% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Fundamental_Theorem_Algebra/prob_189__5369416_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:27:49.562

% Could-be-implicit typings (4)
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (39)
thf(sy_c_Complex_Oimaginary__unit, type,
    imaginary_unit : complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum, type,
    plus_plus_num : num > num > num).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex, type,
    numera632737353omplex : num > complex).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum, type,
    ord_less_num : num > num > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex, type,
    power_power_complex : complex > nat > complex).
thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat, type,
    power_power_nat : nat > nat > nat).
thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal, type,
    power_power_real : real > nat > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex, type,
    real_V306493662omplex : real > complex).
thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal, type,
    real_V1205483228l_real : real > real).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat, type,
    divide_divide_nat : nat > nat > nat).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex, type,
    dvd_dvd_complex : complex > complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal, type,
    dvd_dvd_real : real > real > $o).
thf(sy_v_b, type,
    b : complex).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).

% Relevant facts (234)
thf(fact_0__092_060open_062odd_An_092_060close_062, axiom,
    ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))))). % \<open>odd n\<close>
thf(fact_1__092_060open_062cmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_L_A1_J_A_060_A1_A_092_060or_062_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_N_A1_J_A_060_A1_A_092_060or_062_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_L_A_092_060i_062_J_A_060_A1_A_092_060or_062_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_N_A_092_060i_062_J_A_060_A1_092_060close_062, axiom,
    (((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ one_one_complex)) @ one_one_real) | ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ one_one_complex)) @ one_one_real) | ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ imaginary_unit)) @ one_one_real) | (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ imaginary_unit)) @ one_one_real)))))). % \<open>cmod (complex_of_real (cmod b) / b + 1) < 1 \<or> cmod (complex_of_real (cmod b) / b - 1) < 1 \<or> cmod (complex_of_real (cmod b) / b + \<i>) < 1 \<or> cmod (complex_of_real (cmod b) / b - \<i>) < 1\<close>
thf(fact_2_b, axiom,
    ((~ ((b = zero_zero_complex))))). % b
thf(fact_3_n, axiom,
    ((~ ((na = zero_zero_nat))))). % n
thf(fact_4_th0, axiom,
    (((real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) = one_one_real))). % th0
thf(fact_5_assms_I2_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(2)
thf(fact_6_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_7_of__real__1, axiom,
    (((real_V1205483228l_real @ one_one_real) = one_one_real))). % of_real_1
thf(fact_8_of__real__1, axiom,
    (((real_V306493662omplex @ one_one_real) = one_one_complex))). % of_real_1
thf(fact_9_of__real__eq__1__iff, axiom,
    ((![X3 : real]: (((real_V1205483228l_real @ X3) = one_one_real) = (X3 = one_one_real))))). % of_real_eq_1_iff
thf(fact_10_of__real__eq__1__iff, axiom,
    ((![X3 : real]: (((real_V306493662omplex @ X3) = one_one_complex) = (X3 = one_one_real))))). % of_real_eq_1_iff
thf(fact_11_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_12_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_13_power__inject__exp, axiom,
    ((![A : real, M : nat, N : nat]: ((ord_less_real @ one_one_real @ A) => (((power_power_real @ A @ M) = (power_power_real @ A @ N)) = (M = N)))))). % power_inject_exp
thf(fact_14_power__inject__exp, axiom,
    ((![A : nat, M : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => (((power_power_nat @ A @ M) = (power_power_nat @ A @ N)) = (M = N)))))). % power_inject_exp
thf(fact_15_power__strict__increasing__iff, axiom,
    ((![B : real, X3 : nat, Y2 : nat]: ((ord_less_real @ one_one_real @ B) => ((ord_less_real @ (power_power_real @ B @ X3) @ (power_power_real @ B @ Y2)) = (ord_less_nat @ X3 @ Y2)))))). % power_strict_increasing_iff
thf(fact_16_power__strict__increasing__iff, axiom,
    ((![B : nat, X3 : nat, Y2 : nat]: ((ord_less_nat @ one_one_nat @ B) => ((ord_less_nat @ (power_power_nat @ B @ X3) @ (power_power_nat @ B @ Y2)) = (ord_less_nat @ X3 @ Y2)))))). % power_strict_increasing_iff
thf(fact_17_of__real__power, axiom,
    ((![X3 : real, N : nat]: ((real_V306493662omplex @ (power_power_real @ X3 @ N)) = (power_power_complex @ (real_V306493662omplex @ X3) @ N))))). % of_real_power
thf(fact_18_of__real__power, axiom,
    ((![X3 : real, N : nat]: ((real_V1205483228l_real @ (power_power_real @ X3 @ N)) = (power_power_real @ (real_V1205483228l_real @ X3) @ N))))). % of_real_power
thf(fact_19_of__real__divide, axiom,
    ((![X3 : real, Y2 : real]: ((real_V306493662omplex @ (divide_divide_real @ X3 @ Y2)) = (divide1210191872omplex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2)))))). % of_real_divide
thf(fact_20_of__real__divide, axiom,
    ((![X3 : real, Y2 : real]: ((real_V1205483228l_real @ (divide_divide_real @ X3 @ Y2)) = (divide_divide_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2)))))). % of_real_divide
thf(fact_21_of__real__add, axiom,
    ((![X3 : real, Y2 : real]: ((real_V306493662omplex @ (plus_plus_real @ X3 @ Y2)) = (plus_plus_complex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2)))))). % of_real_add
thf(fact_22_of__real__add, axiom,
    ((![X3 : real, Y2 : real]: ((real_V1205483228l_real @ (plus_plus_real @ X3 @ Y2)) = (plus_plus_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2)))))). % of_real_add
thf(fact_23_norm__less__p1, axiom,
    ((![X3 : complex]: (ord_less_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ (plus_plus_complex @ (real_V306493662omplex @ (real_V638595069omplex @ X3)) @ one_one_complex)))))). % norm_less_p1
thf(fact_24_norm__less__p1, axiom,
    ((![X3 : real]: (ord_less_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ (plus_plus_real @ (real_V1205483228l_real @ (real_V646646907m_real @ X3)) @ one_one_real)))))). % norm_less_p1
thf(fact_25_power__one, axiom,
    ((![N : nat]: ((power_power_real @ one_one_real @ N) = one_one_real)))). % power_one
thf(fact_26_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_27_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_28_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_29_div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % div_by_1
thf(fact_30_div__by__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ one_one_complex) = A)))). % div_by_1
thf(fact_31_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_32_power__one__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_33_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_34_of__real__eq__iff, axiom,
    ((![X3 : real, Y2 : real]: (((real_V306493662omplex @ X3) = (real_V306493662omplex @ Y2)) = (X3 = Y2))))). % of_real_eq_iff
thf(fact_35_of__real__eq__iff, axiom,
    ((![X3 : real, Y2 : real]: (((real_V1205483228l_real @ X3) = (real_V1205483228l_real @ Y2)) = (X3 = Y2))))). % of_real_eq_iff
thf(fact_36_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_37_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_38_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_39_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_40_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_41_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_42_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_43_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_44_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_45_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_46_dvd__add__triv__right__iff, axiom,
    ((![A : complex, B : complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ A)) = (dvd_dvd_complex @ A @ B))))). % dvd_add_triv_right_iff
thf(fact_47_dvd__add__triv__right__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ A)) = (dvd_dvd_nat @ A @ B))))). % dvd_add_triv_right_iff
thf(fact_48_dvd__add__triv__left__iff, axiom,
    ((![A : complex, B : complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ A @ B)) = (dvd_dvd_complex @ A @ B))))). % dvd_add_triv_left_iff
thf(fact_49_dvd__add__triv__left__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ A @ B)) = (dvd_dvd_nat @ A @ B))))). % dvd_add_triv_left_iff
thf(fact_50_div__dvd__div, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => ((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))))). % div_dvd_div
thf(fact_51_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_52_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_53_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_54_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_55_nat__zero__less__power__iff, axiom,
    ((![X3 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ X3 @ N)) = (((ord_less_nat @ zero_zero_nat @ X3)) | ((N = zero_zero_nat))))))). % nat_zero_less_power_iff
thf(fact_56_norm__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (numera632737353omplex @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_57_norm__numeral, axiom,
    ((![W : num]: ((real_V646646907m_real @ (numeral_numeral_real @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_58_of__real__0, axiom,
    (((real_V306493662omplex @ zero_zero_real) = zero_zero_complex))). % of_real_0
thf(fact_59_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_60_of__real__eq__0__iff, axiom,
    ((![X3 : real]: (((real_V306493662omplex @ X3) = zero_zero_complex) = (X3 = zero_zero_real))))). % of_real_eq_0_iff
thf(fact_61_of__real__eq__0__iff, axiom,
    ((![X3 : real]: (((real_V1205483228l_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % of_real_eq_0_iff
thf(fact_62_of__real__numeral, axiom,
    ((![W : num]: ((real_V306493662omplex @ (numeral_numeral_real @ W)) = (numera632737353omplex @ W))))). % of_real_numeral
thf(fact_63_of__real__numeral, axiom,
    ((![W : num]: ((real_V1205483228l_real @ (numeral_numeral_real @ W)) = (numeral_numeral_real @ W))))). % of_real_numeral
thf(fact_64_of__real__diff, axiom,
    ((![X3 : real, Y2 : real]: ((real_V306493662omplex @ (minus_minus_real @ X3 @ Y2)) = (minus_minus_complex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2)))))). % of_real_diff
thf(fact_65_of__real__diff, axiom,
    ((![X3 : real, Y2 : real]: ((real_V1205483228l_real @ (minus_minus_real @ X3 @ Y2)) = (minus_minus_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2)))))). % of_real_diff
thf(fact_66_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_67_div__self, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ A @ A) = one_one_nat))))). % div_self
thf(fact_68_div__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % div_self
thf(fact_69_div__add, axiom,
    ((![C : nat, A : nat, B : nat]: ((dvd_dvd_nat @ C @ A) => ((dvd_dvd_nat @ C @ B) => ((divide_divide_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)))))))). % div_add
thf(fact_70_power__zero__numeral, axiom,
    ((![K : num]: ((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ K)) = zero_zero_complex)))). % power_zero_numeral
thf(fact_71_power__zero__numeral, axiom,
    ((![K : num]: ((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ K)) = zero_zero_nat)))). % power_zero_numeral
thf(fact_72_unit__div__1__div__1, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((divide_divide_nat @ one_one_nat @ (divide_divide_nat @ one_one_nat @ A)) = A))))). % unit_div_1_div_1
thf(fact_73_unit__div__1__unit, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (dvd_dvd_nat @ (divide_divide_nat @ one_one_nat @ A) @ one_one_nat))))). % unit_div_1_unit
thf(fact_74_unit__div, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ (divide_divide_nat @ A @ B) @ one_one_nat)))))). % unit_div
thf(fact_75_zero__less__norm__iff, axiom,
    ((![X3 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X3)) = (~ ((X3 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_76_zero__less__norm__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X3)) = (~ ((X3 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_77_power__eq__0__iff, axiom,
    ((![A : complex, N : nat]: (((power_power_complex @ A @ N) = zero_zero_complex) = (((A = zero_zero_complex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_78_power__eq__0__iff, axiom,
    ((![A : nat, N : nat]: (((power_power_nat @ A @ N) = zero_zero_nat) = (((A = zero_zero_nat)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_79_norm__divide__numeral, axiom,
    ((![A : complex, W : num]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ (numera632737353omplex @ W))) = (divide_divide_real @ (real_V638595069omplex @ A) @ (numeral_numeral_real @ W)))))). % norm_divide_numeral
thf(fact_80_norm__divide__numeral, axiom,
    ((![A : real, W : num]: ((real_V646646907m_real @ (divide_divide_real @ A @ (numeral_numeral_real @ W))) = (divide_divide_real @ (real_V646646907m_real @ A) @ (numeral_numeral_real @ W)))))). % norm_divide_numeral
thf(fact_81_power__strict__decreasing__iff, axiom,
    ((![B : real, M : nat, N : nat]: ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ B @ one_one_real) => ((ord_less_real @ (power_power_real @ B @ M) @ (power_power_real @ B @ N)) = (ord_less_nat @ N @ M))))))). % power_strict_decreasing_iff
thf(fact_82_power__strict__decreasing__iff, axiom,
    ((![B : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ B @ one_one_nat) => ((ord_less_nat @ (power_power_nat @ B @ M) @ (power_power_nat @ B @ N)) = (ord_less_nat @ N @ M))))))). % power_strict_decreasing_iff
thf(fact_83_even__add, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))). % even_add
thf(fact_84_odd__add, axiom,
    ((![A : nat, B : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)))) = (~ (((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))))))). % odd_add
thf(fact_85_zero__eq__power2, axiom,
    ((![A : complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex) = (A = zero_zero_complex))))). % zero_eq_power2
thf(fact_86_zero__eq__power2, axiom,
    ((![A : nat]: (((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat) = (A = zero_zero_nat))))). % zero_eq_power2
thf(fact_87_bits__1__div__2, axiom,
    (((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % bits_1_div_2
thf(fact_88_even__plus__one__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ one_one_nat)) = (~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))))). % even_plus_one_iff
thf(fact_89_zero__less__power2, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (~ ((A = zero_zero_real))))))). % zero_less_power2
thf(fact_90_even__succ__div__two, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((divide_divide_nat @ (plus_plus_nat @ A @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))). % even_succ_div_two
thf(fact_91_odd__succ__div__two, axiom,
    ((![A : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) => ((divide_divide_nat @ (plus_plus_nat @ A @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))))). % odd_succ_div_two
thf(fact_92_even__succ__div__2, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((divide_divide_nat @ (plus_plus_nat @ one_one_nat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))). % even_succ_div_2
thf(fact_93_even__power, axiom,
    ((![A : nat, N : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (power_power_nat @ A @ N)) = (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % even_power
thf(fact_94_power__less__zero__eq__numeral, axiom,
    ((![A : real, W : num]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ W)) @ zero_zero_real) = (((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ W))))) & ((ord_less_real @ A @ zero_zero_real))))))). % power_less_zero_eq_numeral
thf(fact_95_power__less__zero__eq, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ (power_power_real @ A @ N) @ zero_zero_real) = (((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)))) & ((ord_less_real @ A @ zero_zero_real))))))). % power_less_zero_eq
thf(fact_96_even__mask__iff, axiom,
    ((![N : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) @ one_one_nat)) = (N = zero_zero_nat))))). % even_mask_iff
thf(fact_97_zero__less__power__eq__numeral, axiom,
    ((![A : real, W : num]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ W))) = ((((numeral_numeral_nat @ W) = zero_zero_nat)) | ((((((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ W))) & ((~ ((A = zero_zero_real)))))) | ((((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ W))))) & ((ord_less_real @ zero_zero_real @ A))))))))))). % zero_less_power_eq_numeral
thf(fact_98_even__succ__div__exp, axiom,
    ((![A : nat, N : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_nat @ zero_zero_nat @ N) => ((divide_divide_nat @ (plus_plus_nat @ one_one_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)) = (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)))))))). % even_succ_div_exp
thf(fact_99_IH, axiom,
    ((![M2 : nat]: ((ord_less_nat @ M2 @ na) => ((~ ((M2 = zero_zero_nat))) => (?[Z2 : complex]: (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ one_one_complex @ (times_times_complex @ b @ (power_power_complex @ Z2 @ M2)))) @ one_one_real))))))). % IH
thf(fact_100_odd__pos, axiom,
    ((![N : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N))) => (ord_less_nat @ zero_zero_nat @ N))))). % odd_pos
thf(fact_101_nat__induct2, axiom,
    ((![P : nat > $o, N : nat]: ((P @ zero_zero_nat) => ((P @ one_one_nat) => ((![N2 : nat]: ((P @ N2) => (P @ (plus_plus_nat @ N2 @ (numeral_numeral_nat @ (bit0 @ one)))))) => (P @ N))))))). % nat_induct2
thf(fact_102_nat__power__less__imp__less, axiom,
    ((![I : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ I) => ((ord_less_nat @ (power_power_nat @ I @ M) @ (power_power_nat @ I @ N)) => (ord_less_nat @ M @ N)))))). % nat_power_less_imp_less
thf(fact_103_dvd__diff, axiom,
    ((![X3 : complex, Y2 : complex, Z3 : complex]: ((dvd_dvd_complex @ X3 @ Y2) => ((dvd_dvd_complex @ X3 @ Z3) => (dvd_dvd_complex @ X3 @ (minus_minus_complex @ Y2 @ Z3))))))). % dvd_diff
thf(fact_104_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex))))). % zero_power
thf(fact_105_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat))))). % zero_power
thf(fact_106_zero__power2, axiom,
    (((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex))). % zero_power2
thf(fact_107_zero__power2, axiom,
    (((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % zero_power2
thf(fact_108_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_109_even__zero, axiom,
    ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ zero_zero_nat))). % even_zero
thf(fact_110_dvd__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A @ C)))))). % dvd_trans
thf(fact_111_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_112_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_113_even__numeral, axiom,
    ((![N : num]: (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit0 @ N)))))). % even_numeral
thf(fact_114_exp__add__not__zero__imp__left, axiom,
    ((![M : nat, N : nat]: ((~ (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ M @ N)) = zero_zero_nat))) => (~ (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ M) = zero_zero_nat))))))). % exp_add_not_zero_imp_left
thf(fact_115_exp__add__not__zero__imp__right, axiom,
    ((![M : nat, N : nat]: ((~ (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ M @ N)) = zero_zero_nat))) => (~ (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) = zero_zero_nat))))))). % exp_add_not_zero_imp_right
thf(fact_116_zero__less__power__eq, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ N)) = (((N = zero_zero_nat)) | ((((((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)) & ((~ ((A = zero_zero_real)))))) | ((((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)))) & ((ord_less_real @ zero_zero_real @ A))))))))))). % zero_less_power_eq
thf(fact_117_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_118_dvd__div__eq__0__iff, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ A) => (((divide_divide_nat @ A @ B) = zero_zero_nat) = (A = zero_zero_nat)))))). % dvd_div_eq_0_iff
thf(fact_119_dvd__div__eq__0__iff, axiom,
    ((![B : complex, A : complex]: ((dvd_dvd_complex @ B @ A) => (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (A = zero_zero_complex)))))). % dvd_div_eq_0_iff
thf(fact_120_odd__even__add, axiom,
    ((![A : nat, B : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) => ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) => (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B))))))). % odd_even_add
thf(fact_121_odd__one, axiom,
    ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ one_one_nat))))). % odd_one
thf(fact_122_bit__eq__rec, axiom,
    (((^[Y3 : nat]: (^[Z4 : nat]: (Y3 = Z4))) = (^[A2 : nat]: (^[B2 : nat]: ((((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A2) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B2))) & (((divide_divide_nat @ A2 @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ B2 @ (numeral_numeral_nat @ (bit0 @ one))))))))))). % bit_eq_rec
thf(fact_123_power2__commute, axiom,
    ((![X3 : complex, Y2 : complex]: ((power_power_complex @ (minus_minus_complex @ X3 @ Y2) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_complex @ (minus_minus_complex @ Y2 @ X3) @ (numeral_numeral_nat @ (bit0 @ one))))))). % power2_commute
thf(fact_124_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_125_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_126_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_127_dvd__power, axiom,
    ((![N : nat, X3 : real]: (((ord_less_nat @ zero_zero_nat @ N) | (X3 = one_one_real)) => (dvd_dvd_real @ X3 @ (power_power_real @ X3 @ N)))))). % dvd_power
thf(fact_128_dvd__power, axiom,
    ((![N : nat, X3 : complex]: (((ord_less_nat @ zero_zero_nat @ N) | (X3 = one_one_complex)) => (dvd_dvd_complex @ X3 @ (power_power_complex @ X3 @ N)))))). % dvd_power
thf(fact_129_dvd__power, axiom,
    ((![N : nat, X3 : nat]: (((ord_less_nat @ zero_zero_nat @ N) | (X3 = one_one_nat)) => (dvd_dvd_nat @ X3 @ (power_power_nat @ X3 @ N)))))). % dvd_power
thf(fact_130_power__not__zero, axiom,
    ((![A : complex, N : nat]: ((~ ((A = zero_zero_complex))) => (~ (((power_power_complex @ A @ N) = zero_zero_complex))))))). % power_not_zero
thf(fact_131_power__not__zero, axiom,
    ((![A : nat, N : nat]: ((~ ((A = zero_zero_nat))) => (~ (((power_power_nat @ A @ N) = zero_zero_nat))))))). % power_not_zero
thf(fact_132_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_real @ zero_zero_real @ N) = one_one_real)) & ((~ ((N = zero_zero_nat))) => ((power_power_real @ zero_zero_real @ N) = zero_zero_real)))))). % power_0_left
thf(fact_133_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_complex @ zero_zero_complex @ N) = one_one_complex)) & ((~ ((N = zero_zero_nat))) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex)))))). % power_0_left
thf(fact_134_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ N) = one_one_nat)) & ((~ ((N = zero_zero_nat))) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat)))))). % power_0_left
thf(fact_135_power__eq__imp__eq__norm, axiom,
    ((![W : complex, N : nat, Z3 : complex]: (((power_power_complex @ W @ N) = (power_power_complex @ Z3 @ N)) => ((ord_less_nat @ zero_zero_nat @ N) => ((real_V638595069omplex @ W) = (real_V638595069omplex @ Z3))))))). % power_eq_imp_eq_norm
thf(fact_136_power__eq__imp__eq__norm, axiom,
    ((![W : real, N : nat, Z3 : real]: (((power_power_real @ W @ N) = (power_power_real @ Z3 @ N)) => ((ord_less_nat @ zero_zero_nat @ N) => ((real_V646646907m_real @ W) = (real_V646646907m_real @ Z3))))))). % power_eq_imp_eq_norm
thf(fact_137_div__exp__eq, axiom,
    ((![A : nat, M : nat, N : nat]: ((divide_divide_nat @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ M)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)) = (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ M @ N))))))). % div_exp_eq
thf(fact_138_power2__less__0, axiom,
    ((![A : real]: (~ ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_real)))))). % power2_less_0
thf(fact_139_norm__diff__triangle__less, axiom,
    ((![X3 : complex, Y2 : complex, E1 : real, Z3 : complex, E2 : real]: ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Y2)) @ E1) => ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Y2 @ Z3)) @ E2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Z3)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_140_norm__diff__triangle__less, axiom,
    ((![X3 : real, Y2 : real, E1 : real, Z3 : real, E2 : real]: ((ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Y2)) @ E1) => ((ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ Y2 @ Z3)) @ E2) => (ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Z3)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_141_unit__div__eq__0__iff, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => (((divide_divide_nat @ A @ B) = zero_zero_nat) = (A = zero_zero_nat)))))). % unit_div_eq_0_iff
thf(fact_142_is__unit__power__iff, axiom,
    ((![A : nat, N : nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ N) @ one_one_nat) = (((dvd_dvd_nat @ A @ one_one_nat)) | ((N = zero_zero_nat))))))). % is_unit_power_iff
thf(fact_143_sum__power2__gt__zero__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ X3 @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ Y2 @ (numeral_numeral_nat @ (bit0 @ one))))) = (((~ ((X3 = zero_zero_real)))) | ((~ ((Y2 = zero_zero_real))))))))). % sum_power2_gt_zero_iff
thf(fact_144_not__sum__power2__lt__zero, axiom,
    ((![X3 : real, Y2 : real]: (~ ((ord_less_real @ (plus_plus_real @ (power_power_real @ X3 @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ Y2 @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_real)))))). % not_sum_power2_lt_zero
thf(fact_145_add__less__zeroD, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ (plus_plus_real @ X3 @ Y2) @ zero_zero_real) => ((ord_less_real @ X3 @ zero_zero_real) | (ord_less_real @ Y2 @ zero_zero_real)))))). % add_less_zeroD
thf(fact_146_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_147_not__one__less__zero, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ zero_zero_nat))))). % not_one_less_zero
thf(fact_148_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_149_zero__less__one, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % zero_less_one
thf(fact_150_zero__less__power, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (power_power_real @ A @ N)))))). % zero_less_power
thf(fact_151_zero__less__power, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ N)))))). % zero_less_power
thf(fact_152_power__0, axiom,
    ((![A : real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real)))). % power_0
thf(fact_153_power__0, axiom,
    ((![A : complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex)))). % power_0
thf(fact_154_power__0, axiom,
    ((![A : nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat)))). % power_0
thf(fact_155_nonzero__norm__divide, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B))))))). % nonzero_norm_divide
thf(fact_156_nonzero__norm__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B))))))). % nonzero_norm_divide
thf(fact_157_dvd__add__right__iff, axiom,
    ((![A : complex, B : complex, C : complex]: ((dvd_dvd_complex @ A @ B) => ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ C)) = (dvd_dvd_complex @ A @ C)))))). % dvd_add_right_iff
thf(fact_158_dvd__add__right__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) = (dvd_dvd_nat @ A @ C)))))). % dvd_add_right_iff
thf(fact_159_dvd__add__left__iff, axiom,
    ((![A : complex, C : complex, B : complex]: ((dvd_dvd_complex @ A @ C) => ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ C)) = (dvd_dvd_complex @ A @ B)))))). % dvd_add_left_iff
thf(fact_160_dvd__add__left__iff, axiom,
    ((![A : nat, C : nat, B : nat]: ((dvd_dvd_nat @ A @ C) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) = (dvd_dvd_nat @ A @ B)))))). % dvd_add_left_iff
thf(fact_161_dvd__add, axiom,
    ((![A : complex, B : complex, C : complex]: ((dvd_dvd_complex @ A @ B) => ((dvd_dvd_complex @ A @ C) => (dvd_dvd_complex @ A @ (plus_plus_complex @ B @ C))))))). % dvd_add
thf(fact_162_dvd__add, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C))))))). % dvd_add
thf(fact_163_dvd__unit__imp__unit, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)))))). % dvd_unit_imp_unit
thf(fact_164_unit__imp__dvd, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ B @ A))))). % unit_imp_dvd
thf(fact_165_one__dvd, axiom,
    ((![A : real]: (dvd_dvd_real @ one_one_real @ A)))). % one_dvd
thf(fact_166_one__dvd, axiom,
    ((![A : complex]: (dvd_dvd_complex @ one_one_complex @ A)))). % one_dvd
thf(fact_167_one__dvd, axiom,
    ((![A : nat]: (dvd_dvd_nat @ one_one_nat @ A)))). % one_dvd
thf(fact_168_div__div__div__same, axiom,
    ((![D : nat, B : nat, A : nat]: ((dvd_dvd_nat @ D @ B) => ((dvd_dvd_nat @ B @ A) => ((divide_divide_nat @ (divide_divide_nat @ A @ D) @ (divide_divide_nat @ B @ D)) = (divide_divide_nat @ A @ B))))))). % div_div_div_same
thf(fact_169_dvd__div__eq__cancel, axiom,
    ((![A : nat, C : nat, B : nat]: (((divide_divide_nat @ A @ C) = (divide_divide_nat @ B @ C)) => ((dvd_dvd_nat @ C @ A) => ((dvd_dvd_nat @ C @ B) => (A = B))))))). % dvd_div_eq_cancel
thf(fact_170_dvd__div__eq__cancel, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) => ((dvd_dvd_complex @ C @ A) => ((dvd_dvd_complex @ C @ B) => (A = B))))))). % dvd_div_eq_cancel
thf(fact_171_dvd__div__eq__iff, axiom,
    ((![C : nat, A : nat, B : nat]: ((dvd_dvd_nat @ C @ A) => ((dvd_dvd_nat @ C @ B) => (((divide_divide_nat @ A @ C) = (divide_divide_nat @ B @ C)) = (A = B))))))). % dvd_div_eq_iff
thf(fact_172_dvd__div__eq__iff, axiom,
    ((![C : complex, A : complex, B : complex]: ((dvd_dvd_complex @ C @ A) => ((dvd_dvd_complex @ C @ B) => (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (A = B))))))). % dvd_div_eq_iff
thf(fact_173_dvd__power__same, axiom,
    ((![X3 : complex, Y2 : complex, N : nat]: ((dvd_dvd_complex @ X3 @ Y2) => (dvd_dvd_complex @ (power_power_complex @ X3 @ N) @ (power_power_complex @ Y2 @ N)))))). % dvd_power_same
thf(fact_174_dvd__power__same, axiom,
    ((![X3 : nat, Y2 : nat, N : nat]: ((dvd_dvd_nat @ X3 @ Y2) => (dvd_dvd_nat @ (power_power_nat @ X3 @ N) @ (power_power_nat @ Y2 @ N)))))). % dvd_power_same
thf(fact_175_norm__minus__commute, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (minus_minus_complex @ A @ B)) = (real_V638595069omplex @ (minus_minus_complex @ B @ A)))))). % norm_minus_commute
thf(fact_176_norm__minus__commute, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (minus_minus_real @ A @ B)) = (real_V646646907m_real @ (minus_minus_real @ B @ A)))))). % norm_minus_commute
thf(fact_177_one__power2, axiom,
    (((power_power_real @ one_one_real @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real))). % one_power2
thf(fact_178_one__power2, axiom,
    (((power_power_complex @ one_one_complex @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex))). % one_power2
thf(fact_179_one__power2, axiom,
    (((power_power_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat))). % one_power2
thf(fact_180_zero__less__two, axiom,
    ((ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ one_one_real)))). % zero_less_two
thf(fact_181_zero__less__two, axiom,
    ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))). % zero_less_two
thf(fact_182_power__strict__decreasing, axiom,
    ((![N : nat, N3 : nat, A : real]: ((ord_less_nat @ N @ N3) => ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => (ord_less_real @ (power_power_real @ A @ N3) @ (power_power_real @ A @ N)))))))). % power_strict_decreasing
thf(fact_183_power__strict__decreasing, axiom,
    ((![N : nat, N3 : nat, A : nat]: ((ord_less_nat @ N @ N3) => ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (power_power_nat @ A @ N3) @ (power_power_nat @ A @ N)))))))). % power_strict_decreasing
thf(fact_184_one__less__power, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_real @ one_one_real @ (power_power_real @ A @ N))))))). % one_less_power
thf(fact_185_one__less__power, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ one_one_nat @ (power_power_nat @ A @ N))))))). % one_less_power
thf(fact_186_power__eq__1__iff, axiom,
    ((![W : complex, N : nat]: (((power_power_complex @ W @ N) = one_one_complex) => (((real_V638595069omplex @ W) = one_one_real) | (N = zero_zero_nat)))))). % power_eq_1_iff
thf(fact_187_power__eq__1__iff, axiom,
    ((![W : real, N : nat]: (((power_power_real @ W @ N) = one_one_real) => (((real_V646646907m_real @ W) = one_one_real) | (N = zero_zero_nat)))))). % power_eq_1_iff
thf(fact_188_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) => ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_real @ Y2 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_189_linordered__semidom__class_Oadd__diff__inverse, axiom,
    ((![A : real, B : real]: ((~ ((ord_less_real @ A @ B))) => ((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A))))). % linordered_semidom_class.add_diff_inverse
thf(fact_190_linordered__semidom__class_Oadd__diff__inverse, axiom,
    ((![A : nat, B : nat]: ((~ ((ord_less_nat @ A @ B))) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A))))). % linordered_semidom_class.add_diff_inverse
thf(fact_191_dvd__div__unit__iff, axiom,
    ((![B : nat, A : nat, C : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => ((dvd_dvd_nat @ A @ (divide_divide_nat @ C @ B)) = (dvd_dvd_nat @ A @ C)))))). % dvd_div_unit_iff
thf(fact_192_div__unit__dvd__iff, axiom,
    ((![B : nat, A : nat, C : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => ((dvd_dvd_nat @ (divide_divide_nat @ A @ B) @ C) = (dvd_dvd_nat @ A @ C)))))). % div_unit_dvd_iff
thf(fact_193_unit__div__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((divide_divide_nat @ B @ A) = (divide_divide_nat @ C @ A)) = (B = C)))))). % unit_div_cancel
thf(fact_194_div__power, axiom,
    ((![B : nat, A : nat, N : nat]: ((dvd_dvd_nat @ B @ A) => ((power_power_nat @ (divide_divide_nat @ A @ B) @ N) = (divide_divide_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N))))))). % div_power
thf(fact_195_square__norm__one, axiom,
    ((![X3 : complex]: (((power_power_complex @ X3 @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex) => ((real_V638595069omplex @ X3) = one_one_real))))). % square_norm_one
thf(fact_196_square__norm__one, axiom,
    ((![X3 : real]: (((power_power_real @ X3 @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real) => ((real_V646646907m_real @ X3) = one_one_real))))). % square_norm_one
thf(fact_197_unimodular__reduce__norm, axiom,
    ((![Z3 : complex]: (((real_V638595069omplex @ Z3) = one_one_real) => ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ Z3 @ one_one_complex)) @ one_one_real) | ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Z3 @ one_one_complex)) @ one_one_real) | ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ Z3 @ imaginary_unit)) @ one_one_real) | (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Z3 @ imaginary_unit)) @ one_one_real)))))))). % unimodular_reduce_norm
thf(fact_198_power__divide, axiom,
    ((![A : complex, B : complex, N : nat]: ((power_power_complex @ (divide1210191872omplex @ A @ B) @ N) = (divide1210191872omplex @ (power_power_complex @ A @ N) @ (power_power_complex @ B @ N)))))). % power_divide
thf(fact_199_norm__divide, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_divide
thf(fact_200_norm__divide, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_divide
thf(fact_201_norm__power, axiom,
    ((![X3 : complex, N : nat]: ((real_V638595069omplex @ (power_power_complex @ X3 @ N)) = (power_power_real @ (real_V638595069omplex @ X3) @ N))))). % norm_power
thf(fact_202_norm__power, axiom,
    ((![X3 : real, N : nat]: ((real_V646646907m_real @ (power_power_real @ X3 @ N)) = (power_power_real @ (real_V646646907m_real @ X3) @ N))))). % norm_power
thf(fact_203_add__mono1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ one_one_real) @ (plus_plus_real @ B @ one_one_real)))))). % add_mono1
thf(fact_204_add__mono1, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ one_one_nat) @ (plus_plus_nat @ B @ one_one_nat)))))). % add_mono1
thf(fact_205_less__add__one, axiom,
    ((![A : real]: (ord_less_real @ A @ (plus_plus_real @ A @ one_one_real))))). % less_add_one
thf(fact_206_less__add__one, axiom,
    ((![A : nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat))))). % less_add_one
thf(fact_207_power__strict__increasing, axiom,
    ((![N : nat, N3 : nat, A : real]: ((ord_less_nat @ N @ N3) => ((ord_less_real @ one_one_real @ A) => (ord_less_real @ (power_power_real @ A @ N) @ (power_power_real @ A @ N3))))))). % power_strict_increasing
thf(fact_208_power__strict__increasing, axiom,
    ((![N : nat, N3 : nat, A : nat]: ((ord_less_nat @ N @ N3) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ A @ N3))))))). % power_strict_increasing
thf(fact_209_power__less__imp__less__exp, axiom,
    ((![A : real, M : nat, N : nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ (power_power_real @ A @ M) @ (power_power_real @ A @ N)) => (ord_less_nat @ M @ N)))))). % power_less_imp_less_exp
thf(fact_210_power__less__imp__less__exp, axiom,
    ((![A : nat, M : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ M) @ (power_power_nat @ A @ N)) => (ord_less_nat @ M @ N)))))). % power_less_imp_less_exp
thf(fact_211_power__one__over, axiom,
    ((![A : real, N : nat]: ((power_power_real @ (divide_divide_real @ one_one_real @ A) @ N) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ N)))))). % power_one_over
thf(fact_212_power__one__over, axiom,
    ((![A : complex, N : nat]: ((power_power_complex @ (divide1210191872omplex @ one_one_complex @ A) @ N) = (divide1210191872omplex @ one_one_complex @ (power_power_complex @ A @ N)))))). % power_one_over
thf(fact_213_norm__triangle__lt, axiom,
    ((![X3 : complex, Y2 : complex, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_214_norm__triangle__lt, axiom,
    ((![X3 : real, Y2 : real, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_215_norm__add__less, axiom,
    ((![X3 : complex, R : real, Y2 : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X3) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y2) @ S2) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ (plus_plus_real @ R @ S2))))))). % norm_add_less
thf(fact_216_norm__add__less, axiom,
    ((![X3 : real, R : real, Y2 : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X3) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S2) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ (plus_plus_real @ R @ S2))))))). % norm_add_less
thf(fact_217_one__div__two__eq__zero, axiom,
    (((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % one_div_two_eq_zero
thf(fact_218_one__add__one, axiom,
    (((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one))))). % one_add_one
thf(fact_219_one__add__one, axiom,
    (((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % one_add_one
thf(fact_220_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_221_pow__divides__pow__iff, axiom,
    ((![N : nat, A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((dvd_dvd_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N)) = (dvd_dvd_nat @ A @ B)))))). % pow_divides_pow_iff
thf(fact_222_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_223_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_complex @ one_one_complex @ (numera632737353omplex @ N)) = (numera632737353omplex @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_224_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_225_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_real @ (numeral_numeral_real @ N) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_226_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_complex @ (numera632737353omplex @ N) @ one_one_complex) = (numera632737353omplex @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_227_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_nat @ (numeral_numeral_nat @ N) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_228_one__less__numeral__iff, axiom,
    ((![N : num]: ((ord_less_real @ one_one_real @ (numeral_numeral_real @ N)) = (ord_less_num @ one @ N))))). % one_less_numeral_iff
thf(fact_229_one__less__numeral__iff, axiom,
    ((![N : num]: ((ord_less_nat @ one_one_nat @ (numeral_numeral_nat @ N)) = (ord_less_num @ one @ N))))). % one_less_numeral_iff
thf(fact_230_zero__less__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_divide_1_iff
thf(fact_231_less__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)))))). % less_divide_eq_1_pos
thf(fact_232_less__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)))))). % less_divide_eq_1_neg
thf(fact_233_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[V : complex]: (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ (power_power_complex @ V @ na))) @ one_one_real)))).
