855t_bool (hAPP_f618557131t_bool (hAPP_f1505651103t_bool cOMBB_800536526ol_nat _let_35) suc)))) (forall ((W_17 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) (hAPP_int_real number267125858f_real W_17)) (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit1 pls)) W_17)))) (forall ((N $$unsorted)) (= (hAPP_complex_real im (hAPP_nat_complex semiri2020571505omplex N)) zero_zero_real)) (forall ((A $$unsorted) (R_2 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) R_2)) (=> (hBOOL (summable_real A)) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_3) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_f352196356l_real suminf_real (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat A) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat plus_plus_nat) N_2))))) R_2)))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int A_3))) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int _let_1 B_2)) C_1) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int B_2) C_1))))) (= zero_zero_real (hAPP_real_real cos _let_10)) (forall ((I $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat I))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) I)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)))))) (forall ((W $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int W))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) zero_zero_int)) (= (hAPP_P1175774780nt_int product_snd_int_int (hAPP_P1975530577nt_int negateSnd (negDivAlg (hAPP_int_int uminus_uminus_int one_one_int) (hAPP_int_int uminus_uminus_int _let_1)))) (hAPP_int_int (div_mod_int one_one_int) _let_1))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat Z_1))) (let ((_let_2 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (hBOOL (hAPP_nat_bool _let_2 Y)) (=> (and (not (hBOOL (hAPP_nat_bool _let_1 Y))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) Z_1))) (and (hBOOL (hAPP_nat_bool _let_2 Z_1)) (not (hBOOL (hAPP_nat_bool _let_1 X))))))))) (forall ((A_231 $$unsorted) (B_165 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_165) A_231) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_231) B_165))) (forall ((V $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat V))) (let ((_let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_1) (hAPP_int_nat number_number_of_nat V_1)))) (let ((_let_3 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int V_1) pls)))) (let ((_let_4 (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V) (hAPP_int_int uminus_uminus_int V_1))))) (and (=> (not _let_3) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_b992065680at_nat if_nat (hAPP_int_bool nat_neg _let_4)) zero_zero_nat) (hAPP_int_nat nat _let_4)) _let_2)) (=> _let_3 (= _let_1 _let_2)))))))) (forall ((A $$unsorted)) (=> (is_int A) (= (= A zero_zero_int) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) A) zero_zero_int)))) (forall ((N_1 $$unsorted)) (= (= N_1 zero_zero_nat) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) zero_zero_nat)))) (forall ((N $$unsorted)) (= N (hAPP_C498520661umeral (hAPP_C1594335432umeral minus_1690775515umeral (code_S1047413653umeral N)) one_on1645066479umeral))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real exp_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X)))))) (forall ((N_52 $$unsorted) (A_150 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_150)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_150) N_52)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (F $$unsorted)) (=> (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real F X_2) zero_zero_real))) (= (hAPP_real_real F Y_2) (hAPP_real_real F X_1)))) (forall ((M_28 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) one_one_int)) M_28) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int M_28) M_28))) (forall ((A_106 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral zero_z126310315umeral) A_106) A_106)) (is_int zero_zero_int) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_10) _let_8)) (forall ((N_1 $$unsorted)) (=> (is_int N_1) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) N_1)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_f957591787ol_nat finite_card_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_eq_int) N_1))))) N_1)))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (= Y (hAPP_real_real cos (hAPP_real_real arccos Y)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X) Y)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int semiri1621563631at_int X)) (hAPP_nat_int semiri1621563631at_int Y)))) (forall ((B_130 $$unsorted) (A_170 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) A_170)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat B_130) zero_zero_nat)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_130) A_170)) zero_zero_nat))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (exists ((K $$unsorted)) (= N_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) K))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) zero_zero_real)) (exists ((R_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real R_1))) (and (= Y (hAPP_real_real _let_1 (hAPP_real_real sin A_2))) (= (hAPP_real_real _let_1 (hAPP_real_real cos A_2)) X)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (and (is_int N_1) (is_int Ma)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (= (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int Ma) N_1) one_one_int) (and (= one_one_int N_1) (= Ma one_one_int)))))) (forall ((A_58 $$unsorted) (B_49 $$unsorted) (C_28 $$unsorted)) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_58) B_49)) C_28) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_58) C_28)) (hAPP_C498520661umeral (div_mo1740067990umeral B_49) C_28))) C_28))) (forall ((X_7 $$unsorted) (Q_6 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral X_7))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral X_7) (hAPP_n1108039445umeral _let_1 Q_6)) (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat suc Q_6))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (div_mod_nat M) N)) N)))) (forall ((A $$unsorted)) (= (not (= A zero_zero_nat)) (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat zero_zero_nat) A))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A) zero_zero_nat))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= X Y)) (=> (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X) Y))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Y) X))))) (= (hAPP_nat_nat suc _let_12) _let_34) (forall ((A_122 $$unsorted) (B_100 $$unsorted) (V_6 $$unsorted)) (let ((_let_1 (hAPP_int_complex number528085621omplex V_6))) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_122) _let_1)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B_100) _let_1)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A_122) B_100)) _let_1)))) (forall ((N_53 $$unsorted) (M_21 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 M_21)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 N_53)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int M_21) N_53))))))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_n1699378549t_bool (ord_at4362885an_nat L) (hAPP_nat_nat suc U)) (hAPP_n1699378549t_bool (ord_at238088361st_nat L) U))) (forall ((W_12 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) one_one_real)) (hAPP_int_real number267125858f_real W_12)) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 W_12)))) (= (hAPP_real_real cos _let_33) _let_30) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) M)) N) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat suc M)))) N))) (forall ((M_18 $$unsorted) (N_38 $$unsorted) (A_128 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_128))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) A_128)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 M_18)) (hAPP_nat_nat _let_1 N_38))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_18) N_38)))))) (forall ((M_8 $$unsorted) (N_22 $$unsorted)) (= (hAPP_nat_real semiri132038758t_real (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M_8) N_22)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real semiri132038758t_real M_8)) (hAPP_nat_real semiri132038758t_real N_22)))) (not (hBOOL (hAPP_f54304608l_bool finite_finite_nat (collect_nat prime)))) (forall ((K_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) pls)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 K_1)) pls)))) (forall ((Y_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_n546711566l_real root N_1) Y_2))) (hBOOL (hAPP_real_bool _let_1 Y_2)))))) (hBOOL (hAPP_int_bool even_odd_even_int zero_zero_int)) (forall ((X $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2) one_one_nat) (=> (hBOOL (hAPP_nat_bool _let_1 A_3)) (=> (hBOOL (hAPP_nat_bool _let_1 B_2)) (= one_one_nat X)))))) (forall ((A_205 $$unsorted) (B_156 $$unsorted)) (=> (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_205) B_156) zero_zero_complex) (or (= zero_zero_complex B_156) (= zero_zero_complex A_205)))) (forall ((A_3 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool _let_1 Y)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real powr X) A_3)) (hAPP_real_real (hAPP_r1250527377l_real powr Y) A_3)) (hAPP_real_real (hAPP_r1250527377l_real powr (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) Y)) A_3)))))) (forall ((A_110 $$unsorted) (B_88 $$unsorted) (C_48 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat plus_plus_rat A_110))) (=> (= (hAPP_rat_rat _let_1 C_48) (hAPP_rat_rat _let_1 B_88)) (= B_88 C_48)))) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_f1676298106t_real _let_28 suc)) zero_zero_real sequentially)) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real F X_1) L)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) L)) (exists ((D_2 $$unsorted)) (and (forall ((H_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real H_1) D_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F X_1)) (hAPP_real_real F (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) H_1))))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D_2))))))) (forall ((A_27 $$unsorted) (B_22 $$unsorted) (C_9 $$unsorted)) (=> (not (= zero_z126310315umeral C_9)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_27) B_22) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_27) C_9)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_22) C_9))))) (forall ((V_8 $$unsorted) (W_4 $$unsorted)) (= (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int V_8) W_4)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat (hAPP_int_rat number_number_of_rat V_8)) (hAPP_int_rat number_number_of_rat W_4)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (is_int Ma) (=> (not (= zero_zero_int Ma)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Ma) N_1)) Ma)) (= one_one_int (hAPP_int_int abs_abs_int N_1)))))) (forall ((M_25 $$unsorted) (A_185 $$unsorted) (N_60 $$unsorted) (B_142 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int A_185))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int _let_1 N_60)) B_142)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_25) N_60)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_nat_int _let_1 M_25)) B_142)))))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 K_1)) (hAPP_int_int bit1 L))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) L)))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int posDivAlg_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A0) A1))) (=> (forall ((A_2 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool P_1 A_2))) (=> (and (is_int B_4) (is_int A_2)) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int posDivAlg_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A_2) B_4))) (=> (=> (not (or (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_4) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_2) B_4)))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) B_4)))) (hBOOL (hAPP_int_bool _let_1 B_4))))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (F $$unsorted)) (=> (forall ((M_1 $$unsorted) (N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat F M_1)) (hAPP_nat_nat F N_2))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat F Ma)) K_1)) (hAPP_nat_nat F (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) K_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N)) M))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))) (not (= one_one_int (hAPP_int_int (inv P_3) A_3))))))) (forall ((A_220 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int zero_z891286103de_int) A_220) A_220)) (forall ((N_62 $$unsorted)) (= one_one_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat one_one_rat) N_62))) (forall ((M $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat P_3))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M) (hAPP_nat_nat suc (hAPP_nat_nat suc zero_zero_nat))))) (hBOOL (hAPP_nat_bool _let_1 M)))))) (forall ((W_17 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat one_one_rat) (hAPP_int_rat number_number_of_rat W_17)) (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit1 pls)) W_17)))) (forall ((M $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat suc (hAPP_nat_nat suc M))) _let_1) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) _let_1))))) (forall ((M_9 $$unsorted) (N_23 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_9) N_23)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real semiri132038758t_real M_9)) (hAPP_nat_real semiri132038758t_real N_23))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted)) (= (hAPP_complex_real norm_norm_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (of_real_complex R_3)) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real cos A_3)) (hAPP_real_real sin A_3)))) (hAPP_real_real abs_abs_real R_3))) (forall ((P_1 $$unsorted) (I_1 $$unsorted)) (=> (is_int I_1) (= (hBOOL (hAPP_nat_bool P_1 (hAPP_int_nat nat I_1))) (and (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I_1) zero_zero_int)) (hBOOL (hAPP_nat_bool P_1 zero_zero_nat))) (forall ((N_2 $$unsorted)) (=> (= I_1 (hAPP_nat_int semiri1621563631at_int N_2)) (hBOOL (hAPP_nat_bool P_1 N_2)))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real real_nat N_1)) (hAPP_nat_real real_nat Ma))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) Ma)))) (forall ((X $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int minus_minus_int X))) (= (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int Y) M))) M) (hAPP_int_int (div_mod_int (hAPP_int_int _let_1 Y)) M)))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) X))) X)))) (forall ((A_207 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_207) A_207))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1584592887nt_int P (hAPP_int_int Q R)) (hAPP_i1584592887nt_int (hAPP_f1574055885nt_int (hAPP_f2054677283nt_int cOMBB_782625832nt_int P) Q) R))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_int (hAPP_nat_int B_1_1 B_2_1))) (forall ((N $$unsorted) (A_3 $$unsorted)) (= (hAPP_complex_real re (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex (cis A_3)) N)) (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N)) A_3)))) (forall ((V_11 $$unsorted) (W_9 $$unsorted)) (= (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_11) W_9)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_int_rat number_number_of_rat V_11)) (hAPP_int_rat number_number_of_rat W_9)))) (forall ((W $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V_2))) (let ((_let_2 (hAPP_int_int number_number_of_int W))) (let ((_let_3 (negDivAlg _let_2 _let_1))) (let ((_let_4 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_2) _let_1))) (let ((_let_5 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_4)))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) _let_1)) (and (=> _let_5 (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int number_number_of_int min)) _let_4) _let_3)) (=> (not _let_5) (= (hAPP_P1975530577nt_int (adjust _let_1) (negDivAlg _let_2 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) _let_1))) _let_3)))))))))) (forall ((X $$unsorted)) (= (hAPP_real_real sqrt (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hAPP_real_real abs_abs_real X))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real X))) (=> (hBOOL (hAPP_real_bool _let_1 Y)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y)) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))))) (forall ((X_3 $$unsorted)) (=> (hBOOL (vanishes X_3)) (hBOOL (vanishes (hAPP_f2062659861at_rat (hAPP_f1082758869at_rat cOMBB_rat_rat_nat uminus_uminus_rat) X_3))))) (forall ((X_3 $$unsorted) (A $$unsorted)) (=> (hBOOL (hAPP_complex_bool (sums_complex X_3) A)) (hBOOL (hAPP_complex_bool (sums_complex (hAPP_f1646117269omplex (hAPP_f1457396693omplex cOMBB_117013006ex_nat cnj) X_3)) (hAPP_complex_complex cnj A))))) (forall ((A_98 $$unsorted) (C_40 $$unsorted) (B_80 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_98) C_40)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_80) C_40))) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_98) B_80)))) (forall ((K_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int K_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I) J_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) K_2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 I)) (hAPP_int_int _let_1 J_2))))))) (forall ((A_129 $$unsorted) (N_40 $$unsorted) (N_39 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_129))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_40) N_39)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) A_129)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat _let_1 N_40)) (hAPP_nat_nat _let_1 N_39))))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral D) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral X_2) Sa)))))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral X_2) Z)) (= _let_1 _let_1)))))) (forall ((X_39 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral X_39) X_39) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_39) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((A_239 $$unsorted) (B_167 $$unsorted) (V_15 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V_15))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_239) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_167) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_239) B_167)) _let_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (is_int X_1) (is_int Y_2)) (= (= Y_2 X_1) (= (hAPP_int_complex number528085621omplex X_1) (hAPP_int_complex number528085621omplex Y_2))))) (forall ((N_12 $$unsorted) (R_6 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_6)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int R_6) one_one_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int R_6) (hAPP_nat_nat suc N_12))) R_6))))) (forall ((B $$unsorted) (P_5 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_i2112223885l_bool member_int B))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A)) (=> (hBOOL (hAPP_f448129468l_bool _let_1 (hAPP_i1948725293t_bool (wset (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A) one_one_int)) P_5))) (hBOOL (hAPP_f448129468l_bool _let_1 (hAPP_i1948725293t_bool (wset A) P_5))))))) (forall ((N_13 $$unsorted) (A_8 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat one_one_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 A_8)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_8) (hAPP_nat_nat suc N_13))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (and (= N_1 one_one_nat) (= Ma one_one_nat)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat N_1) Ma) one_one_nat))) (forall ((V $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (= (=> (not (hBOOL (hAPP_int_bool nat_neg _let_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_int_nat nat _let_1)) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_int_nat number_number_of_nat V)) (hAPP_nat_nat suc N_1)))))) (forall ((L $$unsorted)) (=> (is_int L) (= (= L min) (= (hAPP_int_int bit1 L) min)))) (not (hBOOL (hAPP_int_bool _let_27 zero_zero_int))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 Y)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Y) Z_1)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P921862901l_bool (hAPP_f365317245l_bool (hAPP_f1961001761l_bool cOMBB_1550063917nt_int P) Q) R) (hAPP_b589554111l_bool P (hAPP_P603027463t_bool Q R)))) (forall ((A_235 $$unsorted)) (= (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A_235) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_235) A_235)) A_235))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool _let_1 Y)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real X) Y))))))) (forall ((B_74 $$unsorted) (A_86 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A_86) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B_74) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_86) B_74)) zero_zero_real))))) (forall ((M_11 $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real semiri132038758t_real M_11)) zero_zero_real)))) (not (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int one_one_int) zEven))) (forall ((C_44 $$unsorted) (D_8 $$unsorted) (A_102 $$unsorted) (B_84 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_102) B_84)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int C_44) D_8)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_102) C_44)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_84) D_8)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (and (= zero_zero_real X_1) (= zero_zero_real Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_1) X_1)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_2) Y_2))) zero_zero_real)))) (forall ((X_20 $$unsorted) (Y_16 $$unsorted) (A_120 $$unsorted) (B_98 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex X_20))) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex _let_1 Y_16)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_120) B_98)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex Y_16) B_98))) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_20) A_120)) B_98))))) (forall ((S $$unsorted)) (= (not (hBOOL (hAPP_f54304608l_bool finite_finite_nat S))) (forall ((M_1 $$unsorted)) (exists ((N_2 $$unsorted)) (and (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat N_2) S)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_2))))))) (forall ((V $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int V))) (let ((_let_2 (hAPP_int_int number_number_of_int W_1))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int _let_1) _let_2)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_2) _let_1))))))) (hBOOL (hAPP_int_bool _let_26 pls)) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_P1333854989l_bool B_1_1 B_2_1))) (forall ((X_44 $$unsorted) (Y_32 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_44) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_32) _let_1))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y_32)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_44) Y_32)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral A))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C)) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral B) A)) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral C) A))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral B) C))))))) (forall ((M_13 $$unsorted)) (= (hAPP_nat_real semiri132038758t_real (hAPP_nat_nat suc M_13)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real one_one_real) (hAPP_nat_real semiri132038758t_real M_13)))) (forall ((X $$unsorted)) (= (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X)) (hAPP_real_real sin X))) (forall ((C_85 $$unsorted) (A_193 $$unsorted) (B_149 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral A_193))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_149)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_149) C_85)))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat D) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat X_2) Sa))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Z) X_2)) (= _let_1 _let_1)))))) (forall ((A_200 $$unsorted) (B_153 $$unsorted) (C_86 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_200) B_153)) C_86) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_200) C_86)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_153) C_86)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real (hAPP_b646336293l_real if_real fTrue) X) Y) X)) (forall ((A_56 $$unsorted) (C_26 $$unsorted) (B_47 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (div_mo1740067990umeral A_56) B_47)) C_26) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_56) C_26)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_47) C_26)))) (forall ((B_131 $$unsorted) (A_171 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_171) zero_zero_nat)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) B_131)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_171) B_131)) zero_zero_nat))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y))) (not (= Y X)))) (forall ((B_73 $$unsorted) (A_85 $$unsorted) (C_36 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real B_73))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) C_36)) (=> (hBOOL (hAPP_real_bool _let_1 A_85)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_85) C_36))))))) (forall ((N $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_3)) (exists ((R_1 $$unsorted)) (and (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real R_1) (hAPP_nat_nat suc N)) A_3) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) R_1)))))) (forall ((V_5 $$unsorted) (W_3 $$unsorted) (C_55 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_5) W_3))) C_55) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real V_5)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_int_real number267125858f_real W_3)) C_55)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1562208522t_bool (hAPP_f2084827628t_bool (hAPP_f1121609875t_bool cOMBB_2125215742l_real P) Q) R) (hAPP_f1902329768t_bool P (hAPP_r285062775l_bool Q R)))) (forall ((F $$unsorted) (G $$unsorted)) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_3) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_nat_real F N_2))) (hAPP_nat_real G N_2)))))) (=> (hBOOL (summable_real G)) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat abs_abs_real) F)))))) (forall ((A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (= (natfloor (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_nat_real real_nat A_3))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (natfloor X)) A_3)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_bool_bool P (hAPP_int_bool Q R)) (hAPP_int_bool (hAPP_f1805168059t_bool (hAPP_f627970963t_bool cOMBB_bool_bool_int P) Q) R))) (forall ((A_190 $$unsorted) (B_146 $$unsorted) (K_7 $$unsorted)) (=> (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_146) K_7) A_190) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real B_146) A_190)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (and (= X_1 zero_zero_rat) (= Y_2 zero_zero_rat)) (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_1) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_2) _let_1)))))) (forall ((Nat $$unsorted)) (= (hAPP_nat_nat nat_size (hAPP_nat_nat suc Nat)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat nat_size Nat)) (hAPP_nat_nat suc zero_zero_nat)))) (forall ((N_1 $$unsorted)) (hBOOL (hAPP_f448129468l_bool finite_finite_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) N_1)))))) (forall ((K_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int min))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int bit1 K_1))) (hBOOL (hAPP_int_bool _let_1 K_1))))) (forall ((A $$unsorted)) (= (= zero_zero_real A) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) A) zero_zero_real))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) (hAPP_nat_int semiri1621563631at_int N_1))))) (forall ((N_11 $$unsorted) (A_7 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) A_7)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_7) one_on1684967323de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_7) (hAPP_nat_nat suc N_11))) one_on1684967323de_int))))) (forall ((A_183 $$unsorted) (M_22 $$unsorted) (N_57 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_183))) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_nat_real _let_1 M_22)) N_57) (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_22) N_57))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N))) (= (hAPP_nat_nat (div_mod_nat M) N) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) N)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_real P (hAPP_nat_real Q R)) (hAPP_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat P) Q) R))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (exists ((K $$unsorted)) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) K)) N)))) (forall ((A_103 $$unsorted) (C_45 $$unsorted) (B_85 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_103) C_45)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_85) C_45))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_103) B_85)))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int min) K_2) (hAPP_int_int uminus_uminus_int K_2))) (forall ((N $$unsorted) (I $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc zero_zero_nat)))) (=> (hBOOL (hAPP_nat_bool _let_1 I)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat I) N)))))) (forall ((M_6 $$unsorted) (N_20 $$unsorted)) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int (hAPP_n522471361de_int semiri1424489471de_int M_6)) N_20) (hAPP_n522471361de_int semiri1424489471de_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M_6) N_20)))) (forall ((X_3 $$unsorted)) (=> (hBOOL (summable_complex X_3)) (hBOOL (summable_complex (hAPP_f1646117269omplex (hAPP_f1457396693omplex cOMBB_117013006ex_nat cnj) X_3))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= N_1 Ma) (= (hAPP_nat_rat semiri151668891at_rat Ma) (hAPP_nat_rat semiri151668891at_rat N_1)))) (forall ((A_134 $$unsorted) (N_47 $$unsorted) (B_103 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_134) N_47)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral B_103) N_47))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) B_103)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_134) B_103))))) (forall ((A_188 $$unsorted) (B_144 $$unsorted) (C_81 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_188) B_144)) C_81)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int B_144) C_81)))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real D) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_2) Sa))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Z) X_2)) (= _let_1 _let_1)))))) (= (hAPP_complex_complex cnj one_one_complex) one_one_complex) (forall ((A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool (zcong A) B))) (= (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int uminus_uminus_int Ma))) (hBOOL (hAPP_int_bool _let_1 Ma))))) (forall ((N_19 $$unsorted)) (= zero_z891286103de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int zero_z891286103de_int) (hAPP_nat_nat suc N_19)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_r481142414t_bool (hAPP_f1845081853t_bool cOMBC_int_real_bool P) Q) R) (hAPP_real_bool (hAPP_i688218208l_bool P R) Q))) (forall ((X_1 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2))) (hBOOL (hAPP_real_bool (isCont_real_real F) X_2)))) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) X_2))) (hBOOL (hAPP_real_bool (deriv_real F X_2) zero_zero_real)))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) B)) (= (hAPP_real_real F A) (hAPP_real_real F X_1)))))))) (forall ((N $$unsorted)) (= (natceiling (hAPP_int_real number267125858f_real N)) (hAPP_int_nat number_number_of_nat N))) (forall ((N_54 $$unsorted) (A_151 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 A_151)) (hBOOL (hAPP_real_bool _let_1 (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_151) N_54)))))) (forall ((M_12 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) (hAPP_n522471361de_int semiri1424489471de_int M_12)))) (forall ((C_68 $$unsorted) (A_162 $$unsorted) (B_123 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_162) B_123)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) C_68)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_162) C_68)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_123) C_68)))))) (forall ((Ma $$unsorted) (X_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X_1) zero_zero_int) Ma)) (= zero_zero_int (hAPP_int_int (standardRes Ma) X_1)))) (forall ((N $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real real_nat N)))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex times_times_complex Lx_3))) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex _let_1 Ly_1)) Rx_3) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex _let_1 Rx_3)) Ly_1)))) (forall ((N_1 $$unsorted) (X_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (=> (and (not (= X_1 zero_zero_real)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (forall ((M_1 $$unsorted) (X_2 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) X_2) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) X_2)))) (= (hAPP_n546711566l_real Diff zero_zero_nat) F)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_real_real abs_abs_real T))) (let ((_let_2 (hAPP_r474017924t_real power_power_real X_1))) (and (= (hAPP_real_real F X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_2)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_2 N_1)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) (hAPP_real_real abs_abs_real X_1))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) _let_1)))))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_2))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int M) N))) (=> (hBOOL (hAPP_int_bool _let_1 N)) (hBOOL (hAPP_int_bool _let_1 M)))))) (forall ((N_33 $$unsorted) (A_123 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat one_one_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_123)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_33)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_123) N_33))))))) (not (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral one_on1645066479umeral) zero_z126310315umeral))) (forall ((V_9 $$unsorted) (U_2 $$unsorted) (Y_19 $$unsorted) (X_25 $$unsorted) (A_127 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat X_25) A_127)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat Y_19) A_127)) (=> (hBOOL (hAPP_rat_bool _let_1 U_2)) (=> (hBOOL (hAPP_rat_bool _let_1 V_9)) (=> (= one_one_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat U_2) V_9)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat U_2) X_25)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat V_9) Y_19))) A_127))))))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) X))) (hAPP_real_real uminus_uminus_real X)))))) (forall ((Xa_3 $$unsorted) (X_13 $$unsorted) (Y_10 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Xa_3))) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_13) Y_10)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real _let_1 X_13)) (hAPP_real_real _let_1 Y_10))))) (forall ((B_132 $$unsorted) (A_172 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_172) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B_132) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_172) B_132)))))) (forall ((R_3 $$unsorted)) (exists ((N_2 $$unsorted)) (and (is_int N_2) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int N_2) one_one_int)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int N_2)) R_3))))) (forall ((N_43 $$unsorted) (A_131 $$unsorted)) (let ((_let_1 (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_131) N_43))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_131)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int _let_1) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_131) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real real_int X)) (hAPP_int_real real_int Y)) (hAPP_int_real real_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) Y)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B_2) one_one_int)) A_3) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) (hAPP_int_int _let_1 B_2))) (hAPP_int_int _let_1 A_3)))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (legacy_zgcd I) J_2)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f561022312t_bool P (hAPP_i614188481l_bool Q R)) (hAPP_i1796122964t_bool (hAPP_f1902329768t_bool (hAPP_f1182713365t_bool cOMBB_2087181719ol_int P) Q) R))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat D) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat X_2) Sa))))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat X_2) Z)) (= _let_1 _let_1)))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_C24501650l_bool B_1_1 B_2_1))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root N))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (= (hAPP_real_real _let_1 (hAPP_real_real abs_abs_real X)) (hAPP_real_real abs_abs_real (hAPP_real_real _let_1 X)))))) (forall ((X_15 $$unsorted) (Y_12 $$unsorted) (Ya_2 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_15) Ya_2)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Y_12) Ya_2)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X_15) Y_12)) Ya_2))) (= zero_zero_real (ratreal zero_zero_rat)) (forall ((N_26 $$unsorted)) (= (hAPP_int_rat number_number_of_rat (hAPP_nat_int semiri1621563631at_int N_26)) (hAPP_nat_rat semiri151668891at_rat N_26))) (forall ((C_34 $$unsorted) (D_6 $$unsorted) (A_80 $$unsorted) (B_68 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_80) B_68)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat C_34) D_6)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_80) C_34)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat B_68) D_6)))))) (forall ((X_1 $$unsorted)) (=> (is_int X_1) (= (= zero_zero_int X_1) (= (hAPP_int_real real_int X_1) zero_zero_real)))) (= one_one_nat (natceiling one_one_real)) (forall ((Sa $$unsorted) (Ta $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A) B)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Sa) Ta)) (hBOOL (hAPP_f115998247l_bool (hAPP_P1876494581l_bool member180897546at_nat (hAPP_P369611207at_nat (hAPP_P402336767at_nat produc494345619at_nat (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat A) Sa)) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat B) Ta))) pair_leq))))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Q_1))) (let ((_let_2 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int R_2) B))) (= (hAPP_P1975530577nt_int (hAPP_P1145851913nt_int (hAPP_b40753821nt_int if_Pro1731782967nt_int (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_2)) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_1) one_one_int)) _let_2)) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int _let_1) R_2)) (hAPP_P1975530577nt_int (adjust B) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_1) R_2)))))) (forall ((A $$unsorted) (B $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (=> (and (is_int B) (is_int A)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Ma)) (=> (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) A_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) A_1)) (= A B)))))))) (forall ((K_2 $$unsorted)) (=> (is_int K_2) (= K_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int K_2) pls)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i418383825t_bool (hAPP_f289318786t_bool (hAPP_f729588221t_bool cOMBC_678732631t_bool P) Q) R) (hAPP_f800510211t_bool (hAPP_i1796122964t_bool P R) Q))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_int_real real_int N_1))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N_1)))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X)) (=> (hBOOL (hAPP_int_bool nat_is_nat Y)) (hBOOL (hAPP_int_bool nat_is_nat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) Y)))))) (forall ((A_149 $$unsorted)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_149) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_149) one_on1645066479umeral)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat nat X)) (hAPP_int_nat nat Y)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y))))))) (forall ((A_94 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A_94) A_94) zero_zero_rat)) (forall ((W_17 $$unsorted)) (= (hAPP_int_complex number528085621omplex (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit1 pls)) W_17)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex one_one_complex) (hAPP_int_complex number528085621omplex W_17)))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int pred K_2) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int min) K_2))) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real zero_zero_real) _let_4) zero_zero_real) (= zero_zero_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex zero_zero_complex) _let_4)) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int D) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int X_2) Sa)))))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int Z) X_2)) (= _let_1 _let_1)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat Ma))) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat suc N_1))) (or (= Ma N_1) (hBOOL (hAPP_nat_bool _let_1 N_1)))))) (forall ((F $$unsorted) (K_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (not (= B A)) (=> (forall ((X_2 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real F X_2) K_1))) (= K_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real F B)) (hAPP_real_real F A))) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real B) A)))))) (forall ((Ta $$unsorted) (A_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Ta) A_1)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa) X_2)))))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) Ta)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) D_1)) Ta))))))))) (forall ((X $$unsorted)) (= X (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) X))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (= (hAPP_real_real sin (hAPP_real_real _let_1 X)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 (hAPP_real_real sin X))) (hAPP_real_real cos X))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) M)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat N) M)))))) (forall ((N $$unsorted) (M $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int N) (hAPP_int_int (hAPP_int_fun_int_int div_div_int M) N)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int M) (hAPP_int_int (div_mod_int M) N)))) (forall ((N_25 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real semiri132038758t_real N_25)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= Y X) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)))) (forall ((C_1 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong C_1) D_3) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_3) C_1)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B_2) D_3)) M))))) (forall ((F $$unsorted) (L $$unsorted)) (=> (hBOOL (tendsto_nat_real F L sequentially)) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat abs_abs_real) F) (hAPP_real_real abs_abs_real L) sequentially)))) (forall ((A_134 $$unsorted) (N_47 $$unsorted) (B_103 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_134) N_47)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_103) N_47))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) B_103)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_134) B_103))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (=> (is_int K_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N)) (=> (= K_2 (hAPP_int_int (legacy_zgcd M) N)) (exists ((S_2 $$unsorted) (T $$unsorted)) (and (is_int S_2) (is_int T) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int S_2) M)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int T) N)) K_2))))))) (forall ((V_2 $$unsorted) (W $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 V_2))) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 W))))) (let ((_let_2 (hAPP_int_int number_number_of_int W))) (let ((_let_3 (hAPP_int_int number_number_of_int V_2))) (let ((_let_4 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_2)))) (and (=> _let_4 (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int _let_3) _let_2) _let_1)) (=> (not _let_4) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int _let_3) one_one_int)) _let_2) _let_1)))))))) (forall ((N_65 $$unsorted) (A_199 $$unsorted)) (=> (is_int A_199) (=> (not (= A_199 zero_zero_int)) (not (= zero_zero_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_199) N_65)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_bool_bool P (hAPP_P603027463t_bool Q R)) (hAPP_P603027463t_bool (hAPP_f237669397t_bool (hAPP_f513299955t_bool cOMBB_1344650379nt_int P) Q) R))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral C))) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral _let_1 A)) (hAPP_C498520661umeral _let_1 B))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral A) B))))) (forall ((A_201 $$unsorted) (E_3 $$unsorted) (B_154 $$unsorted) (C_87 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_201) E_3)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_154) E_3)) C_87)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_201) B_154)) E_3)) C_87))) (= _let_25 one_one_complex) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_1) J)) (= (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat K_1) I_1) J) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J) I_1) K_1)))) (forall ((N $$unsorted) (K_2 $$unsorted)) (=> (is_int K_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_2)) (= K_2 (hAPP_int_int (legacy_zgcd K_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) N)))))) (forall ((Y_14 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real zero_zero_real) Y_14) zero_zero_real)) (forall ((A_108 $$unsorted)) (= A_108 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_108) zero_z126310315umeral))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral) A)) (= (= Ma N_1) (= (hAPP_n1108039445umeral _let_1 N_1) (hAPP_n1108039445umeral _let_1 Ma)))))) (forall ((D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat D_3))) (=> (= one_one_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))) (= one_one_nat (hAPP_nat_nat _let_1 A_3))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (and (is_int Y_2) (is_int X_1)) (= (and (= X_1 zero_zero_int) (= zero_zero_int Y_2)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_1) _let_1)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_2) _let_1))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_1) A_1)) (hBOOL (hAPP_real_bool A_1 X_1)))) (forall ((X_46 $$unsorted) (Y_34 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (and (is_int X_46) (is_int Y_34)) (=> (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_46) _let_2) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_34) _let_2)) (=> (hBOOL (hAPP_int_bool _let_1 X_46)) (=> (hBOOL (hAPP_int_bool _let_1 Y_34)) (= Y_34 X_46)))))))) (forall ((M $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int fact_fact_int M)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (hBOOL P)) (hBOOL Q) (not (hBOOL (hAPP_bool_bool (fimplies P) Q))))) (forall ((X_19 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex X_19) X_19)) one_one_complex) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X_19) one_one_complex)) (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex X_19) one_one_complex)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (or (= C zero_zero_complex) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex A) B))) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A) C)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B) C))))) (forall ((K_1 $$unsorted) (N_1 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (ord_at4362885an_nat zero_zero_nat))) (let ((_let_2 (hAPP_f1509287679l_real big_co604158596t_real F_2))) (= (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat F_2) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat plus_plus_nat) K_1))) (hAPP_n1699378549t_bool _let_1 N_1)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_f1406902706l_real _let_2 (hAPP_n1699378549t_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N_1) K_1)))) (hAPP_f1406902706l_real _let_2 (hAPP_n1699378549t_bool _let_1 K_1))))))) (forall ((Z_1 $$unsorted)) (=> (is_int Z_1) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_1)) (= Z_1 (hAPP_nat_int semiri1621563631at_int (hAPP_int_nat nat Z_1)))))) (forall ((C_71 $$unsorted) (B_126 $$unsorted) (A_165 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_126) A_165)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C_71) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_165) C_71)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_126) C_71)))))) (forall ((X_1 $$unsorted) (K_1 $$unsorted)) (=> (= X_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) K_1)) one_one_int)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)))) (forall ((Y $$unsorted)) (let ((_let_1 (hAPP_real_real arcsin Y))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) pi)) (= (hAPP_real_real sin _let_1) Y) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) _let_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool (wset A) P_5))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (and (= A one_one_real) (= B zero_zero_real)) (= (hAPP_real_complex (hAPP_r265291036omplex complex A) B) one_one_complex))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Y)) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y) (hAPP_real_real tan X_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_2)))))) (forall ((Lx_4 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (let ((_let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int Rx_4) Ry_2))) (let ((_let_2 (hAPP_Q1729056540de_int times_123202395de_int Lx_4))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int _let_2 Ly_2)) _let_1) (hAPP_Q1762011733de_int _let_2 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int Ly_2) _let_1)))))) (not (= zero_zero_int one_one_int)) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X)) (=> (= zero_zero_real (hAPP_real_real sqrt X)) (= X zero_zero_real)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B_2) one_one_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) B_2)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) B_2)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_1)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) _let_1)) (= X (hAPP_real_real arctan (hAPP_real_real tan X))))))) (forall ((R_3 $$unsorted) (A_3 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real R_3) (hAPP_real_real sin A_3)) (hAPP_complex_real im (rcis R_3 A_3)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj))) (let ((_let_2 (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B))) (= (produc93441119t_bool (hAPP_f1048215610t_bool (hAPP_f472159229t_bool cOMBC_1683390479t_bool (hAPP_f1545556668t_bool (hAPP_f85237525t_bool cOMBB_389152643ol_int cOMBS_int_bool_bool) (hAPP_f1344929775l_bool (hAPP_f1830214065l_bool cOMBB_793166024ol_int _let_1) (hAPP_f720654810t_bool (hAPP_f908327869t_bool cOMBB_1290694363ol_int (hAPP_f1512942609t_bool cOMBB_int_bool_int (hAPP_i1948725293t_bool fequal_int A))) (hAPP_f1760145644nt_int (hAPP_f1629352853nt_int cOMBB_1496585939nt_int plus_plus_int) (hAPP_int_fun_int_int times_times_int B)))))) (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool _let_1 (hAPP_f1805168059t_bool (hAPP_f627970963t_bool cOMBB_bool_bool_int (fimplies _let_2)) (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool _let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) B))))) (hAPP_f1805168059t_bool (hAPP_f627970963t_bool cOMBB_bool_bool_int (fimplies (hAPP_bool_bool fNot _let_2))) (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool _let_1 (hAPP_i1948725293t_bool ord_less_int B))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_eq_int) zero_zero_int)))))) (divmod_int_rel A B))))) (forall ((A_3 $$unsorted)) (= one_one_real (hAPP_complex_real norm_norm_complex (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real cos A_3)) (hAPP_real_real sin A_3))))) (forall ((A $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (= (hBOOL (hAPP_real_bool _let_1 A)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) A)))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3_1 $$unsorted)) (is_bool (tendsto_nat_complex B_1_1 B_2_1 B_3_1))) (forall ((Z_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_2)))) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_int_nat nat Z_2)) Ma)) (and (=> (not _let_1) (= Ma zero_zero_nat)) (=> _let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Z_2) (hAPP_nat_int semiri1621563631at_int Ma)))))))) (forall ((F $$unsorted) (L $$unsorted) (C $$unsorted)) (=> (hBOOL (tendsto_real_real F L (at_real C))) (=> (not (= zero_zero_real L)) (exists ((R_1 $$unsorted)) (and (forall ((X_2 $$unsorted)) (=> (and (not (= C X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real C) X_2))) R_1))) (not (= (hAPP_real_real F X_2) zero_zero_real)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) R_1))))))) (forall ((B_141 $$unsorted) (A_181 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (or (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_181) zero_zero_rat)) (hBOOL (hAPP_rat_bool _let_1 B_141))) (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat B_141) zero_zero_rat)) (hBOOL (hAPP_rat_bool _let_1 A_181)))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_181) B_141)) zero_zero_rat))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int M) N)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int fact_fact_int M)) (hAPP_int_int fact_fact_int N)))))) (forall ((M_13 $$unsorted)) (= (hAPP_nat_complex semiri2020571505omplex (hAPP_nat_nat suc M_13)) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex one_one_complex) (hAPP_nat_complex semiri2020571505omplex M_13)))) (forall ((R_3 $$unsorted) (Q_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (= A_3 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int R_3) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) Q_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) R_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Q_2) one_one_int)))))) (is_int s) (= (hAPP_i1732201573de_int quickcheck_of_int zero_zero_int) zero_z891286103de_int) (forall ((A_19 $$unsorted) (B_15 $$unsorted)) (=> (is_int B_15) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_19) B_15)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_19) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_15) A_19)) B_15)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_real_real sgn_sgn_real X))) (let ((_let_2 (= zero_zero_real X))) (let ((_let_3 (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)))) (and (=> (not _let_2) (and (=> (not _let_3) (= _let_1 (hAPP_real_real uminus_uminus_real one_one_real))) (=> _let_3 (= _let_1 one_one_real)))) (=> _let_2 (= _let_1 zero_zero_real))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool even_odd_even_int X)) (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_bool (hAPP_P252494982t_bool P R) (hAPP_P1175774780nt_int Q R)) (hAPP_P603027463t_bool (hAPP_f892584630t_bool (hAPP_f1325804733t_bool cOMBS_480885903t_bool P) Q) R))) (= (hAPP_nat_real semiri132038758t_real one_one_nat) one_one_real) (forall ((M $$unsorted)) (not (= zero_zero_nat (hAPP_nat_nat suc M)))) (forall ((P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_3)))) (forall ((X_36 $$unsorted) (Y_28 $$unsorted) (Z_9 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral X_36))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 Y_28)) (hAPP_C498520661umeral _let_1 Z_9)) (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral Y_28) Z_9))))) (forall ((A_66 $$unsorted) (B_54 $$unsorted)) (=> (is_int A_66) (= A_66 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_66) B_54)) B_54)) (hAPP_int_int (div_mod_int A_66) B_54))))) (forall ((A $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (tendsto_nat_real X_3 X_1 sequentially)) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_3) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) (hAPP_nat_real X_3 N_2)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_1))))) (forall ((A_91 $$unsorted)) (= A_91 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_91) one_one_nat))) (forall ((A_149 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_149) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_149) one_on1684967323de_int)))) (forall ((P_3 $$unsorted) (Q_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_3) Q_2))) (or (= one_one_nat Q_2) (= one_one_nat P_3)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1195171167l_real (hAPP_r2019696015l_real P R) (hAPP_real_real Q R)) (hAPP_r1195171167l_real (hAPP_f617735571l_real (hAPP_f1730463541l_real cOMBS_511527878l_real P) Q) R))) (forall ((A_106 $$unsorted)) (= A_106 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat zero_zero_nat) A_106))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_int (hAPP_nat_fun_int_int P R) Q) (hAPP_nat_int (hAPP_int_fun_nat_int (hAPP_f1673103573at_int cOMBC_nat_int_int P) Q) R))) (forall ((N $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (= (hAPP_int_int (legacy_zgcd A_3) B_2) one_one_int) (= one_one_int (hAPP_int_int (legacy_zgcd (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_3) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_2) N))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral B))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral one_on1645066479umeral) B)) (= (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_n1108039445umeral _let_1 X_1)) (hAPP_n1108039445umeral _let_1 Y_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)))))) (forall ((A_196 $$unsorted) (N_63 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_196) N_63))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_196) _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) A_196)))) (forall ((A_158 $$unsorted) (B_119 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_158) B_119))) (=> (hBOOL (hAPP_rat_bool _let_1 A_158)) (hBOOL (hAPP_rat_bool _let_1 B_119)))))) (forall ((X_1 $$unsorted)) (= (or (exists ((N_2 $$unsorted)) (and (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_2)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X_1) (hBOOL (hAPP_nat_bool even_odd_even_nat N_2)))) (exists ((N_2 $$unsorted)) (and (= X_1 (hAPP_real_real uminus_uminus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real real_nat N_2)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real pi) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (hBOOL (hAPP_nat_bool even_odd_even_nat N_2))))) (= (hAPP_real_real sin X_1) zero_zero_real))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1134773055l_bool (hAPP_f1884005689l_bool (hAPP_f172451459l_bool cOMBB_421479067l_real P) Q) R) (hAPP_f330985925l_bool P (hAPP_r2019696015l_real Q R)))) (forall ((K_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int min))) (= (hBOOL (hAPP_int_bool _let_1 K_1)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int bit0 K_1)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_3)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) (hAPP_int_int _let_1 B_2))) (hAPP_int_int _let_1 A_3)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_2) A_3))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (is_int Ma) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (= (= (hAPP_int_int (legacy_zgcd N_1) Ma) Ma) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Ma) N_1)))))) (forall ((A_201 $$unsorted) (E_3 $$unsorted) (B_154 $$unsorted) (C_87 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_201) B_154)) E_3)) C_87) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_201) E_3)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_154) E_3)) C_87)))) (forall ((A_32 $$unsorted)) (= (hAPP_int_int (div_mod_int A_32) one_one_int) zero_zero_int)) (forall ((A_109 $$unsorted) (B_87 $$unsorted) (C_47 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real A_109))) (= (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real B_87) C_47)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 B_87)) C_47)))) (forall ((A_44 $$unsorted) (B_35 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_44) B_35)) B_35) (hAPP_nat_nat (div_mod_nat A_44) B_35))) (forall ((A_146 $$unsorted)) (= one_on1645066479umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A_146) zero_zero_nat))) (forall ((A_124 $$unsorted) (N_34 $$unsorted) (B_102 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (= (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat B_102) N_34) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_124) N_34)) (=> (hBOOL (hAPP_rat_bool _let_1 A_124)) (=> (hBOOL (hAPP_rat_bool _let_1 B_102)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_34)) (= A_124 B_102))))))) (forall ((A_20 $$unsorted) (C_6 $$unsorted) (B_16 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int A_20))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int C_6) B_16)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int _let_1 B_16)) C_6) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_16) C_6)))))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) (hAPP_nat_nat suc N)))) (forall ((W $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W))) (let ((_let_2 (hAPP_int_int number_number_of_int V_2))) (let ((_let_3 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_int_nat number_number_of_nat V_2)) _let_1))) (let ((_let_4 (hBOOL (hAPP_int_bool nat_neg _let_2)))) (and (=> _let_4 (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat zero_zero_nat) _let_1) _let_3)) (=> (not _let_4) (= _let_3 (hAPP_int_nat nat (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int _let_2) _let_1)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real uminus_uminus_real (hAPP_real_real sin X_1))) (hAPP_real_real cos X_1)))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real times_times_real) cos)) cos) X_1) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) _let_1))))) (forall ((M_9 $$unsorted) (N_23 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_9) N_23)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int semiri1621563631at_int M_9)) (hAPP_nat_int semiri1621563631at_int N_23))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_f284875647l_bool ord_le951220754t_bool (image_nat_int semiri1621563631at_int A_1)) (image_nat_int semiri1621563631at_int B_1))) (hBOOL (hAPP_f54304608l_bool (hAPP_f103356543l_bool ord_le1568362934t_bool A_1) B_1)))) (forall ((X_6 $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat X_6))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat suc Q_5)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat X_6) (hAPP_nat_nat _let_1 Q_5))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (hAPP_complex_real re (hAPP_real_complex (hAPP_r265291036omplex complex X) Y)))) (forall ((Diff $$unsorted) (F $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (forall ((M_1 $$unsorted) (T $$unsorted)) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_1) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real T) H)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) T))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real Diff M_1) T) (hAPP_real_real (hAPP_n546711566l_real Diff (hAPP_nat_nat suc M_1)) T))))) (= (hAPP_n546711566l_real Diff zero_zero_nat) F)) (exists ((T $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real H))) (and (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat inverse_divide_real) (hAPP_r474017924t_real (hAPP_f42270917t_real cOMBC_nat_real_real Diff) zero_zero_real))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) fact_fact_nat)))) _let_1)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) N_1))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real (hAPP_n546711566l_real Diff N_1) T)) (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N_1)))) (hAPP_nat_real _let_1 N_1))) (hAPP_real_real F H)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real T) H)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) T))))))) (= one_one_complex (expi zero_zero_complex)) (forall ((Z_2 $$unsorted)) (= (= zero_zero_complex Z_2) (= (hAPP_complex_complex cnj Z_2) zero_zero_complex))) (forall ((A_3 $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) A_3)) (exists ((X_2 $$unsorted)) (and (= A_3 (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_2) N)) (forall ((Y_1 $$unsorted)) (=> (and (= A_3 (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_1) N)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) Y_1))) (= Y_1 X_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_2))))))) (forall ((A_35 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_35) one_on1645066479umeral) A_35)) (forall ((X_47 $$unsorted) (Y_35 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_47) X_47)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Y_35) Y_35))))) (forall ((X_37 $$unsorted)) (= X_37 (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex X_37) one_one_nat))) (is_int (undefined_int int)) (forall ((A $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A) A)) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) zero_zero_real)))) (forall ((C_80 $$unsorted) (A_187 $$unsorted) (B_143 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral A_187))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 B_143)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C_80)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_143) C_80))))))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool _let_24 _let_22) _let_18)) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_rat_rat times_times_rat Lx_3))) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat _let_1 Rx_3)) Ly_1) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat _let_1 Ly_1)) Rx_3)))) (forall ((R_2 $$unsorted)) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real plus_plus_real R_2)) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat uminus_uminus_real) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) suc)))) R_2 sequentially))) (forall ((Z_14 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex Z_14) Z_14) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_int_complex number528085621omplex (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_14))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int number_number_of_int K_2)) (hAPP_int_int number_number_of_int L_2)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat (hAPP_int_rat number_number_of_rat K_2)) (hAPP_int_rat number_number_of_rat L_2)))) (forall ((P_1 $$unsorted) (A0 $$unsorted)) (=> (hBOOL (hAPP_int_bool (accp_int quickc1265749348ro_rel) A0)) (=> (forall ((I_2 $$unsorted)) (=> (is_int I_2) (=> (hBOOL (hAPP_int_bool (accp_int quickc1265749348ro_rel) I_2)) (=> (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I_2) zero_zero_int))) (=> (not (= I_2 zero_zero_int)) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int I_2) one_one_int))))) (hBOOL (hAPP_int_bool P_1 I_2)))))) (hBOOL (hAPP_int_bool P_1 A0))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat I))) (=> (hBOOL (hAPP_nat_bool _let_1 J_2)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) J_2)))))) (forall ((M_14 $$unsorted) (D_4 $$unsorted)) (=> (is_int M_14) (=> (= (hAPP_int_int (div_mod_int M_14) D_4) zero_zero_int) (exists ((Q_4 $$unsorted)) (and (is_int Q_4) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int D_4) Q_4) M_14)))))) (forall ((A_6 $$unsorted) (N_8 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_nat_fun_nat_nat power_power_nat A_6))) (= (hAPP_nat_nat _let_2 (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_8))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_6) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat _let_2 N_8)) _let_1)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (= (hAPP_nat_real real_nat N_1) (hAPP_nat_real real_nat Ma)) (= Ma N_1))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) zero_zero_int))) (forall ((X_1 $$unsorted)) (=> (is_int X_1) (= (exists ((Y_1 $$unsorted)) (and (is_int Y_1) (= X_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Y_1)))) (hBOOL (hAPP_int_bool even_odd_even_int X_1))))) (forall ((X_7 $$unsorted) (Q_6 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int X_7))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int X_7) (hAPP_n522471361de_int _let_1 Q_6)) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat suc Q_6))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat fact_fact_nat N)) (hAPP_nat_nat fact_fact_nat M))))) (forall ((A_11 $$unsorted) (N_17 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real A_11))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_11) (hAPP_nat_real _let_1 N_17)) (hAPP_nat_real _let_1 (hAPP_nat_nat suc N_17))))) (forall ((X $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X) N))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat P_3) _let_1)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_3) N)) _let_1)))))) (forall ((X $$unsorted)) (= (hAPP_int_int abs_abs_int X) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) X))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1)))))) one_one_real)))) (forall ((A_207 $$unsorted)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_207) A_207))) (forall ((A_109 $$unsorted) (B_87 $$unsorted) (C_47 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_109))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 B_87)) C_47) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat B_87) C_47))))) (forall ((P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int zfact (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))) (hAPP_int_int number_number_of_int min)) P_3)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat M))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat suc N))) (=> (not (hBOOL (hAPP_nat_bool _let_1 N))) (= N M))))) (forall ((X_47 $$unsorted) (Y_35 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real X_47) X_47)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real Y_35) Y_35))))) (forall ((Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) (hAPP_int_real number267125858f_real Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 pls)) Y_2)))) (forall ((X_24 $$unsorted) (N_32 $$unsorted)) (=> (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_32)) (= X_24 one_on1645066479umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral X_24) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_24) N_32))))) (forall ((W_1 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int X_1))) (let ((_let_2 (hAPP_int_fun_int_int times_times_int W_1))) (=> (and (is_int W_1) (is_int X_1) (is_int Z_2) (is_int Y_2)) (= (or (= X_1 W_1) (= Y_2 Z_2)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_2 Z_2)) (hAPP_int_int _let_1 Y_2)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_2 Y_2)) (hAPP_int_int _let_1 Z_2)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) P_5))) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool quadRes P_5) A))) (=> (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool X_1) (setS A P_5))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (big_co1548731110nt_int cOMBI_int X_1)) A) P_5)))))))) (forall ((A_1 $$unsorted) (Ma $$unsorted)) (= (and (= (hAPP_int_nat phi Ma) (hAPP_f957591787ol_nat finite_card_int A_1)) (hBOOL (hAPP_f215623910l_bool (hAPP_f628503027l_bool member_fun_int_bool A_1) (rsetR Ma)))) (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)))) (forall ((D $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime D) zero_zero_nat)) (= D one_one_nat))) (forall ((N_1 $$unsorted) (K_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat K_1))) (=> (hBOOL (hAPP_nat_bool _let_1 Ma)) (=> (hBOOL (hAPP_nat_bool _let_1 N_1)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat Ma) K_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_1) K_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1))))))) (forall ((N_65 $$unsorted) (A_199 $$unsorted)) (=> (not (= zero_zero_complex A_199)) (not (= zero_zero_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex A_199) N_65))))) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) (hAPP_i1948725293t_bool sRStar P_5))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X_1) zero_zero_int) P_5))))) (forall ((M_12 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) (hAPP_nat_nat semiri984289939at_nat M_12)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_P1668131738nt_int (hAPP_f167782601nt_int (hAPP_f400538607nt_int cOMBB_866192175nt_int P) Q) R) (hAPP_i61245889nt_int P (hAPP_P1175774780nt_int Q R)))) (forall ((A_91 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real A_91) one_one_real) A_91)) (forall ((X_34 $$unsorted) (P_7 $$unsorted) (Q_10 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat X_34))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat _let_1 P_7)) (hAPP_nat_nat _let_1 Q_10)) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat P_7) Q_10))))) (is_int one_one_int) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int M))) (= (hAPP_int_int _let_1 N) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int M) N))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_real_complex (hAPP_r265291036omplex complex A_3) B_2)) ii) (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real uminus_uminus_real B_2)) A_3))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (= (hAPP_n1699378549t_bool (ord_at238088361st_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat I_1) K_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat J) K_1)) (image_nat_nat (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat plus_plus_nat) K_1) (hAPP_n1699378549t_bool (ord_at238088361st_nat I_1) J)))) (forall ((A_110 $$unsorted) (B_88 $$unsorted) (C_48 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex A_110))) (=> (= (hAPP_complex_complex _let_1 B_88) (hAPP_complex_complex _let_1 C_48)) (= B_88 C_48)))) (forall ((P_1 $$unsorted)) (= (collec1347809874nt_int P_1) P_1)) (forall ((N $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int N) one_one_int)) N) one_one_int)) (forall ((A_207 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat A_207) A_207))) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real F X_1) L)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) L)) (exists ((D_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D_2)) (forall ((H_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real H_1) D_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_1) H_1))) (hAPP_real_real F X_1))))))))))) (forall ((C_83 $$unsorted) (D_16 $$unsorted) (A_191 $$unsorted) (B_147 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_191) B_147)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral C_83) D_16)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_191) C_83)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_147) D_16)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool even_odd_even_int X)) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int Y))) (not (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) Y))))))) (forall ((A_238 $$unsorted)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_238) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (= zero_zero_int (hAPP_int_int (div_mod_int X_1) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) K_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 K_1)) (hAPP_int_int bit1 L))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K_1) L)))) (forall ((B_69 $$unsorted) (A_81 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_81)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 B_69)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_81) B_69))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_complex_real re X)) (hAPP_complex_real re Y))) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_complex_real im X)) (hAPP_complex_real im Y))) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X) Y))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) M)) (not (= N M)))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat C_1))) (=> (= B_2 A_3) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) C_1)) (not (hBOOL (hAPP_nat_bool _let_1 B_2)))) (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) C_1)) (not (hBOOL (hAPP_nat_bool _let_1 A_3)))))))) (forall ((X_3 $$unsorted)) (=> (hBOOL (summable_complex X_3)) (= (hAPP_f213450978omplex suminf_complex (hAPP_f1646117269omplex (hAPP_f1457396693omplex cOMBB_117013006ex_nat cnj) X_3)) (hAPP_complex_complex cnj (hAPP_f213450978omplex suminf_complex X_3))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_nat_bool even_odd_even_nat N)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) one_one_nat)) _let_1))))) (forall ((Y_20 $$unsorted) (X_26 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 X_26)) (=> (hBOOL (hAPP_rat_bool _let_1 Y_20)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat Y_20) one_one_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat X_26) Y_20)) X_26))))))) (forall ((A_240 $$unsorted)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_240) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) zero_zero_real)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real exp_real X_1)) (hAPP_real_real exp_real Y_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (ratreal X_1)) (ratreal Y_2))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat X_1) Y_2)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real P R) (hAPP_real_real Q R)) (hAPP_real_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real P) Q) R))) (forall ((Z_1 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_nat_int semiri1621563631at_int Z_1)))) (forall ((V_19 $$unsorted) (W_15 $$unsorted)) (= (hAPP_int_rat number_number_of_rat (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_19) W_15)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat number_number_of_rat V_19)) (hAPP_int_rat number_number_of_rat W_15)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B))))))) (forall ((C_73 $$unsorted) (A_173 $$unsorted) (B_133 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_173) B_133)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) C_73)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_173) C_73)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_133) C_73)))))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (of_real_complex (hAPP_real_real exp_real (hAPP_complex_real re Z_1)))) (cis (hAPP_complex_real im Z_1))) (expi Z_1))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (= (= N_1 Ma) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N_1) K_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) K_1)))) (forall ((X $$unsorted)) (= (hAPP_complex_complex sgn_sgn_complex X) (hAPP_complex_complex (scaleR1652505878omplex (hAPP_real_real inverse_inverse_real (hAPP_complex_real norm_norm_complex X))) X))) (forall ((N_41 $$unsorted)) (let ((_let_1 (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex zero_zero_complex) N_41))) (and (=> (not (= zero_zero_nat N_41)) (= zero_zero_complex _let_1)) (=> (= N_41 zero_zero_nat) (= _let_1 one_one_complex))))) (forall ((K_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_1))) (= (and (hBOOL (hAPP_int_bool _let_1 N_1)) (hBOOL (hAPP_int_bool _let_1 Ma))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int Ma) N_1)))))) (forall ((B_72 $$unsorted) (C_35 $$unsorted) (A_84 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int B_72))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_84)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C_35)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_84) C_35))))))) (forall ((C $$unsorted) (D $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat B))) (let ((_let_2 (hAPP_nat_fun_nat_nat times_times_nat A))) (= (and (not (= C D)) (not (= A B))) (not (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_2 D)) (hAPP_nat_nat _let_1 C)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_2 C)) (hAPP_nat_nat _let_1 D)))))))) (forall ((A_33 $$unsorted) (B_27 $$unsorted)) (= zero_z126310315umeral (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_33) B_27)) B_27))) (forall ((X $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) P_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (standardRes P_3) X))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)))) (forall ((X_1 $$unsorted)) (= (= (hAPP_int_real real_int (archim856651990g_real X_1)) X_1) (exists ((N_2 $$unsorted)) (and (= (hAPP_int_real real_int N_2) X_1) (is_int N_2))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (legacy_zgcd I) J_2)) I))) (forall ((N_53 $$unsorted) (M_21 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat one_one_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 M_21)) (=> (hBOOL (hAPP_rat_bool _let_1 N_53)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat M_21) N_53))))))) (forall ((C_63 $$unsorted) (A_141 $$unsorted) (B_110 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C_63))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A_141)) (hAPP_int_int _let_1 B_110))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) C_63)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_141) B_110)))))) (forall ((X_34 $$unsorted) (P_7 $$unsorted) (Q_10 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat X_34))) (= (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat P_7) Q_10)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat _let_1 P_7)) (hAPP_nat_rat _let_1 Q_10))))) (is_bool fFalse) (forall ((B_2 $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) C_1)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat B_2) D_3)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat C_1) D_3)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) C_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_2) D_3)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)) (hAPP_int_rat (hAPP_int_fun_int_rat fract C_1) D_3)))) (forall ((X $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (log A_3))) (let ((_let_2 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_2 A_3)) (=> (not (= one_one_real A_3)) (=> (hBOOL (hAPP_real_bool _let_2 X)) (= (hAPP_real_real uminus_uminus_real (hAPP_real_real _let_1 X)) (hAPP_real_real _let_1 (hAPP_real_real inverse_inverse_real X))))))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (=> (is_int C) (= (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B) E_2)) D) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) E_2)) C)) (= C (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int B) A)) E_2)) D))))) (forall ((L $$unsorted) (U $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (hAPP_n1699378549t_bool (ord_at238088361st_nat L) U)))) (forall ((N $$unsorted) (M $$unsorted)) (= (code_d418564891umeral N M) (hAPP_C2132160860umeral (hAPP_C1614127039umeral produc2136830103umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral N) M)) (hAPP_C498520661umeral (div_mo1740067990umeral N) M)))) (forall ((C_59 $$unsorted) (D_12 $$unsorted) (A_137 $$unsorted) (B_106 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_137) B_106)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral C_59) D_12)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_137)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) C_59)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_137) C_59)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_106) D_12)))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) Y_2)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_int_rat number_number_of_rat X_1)) (hAPP_int_rat number_number_of_rat Y_2))))) (forall ((X_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool even_odd_even_nat X_1)) (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_nat_int semiri1621563631at_int X_1))))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat V_2))) (let ((_let_2 (hAPP_int_nat number_number_of_nat V_3))) (let ((_let_3 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat _let_1) _let_2))) (let ((_let_4 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int V_3) pls)))) (let ((_let_5 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int V_2) pls)))) (and (=> _let_5 (= _let_3 _let_2)) (=> (not _let_5) (and (=> (not _let_4) (= (hAPP_int_nat number_number_of_nat (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_2) V_3)) _let_3)) (=> _let_4 (= _let_3 _let_1))))))))))) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (standardRes P_5) X_1)) (hAPP_i1948725293t_bool sRStar P_5))) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X_1) zero_zero_int) P_5)))))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (and (is_int Z) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) Sa)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Z) X_2)) (= _let_1 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real C) D)) (= (= C D) (= A B)))) (forall ((A_94 $$unsorted)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int A_94) A_94))) (forall ((P $$unsorted) (Q $$unsorted)) (or (hBOOL (hAPP_bool_bool (fimplies P) Q)) (not (hBOOL Q)))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int semiri1621563631at_int M)) N))) (forall ((A_3 $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_nat_real real_nat A_3))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) X)) (= (natfloor (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (natfloor X)) A_3))))) (forall ((A_225 $$unsorted) (B_162 $$unsorted) (C_91 $$unsorted) (D_18 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_225))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 B_162)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral C_91) D_18)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 C_91)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_162) D_18))))) (forall ((X $$unsorted)) (= (hAPP_complex_complex cnj (hAPP_complex_complex uminus473333897omplex X)) (hAPP_complex_complex uminus473333897omplex (hAPP_complex_complex cnj X)))) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool sRStar P_5))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) _let_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (standardRes P_5) X_1)) _let_1))))))) (forall ((M $$unsorted) (K_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_1 N)) (=> (hBOOL (hAPP_nat_bool _let_1 K_2)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc zero_zero_nat)) M)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M) N) K_2) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) K_2)))))))) (forall ((U $$unsorted)) (= (hAPP_int_nat nat U) (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool (ord_at641636577an_int zero_zero_int) U)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real B))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real one_one_real) B)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real _let_1 X_1)) (hAPP_nat_real _let_1 Y_2))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc N_1)) (hAPP_nat_nat suc Ma))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_1) Ma)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zOdd)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_1) Y_2)) zEven))))) (hBOOL (hAPP_real_bool _let_21 _let_10)) (forall ((M_6 $$unsorted) (N_20 $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M_6) N_20)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int semiri1621563631at_int M_6)) N_20))) (forall ((Ta $$unsorted) (A_1 $$unsorted) (D_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Ta) one_one_int)) A_1)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D_1))) (forall ((Xb $$unsorted)) (=> (is_int Xb) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xb) A_1)) (not (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int Xb) Xa) X_2)))))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_2) Ta)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) D_1)) Ta))))))))) (forall ((N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) one_one_nat) (hAPP_nat_nat suc N))) (forall ((V_9 $$unsorted) (U_2 $$unsorted) (Y_19 $$unsorted) (X_25 $$unsorted) (A_127 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_25) A_127)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Y_19) A_127)) (=> (hBOOL (hAPP_int_bool _let_1 U_2)) (=> (hBOOL (hAPP_int_bool _let_1 V_9)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int U_2) V_9) one_one_int) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int U_2) X_25)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int V_9) Y_19))) A_127))))))))) (forall ((K_1 $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_eq_nat) K_1))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (=> (is_int Z_2) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) Z_2)) (exists ((N_2 $$unsorted)) (= Z_2 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int W_1) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat suc N_2)))))))) (forall ((A_133 $$unsorted) (N_46 $$unsorted) (N_45 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat A_133))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_46) N_45)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat) A_133)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_133) one_one_rat)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_nat_rat _let_1 N_45)) (hAPP_nat_rat _let_1 N_46)))))))) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (hAPP_n546711566l_real root M))) (let ((_let_2 (hAPP_n546711566l_real root N))) (let ((_let_3 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool _let_3 M)) (=> (hBOOL (hAPP_nat_bool _let_3 N)) (= (hAPP_real_real _let_1 (hAPP_real_real _let_2 X)) (hAPP_real_real _let_2 (hAPP_real_real _let_1 X))))))))) (forall ((A_228 $$unsorted) (C_94 $$unsorted) (D_19 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_228))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral _let_1 C_94)) D_19) (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral C_94) D_19))))) (forall ((N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat zero_zero_nat) N) N)) (forall ((C_59 $$unsorted) (D_12 $$unsorted) (A_137 $$unsorted) (B_106 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_137) B_106)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int C_59) D_12)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_137)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C_59)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_137) C_59)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_106) D_12)))))))) (forall ((A_215 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_215) one_one_rat) A_215)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat nat X_1))) (=> (and (is_int A) (is_int C) (is_int B)) (=> (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) B)) C) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int D) _let_1)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) _let_1)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zOdd)) (=> (= (hAPP_int_int (legacy_zgcd A) B) one_one_int) (=> (= (hAPP_int_int (legacy_zgcd B) C) one_one_int) (=> (= one_one_int (hAPP_int_int (legacy_zgcd C) A)) (exists ((K $$unsorted) (L_1 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat nat X_1))) (and (is_int K) (is_int M_1) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int K) _let_1) A) (= B (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int L_1) _let_1)) (= C (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int M_1) _let_1)) (is_int L_1))))))))))))) (forall ((N $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_nat_nat fact N)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B_2)) (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (posDivAlg A_3 B_2)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) zero_zero_real)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real uminus_uminus_real pi)) X)) (= (hAPP_real_real arccos (hAPP_real_real cos X)) (hAPP_real_real uminus_uminus_real X))))) (forall ((A_21 $$unsorted) (B_17 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_21) B_17)) (= B_17 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat B_17) A_21)) A_21)))) (forall ((A_190 $$unsorted) (B_146 $$unsorted) (K_7 $$unsorted)) (=> (= A_190 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_146) K_7)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat B_146) A_190)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1524277240nt_int (hAPP_f883232462nt_int (hAPP_f2002277285nt_int cOMBB_1846624359nt_int P) Q) R) (hAPP_i1524277240nt_int P (hAPP_int_int Q R)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_int_real real_int X_1)) (hAPP_int_real real_int Y_2))))) (forall ((B_93 $$unsorted) (A_115 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int A_115) zero_z891286103de_int)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int B_93) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_115) B_93)) zero_z891286103de_int))))) (forall ((N_42 $$unsorted) (A_130 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int one_on1684967323de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_130)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_130) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int A_130) N_42))))))) (forall ((X_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (=> (= (hAPP_int_int (legacy_zgcd X_1) Ma) one_one_int) (= (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool norRRset Ma)) (hAPP_f957591787ol_nat finite_card_int (hAPP_i1948725293t_bool (noXRRset Ma) X_1)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_nat_bool (hAPP_f1154658180t_bool (hAPP_f1361476881t_bool cOMBB_int_bool_nat P) Q) R) (hAPP_int_bool P (hAPP_nat_int Q R)))) (forall ((K_2 $$unsorted)) (= (hAPP_int_int bit1 (hAPP_int_int pred (hAPP_int_int uminus_uminus_int K_2))) (hAPP_int_int uminus_uminus_int (hAPP_int_int bit1 K_2)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)))) (let ((_let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) (hAPP_nat_real semiri132038758t_real N_1))))) (forall ((A_29 $$unsorted) (B_24 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_29) B_24)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int B_24) A_29) zero_z891286103de_int))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N))) (=> (not (= zero_zero_nat N)) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_1) one_one_nat)) _let_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real sqrt X)) (hAPP_real_real sqrt Y)) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i744251628nt_int (hAPP_f836602773nt_int (hAPP_f888249301nt_int cOMBB_1875755114nt_int P) Q) R) (hAPP_f747162069nt_int P (hAPP_int_fun_int_int Q R)))) (forall ((V_12 $$unsorted) (W_10 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int number_number_of_int V_12)) (hAPP_int_int number_number_of_int W_10)) (hAPP_int_int number_number_of_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_12) W_10)))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) one_on1645066479umeral)) (forall ((A_183 $$unsorted) (M_22 $$unsorted) (N_57 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_183))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_22) N_57)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat (hAPP_nat_nat _let_1 M_22)) N_57)))) (forall ((A_64 $$unsorted) (B_52 $$unsorted) (C_31 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_64) B_52)) B_52)) (hAPP_C498520661umeral (div_mo1740067990umeral A_64) B_52))) C_31) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_64) C_31))) (forall ((K_2 $$unsorted)) (not (= (hAPP_int_int bit0 K_2) min))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r931665397l_real (hAPP_f1607917947l_real (hAPP_f1076489843l_real cOMBB_415306361l_real P) Q) R) (hAPP_b1482221219l_real P (hAPP_real_bool Q R)))) (forall ((N_1 $$unsorted)) (= zero_zero_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min))) suc)) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_1))))) (forall ((A_221 $$unsorted)) (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_221) zero_zero_rat))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= Ma N_1) (= (hAPP_nat_int semiri1621563631at_int N_1) (hAPP_nat_int semiri1621563631at_int Ma)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_rat_rat inverse_inverse_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)) (hAPP_int_rat (hAPP_int_fun_int_rat fract B_2) A_3))) (forall ((M_10 $$unsorted) (N_24 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_nat_real semiri132038758t_real M_10)) (hAPP_nat_real semiri132038758t_real N_24))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_10) N_24)))) (forall ((N $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) zero_zero_nat)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (not (hBOOL (hAPP_nat_bool even_odd_even_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat Ma) N_1)))) (not (= (not (hBOOL (hAPP_nat_bool even_odd_even_nat Ma))) (not (hBOOL (hAPP_nat_bool even_odd_even_nat N_1))))))) (forall ((A $$unsorted)) (= (= zero_zero_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A) A)) (= A zero_zero_rat))) (forall ((M_17 $$unsorted) (N_30 $$unsorted)) (let ((_let_1 (hAPP_r474017924t_real power_power_real M_17))) (let ((_let_2 (hAPP_nat_real _let_1 N_30))) (let ((_let_3 (= N_30 zero_zero_nat))) (and (=> (not _let_3) (= _let_2 (hAPP_real_real (hAPP_r1250527377l_real times_times_real M_17) (hAPP_nat_real _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_30) one_one_nat))))) (=> _let_3 (= one_one_real _let_2))))))) (forall ((N $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc N)) N)))) (forall ((A_201 $$unsorted) (E_3 $$unsorted) (B_154 $$unsorted) (C_87 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_201) E_3)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_154) E_3)) C_87)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_201) B_154)) E_3)) C_87))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat X))) (=> (hBOOL (hAPP_nat_bool _let_1 Y)) (=> (hBOOL (hAPP_nat_bool _let_1 Z_1)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Y) Z_1))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1250527377l_real (hAPP_r337325687l_real (hAPP_f1644353557l_real cOMBC_1508019322l_real P) Q) R) (hAPP_r1250527377l_real (hAPP_r337325687l_real P R) Q))) (forall ((M $$unsorted) (N $$unsorted)) (=> (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)) (= M N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X)) (=> (hBOOL (hAPP_int_bool nat_is_nat Y)) (hBOOL (hAPP_int_bool nat_is_nat (hAPP_int_int (hAPP_int_fun_int_int times_times_int X) Y)))))) (forall ((A_87 $$unsorted) (B_75 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat minus_minus_rat A_87) B_75)) B_75) A_87)) (forall ((N_1 $$unsorted)) (= (hAPP_n1699378549t_bool ord_atMost_nat N_1) (image_int_nat nat (hAPP_i1948725293t_bool (ord_at875362053st_int zero_zero_int) (hAPP_nat_int semiri1621563631at_int N_1))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (not (hBOOL (hAPP_int_bool even_odd_even_int X))) (=> (hBOOL (hAPP_int_bool even_odd_even_int Y)) (not (hBOOL (hAPP_int_bool even_odd_even_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X) Y))))))) (forall ((B_155 $$unsorted) (A_204 $$unsorted)) (=> (and (is_int A_204) (is_int B_155)) (=> (not (= A_204 zero_zero_int)) (=> (not (= zero_zero_int B_155)) (not (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_204) B_155))))))) (= (hAPP_real_real sqrt zero_zero_real) zero_zero_real) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y)) Y))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r337325687l_real (hAPP_f1732848529l_real (hAPP_f1310479593l_real cOMBB_2092576745l_real P) Q) R) (hAPP_f556082547l_real P (hAPP_r1250527377l_real Q R)))) (forall ((N $$unsorted)) (exists ((P_4 $$unsorted)) (and (hBOOL (hAPP_nat_bool prime P_4)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_4) (hAPP_nat_nat suc (hAPP_nat_nat fact N)))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) P_4))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (is_int Y_2) (is_int X_1)) (= (and (= X_1 zero_zero_int) (= zero_zero_int Y_2)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_1) X_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Y_2) Y_2)))))) (forall ((F $$unsorted) (G $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real F N_2)) (hAPP_nat_real G N_2)))) (=> (hBOOL (summable_real F)) (=> (hBOOL (summable_real G)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f352196356l_real suminf_real F)) (hAPP_f352196356l_real suminf_real G))))))) (forall ((Z_7 $$unsorted) (W_2 $$unsorted) (Y_9 $$unsorted) (X_12 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int Y_9) X_12)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int Z_7) W_2)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int X_12) W_2)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int Y_9) Z_7)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int X_12) Y_9)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int W_2) Z_7)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= Ma N_1) (= (hAPP_nat_nat semiri984289939at_nat Ma) (hAPP_nat_nat semiri984289939at_nat N_1)))) (forall ((Z_2 $$unsorted) (W_1 $$unsorted)) (= (and (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat Z_2) W_1)) (not (= Z_2 W_1))) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat Z_2) W_1)))) (= (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int one_on1684967323de_int) _let_4) one_on1684967323de_int) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (=> (and (is_int Q_2) (is_int B_2)) (=> (hBOOL (hAPP_P603027463t_bool (divmod_int_rel A_3 B_2) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int Q_2) R_3))) (=> (not (= B_2 zero_zero_int)) (= Q_2 (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit1 K1)) (hAPP_int_int bit0 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K1) K2)))) (forall ((D_3 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat D_3))) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime D_3) A_3)) (hBOOL (hAPP_nat_bool _let_1 B_2)))))) (forall ((X $$unsorted) (Y $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y)) Y))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) L)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int bit1 K_1)) (hAPP_int_int bit0 L))))) (forall ((Z_1 $$unsorted)) (= (hAPP_complex_real norm_norm_complex Z_1) (hAPP_real_real sqrt (hAPP_complex_real re (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Z_1) (hAPP_complex_complex cnj Z_1)))))) (forall ((X_37 $$unsorted)) (= X_37 (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_37) one_one_nat))) (forall ((B_94 $$unsorted) (C_52 $$unsorted) (A_116 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral B_94))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_116)) (=> (hBOOL (hAPP_C24501650l_bool _let_1 C_52)) (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_116) C_52))))))) (forall ((M_10 $$unsorted) (N_24 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int semiri1424489471de_int M_10)) (hAPP_n522471361de_int semiri1424489471de_int N_24))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_10) N_24)))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int bit1 K_2)) L_2) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int bit0 (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) L_2))) L_2))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y))))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat (hAPP_nat_nat suc M)) (hAPP_nat_nat suc N)) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_min_nat M) N)))) (forall ((X_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (=> (= one_one_int (hAPP_int_int (legacy_zgcd X_1) Ma)) (hBOOL (hAPP_int_bool (is_RRset (hAPP_i1948725293t_bool (noXRRset Ma) X_1)) Ma))))) (forall ((Z_11 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat Z_11) Z_11) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Z_11) (hAPP_int_rat number_number_of_rat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((R_3 $$unsorted)) (let ((_let_1 (hAPP_real_real abs_abs_real R_3))) (let ((_let_2 (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_3) zero_zero_real)))) (and (=> _let_2 (= _let_1 (hAPP_real_real uminus_uminus_real R_3))) (=> (not _let_2) (= R_3 _let_1)))))) (forall ((W_1 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real X_1))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real W_1))) (= (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_2 Y_2)) (hAPP_real_real _let_1 Z_2)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_2 Z_2)) (hAPP_real_real _let_1 Y_2))) (or (= Z_2 Y_2) (= X_1 W_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat (hAPP_nat_nat suc M)) (hAPP_nat_nat suc N)) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat M) N)))) (forall ((X_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_1)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) X_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real ln X_1)))))) (forall ((V_11 $$unsorted) (W_9 $$unsorted)) (= (hAPP_int_real number267125858f_real (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int V_11) W_9)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_int_real number267125858f_real V_11)) (hAPP_int_real number267125858f_real W_9)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) pi)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sin X))))))) (forall ((B_120 $$unsorted) (A_159 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_120) A_159))) (=> (hBOOL (hAPP_int_bool _let_1 A_159)) (hBOOL (hAPP_int_bool _let_1 B_120)))))) (forall ((N_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (hAPP_nat_nat suc N_1))) (let ((_let_2 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat (hAPP_b992065680at_nat if_nat (hAPP_int_bool nat_neg _let_2)) _let_1) (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat N_1) (hAPP_int_nat nat _let_2)))) (hAPP_nat_nat (hAPP_nat_fun_nat_nat ord_max_nat _let_1) (hAPP_int_nat number_number_of_nat V)))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (isCont_real_real sqrt) X_1))) (forall ((A_223 $$unsorted) (K_8 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_223) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) K_8))) zero_zero_real)) (= zero_zero_real A_223))) (forall ((P_1 $$unsorted) (P1 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D)) (=> (forall ((X_2 $$unsorted) (K $$unsorted)) (=> (and (is_int K) (is_int X_2)) (= (hBOOL (hAPP_int_bool P1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K) D)))) (hBOOL (hAPP_int_bool P1 X_2))))) (=> (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) Z)) (= (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_int_bool P1 X_2))))))) (=> (exists ((X1 $$unsorted)) (hBOOL (hAPP_int_bool P1 X1))) (exists ((X1 $$unsorted)) (and (hBOOL (hAPP_int_bool P_1 X1)) (is_int X1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (bezw Y (hAPP_nat_nat (div_mod_nat X) Y)))) (let ((_let_2 (hAPP_P1175774780nt_int product_snd_int_int _let_1))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) Y)) (= (bezw X Y) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int _let_2) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_P1175774780nt_int product_fst_int_int _let_1)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int _let_2) (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat X) Y)))))))))) (forall ((N_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))) (let ((_let_2 (not (hBOOL (hAPP_int_bool nat_neg _let_1))))) (= (= (hAPP_nat_nat suc N_1) (hAPP_int_nat number_number_of_nat V)) (and (=> _let_2 (= N_1 (hAPP_int_nat nat _let_1))) _let_2))))) (forall ((A_3 $$unsorted)) (= one_one_real (hAPP_real_real (hAPP_r1250527377l_real powr one_one_real) A_3))) (forall ((A_17 $$unsorted) (C_4 $$unsorted) (B_13 $$unsorted)) (=> (not (= zero_z126310315umeral B_13)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral C_4) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_17) B_13)) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_17) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_13) C_4))) B_13)))) (forall ((R_2 $$unsorted)) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real times_times_real R_2)) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real plus_plus_real one_one_real)) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat uminus_uminus_real) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) suc))))) R_2 sequentially))) (forall ((N $$unsorted) (M $$unsorted)) (=> (is_int M) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int N) M)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int N) (hAPP_int_int (hAPP_int_fun_int_int div_div_int M) N)) M)))) (forall ((M $$unsorted) (N $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (not (= N zero_zero_nat)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat P_3) M) N) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) N)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat Ma)) (=> (hBOOL (hAPP_int_bool nat_is_nat N_1)) (= (image_nat_int semiri1621563631at_int (hAPP_n1699378549t_bool (ord_at238088361st_nat (hAPP_int_nat nat Ma)) (hAPP_int_nat nat N_1))) (hAPP_i1948725293t_bool (ord_at875362053st_int Ma) N_1))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int K_2))) (=> (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (div_mod_int M) N))) (=> (hBOOL (hAPP_int_bool _let_1 N)) (hBOOL (hAPP_int_bool _let_1 M)))))) (forall ((A_235 $$unsorted)) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_235) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 (hAPP_int_int bit1 pls)))) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_235) A_235)) A_235))) (forall ((M_25 $$unsorted) (A_185 $$unsorted) (N_60 $$unsorted) (B_142 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_185))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_n1108039445umeral _let_1 N_60)) B_142)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_25) N_60)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_n1108039445umeral _let_1 M_25)) B_142)))))) (forall ((Ma $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool dvd_dv174992974umeral K_1))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 N_1)) (= (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (div_mo1740067990umeral Ma) N_1))) (hBOOL (hAPP_C24501650l_bool _let_1 Ma)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X)))) (let ((_let_2 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)))) (=> (and (not _let_1) _let_2) (not (and (not _let_2) _let_1)))))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) N)) (not (= zero_zero_int (hAPP_int_int fact_fact_int N))))) (forall ((X $$unsorted)) (= (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) pi)) (hAPP_real_real uminus_uminus_real (hAPP_real_real cos X)))) (forall ((A_26 $$unsorted) (B_21 $$unsorted)) (=> (and (is_int A_26) (is_int B_21)) (=> (not (= B_21 zero_zero_int)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_21) A_26)) B_21) A_26)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1823918693l_bool (hAPP_f1344929775l_bool (hAPP_f1830214065l_bool cOMBB_793166024ol_int P) Q) R) (hAPP_f2144054103l_bool P (hAPP_i1948725293t_bool Q R)))) (forall ((F $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (resSet Ma))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (=> (hBOOL (hAPP_f448129468l_bool _let_1 A_1)) (=> (forall ((X_2 $$unsorted)) (=> (is_int X_2) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_2) A_1)) (forall ((Xa $$unsorted)) (=> (is_int Xa) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Xa) A_1)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int F X_2)) (hAPP_int_int F Xa)) Ma)) (= Xa X_2)))))))) (hBOOL (hAPP_f448129468l_bool _let_1 (image_int_int F A_1)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 X)) (=> (hBOOL (hAPP_int_bool _let_1 Y)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_int_nat nat X)) (hAPP_int_nat nat Y)) (hAPP_int_nat nat (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y))))))) (forall ((B_115 $$unsorted) (C_67 $$unsorted) (A_153 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le1860547276de_int B_115))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int zero_z891286103de_int) A_153)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C_67)) (hBOOL (hAPP_Q2096512830t_bool _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_153) C_67))))))) (forall ((A_3 $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) M)) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) X_2)) (forall ((Y_1 $$unsorted)) (=> (is_int Y_1) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Y_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) Y_1) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int Y_1) M))) (= Y_1 X_2)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) X_2) M)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) M)) (is_int X_2))))) (= one_one_complex (hAPP_nat_complex (hAPP_c1088319240omplex power_power_complex one_one_complex) _let_4)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_nat_int semiri1621563631at_int Ma)) (hAPP_nat_int semiri1621563631at_int N_1))))) (forall ((A_98 $$unsorted) (C_40 $$unsorted) (B_80 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral A_98) C_40)) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_80) C_40))) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_98) B_80)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int X_1)) (hAPP_int_int number_number_of_int Y_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_1) Y_2)))) (forall ((A_108 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat A_108) zero_zero_rat) A_108)) (forall ((A_30 $$unsorted) (B_25 $$unsorted) (C_11 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_30) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_25) C_11))) B_25) (hAPP_nat_nat (div_mod_nat A_30) B_25))) (forall ((C_73 $$unsorted) (A_173 $$unsorted) (B_133 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat A_173) B_133)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_73)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_173) C_73)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_133) C_73)))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_3) B_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int B_2) A_3)) (= (hAPP_int_int abs_abs_int B_2) (hAPP_int_int abs_abs_int A_3))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X)))) (not (= X Y)))) (forall ((X $$unsorted) (Q_2 $$unsorted) (N $$unsorted) (R_3 $$unsorted)) (=> (= X (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Q_2) N)) R_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) R_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat R_3) N)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat N) X))))))) (forall ((A_29 $$unsorted) (B_24 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral A_29) B_24)) (= (hAPP_C498520661umeral (div_mo1740067990umeral B_24) A_29) zero_z126310315umeral))) (forall ((X_31 $$unsorted) (Y_25 $$unsorted)) (=> (not (= X_31 Y_25)) (=> (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_31) Y_25))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_25) X_31))))) (forall ((A_13 $$unsorted) (B_9 $$unsorted)) (=> (is_int A_13) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_13) B_9)) B_9)) (hAPP_int_int (div_mod_int A_13) B_9)) A_13))) (forall ((B_2 $$unsorted) (A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_3) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) B_2)) (exists ((D_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D_2)) (forall ((Y_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real abs_abs_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X) Y_1))) D_2)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A_3) Y_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_1) B_2)))))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int uminus_uminus_int A_3)) B_2))) (let ((_let_2 (hAPP_int_int uminus_uminus_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2)))) (let ((_let_3 (= zero_zero_int (hAPP_int_int (div_mod_int A_3) B_2)))) (=> (is_int B_2) (=> (not (= B_2 zero_zero_int)) (and (=> (not _let_3) (= (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int _let_2) one_one_int) _let_1)) (=> _let_3 (= _let_2 _let_1))))))))) (forall ((X_35 $$unsorted) (Y_27 $$unsorted) (Q_11 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int X_35) Q_11)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y_27) Q_11)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int X_35) Y_27)) Q_11))) (forall ((S_1 $$unsorted) (T_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat S_1) T_1)) (not (= S_1 T_1)))) (forall ((C_88 $$unsorted) (A_206 $$unsorted) (B_157 $$unsorted)) (let ((_let_1 (hAPP_c1403687985x_bool dvd_dvd_complex A_206))) (=> (hBOOL (hAPP_complex_bool _let_1 B_157)) (=> (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex B_157) C_88)) (hBOOL (hAPP_complex_bool _let_1 C_88)))))) (forall ((N_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_r474017924t_real power_power_real (hAPP_int_real number267125858f_real min)))) A))) (=> (hBOOL (tendsto_nat_real A zero_zero_real sequentially)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real A N_2)))) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real A (hAPP_nat_nat suc N_2))) (hAPP_nat_real A N_2)))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_f352196356l_real suminf_real _let_1)) (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real _let_1) (hAPP_n1699378549t_bool (ord_at4362885an_nat zero_zero_nat) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_1)) one_one_nat)))))))))) (forall ((X $$unsorted) (M $$unsorted) (Y $$unsorted)) (= (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X) Y)) M) (hAPP_int_int (div_mod_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_int_int (div_mod_int X) M)) Y)) M))) (forall ((A_226 $$unsorted) (B_163 $$unsorted) (C_92 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat A_226))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 B_163)) C_92) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 C_92)) B_163)))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int Z_1))) (let ((_let_2 (hAPP_nat_int _let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit1 W))))) (let ((_let_3 (hAPP_nat_int _let_1 (hAPP_int_nat number_number_of_nat W)))) (let ((_let_4 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int number_number_of_int W))))) (and (=> (not _let_4) (= one_one_int _let_2)) (=> _let_4 (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z_1) _let_3)) _let_3) _let_2)))))))) (forall ((A $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_1))) (= (= zero_z126310315umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral A) _let_1)) (and (= zero_z126310315umeral A) (not (= zero_zero_nat _let_1)))))) (forall ((P_1 $$unsorted) (D $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) D)) (=> (forall ((X_2 $$unsorted) (K $$unsorted)) (=> (and (is_int X_2) (is_int K)) (= (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_2) (hAPP_int_int (hAPP_int_fun_int_int times_times_int K) D)))) (hBOOL (hAPP_int_bool P_1 X_2))))) (= (exists ((X1 $$unsorted)) (and (is_int X1) (hBOOL (hAPP_int_bool P_1 X1)))) (exists ((X_2 $$unsorted)) (and (is_int X_2) (hBOOL (hAPP_int_bool P_1 X_2)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_2) (hAPP_i1948725293t_bool (ord_at875362053st_int one_one_int) D))))))))) (forall ((B $$unsorted) (A $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool (wset A) P_5))) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) _let_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (inv P_5) B)) _let_1)))))))) (= one_one_nat _let_20) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat Y) X)) (= Y (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y)))) (forall ((N_53 $$unsorted) (M_21 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real one_one_real))) (=> (hBOOL (hAPP_real_bool _let_1 M_21)) (=> (hBOOL (hAPP_real_bool _let_1 N_53)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real M_21) N_53))))))) (forall ((A_215 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_215) one_one_complex) A_215)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_1) Y_2)) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_1) Y_2)))) (forall ((A_139 $$unsorted) (C_61 $$unsorted) (B_108 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_139) C_61)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_108) C_61))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat zero_zero_nat) C_61)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat A_139) B_108))))) (forall ((X_6 $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral X_6))) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral X_6) (hAPP_n1108039445umeral _let_1 Q_5)) (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat suc Q_5))))) _let_19 (forall ((A_28 $$unsorted) (B_23 $$unsorted) (C_10 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral times_1655362735umeral C_10))) (=> (not (= zero_z126310315umeral C_10)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_28) B_23) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral _let_1 A_28)) (hAPP_C498520661umeral _let_1 B_23)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y))) (and (=> (not (= zero_zero_nat Y)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat Y) (hAPP_nat_nat (div_mod_nat X) Y)) _let_1)) (=> (= Y zero_zero_nat) (= X _let_1))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat times_times_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) one_one_nat))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X_1)) one_one_real)) (hBOOL (monoseq_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real inverse_divide_real one_one_real)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) _let_1)))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1))))))) (forall ((C_85 $$unsorted) (A_193 $$unsorted) (B_149 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool dvd_dvd_rat A_193))) (=> (hBOOL (hAPP_rat_bool _let_1 B_149)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_149) C_85)))))) (forall ((A_3 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_3) one_one_int))) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) _let_1)) (not (= _let_1 (hAPP_int_int (inv P_3) A_3)))))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (= (hAPP_int_int (legacy_zgcd I) J_2) (hAPP_int_int (legacy_zgcd (hAPP_int_int uminus_uminus_int I)) J_2))) (forall ((X_45 $$unsorted) (Y_33 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int X_45) _let_1)) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int Y_33) _let_1))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) Y_33)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int X_45) Y_33)))))) (forall ((Y_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_1)) (= (hBOOL (hAPP_real_bool _let_1 Y_2)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_n546711566l_real root N_1) Y_2))))))) (forall ((C_80 $$unsorted) (A_187 $$unsorted) (B_143 $$unsorted)) (let ((_let_1 (hAPP_c1403687985x_bool dvd_dvd_complex A_187))) (=> (hBOOL (hAPP_complex_bool _let_1 B_143)) (=> (hBOOL (hAPP_complex_bool _let_1 C_80)) (hBOOL (hAPP_complex_bool _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_143) C_80))))))) (forall ((I $$unsorted)) (let ((_let_1 (hAPP_int_int abs_abs_int I))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int I) zero_zero_int)))) (=> (is_int I) (and (=> (not _let_2) (= _let_1 I)) (=> _let_2 (= _let_1 (hAPP_int_int uminus_uminus_int I)))))))) (hBOOL (hAPP_int_bool _let_16 pls)) (hBOOL (hAPP_real_bool _let_15 _let_14)) (forall ((Z_12 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_12) Z_12) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z_12) (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (ratreal X_1)) (ratreal Y_2))))) (forall ((A_219 $$unsorted)) (= A_219 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_219) zero_zero_real))) (forall ((A $$unsorted)) (hBOOL (hAPP_complex_bool (isCont156215680omplex cnj) A))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_1) Y_2)) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_2) (hAPP_real_real uminus_uminus_real X_1))))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex B) E_2)) D) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A) E_2)) C)) (= D (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex minus_minus_complex A) B)) E_2)) C)))) (forall ((N_42 $$unsorted) (A_130 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_rat one_one_rat))) (=> (hBOOL (hAPP_rat_bool _let_1 A_130)) (hBOOL (hAPP_rat_bool _let_1 (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_130) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_130) N_42))))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (= (archim1246769320r_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_int_real real_int A_3))) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (archim1246769320r_real X)) A_3))) (forall ((X0 $$unsorted) (F $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real))) (let ((_let_2 (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_1 F)))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real))) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X_2) (hAPP_r1134773055l_bool (ord_gr788844697n_real (hAPP_real_real uminus_uminus_real R_4)) R_4))) (hBOOL (summable_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_1 (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_1 F)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) suc)))) (hAPP_r474017924t_real power_power_real X_2))))))) (=> (hBOOL (hAPP_f1501066425l_bool (hAPP_r1130899993l_bool member_real X0) (hAPP_r1134773055l_bool (ord_gr788844697n_real (hAPP_real_real uminus_uminus_real R_4)) R_4))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) R_4)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1122023986l_real (hAPP_f1786887945l_real cOMBB_1896127834l_real suminf_real) (hAPP_f1993765077t_real (hAPP_f895854793t_real cOMBB_1948233853l_real _let_2) (hAPP_f1501741374t_real (hAPP_f1135648319t_real cOMBC_1329014627t_real (hAPP_f1163894827t_real (hAPP_f1998755145t_real cOMBB_421464275l_real cOMBB_nat_real_nat) power_power_real)) suc))) X0) (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real _let_1 (hAPP_f1888375463t_real _let_2 (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) suc)))) (hAPP_r474017924t_real power_power_real X0))))))))))) (forall ((P_1 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int gcd_gcd_int X_1))) (let ((_let_2 (hBOOL (hAPP_int_bool P_1 (hAPP_int_int _let_1 Y_2))))) (let ((_let_3 (hAPP_int_int uminus_uminus_int Y_2))) (let ((_let_4 (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int uminus_uminus_int X_1)))) (let ((_let_5 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int Y_2) zero_zero_int)))) (let ((_let_6 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int X_1) zero_zero_int)))) (let ((_let_7 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_8 (hBOOL (hAPP_int_bool _let_7 Y_2)))) (let ((_let_9 (hBOOL (hAPP_int_bool _let_7 X_1)))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (hBOOL (hAPP_int_bool P_1 (hAPP_int_int _let_1 _let_3))))) (=> (=> _let_6 (=> _let_8 (hBOOL (hAPP_int_bool P_1 (hAPP_int_int _let_4 Y_2))))) (=> (=> _let_6 (=> _let_5 (hBOOL (hAPP_int_bool P_1 (hAPP_int_int _let_4 _let_3))))) _let_2)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real one_one_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sqrt X)))))) (forall ((X_36 $$unsorted) (Y_28 $$unsorted) (Z_9 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real X_36))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real _let_1 Y_28)) (hAPP_real_real _let_1 Z_9)) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Y_28) Z_9))))) (forall ((N_1 $$unsorted)) (= (not (hBOOL (hAPP_nat_bool even_odd_even_nat N_1))) (exists ((M_1 $$unsorted)) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) M_1)) N_1)))) (forall ((A_105 $$unsorted)) (= A_105 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int zero_z891286103de_int) A_105))) (forall ((W_8 $$unsorted)) (let ((_let_1 (hAPP_i1732201573de_int number1226105091de_int W_8))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int _let_1) _let_1) (hAPP_n522471361de_int (hAPP_Q125967240de_int power_881366806de_int _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((P_1 $$unsorted)) (= (collect_real P_1) P_1)) (forall ((A $$unsorted) (B $$unsorted)) (= (forall ((D_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat D_2))) (= (= one_one_nat D_2) (and (hBOOL (hAPP_nat_bool _let_1 A)) (hBOOL (hAPP_nat_bool _let_1 B)))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A) B)))) (forall ((A_75 $$unsorted) (A_74 $$unsorted) (B_62 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_75) B_62)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_74) B_62)) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex A_75) A_74)) B_62))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral D) (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral X_2) Sa))))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral X_2) Z)) (= _let_1 _let_1)))))) (forall ((A_113 $$unsorted) (B_91 $$unsorted) (C_51 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int A_113))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int _let_1 B_91)) C_51) (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_91) C_51))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (not (= zero_zero_real C)) (= (= B A) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) C) (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real plus_plus_real A))) (= (= B C) (= (hAPP_real_real _let_1 C) (hAPP_real_real _let_1 B))))) (forall ((P_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool P_1 N_1) Ma)))) (=> (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) _let_1) (=> (=> (= N_1 Ma) _let_1) (=> (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) Ma)) _let_1) _let_1))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N) M) (= N zero_zero_nat))) (forall ((N $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) N)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int N) P_3)) (= one_one_int (hAPP_int_int (legacy_zgcd N) P_3)))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_int_real real_int N))) (=> (is_int N) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_1) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real _let_1) one_one_real))) (= N (archim1246769320r_real X))))))) (forall ((A_55 $$unsorted) (C_25 $$unsorted) (B_46 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_55) B_46)) C_25) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_55) C_25)) B_46)) C_25))) (forall ((M_19 $$unsorted) (N_44 $$unsorted) (A_132 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat A_132))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat one_one_nat) A_132)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat _let_1 M_19)) (hAPP_nat_nat _let_1 N_44))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_19) N_44)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (= (or (and (hBOOL (hAPP_int_bool _let_1 A)) (hBOOL (hAPP_int_bool _let_1 B))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) zero_zero_int)))) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) B)))))) (forall ((A $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (hAPP_int_int (rRset2norRR A_1 Ma) A))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Ma)) (=> (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) A_1)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) _let_1) Ma)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int _let_1) (hAPP_i1948725293t_bool norRRset Ma))))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f883232462nt_int (hAPP_i998473677nt_int P R) Q) (hAPP_i1584592887nt_int (hAPP_f1574055885nt_int (hAPP_f960630521nt_int cOMBC_1805044090nt_int P) Q) R))) (forall ((C_78 $$unsorted) (D_14 $$unsorted) (A_178 $$unsorted) (B_138 $$unsorted)) (let ((_let_1 (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int A_178) B_138)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int C_78) D_14)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 A_178)) (=> (hBOOL (hAPP_Q2096512830t_bool _let_1 C_78)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_178) C_78)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_138) D_14))))))))) (forall ((K_2 $$unsorted)) (=> (is_int K_2) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) K_2)) (exists ((N_2 $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int N_2) K_2))))) (forall ((A_234 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_234) A_234) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat A_234) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real sin X)) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real cos X)) _let_1)) one_one_real))) (forall ((K_2 $$unsorted)) (= (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_nat_int semiri1621563631at_int K_2)) one_one_int) (hAPP_nat_rat semiri151668891at_rat K_2))) (forall ((A_186 $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat one_one_nat) A_186))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) Ma)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real real_nat N_1)) one_one_real)) (hAPP_nat_real real_nat Ma))))) (forall ((N_1 $$unsorted)) (= (= N_1 zero_zero_nat) (= zero_zero_real (hAPP_nat_real real_nat N_1)))) (forall ((A_6 $$unsorted) (N_8 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (let ((_let_2 (hAPP_int_fun_nat_int power_power_int A_6))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_6) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int _let_2 N_8)) _let_1)) (hAPP_nat_int _let_2 (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) N_8))))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) M)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) N)) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int (hAPP_nat_int semiri1621563631at_int M)) (hAPP_nat_int semiri1621563631at_int N))))) (forall ((N_1 $$unsorted) (N_7 $$unsorted) (F $$unsorted)) (let ((_let_1 (hAPP_nat_nat F N_7))) (let ((_let_2 (hAPP_nat_nat F N_1))) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (hAPP_nat_nat F (hAPP_nat_nat suc N_2)))) (let ((_let_2 (hAPP_nat_nat F N_2))) (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_1) _let_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_2) _let_1)))))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N_1) N_7)) (and (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_1) _let_2))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat _let_2) _let_1)))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real exp_real X_1)) (hAPP_real_real exp_real Y_2))))) (forall ((Y $$unsorted) (X $$unsorted) (P_3 $$unsorted)) (=> (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong X) zero_zero_int) P_3))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int Y) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X) P_3)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int P_3) Y)))))) (forall ((Nat_2 $$unsorted)) (not (= (hAPP_nat_nat suc Nat_2) zero_zero_nat))) (forall ((A $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int))) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) _let_1)) one_one_int) P_5)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) _let_1) P_5))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real sin X)) one_one_real))) (forall ((W_12 $$unsorted)) (= (hAPP_int_int number_number_of_int (hAPP_int_int bit0 W_12)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int one_one_int) one_one_int)) (hAPP_int_int number_number_of_int W_12)))) (forall ((A_68 $$unsorted) (B_56 $$unsorted)) (=> (is_int A_68) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (div_mod_int A_68) B_56)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_68) B_56)) B_56)) A_68))) (forall ((Z_2 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_int_nat nat Z_2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Z_2)))) (forall ((A_12 $$unsorted) (N_18 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_12))) (= (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat suc N_18)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral _let_1 N_18)) A_12)))) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (and (is_int Z) (forall ((X_2 $$unsorted)) (let ((_let_1 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int D) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) Sa))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int X_2) Z)) (= _let_1 _let_1))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (or (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (= N_1 Ma)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat X) Y)) (= X (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat X) Y)))) (forall ((N_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) N_1)) (= (hAPP_int_nat nat N_1) (hAPP_f957591787ol_nat finite_card_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_eq_int) N_1))))))) (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool sRStar P_5))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) P_5)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) _let_1)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (standardRes P_5) (hAPP_int_int (multInv P_5) X_1))) _let_1))))))) (forall ((U_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) U_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real U_1) (hAPP_real_real sqrt (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) U_1)))) (forall ((L $$unsorted) (U $$unsorted)) (hBOOL (hAPP_f54304608l_bool finite_finite_nat (hAPP_n1699378549t_bool (ord_at4362885an_nat L) U)))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (hAPP_int_int uminus_uminus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z_1) W)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int uminus_uminus_int Z_1)) W))) (forall ((F $$unsorted)) (= (hBOOL (tendsto_nat_real F zero_zero_real sequentially)) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat abs_abs_real) F) zero_zero_real sequentially)))) (forall ((B_1_1 $$unsorted)) (is_int (archim1246769320r_real B_1_1))) (forall ((X_35 $$unsorted) (Y_27 $$unsorted) (Q_11 $$unsorted)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_35) Q_11)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral Y_27) Q_11)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral X_35) Y_27)) Q_11))) (forall ((M_7 $$unsorted) (N_21 $$unsorted)) (= (hAPP_nat_real semiri132038758t_real (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_7) N_21)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_nat_real semiri132038758t_real M_7)) (hAPP_nat_real semiri132038758t_real N_21)))) (forall ((A_113 $$unsorted) (B_91 $$unsorted) (C_51 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real A_113))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real _let_1 B_91)) C_51) (hAPP_real_real _let_1 (hAPP_real_real (hAPP_r1250527377l_real times_times_real B_91) C_51))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f513299955t_bool P (hAPP_P921862901l_bool Q R)) (hAPP_P877703507t_bool (hAPP_f1965248563t_bool (hAPP_f1273270095t_bool cOMBB_595786433nt_int P) Q) R))) (forall ((K_1 $$unsorted) (L $$unsorted)) (= (hAPP_int_int abs_abs_int (hAPP_int_int (hAPP_int_fun_int_int (hAPP_b1463609396nt_int if_int (hAPP_int_bool (hAPP_i1948725293t_bool fequal_int L) zero_zero_int)) K_1) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int L) (hAPP_int_int (div_mod_int (hAPP_int_int abs_abs_int K_1)) (hAPP_int_int abs_abs_int L))))) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int K_1) L))) (forall ((C_78 $$unsorted) (D_14 $$unsorted) (A_178 $$unsorted) (B_138 $$unsorted)) (let ((_let_1 (hAPP_r2115560837t_bool ord_less_eq_rat zero_zero_rat))) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat A_178) B_138)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat C_78) D_14)) (=> (hBOOL (hAPP_rat_bool _let_1 A_178)) (=> (hBOOL (hAPP_rat_bool _let_1 C_78)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_178) C_78)) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat B_138) D_14))))))))) (forall ((X_3 $$unsorted) (A $$unsorted)) (=> (hBOOL (hAPP_complex_bool (sums_complex X_3) A)) (hBOOL (hAPP_real_bool (sums_real (hAPP_f1290670424t_real (hAPP_f327026105t_real cOMBB_722610049al_nat im) X_3)) (hAPP_complex_real im A))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) one_one_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real ln X)) zero_zero_real))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat times_times_nat) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) one_one_nat))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real abs_abs_real X_1)) one_one_real)) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat (hAPP_r1250527377l_real inverse_divide_real one_one_real)) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat real_nat) _let_1)))) (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat (hAPP_r474017924t_real power_power_real X_1)) _let_1)) zero_zero_real sequentially))))) (forall ((Q_2 $$unsorted) (P_3 $$unsorted)) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool prime Q_2)) (=> (not (= P_3 Q_2)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime P_3) Q_2)))))) (forall ((I $$unsorted) (K_2 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat plus_plus_nat I))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K_2) J_2)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat _let_1 J_2)) K_2) (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J_2) K_2)))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X_1)) (=> (hBOOL (hAPP_real_bool _let_1 Y_2)) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real ln X_1)) (hAPP_real_real ln Y_2))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_1) Y_2))))))) (forall ((A_48 $$unsorted) (B_39 $$unsorted) (C_20 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (div_mod_nat A_48) C_20)) (hAPP_nat_nat (div_mod_nat B_39) C_20))) C_20) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat A_48) B_39)) C_20))) (forall ((A $$unsorted) (E_2 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (= (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real A) B)) E_2)) C) D) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) E_2)) C) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real B) E_2)) D)))) (forall ((X $$unsorted)) (= (hAPP_real_real tan (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) pi))) (hAPP_real_real tan X))) (forall ((M $$unsorted) (N $$unsorted)) (not (forall ((Q_4 $$unsorted) (R_1 $$unsorted)) (not (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel M N) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat Q_4) R_1))))))) (forall ((K_2 $$unsorted)) (= (hAPP_int_rat number_number_of_rat K_2) (hAPP_int_rat (hAPP_int_fun_int_rat fract (hAPP_int_int number_number_of_int K_2)) one_one_int))) (forall ((Y_6 $$unsorted) (P_6 $$unsorted) (N_10 $$unsorted)) (let ((_let_1 (hAPP_int_fun_nat_int power_power_int Y_6))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_6) N_10)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_10) P_6))) Y_6) (hAPP_nat_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc N_10)) P_6)))))) (forall ((A_184 $$unsorted) (M_23 $$unsorted) (N_58 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_184))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M_23) N_58)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool dvd_dv174992974umeral (hAPP_n1108039445umeral _let_1 M_23)) (hAPP_n1108039445umeral _let_1 N_58)))))) (forall ((Z_2 $$unsorted)) (=> (is_int Z_2) (= (or (= Z_2 one_one_int) (= (hAPP_int_int number_number_of_int min) Z_2)) (= (hAPP_int_int abs_abs_int Z_2) one_one_int)))) (forall ((N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N)) (exists ((M_1 $$unsorted)) (= N (hAPP_nat_nat suc M_1))))) (forall ((M_6 $$unsorted) (N_20 $$unsorted)) (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral (hAPP_n1108039445umeral semiri1619134803umeral M_6)) N_20) (hAPP_n1108039445umeral semiri1619134803umeral (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat M_6) N_20)))) (forall ((A $$unsorted) (B $$unsorted) (W_1 $$unsorted)) (= (and (= zero_zero_real B) (= (hAPP_int_real number267125858f_real W_1) A)) (= (hAPP_real_complex (hAPP_r265291036omplex complex A) B) (hAPP_int_complex number528085621omplex W_1)))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat Lx))) (let ((_let_2 (hAPP_nat_fun_nat_nat times_times_nat Rx))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat _let_2 Ry)) (hAPP_nat_nat _let_2 (hAPP_nat_nat _let_1 Ry)))))) (forall ((B_129 $$unsorted) (A_169 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) A_169)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral B_129) zero_z126310315umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_169) B_129)) zero_z126310315umeral))))) (forall ((X_3 $$unsorted)) (= (hBOOL (vanishes X_3)) (forall ((R_1 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat zero_zero_rat) R_1)) (exists ((K $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K) N_2)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_rat_rat abs_abs_rat (hAPP_nat_rat X_3 N_2))) R_1))))))))) (forall ((Real1 $$unsorted) (Real2 $$unsorted)) (= (complex_size (hAPP_real_complex (hAPP_r265291036omplex complex Real1) Real2)) zero_zero_nat)) (forall ((A_189 $$unsorted) (B_145 $$unsorted) (C_82 $$unsorted)) (=> (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_189) B_145)) C_82)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool dvd_dvd_rat A_189) C_82)))) (forall ((A_158 $$unsorted) (B_119 $$unsorted)) (let ((_let_1 (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_158) B_119))) (=> (hBOOL (hAPP_C24501650l_bool _let_1 A_158)) (hBOOL (hAPP_C24501650l_bool _let_1 B_119)))))) (forall ((X_1 $$unsorted)) (= (hAPP_nat_nat suc X_1) (hAPP_f22106695ol_nat finite_card_nat (collect_nat (hAPP_n1699378549t_bool (hAPP_f229349961t_bool cOMBC_nat_nat_bool ord_less_eq_nat) X_1))))) (forall ((A_149 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_149) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A_149) one_one_int)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc zero_zero_nat)))) (= (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat Ma) N_1))) (and (hBOOL (hAPP_nat_bool _let_1 Ma)) (hBOOL (hAPP_nat_bool _let_1 N_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N)))) (forall ((B_148 $$unsorted) (A_192 $$unsorted) (C_84 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool dvd_dvd_int A_192))) (=> (hBOOL (hAPP_int_bool _let_1 C_84)) (hBOOL (hAPP_int_bool _let_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_148) C_84)))))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 _let_1))) N))) (=> (not (= zero_zero_nat N)) (= _let_2 (hAPP_nat_nat suc (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat _let_2) (hAPP_int_nat number_number_of_nat _let_1))))))))) (forall ((M_7 $$unsorted) (N_21 $$unsorted)) (= (hAPP_n1108039445umeral semiri1619134803umeral (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat M_7) N_21)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral (hAPP_n1108039445umeral semiri1619134803umeral M_7)) (hAPP_n1108039445umeral semiri1619134803umeral N_21)))) (= (diffs_real sin_coeff) cos_coeff) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit0 K1)) (hAPP_int_int bit0 K2))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K1) K2)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) B)) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) B))) (hBOOL (hAPP_real_bool (isCont_real_real F) X_2)))) (=> (forall ((X_2 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_2) B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real A) X_2))) (hBOOL (hAPP_real_bool (deriv_real F X_2) zero_zero_real)))) (= (hAPP_real_real F B) (hAPP_real_real F A)))))) (forall ((Z_11 $$unsorted)) (= (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex Z_11) (hAPP_int_complex number528085621omplex (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex Z_11) Z_11))) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (=> (hBOOL (hAPP_real_bool (deriv_real F X_1) L)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real L) zero_zero_real)) (exists ((D_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) D_2)) (forall ((H_1 $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) H_1)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real H_1) D_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real F X_1)) (hAPP_real_real F (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real X_1) H_1)))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_nat_nat (div_mod_nat M) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat M) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat M) N)) N)))) (forall ((A_3 $$unsorted)) (= (hAPP_int_int (div_mod_int A_3) (hAPP_int_int number_number_of_int min)) zero_zero_int)) (forall ((X_40 $$unsorted) (N_69 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat power_power_nat X_40))) (let ((_let_2 (hAPP_nat_nat _let_1 N_69))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) N_69)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_2) _let_2))))) (forall ((R_3 $$unsorted) (P_3 $$unsorted) (Q_2 $$unsorted)) (=> (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2) (normalize R_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Q_2)))) (forall ((X $$unsorted) (N $$unsorted)) (= (hAPP_nat_int semiri1621563631at_int (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat X) N)) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int (hAPP_nat_int semiri1621563631at_int X)) N))) (forall ((A_3 $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) (archim1246769320r_real X))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real real_int A_3)) X)))) (forall ((X_6 $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int X_6))) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int X_6) (hAPP_n522471361de_int _let_1 Q_5)) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat suc Q_5))))) (forall ((X_21 $$unsorted) (N_31 $$unsorted)) (let ((_let_1 (hAPP_rat_fun_nat_rat power_power_rat X_21))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_31)) (= (hAPP_nat_rat _let_1 N_31) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat (hAPP_nat_rat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_31) one_one_nat))) X_21))))) (forall ((Q_2 $$unsorted) (R_3 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat inverse_divide_rat Q_2) R_3) (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat Q_2) (hAPP_rat_rat inverse_inverse_rat R_3)))) (forall ((A_20 $$unsorted) (C_6 $$unsorted) (B_16 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int A_20))) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int C_6) B_16)) (= (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int B_16) C_6)) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int (hAPP_Q1762011733de_int _let_1 B_16)) C_6))))) (forall ((V_10 $$unsorted) (U_3 $$unsorted) (Y_26 $$unsorted) (X_32 $$unsorted) (A_209 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X_32) A_209)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Y_26) A_209)) (=> (hBOOL (hAPP_real_bool _let_1 U_3)) (=> (hBOOL (hAPP_real_bool _let_1 V_10)) (=> (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real U_3) V_10) one_one_real) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real U_3) X_32)) (hAPP_real_real (hAPP_r1250527377l_real times_times_real V_10) Y_26))) A_209))))))))) (forall ((N $$unsorted)) (not (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat N) N)))) (forall ((A_222 $$unsorted)) (= zero_zero_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat zero_zero_nat) A_222))) (forall ((B_94 $$unsorted) (C_52 $$unsorted) (A_116 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real B_94))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) A_116)) (=> (hBOOL (hAPP_real_bool _let_1 C_52)) (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real A_116) C_52))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (hAPP_int_rat ring_1_of_int_rat (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int sgn_sgn_int A_3)) (hAPP_int_int sgn_sgn_int B_2))) (hAPP_rat_rat sgn_sgn_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A_3) B_2)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (is_int A) (is_int B)) (= (or (= zero_zero_int A) (= B zero_zero_int)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int A) B))))) (forall ((A_46 $$unsorted) (B_37 $$unsorted) (C_18 $$unsorted)) (let ((_let_1 (hAPP_C1594335432umeral plus_p1627245867umeral A_46))) (= (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral _let_1 (hAPP_C498520661umeral (div_mo1740067990umeral B_37) C_18))) C_18) (hAPP_C498520661umeral (div_mo1740067990umeral (hAPP_C498520661umeral _let_1 B_37)) C_18)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f291087797t_bool P (hAPP_P1668131738nt_int Q R)) (hAPP_P2053772734t_bool (hAPP_f1198736473t_bool (hAPP_f2042071795t_bool cOMBB_773384995nt_int P) Q) R))) (forall ((A $$unsorted) (B $$unsorted)) (= (= one_one_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A) B)) (forall ((D_2 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat D_2))) (= (and (hBOOL (hAPP_nat_bool _let_1 B)) (hBOOL (hAPP_nat_bool _let_1 A))) (= D_2 (hAPP_nat_nat suc zero_zero_nat))))))) (forall ((A_195 $$unsorted) (B_151 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool dvd_dv1760642554de_int A_195) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_195) B_151)))) (forall ((B_53 $$unsorted) (A_65 $$unsorted) (C_32 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_65) C_32) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_53) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int div_di1430059507de_int A_65) B_53))) (hAPP_Q1762011733de_int (div_mo231679042de_int A_65) B_53))) C_32))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int M) N) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int M) N)) N))) (forall ((R_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real R_3))) (= (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real A_3) R_3) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real _let_1 A_3)) (hAPP_real_real _let_1 R_3))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat B_2))) (let ((_let_2 (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat))) (=> (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel A_3 B_2) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat Q_2) R_3))) (=> (hBOOL (hAPP_nat_bool _let_2 B_2)) (=> (hBOOL (hAPP_nat_bool _let_2 C_1)) (hBOOL (hAPP_P1555980039t_bool (divmod_nat_rel A_3 (hAPP_nat_nat _let_1 C_1)) (hAPP_n1289843868at_nat (hAPP_n1865633855at_nat product_Pair_nat_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat Q_2) C_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat Q_2) C_1))) R_3)))))))))) (forall ((Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) Y)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y) one_one_real)) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) X_2)) (forall ((Y_1 $$unsorted)) (=> (and (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real Y_1) pi)) (= (hAPP_real_real cos Y_1) Y) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y_1))) (= Y_1 X_2))) (= Y (hAPP_real_real cos X_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X_2) pi))))))) (= _let_4 _let_12) (forall ((A_227 $$unsorted) (B_164 $$unsorted) (C_93 $$unsorted)) (let ((_let_1 (hAPP_c172932010omplex plus_plus_complex A_227))) (= (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex (hAPP_complex_complex _let_1 B_164)) C_93) (hAPP_complex_complex _let_1 (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex B_164) C_93))))) (forall ((I_1 $$unsorted) (J $$unsorted)) (=> (and (is_int J) (is_int I_1)) (= (= (hAPP_int_int (legacy_zgcd I_1) J) zero_zero_int) (and (= I_1 zero_zero_int) (= J zero_zero_int))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (hAPP_complex_real norm_norm_complex (hAPP_real_complex (hAPP_r265291036omplex complex X) Y)) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_1)))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int W_1) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z_2) one_one_int))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int W_1) Z_2)))) (forall ((A $$unsorted)) (=> (is_int A) (= (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) A)) (= A zero_zero_int)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) Y)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real arctan X)) (hAPP_real_real arctan Y))))) (forall ((K_2 $$unsorted)) (= K_2 (hAPP_i1732201573de_int quickcheck_of_int (quickcheck_int_of K_2)))) (forall ((A_44 $$unsorted) (B_35 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int A_44) B_35) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int A_44) B_35)) B_35))) (forall ((A_203 $$unsorted)) (= (hAPP_rat_rat (hAPP_rat_fun_rat_rat times_times_rat A_203) zero_zero_rat) zero_zero_rat)) (forall ((A_195 $$unsorted) (B_151 $$unsorted)) (hBOOL (hAPP_complex_bool (hAPP_c1403687985x_bool dvd_dvd_complex A_195) (hAPP_complex_complex (hAPP_c172932010omplex times_times_complex A_195) B_151)))) (forall ((A $$unsorted) (B $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) Ma)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) B) Ma)) (= (hAPP_int_int (div_mod_int A) Ma) (hAPP_int_int (div_mod_int B) Ma))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real uminus_uminus_real pi)) (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real tan X)) zero_zero_real))))) (forall ((A_60 $$unsorted) (B_51 $$unsorted) (C_30 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int times_123202395de_int A_60))) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int _let_1 B_51)) C_30) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int B_51) C_30))) C_30)))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int K1) K2)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int bit0 K1)) (hAPP_int_int bit1 K2))))) (hBOOL (hAPP_int_bool _let_11 zero_zero_int)) (forall ((X_4 $$unsorted) (N_6 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_6)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X_4)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_real_real (hAPP_n546711566l_real root N_6) X_4)))))) (forall ((A_238 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real A_238) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((A_194 $$unsorted) (B_150 $$unsorted)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int A_194) (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_150) A_194)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real X) _let_1)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real times_times_real _let_1) X))) one_one_real)))))) (forall ((W_8 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_8))) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat _let_1) _let_1) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))))) (forall ((Code_numeral_1 $$unsorted)) (= (hAPP_C2129356693al_nat size_s945831648umeral (code_S1047413653umeral Code_numeral_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_C2129356693al_nat size_s945831648umeral Code_numeral_1)) (hAPP_nat_nat suc zero_zero_nat)))) (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X_1)) (=> (hBOOL (hAPP_f448129468l_bool nat_nat_set A_1)) (= (hBOOL (hAPP_f54304608l_bool (hAPP_n215258509l_bool member_nat (hAPP_int_nat nat X_1)) (image_int_nat nat A_1))) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) A_1)))))) (forall ((M_28 $$unsorted)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int M_28) M_28) (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int one_on1684967323de_int) one_on1684967323de_int)) M_28))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real times_times_real Lx))) (let ((_let_2 (hAPP_r1250527377l_real times_times_real Rx))) (= (hAPP_real_real _let_1 (hAPP_real_real _let_2 Ry)) (hAPP_real_real _let_2 (hAPP_real_real _let_1 Ry)))))) (forall ((A_58 $$unsorted) (B_49 $$unsorted) (C_28 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_Q1762011733de_int (div_mo231679042de_int A_58) C_28)) (hAPP_Q1762011733de_int (div_mo231679042de_int B_49) C_28))) C_28) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_58) B_49)) C_28))) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int L) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int X_2) zero_zero_int))) (hBOOL (hAPP_int_bool P_1 X_2)) (is_int X_2))) (exists ((X_2 $$unsorted)) (and (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int times_times_int L) X_2))) (is_int X_2))))) (forall ((A_215 $$unsorted)) (= A_215 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_215) one_one_nat))) (forall ((N $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (P_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat P_3) N)))) (=> (hBOOL (hAPP_nat_bool prime P_3)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime A_3) B_2)) (=> (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_3) B_2))) (or (hBOOL (hAPP_nat_bool _let_1 A_3)) (hBOOL (hAPP_nat_bool _let_1 B_2)))))))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (is_bool B_2_1) (is_bool B_1_1)) (is_bool (fdisj B_1_1 B_2_1)))) (forall ((B_130 $$unsorted) (A_170 $$unsorted)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) A_170)) (=> (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int B_130) zero_z891286103de_int)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int B_130) A_170)) zero_z891286103de_int))))) (forall ((X $$unsorted)) (= (hAPP_real_real tan X) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real (hAPP_real_real sin X)) (hAPP_real_real cos X)))) (forall ((A_111 $$unsorted) (B_89 $$unsorted) (C_49 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int plus_plus_int A_111))) (=> (and (is_int C_49) (is_int B_89)) (=> (= (hAPP_int_int _let_1 C_49) (hAPP_int_int _let_1 B_89)) (= C_49 B_89))))) (forall ((N $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_n1699378549t_bool coprime D_3))) (=> (hBOOL (hAPP_nat_bool _let_1 A_3)) (hBOOL (hAPP_nat_bool _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_3) N)))))) (forall ((K_2 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat K_2))) (= (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat M) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat _let_1 M)) (hAPP_nat_nat _let_1 N))))) (forall ((B_118 $$unsorted) (A_157 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) A_157)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral B_118) zero_z126310315umeral)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral B_118) A_157)) zero_z126310315umeral))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (hBOOL (hAPP_int_bool nat_is_nat X)) (=> (hBOOL (hAPP_int_bool nat_is_nat Y)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) (hAPP_int_int (hAPP_int_fun_int_int gcd_gcd_int X) Y)))))) (forall ((V $$unsorted)) (= (= zero_zero_nat (hAPP_int_nat number_number_of_nat V)) (hBOOL (hAPP_int_bool nat_neg (hAPP_int_int number_number_of_int (hAPP_int_int pred V)))))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int zero_zero_int) _let_4) zero_zero_int) (forall ((Ma $$unsorted) (Z_2 $$unsorted)) (=> (is_int Z_2) (= (and (= (hAPP_int_nat nat Z_2) Ma) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) Z_2))) (= Z_2 (hAPP_nat_int semiri1621563631at_int Ma))))) (forall ((Ma $$unsorted) (D $$unsorted)) (=> (is_int Ma) (= (exists ((Q_4 $$unsorted)) (and (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int D) Q_4) Ma) (is_int Q_4))) (= (hAPP_int_int (div_mod_int Ma) D) zero_zero_int)))) (forall ((A_60 $$unsorted) (B_51 $$unsorted) (C_30 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat A_60))) (= (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 B_51)) C_30) (hAPP_nat_nat (div_mod_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (div_mod_nat B_51) C_30))) C_30)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M) (hAPP_nat_nat suc N))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (= (and (=> (not (= K_1 zero_zero_nat)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat J_1) K_1)) (=> (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat K_1) I_2)) J_1) N_1) (hBOOL (hAPP_nat_bool P_1 J_1)))))) (=> (= zero_zero_nat K_1) (hBOOL (hAPP_nat_bool P_1 N_1)))) (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat (div_mod_nat N_1) K_1))))) (forall ((B_121 $$unsorted) (A_160 $$unsorted)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral A_160) zero_z126310315umeral)) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral zero_z126310315umeral) B_121)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le1304079648umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_160) B_121)) zero_z126310315umeral))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int C))) (= (or (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int C) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B) A))) (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) C)))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int _let_1 A)) (hAPP_int_int _let_1 B)))))) (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (=> (not (hBOOL (hAPP_nat_bool P_1 zero_zero_nat))) (=> (hBOOL (hAPP_nat_bool P_1 N_1)) (exists ((K $$unsorted)) (and (hBOOL (hAPP_nat_bool P_1 K)) (forall ((I_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_2) K)) (not (hBOOL (hAPP_nat_bool P_1 I_2))))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat K) N_1))))))) (forall ((W_8 $$unsorted)) (let ((_let_1 (hAPP_i769753017umeral number1443263063umeral W_8))) (= (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral _let_1) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral _let_1) _let_1)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)) (and (not (= N_1 Ma)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat Ma) N_1))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) (hAPP_real_real cos X_2))) (hAPP_real_real sin X_2)))) (let ((_let_3 (hAPP_int_nat number_number_of_nat _let_1))) (let ((_let_4 (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real))) (hBOOL (hAPP_real_bool (deriv_real (hAPP_f1950183573l_real (hAPP_f2069516469l_real cOMBS_real_real_real (hAPP_f556082547l_real (hAPP_f1960414057l_real cOMBB_882763271l_real plus_plus_real) (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real _let_4 sin)) _let_3))) (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real _let_4 cos)) _let_3)) X_2) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real _let_2) _let_2)))))))) (forall ((X $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) (hAPP_real_real cos X)))) (forall ((I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (legacy_zgcd I))) (= (hAPP_int_int _let_1 J_2) (hAPP_int_int _let_1 (hAPP_int_int uminus_uminus_int J_2))))) (forall ((V $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int pls) V)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) (hAPP_int_nat number_number_of_nat V))))) (forall ((B_2 $$unsorted) (M $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (=> (and (is_int B_2) (is_int A_3)) (=> (hBOOL (hAPP_int_bool _let_1 A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A_3) M)) (=> (hBOOL (hAPP_int_bool _let_1 B_2)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) M)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A_3) B_2) M)) (= A_3 B_2))))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool d22set A))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) A)))) (forall ((P $$unsorted)) (=> (is_bool P) (or (= fTrue P) (= fFalse P)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (=> (hBOOL (hAPP_real_bool _let_1 X)) (=> (hBOOL (hAPP_real_bool _let_1 Y)) (= (hAPP_real_real ln (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real X) Y)) (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real (hAPP_real_real ln X)) (hAPP_real_real ln Y))))))) (forall ((A_46 $$unsorted) (B_37 $$unsorted) (C_18 $$unsorted)) (let ((_let_1 (hAPP_Q1729056540de_int plus_p1446045655de_int A_46))) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int _let_1 (hAPP_Q1762011733de_int (div_mo231679042de_int B_37) C_18))) C_18) (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int _let_1 B_37)) C_18)))) (forall ((X $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 _let_1))) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) X)) _let_2))))) (forall ((N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool coprime N_1) N_1)) (= N_1 one_one_nat))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (hAPP_int_fun_int_int times_times_int A_3))) (= (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int _let_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_2) C_1))) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int _let_1 (hAPP_int_int (div_mod_int B_2) C_1))) C_1)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int (hAPP_int_int _let_1 B_2)) C_1)))) (forall ((A $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) zero_zero_int) Ma)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int Ma) A)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_i1948725293t_bool P (hAPP_int_int Q R)) (hAPP_i1948725293t_bool (hAPP_f1791153283t_bool (hAPP_f1399575567t_bool cOMBB_118231410ol_int P) Q) R))) (forall ((X $$unsorted) (Y $$unsorted)) (= (hAPP_complex_real re (hAPP_complex_complex (hAPP_c172932010omplex plus_plus_complex X) Y)) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_complex_real re X)) (hAPP_complex_real re Y)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (is_bool (hAPP_f1469637905l_bool B_1_1 B_2_1))) (forall ((M $$unsorted) (N $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat M) N)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N) M)) N) (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat M) N)))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_int_int (legacy_zgcd A_3) B_2))) (=> (and (is_int B_2) (is_int A_3)) (=> (or (not (= A_3 zero_zero_int)) (not (= zero_zero_int B_2))) (= one_one_int (hAPP_int_int (legacy_zgcd (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) _let_1)) (hAPP_int_int (hAPP_int_fun_int_int div_div_int B_2) _let_1))))))) (forall ((L $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real F N_2)) (hAPP_nat_real F (hAPP_nat_nat suc N_2))))) (=> (forall ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_nat_real F N_2)) L))) (=> (forall ((E $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real zero_zero_real) E)) (exists ((N_2 $$unsorted)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real L) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real F N_2)) E)))))) (hBOOL (tendsto_nat_real F L sequentially)))))) (forall ((X $$unsorted)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_int_real number267125858f_real min)) X)) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real X) one_one_real)) (= (hAPP_real_real sin (hAPP_real_real arccos X)) (hAPP_real_real sqrt (hAPP_real_real (hAPP_r1250527377l_real minus_minus_real one_one_real) (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))))))) (forall ((X_45 $$unsorted) (Y_33 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral X_45) _let_1)) (hAPP_n1108039445umeral (hAPP_C471253896umeral power_2100829034umeral Y_33) _let_1))) (=> (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral zero_z126310315umeral) Y_33)) (hBOOL (hAPP_C24501650l_bool (hAPP_C10902773l_bool ord_le565307924umeral X_45) Y_33)))))) (forall ((Z_1 $$unsorted)) (= (hAPP_real_complex (hAPP_r265291036omplex complex (hAPP_complex_real re Z_1)) (hAPP_complex_real im Z_1)) Z_1)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (and (= zero_zero_real X_1) (= Y_2 zero_zero_real)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_1) _let_1)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_2) _let_1))) zero_zero_real))))) (forall ((X_3 $$unsorted)) (=> (forall ((R_1 $$unsorted)) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat N_3) N_2)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real R_1) (hAPP_nat_real X_3 N_2))))))) (hBOOL (tendsto_nat_real (hAPP_f1888375463t_real (hAPP_f1690286043t_real cOMBB_real_real_nat inverse_inverse_real) X_3) zero_zero_real sequentially)))) (forall ((M_9 $$unsorted) (N_23 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat M_9) N_23)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le1860547276de_int (hAPP_n522471361de_int semiri1424489471de_int M_9)) (hAPP_n522471361de_int semiri1424489471de_int N_23))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) B_2)) (= (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2) (hAPP_P1175774780nt_int product_fst_int_int (posDivAlg A_3 B_2)))))) (forall ((A_10 $$unsorted) (N_15 $$unsorted) (B_8 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int))) (let ((_let_2 (hAPP_nat_nat suc N_15))) (=> (and (is_int A_10) (is_int B_8)) (=> (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int B_8) _let_2) (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_10) _let_2)) (=> (hBOOL (hAPP_int_bool _let_1 A_10)) (=> (hBOOL (hAPP_int_bool _let_1 B_8)) (= B_8 A_10)))))))) (forall ((A_16 $$unsorted) (B_12 $$unsorted)) (=> (not (= zero_z126310315umeral B_12)) (= (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral A_16) B_12)) one_on1645066479umeral) (hAPP_C498520661umeral (hAPP_C1594335432umeral div_di1218280263umeral (hAPP_C498520661umeral (hAPP_C1594335432umeral plus_p1627245867umeral B_12) A_16)) B_12)))) (forall ((Z_13 $$unsorted)) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real Z_13) Z_13) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) Z_13))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int A_3) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int B_2) A_3)) (= zero_zero_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int A_3) B_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int X_1) Y_2)) zEven)) (= (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int X_1) zEven)) (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int Y_2) zEven))))) (forall ((P_3 $$unsorted) (R_3 $$unsorted) (S_1 $$unsorted) (Q_2 $$unsorted)) (=> (and (is_int S_1) (is_int Q_2)) (=> (not (= zero_zero_int Q_2)) (=> (not (= S_1 zero_zero_int)) (=> (= (normalize (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int R_3) S_1)) (normalize (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int P_3) Q_2))) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int P_3) S_1) (hAPP_int_int (hAPP_int_fun_int_int times_times_int R_3) Q_2))))))) (forall ((X_2 $$unsorted)) (= (hAPP_n1699378549t_bool ord_less_nat X_2) (hAPP_n1699378549t_bool ord_less_eq_nat (hAPP_nat_nat suc X_2)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= Y X)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool fequal_real X) Y)))) (forall ((N $$unsorted) (D_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat gcd_gcd_nat D_3))) (=> (= (hAPP_nat_nat _let_1 A_3) one_one_nat) (= one_one_nat (hAPP_nat_nat _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_3) N)))))) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real (hAPP_real_real uminus_uminus_real _let_10)) zero_zero_real)) (forall ((L_2 $$unsorted) (K_2 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_2) zero_zero_int)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) L_2)) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int K_2) L_2)) (hAPP_int_int (div_mod_int K_2) L_2)) (negDivAlg K_2 L_2))))) (forall ((X_1 $$unsorted)) (hBOOL (hAPP_real_bool (deriv_real (hAPP_n546711566l_real (hAPP_f248847589l_real cOMBC_real_nat_real (hAPP_f1407095736t_real (hAPP_f1796904975t_real cOMBB_599996122l_real power_power_real) cos)) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) X_1) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 min))) (hAPP_real_real cos X_1))) (hAPP_real_real sin X_1))))) (forall ((K_2 $$unsorted) (L_2 $$unsorted)) (= (hAPP_int_int bit0 (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_2) L_2)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int bit0 K_2)) L_2))) (forall ((R_3 $$unsorted) (Q_2 $$unsorted) (A_3 $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) A_3)) (=> (= A_3 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int R_3) (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_3) Q_2))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int R_3) A_3)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int one_one_int) Q_2)))))) (forall ((N $$unsorted)) (= (hAPP_real_real cos (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (hAPP_nat_real real_nat N))) pi)) one_one_real)) (forall ((D $$unsorted) (Sa $$unsorted)) (exists ((Z $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool dvd_dvd_real D) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X_2) Sa)))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real Z) X_2)) (= _let_1 _let_1)))))) (forall ((A_63 $$unsorted)) (= (hAPP_nat_nat (div_mod_nat A_63) A_63) zero_zero_nat)) (forall ((B $$unsorted) (A $$unsorted) (P_5 $$unsorted)) (=> (hBOOL (hAPP_int_bool zprime P_5)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int P_5) one_one_int))) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int B) (hAPP_i1948725293t_bool (wset A) P_5))) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) B)))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r1134773055l_bool (hAPP_f1393328161l_bool (hAPP_f1900646853l_bool cOMBB_430461877l_real P) Q) R) (hAPP_r1134773055l_bool P (hAPP_real_real Q R)))) (forall ((A_3 $$unsorted) (N $$unsorted) (B_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_3) N)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat B_2) N))) (=> (not (= zero_zero_nat N)) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool dvd_dvd_nat A_3) B_2))))) (forall ((X_1 $$unsorted)) (= (hAPP_f352196356l_real suminf_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f1092742621l_real cOMBB_1308947378al_nat times_times_real) cos_coeff)) (hAPP_r474017924t_real power_power_real X_1))) (hAPP_real_real cos X_1))) (forall ((A_11 $$unsorted) (N_17 $$unsorted)) (let ((_let_1 (hAPP_C471253896umeral power_2100829034umeral A_11))) (= (hAPP_n1108039445umeral _let_1 (hAPP_nat_nat suc N_17)) (hAPP_C498520661umeral (hAPP_C1594335432umeral times_1655362735umeral A_11) (hAPP_n1108039445umeral _let_1 N_17))))) (hBOOL (hAPP_nat_bool _let_7 _let_4)) (forall ((B_36 $$unsorted) (A_45 $$unsorted)) (= (hAPP_Q1762011733de_int (div_mo231679042de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int plus_p1446045655de_int B_36) A_45)) B_36) (hAPP_Q1762011733de_int (div_mo231679042de_int A_45) B_36))) (forall ((A $$unsorted) (B $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) B)) (= (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_rat (hAPP_int_rat (hAPP_int_fun_int_rat fract A) B)) one_one_rat)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat suc Ma)) (hAPP_nat_nat suc N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) N_1)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real A) B)) zero_zero_real)) (or (and (hBOOL (hAPP_real_bool _let_1 A)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real B) zero_zero_real))) (and (hBOOL (hAPP_real_bool _let_1 B)) (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real A) zero_zero_real))))))) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real one_one_real) zero_zero_real))) (forall ((A_190 $$unsorted) (B_146 $$unsorted) (K_7 $$unsorted)) (=> (= A_190 (hAPP_int_int (hAPP_int_fun_int_int times_times_int B_146) K_7)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool dvd_dvd_int B_146) A_190)))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_real zero_zero_real))) (= (hBOOL (hAPP_real_bool _let_1 (hAPP_real_real sqrt Y_2))) (hBOOL (hAPP_real_bool _let_1 Y_2))))) (forall ((F $$unsorted) (G $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (hAPP_nat_fun_nat_nat times_times_nat (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))))) (let ((_let_2 (ord_at4362885an_nat zero_zero_nat))) (let ((_let_3 (hAPP_n1699378549t_bool _let_2 N_1))) (= (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat F) _let_1)) _let_3)) (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1676298106t_real (hAPP_f1566856189t_real cOMBB_nat_real_nat G) (hAPP_nat_fun_nat_nat (hAPP_f416620757at_nat cOMBC_nat_nat_nat (hAPP_f1639111240at_nat (hAPP_f1731313045at_nat cOMBB_963856155at_nat plus_plus_nat) _let_1)) one_one_nat))) _let_3)) (hAPP_f1406902706l_real (hAPP_f1509287679l_real big_co604158596t_real (hAPP_f1888375463t_real (hAPP_f197615720t_real cOMBS_nat_real_real (hAPP_f451358433l_real (hAPP_f335634176l_real cOMBS_337378985l_real (hAPP_f1129044203l_real (hAPP_f264196187l_real cOMBB_1480366270al_nat if_real) even_odd_even_nat)) F)) G)) (hAPP_n1699378549t_bool _let_2 (hAPP_nat_nat _let_1 N_1)))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_int_real (hAPP_f563293398t_real (hAPP_f134192053t_real cOMBB_int_real_int P) Q) R) (hAPP_int_real P (hAPP_int_int Q R)))) (forall ((P_1 $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_1) J)) (=> (hBOOL (hAPP_nat_bool P_1 J)) (=> (forall ((I_2 $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat I_2) J)) (=> (hBOOL (hAPP_nat_bool P_1 (hAPP_nat_nat suc I_2))) (hBOOL (hAPP_nat_bool P_1 I_2))))) (hBOOL (hAPP_nat_bool P_1 I_1)))))) (= _let_6 _let_5) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real one_one_real) _let_4) one_one_real) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int Z1) Z2)) W) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z1) W)) (hAPP_int_int (hAPP_int_fun_int_int times_times_int Z2) W)))) (forall ((A $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat W_1))) (= (and (not (= zero_zero_nat _let_1)) (= zero_zero_nat A)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A) _let_1) zero_zero_nat)))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (=> (and (is_int N_1) (is_int K_1)) (= (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (hAPP_int_fun_int_int div_div_int N_1) K_1))) (and (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) zero_zero_int)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (and (is_int I_2) (is_int J_1)) (=> (and (= N_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) I_2)) J_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int J_1) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) J_1))) (hBOOL (hAPP_int_bool P_1 I_2)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) K_1)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (and (is_int J_1) (is_int I_2)) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int J_1) K_1)) (= N_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) I_2)) J_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) J_1))) (hBOOL (hAPP_int_bool P_1 I_2)))))) (=> (= K_1 zero_zero_int) (hBOOL (hAPP_int_bool P_1 zero_zero_int))))))) (forall ((N $$unsorted)) (not (= (hAPP_nat_real real_nat (hAPP_nat_nat fact_fact_nat N)) zero_zero_real))) (forall ((A_222 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int zero_zero_int) A_222) zero_zero_int)) (forall ((A_240 $$unsorted)) (not (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int A_240) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) zero_zero_int)))) (forall ((L $$unsorted) (U $$unsorted)) (= (hAPP_f22106695ol_nat finite_card_nat (hAPP_n1699378549t_bool (ord_gr660468384an_nat L) U)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat U) (hAPP_nat_nat suc L)))) (forall ((Y_6 $$unsorted) (P_6 $$unsorted) (N_10 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int Y_6))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat P_6) N_10)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_10) P_6))) Y_6) (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_nat_nat suc N_10)) P_6)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (= X (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real) Y)) (= (hAPP_real_real sqrt X) Y)))) (forall ((U $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_eq_nat I_1) J)) (= (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat Ma) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat J) I_1)) U)) N_1))) (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat I_1) U)) Ma)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat J) U)) N_1)))))) (forall ((X $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (hAPP_r1250527377l_real powr X))) (= (hAPP_real_real _let_1 (hAPP_real_real uminus_uminus_real A_3)) (hAPP_real_real (hAPP_r1250527377l_real inverse_divide_real one_one_real) (hAPP_real_real _let_1 A_3))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (hAPP_i1948725293t_bool ord_less_int zero_zero_int))) (=> (hBOOL (hAPP_int_bool _let_1 N_1)) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat (hAPP_int_nat nat N_1)) one_one_nat) (hAPP_f957591787ol_nat finite_card_int (collect_int (hAPP_f1805168059t_bool (hAPP_f727283836t_bool cOMBS_int_bool_bool (hAPP_f2144054103l_bool (hAPP_f1734373249l_bool cOMBB_1652995168ol_int fconj) _let_1)) (hAPP_i1948725293t_bool (hAPP_f428220345t_bool cOMBC_int_int_bool ord_less_int) N_1)))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int A) B)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) C)) (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int B) C))))) (forall ((V $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (hAPP_int_real number267125858f_real V))) (let ((_let_2 (hAPP_int_real number267125858f_real W_1))) (= (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_eq_real _let_1) _let_2)) (not (hBOOL (hAPP_real_bool (hAPP_r1134773055l_bool ord_less_real _let_2) _let_1))))))) (= (hAPP_nat_int (hAPP_int_fun_nat_int power_power_int one_one_int) _let_4) one_one_int) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) (let ((_let_2 (hAPP_int_nat number_number_of_nat _let_1))) (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real X) Y)) _let_2) (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_real_real (hAPP_r1250527377l_real plus_plus_real (hAPP_nat_real (hAPP_r474017924t_real power_power_real X) _let_2)) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y) _let_2))) (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_real_real (hAPP_r1250527377l_real times_times_real (hAPP_int_real number267125858f_real _let_1)) X)) Y)))))) (forall ((A_182 $$unsorted)) (= A_182 (hAPP_nat_nat (hAPP_nat_fun_nat_nat power_power_nat A_182) one_one_nat))) (forall ((N $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (not (hBOOL (hAPP_nat_bool even_odd_even_nat N))) (= (hAPP_nat_nat suc (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat N) _let_1)) (hAPP_nat_nat (hAPP_nat_fun_nat_nat div_div_nat (hAPP_nat_nat (hAPP_nat_fun_nat_nat plus_plus_nat N) one_one_nat)) _let_1))))) (forall ((A_221 $$unsorted)) (= (hAPP_int_int (hAPP_int_fun_int_int times_times_int A_221) zero_zero_int) zero_zero_int)) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (=> (and (is_int N_1) (is_int K_1)) (= (and (=> (= zero_zero_int K_1) (hBOOL (hAPP_int_bool P_1 N_1))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int zero_zero_int) K_1)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (and (is_int I_2) (is_int J_1)) (=> (and (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int J_1) K_1)) (= N_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) I_2)) J_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) J_1))) (hBOOL (hAPP_int_bool P_1 J_1)))))) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) zero_zero_int)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (=> (and (is_int J_1) (is_int I_2)) (=> (and (= N_1 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int (hAPP_int_int (hAPP_int_fun_int_int times_times_int K_1) I_2)) J_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int J_1) zero_zero_int)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int K_1) J_1))) (hBOOL (hAPP_int_bool P_1 J_1))))))) (hBOOL (hAPP_int_bool P_1 (hAPP_int_int (div_mod_int N_1) K_1)))))) (forall ((I_1 $$unsorted)) (= (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int I_1) zero_zero_int)) (= (hAPP_int_nat nat I_1) zero_zero_nat))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (negDivAlg A B))) (let ((_let_2 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int B) zero_zero_int)))) (let ((_let_3 (hAPP_int_int (hAPP_int_fun_int_int plus_plus_int A) B))) (let ((_let_4 (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_eq_int zero_zero_int) _let_3)))) (=> (hBOOL (hAPP_P603027463t_bool (accp_P2006205492nt_int negDivAlg_rel) (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int A) B))) (and (=> (or _let_2 _let_4) (= (hAPP_i1524277240nt_int (hAPP_i1584592887nt_int product_Pair_int_int (hAPP_int_int number_number_of_int min)) _let_3) _let_1)) (=> (not (or _let_4 _let_2)) (= _let_1 (hAPP_P1975530577nt_int (adjust B) (negDivAlg A (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit0 (hAPP_int_int bit1 pls)))) B)))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (= (hAPP_int_int (div_mod_int M) N) (hAPP_int_int (hAPP_int_fun_int_int minus_minus_int M) (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int (hAPP_int_fun_int_int div_div_int M) N)) N)))) (forall ((A_221 $$unsorted)) (= zero_z891286103de_int (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_221) zero_z891286103de_int))) (forall ((A_237 $$unsorted)) (=> (is_int A_237) (= A_237 (hAPP_int_int (hAPP_int_fun_int_int times_times_int (hAPP_int_int number_number_of_int (hAPP_int_int bit1 pls))) A_237)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (=> (not (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2) zero_zero_nat)) (exists ((A_4 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_3) B_2))) (and (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat A_4) _let_1) A_3) (= (hAPP_nat_nat (hAPP_nat_fun_nat_nat gcd_gcd_nat A_4) B_3) one_one_nat) (= B_2 (hAPP_nat_nat (hAPP_nat_fun_nat_nat times_times_nat B_3) _let_1))))))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_f1805168059t_bool (hAPP_i1529485324t_bool P R) Q) (hAPP_i1948725293t_bool (hAPP_f1048215610t_bool (hAPP_f472159229t_bool cOMBC_1683390479t_bool P) Q) R))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (= (and (= Y_2 zero_zero_rat) (= zero_zero_rat X_1)) (hBOOL (hAPP_rat_bool (hAPP_r2115560837t_bool ord_less_eq_rat (hAPP_rat_rat (hAPP_rat_fun_rat_rat plus_plus_rat (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat X_1) _let_1)) (hAPP_nat_rat (hAPP_rat_fun_nat_rat power_power_rat Y_2) _let_1))) zero_zero_rat))))) (forall ((M $$unsorted) (X $$unsorted)) (= (hAPP_int_int (div_mod_int X) M) (hAPP_int_int (standardRes M) X))) (forall ((X_46 $$unsorted) (Y_34 $$unsorted)) (let ((_let_1 (hAPP_r1134773055l_bool ord_less_eq_real zero_zero_real))) (let ((_let_2 (hAPP_int_nat number_number_of_nat (hAPP_int_int bit0 (hAPP_int_int bit1 pls))))) (=> (= (hAPP_nat_real (hAPP_r474017924t_real power_power_real X_46) _let_2) (hAPP_nat_real (hAPP_r474017924t_real power_power_real Y_34) _let_2)) (=> (hBOOL (hAPP_real_bool _let_1 X_46)) (=> (hBOOL (hAPP_real_bool _let_1 Y_34)) (= Y_34 X_46))))))) (= _let_1 one_one_nat) (= (hAPP_real_real arctan zero_zero_real) zero_zero_real) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (hAPP_r712953929l_real (hAPP_f1119546819l_real (hAPP_f555557763l_real cOMBB_422423973l_real P) Q) R) (hAPP_f800361423l_real P (hAPP_r2019696015l_real Q R)))) (forall ((P $$unsorted)) (=> (is_bool P) (or (= P fTrue) (= fFalse P)))) (forall ((Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (hAPP_i1584592887nt_int product_Pair_int_int Q_2))) (= (hAPP_i1524277240nt_int _let_1 (hAPP_int_int uminus_uminus_int R_3)) (hAPP_P1975530577nt_int negateSnd (hAPP_i1524277240nt_int _let_1 R_3))))) (forall ((X_21 $$unsorted) (N_31 $$unsorted)) (let ((_let_1 (hAPP_Q125967240de_int power_881366806de_int X_21))) (=> (hBOOL (hAPP_nat_bool (hAPP_n1699378549t_bool ord_less_nat zero_zero_nat) N_31)) (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int (hAPP_n522471361de_int _let_1 (hAPP_nat_nat (hAPP_nat_fun_nat_nat minus_minus_nat N_31) one_one_nat))) X_21) (hAPP_n522471361de_int _let_1 N_31))))) (forall ((A_205 $$unsorted) (B_156 $$unsorted)) (=> (= (hAPP_Q1762011733de_int (hAPP_Q1729056540de_int times_123202395de_int A_205) B_156) zero_z891286103de_int) (or (= B_156 zero_z891286103de_int) (= zero_z891286103de_int A_205)))) (forall ((A $$unsorted) (A_1 $$unsorted) (Ma $$unsorted)) (=> (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool ord_less_int one_one_int) Ma)) (=> (hBOOL (hAPP_int_bool (is_RRset A_1) Ma)) (=> (hBOOL (hAPP_f448129468l_bool (hAPP_i2112223885l_bool member_int A) A_1)) (hBOOL (hAPP_int_bool (hAPP_i1948725293t_bool (zcong A) (hAPP_int_int (rRset2norRR A_1 Ma) A)) Ma)))))) (forall ((M $$unsorted)) (not (= (hAPP_nat_nat suc M) zero_zero_nat))) (forall ((N_25 $$unsorted)) (hBOOL (hAPP_Q2096512830t_bool (hAPP_Q1010094925t_bool ord_le258702272de_int zero_z891286103de_int) (hAPP_n522471361de_int semiri1424489471de_int N_25)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 7.13/7.39 % SZS output end Proof for theBenchmark 7.13/7.39 EOF