% 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_201__5369552_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:07.062

% Could-be-implicit typings (5)
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).
thf(ty_n_t__Int__Oint, type,
    int : $tType).

% Explicit typings (48)
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__Int__Oint, type,
    minus_minus_int : int > int > int).
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__Int__Oint, type,
    one_one_int : int).
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__Int__Oint, type,
    plus_plus_int : int > int > int).
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_Otimes__class_Otimes_001t__Int__Oint, type,
    times_times_int : int > int > int).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum, type,
    times_times_num : num > num > num).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint, type,
    zero_zero_int : int).
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__Int__Oint, type,
    numeral_numeral_int : num > int).
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__Int__Oint, type,
    ord_less_int : int > int > $o).
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__Int__Oint, type,
    power_power_int : int > nat > int).
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_Oof__real_001t__Complex__Ocomplex, type,
    real_V306493662omplex : real > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint, type,
    divide_divide_int : int > int > int).
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__Int__Oint, type,
    dvd_dvd_int : int > int > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_v_b, type,
    b : complex).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).

% Relevant facts (249)
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_b, axiom,
    ((~ ((b = zero_zero_complex))))). % b
thf(fact_2_n, axiom,
    ((~ ((na = zero_zero_nat))))). % n
thf(fact_3_th0, axiom,
    (((real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) = one_one_real))). % th0
thf(fact_4__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_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_unimodular__reduce__norm, axiom,
    ((![Z2 : complex]: (((real_V638595069omplex @ Z2) = one_one_real) => ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ Z2 @ one_one_complex)) @ one_one_real) | ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Z2 @ one_one_complex)) @ one_one_real) | ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ Z2 @ imaginary_unit)) @ one_one_real) | (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Z2 @ imaginary_unit)) @ one_one_real)))))))). % unimodular_reduce_norm
thf(fact_8_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_9_even__succ__div__2, axiom,
    ((![A : int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((divide_divide_int @ (plus_plus_int @ one_one_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))))). % even_succ_div_2
thf(fact_10_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_11_odd__succ__div__two, axiom,
    ((![A : int]: ((~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) => ((divide_divide_int @ (plus_plus_int @ A @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (plus_plus_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))))). % odd_succ_div_two
thf(fact_12_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_13_even__succ__div__two, axiom,
    ((![A : int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((divide_divide_int @ (plus_plus_int @ A @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))))). % even_succ_div_two
thf(fact_14_even__diff, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ A @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B)))))). % even_diff
thf(fact_15_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_16_even__plus__one__iff, axiom,
    ((![A : int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ one_one_int)) = (~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))))). % even_plus_one_iff
thf(fact_17_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_18_odd__add, axiom,
    ((![A : int, B : int]: ((~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B)))) = (~ (((~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) = (~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))))))). % odd_add
thf(fact_19_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_20_even__add, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))). % even_add
thf(fact_21_one__add__one, axiom,
    (((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one))))). % one_add_one
thf(fact_22_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_23_one__add__one, axiom,
    (((plus_plus_int @ one_one_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one))))). % one_add_one
thf(fact_24_one__add__one, axiom,
    (((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % one_add_one
thf(fact_25_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_26_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_27_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_int @ (numeral_numeral_int @ N) @ one_one_int) = (numeral_numeral_int @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_28_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_29_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_30_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_31_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ N)) = (numeral_numeral_int @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_32_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_33_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_34_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_35_one__less__numeral__iff, axiom,
    ((![N : num]: ((ord_less_int @ one_one_int @ (numeral_numeral_int @ N)) = (ord_less_num @ one @ N))))). % one_less_numeral_iff
thf(fact_36_norm__ii, axiom,
    (((real_V638595069omplex @ imaginary_unit) = one_one_real))). % norm_ii
thf(fact_37_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_38_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_39_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_40_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_41_bits__div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % bits_div_by_0
thf(fact_42_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_43_bits__div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % bits_div_0
thf(fact_44_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_45_bits__div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % bits_div_by_1
thf(fact_46_diff__numeral__special_I9_J, axiom,
    (((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real))). % diff_numeral_special(9)
thf(fact_47_diff__numeral__special_I9_J, axiom,
    (((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex))). % diff_numeral_special(9)
thf(fact_48_diff__numeral__special_I9_J, axiom,
    (((minus_minus_int @ one_one_int @ one_one_int) = zero_zero_int))). % diff_numeral_special(9)
thf(fact_49_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_real = (numeral_numeral_real @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_50_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_51_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_int = (numeral_numeral_int @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_52_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_53_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_real @ N) = one_one_real) = (N = one))))). % numeral_eq_one_iff
thf(fact_54_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_55_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_int @ N) = one_one_int) = (N = one))))). % numeral_eq_one_iff
thf(fact_56_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_57_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_58_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N)) = (numeral_numeral_int @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_59_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_complex @ (numera632737353omplex @ M) @ (numera632737353omplex @ N)) = (numera632737353omplex @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_60_add__numeral__left, axiom,
    ((![V : num, W : num, Z2 : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ (numeral_numeral_nat @ W) @ Z2)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ V @ W)) @ Z2))))). % add_numeral_left
thf(fact_61_add__numeral__left, axiom,
    ((![V : num, W : num, Z2 : int]: ((plus_plus_int @ (numeral_numeral_int @ V) @ (plus_plus_int @ (numeral_numeral_int @ W) @ Z2)) = (plus_plus_int @ (numeral_numeral_int @ (plus_plus_num @ V @ W)) @ Z2))))). % add_numeral_left
thf(fact_62_add__numeral__left, axiom,
    ((![V : num, W : num, Z2 : complex]: ((plus_plus_complex @ (numera632737353omplex @ V) @ (plus_plus_complex @ (numera632737353omplex @ W) @ Z2)) = (plus_plus_complex @ (numera632737353omplex @ (plus_plus_num @ V @ W)) @ Z2))))). % add_numeral_left
thf(fact_63_numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (ord_less_num @ M @ N))))). % numeral_less_iff
thf(fact_64_numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (ord_less_num @ M @ N))))). % numeral_less_iff
thf(fact_65_numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N)) = (ord_less_num @ M @ N))))). % numeral_less_iff
thf(fact_66_even__diff__nat, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ M @ N)) = (((ord_less_nat @ M @ N)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ M @ N)))))))). % even_diff_nat
thf(fact_67_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_68_bits__1__div__2, axiom,
    (((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))). % bits_1_div_2
thf(fact_69_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_70_even__power, axiom,
    ((![A : int, N : nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (power_power_int @ A @ N)) = (((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % even_power
thf(fact_71_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_72_power__less__zero__eq__numeral, axiom,
    ((![A : int, W : num]: ((ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ W)) @ zero_zero_int) = (((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ W))))) & ((ord_less_int @ A @ zero_zero_int))))))). % power_less_zero_eq_numeral
thf(fact_73_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_74_power__less__zero__eq, axiom,
    ((![A : int, N : nat]: ((ord_less_int @ (power_power_int @ A @ N) @ zero_zero_int) = (((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)))) & ((ord_less_int @ A @ zero_zero_int))))))). % power_less_zero_eq
thf(fact_75_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_76_even__mask__iff, axiom,
    ((![N : nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ N) @ one_one_int)) = (N = zero_zero_nat))))). % even_mask_iff
thf(fact_77_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_78_zero__less__power__eq__numeral, axiom,
    ((![A : int, W : num]: ((ord_less_int @ zero_zero_int @ (power_power_int @ 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_int)))))) | ((((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ W))))) & ((ord_less_int @ zero_zero_int @ A))))))))))). % zero_less_power_eq_numeral
thf(fact_79_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_80_even__succ__div__exp, axiom,
    ((![A : int, N : nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((ord_less_nat @ zero_zero_nat @ N) => ((divide_divide_int @ (plus_plus_int @ one_one_int @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ N)) = (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ N)))))))). % even_succ_div_exp
thf(fact_81_IH, axiom,
    ((![M2 : nat]: ((ord_less_nat @ M2 @ na) => ((~ ((M2 = zero_zero_nat))) => (?[Z3 : complex]: (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ one_one_complex @ (times_times_complex @ b @ (power_power_complex @ Z3 @ M2)))) @ one_one_real))))))). % IH
thf(fact_82_even__diff__iff, axiom,
    ((![K : int, L : int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ K @ L)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ K @ L)))))). % even_diff_iff
thf(fact_83_add__One__commute, axiom,
    ((![N : num]: ((plus_plus_num @ one @ N) = (plus_plus_num @ N @ one))))). % add_One_commute
thf(fact_84_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_85_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_86_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_numeral_extra(3)
thf(fact_87_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_88_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N))))))). % zero_neq_numeral
thf(fact_89_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N))))))). % zero_neq_numeral
thf(fact_90_complex__i__not__numeral, axiom,
    ((![W : num]: (~ ((imaginary_unit = (numera632737353omplex @ W))))))). % complex_i_not_numeral
thf(fact_91_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_92_complex__i__not__zero, axiom,
    ((~ ((imaginary_unit = zero_zero_complex))))). % complex_i_not_zero
thf(fact_93_nat__1__add__1, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % nat_1_add_1
thf(fact_94_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_95_less__numeral__extra_I1_J, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % less_numeral_extra(1)
thf(fact_96_less__numeral__extra_I1_J, axiom,
    ((ord_less_int @ zero_zero_int @ one_one_int))). % less_numeral_extra(1)
thf(fact_97_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ zero_zero_real)))))). % not_numeral_less_zero
thf(fact_98_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ zero_zero_nat)))))). % not_numeral_less_zero
thf(fact_99_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N) @ zero_zero_int)))))). % not_numeral_less_zero
thf(fact_100_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ N))))). % zero_less_numeral
thf(fact_101_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ N))))). % zero_less_numeral
thf(fact_102_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ N))))). % zero_less_numeral
thf(fact_103_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_104_exp__not__zero__imp__exp__diff__not__zero, axiom,
    ((![N : nat, M : nat]: ((~ (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) = zero_zero_nat))) => (~ (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ N @ M)) = zero_zero_nat))))))). % exp_not_zero_imp_exp_diff_not_zero
thf(fact_105_exp__not__zero__imp__exp__diff__not__zero, axiom,
    ((![N : nat, M : nat]: ((~ (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ N) = zero_zero_int))) => (~ (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ N @ M)) = zero_zero_int))))))). % exp_not_zero_imp_exp_diff_not_zero
thf(fact_106_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_107_exp__add__not__zero__imp__right, axiom,
    ((![M : nat, N : nat]: ((~ (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ M @ N)) = zero_zero_int))) => (~ (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ N) = zero_zero_int))))))). % exp_add_not_zero_imp_right
thf(fact_108_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_109_exp__add__not__zero__imp__left, axiom,
    ((![M : nat, N : nat]: ((~ (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ M @ N)) = zero_zero_int))) => (~ (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ M) = zero_zero_int))))))). % exp_add_not_zero_imp_left
thf(fact_110_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_111_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_112_zero__less__power__eq, axiom,
    ((![A : int, N : nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ N)) = (((N = zero_zero_nat)) | ((((((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)) & ((~ ((A = zero_zero_int)))))) | ((((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)))) & ((ord_less_int @ zero_zero_int @ A))))))))))). % zero_less_power_eq
thf(fact_113_even__zero, axiom,
    ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ zero_zero_nat))). % even_zero
thf(fact_114_even__zero, axiom,
    ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ zero_zero_int))). % even_zero
thf(fact_115_is__num__normalize_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % is_num_normalize(1)
thf(fact_116_is__num__normalize_I1_J, axiom,
    ((![A : int, B : int, C : int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C)))))). % is_num_normalize(1)
thf(fact_117_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_118_div__exp__eq, axiom,
    ((![A : int, M : nat, N : nat]: ((divide_divide_int @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ M)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ N)) = (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ M @ N))))))). % div_exp_eq
thf(fact_119_half__gt__zero__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) = (ord_less_real @ zero_zero_real @ A))))). % half_gt_zero_iff
thf(fact_120_half__gt__zero, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))))))). % half_gt_zero
thf(fact_121_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_122_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ one_one_nat))))). % less_numeral_extra(4)
thf(fact_123_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_int @ one_one_int @ one_one_int))))). % less_numeral_extra(4)
thf(fact_124_complex__i__not__one, axiom,
    ((~ ((imaginary_unit = one_one_complex))))). % complex_i_not_one
thf(fact_125_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ one_one_real)))))). % not_numeral_less_one
thf(fact_126_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ one_one_nat)))))). % not_numeral_less_one
thf(fact_127_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N) @ one_one_int)))))). % not_numeral_less_one
thf(fact_128_one__plus__numeral__commute, axiom,
    ((![X3 : num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ X3)) = (plus_plus_real @ (numeral_numeral_real @ X3) @ one_one_real))))). % one_plus_numeral_commute
thf(fact_129_one__plus__numeral__commute, axiom,
    ((![X3 : num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ X3)) = (plus_plus_nat @ (numeral_numeral_nat @ X3) @ one_one_nat))))). % one_plus_numeral_commute
thf(fact_130_one__plus__numeral__commute, axiom,
    ((![X3 : num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ X3)) = (plus_plus_int @ (numeral_numeral_int @ X3) @ one_one_int))))). % one_plus_numeral_commute
thf(fact_131_one__plus__numeral__commute, axiom,
    ((![X3 : num]: ((plus_plus_complex @ one_one_complex @ (numera632737353omplex @ X3)) = (plus_plus_complex @ (numera632737353omplex @ X3) @ one_one_complex))))). % one_plus_numeral_commute
thf(fact_132_numeral__Bit0, axiom,
    ((![N : num]: ((numeral_numeral_nat @ (bit0 @ N)) = (plus_plus_nat @ (numeral_numeral_nat @ N) @ (numeral_numeral_nat @ N)))))). % numeral_Bit0
thf(fact_133_numeral__Bit0, axiom,
    ((![N : num]: ((numeral_numeral_int @ (bit0 @ N)) = (plus_plus_int @ (numeral_numeral_int @ N) @ (numeral_numeral_int @ N)))))). % numeral_Bit0
thf(fact_134_numeral__Bit0, axiom,
    ((![N : num]: ((numera632737353omplex @ (bit0 @ N)) = (plus_plus_complex @ (numera632737353omplex @ N) @ (numera632737353omplex @ N)))))). % numeral_Bit0
thf(fact_135_numeral__One, axiom,
    (((numeral_numeral_real @ one) = one_one_real))). % numeral_One
thf(fact_136_numeral__One, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numeral_One
thf(fact_137_numeral__One, axiom,
    (((numeral_numeral_int @ one) = one_one_int))). % numeral_One
thf(fact_138_numeral__One, axiom,
    (((numera632737353omplex @ one) = one_one_complex))). % numeral_One
thf(fact_139_divide__numeral__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ (numera632737353omplex @ one)) = A)))). % divide_numeral_1
thf(fact_140_even__numeral, axiom,
    ((![N : num]: (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit0 @ N)))))). % even_numeral
thf(fact_141_even__numeral, axiom,
    ((![N : num]: (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit0 @ N)))))). % even_numeral
thf(fact_142_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_143_odd__even__add, axiom,
    ((![A : int, B : int]: ((~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) => ((~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) => (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))))). % odd_even_add
thf(fact_144_odd__one, axiom,
    ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ one_one_nat))))). % odd_one
thf(fact_145_odd__one, axiom,
    ((~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ one_one_int))))). % odd_one
thf(fact_146_bit__eq__rec, axiom,
    (((^[Y2 : nat]: (^[Z4 : nat]: (Y2 = 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_147_bit__eq__rec, axiom,
    (((^[Y2 : int]: (^[Z4 : int]: (Y2 = Z4))) = (^[A2 : int]: (^[B2 : int]: ((((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A2) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B2))) & (((divide_divide_int @ A2 @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ B2 @ (numeral_numeral_int @ (bit0 @ one))))))))))). % bit_eq_rec
thf(fact_148_sum__power2__eq__zero__iff, axiom,
    ((![X3 : int, Y3 : int]: (((plus_plus_int @ (power_power_int @ X3 @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ Y3 @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_int) = (((X3 = zero_zero_int)) & ((Y3 = zero_zero_int))))))). % sum_power2_eq_zero_iff
thf(fact_149_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_150_zero__less__power2, axiom,
    ((![A : int]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (~ ((A = zero_zero_int))))))). % zero_less_power2
thf(fact_151_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_152_one__div__two__eq__zero, axiom,
    (((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))). % one_div_two_eq_zero
thf(fact_153_zero__eq__power2, axiom,
    ((![A : int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int) = (A = zero_zero_int))))). % zero_eq_power2
thf(fact_154_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_155_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_156_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_157_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_158_power__strict__decreasing__iff, axiom,
    ((![B : int, M : nat, N : nat]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_int @ B @ one_one_int) => ((ord_less_int @ (power_power_int @ B @ M) @ (power_power_int @ B @ N)) = (ord_less_nat @ N @ M))))))). % power_strict_decreasing_iff
thf(fact_159_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_160_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_161_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_162_divide__less__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)))))). % divide_less_eq_1_pos
thf(fact_163_divide__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % divide_eq_0_iff
thf(fact_164_divide__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((divide1210191872omplex @ C @ A) = (divide1210191872omplex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_left
thf(fact_165_divide__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_right
thf(fact_166_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_167_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z2 : nat]: ((times_times_nat @ (numeral_numeral_nat @ V) @ (times_times_nat @ (numeral_numeral_nat @ W) @ Z2)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ V @ W)) @ Z2))))). % mult_numeral_left_semiring_numeral
thf(fact_168_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z2 : int]: ((times_times_int @ (numeral_numeral_int @ V) @ (times_times_int @ (numeral_numeral_int @ W) @ Z2)) = (times_times_int @ (numeral_numeral_int @ (times_times_num @ V @ W)) @ Z2))))). % mult_numeral_left_semiring_numeral
thf(fact_169_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z2 : complex]: ((times_times_complex @ (numera632737353omplex @ V) @ (times_times_complex @ (numera632737353omplex @ W) @ Z2)) = (times_times_complex @ (numera632737353omplex @ (times_times_num @ V @ W)) @ Z2))))). % mult_numeral_left_semiring_numeral
thf(fact_170_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_171_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N)) = (numeral_numeral_int @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_172_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_complex @ (numera632737353omplex @ M) @ (numera632737353omplex @ N)) = (numera632737353omplex @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_173_times__divide__eq__left, axiom,
    ((![B : complex, C : complex, A : complex]: ((times_times_complex @ (divide1210191872omplex @ B @ C) @ A) = (divide1210191872omplex @ (times_times_complex @ B @ A) @ C))))). % times_divide_eq_left
thf(fact_174_divide__divide__eq__left, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ A @ B) @ C) = (divide1210191872omplex @ A @ (times_times_complex @ B @ C)))))). % divide_divide_eq_left
thf(fact_175_divide__divide__eq__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ A @ (divide1210191872omplex @ B @ C)) = (divide1210191872omplex @ (times_times_complex @ A @ C) @ B))))). % divide_divide_eq_right
thf(fact_176_times__divide__eq__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ A @ (divide1210191872omplex @ B @ C)) = (divide1210191872omplex @ (times_times_complex @ A @ B) @ C))))). % times_divide_eq_right
thf(fact_177_power__one, axiom,
    ((![N : nat]: ((power_power_real @ one_one_real @ N) = one_one_real)))). % power_one
thf(fact_178_power__one, axiom,
    ((![N : nat]: ((power_power_int @ one_one_int @ N) = one_one_int)))). % power_one
thf(fact_179_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_180_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_181_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_182_div__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => ((divide_divide_nat @ M @ N) = zero_zero_nat))))). % div_less
thf(fact_183_power__one__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_184_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_185_sum__squares__eq__zero__iff, axiom,
    ((![X3 : int, Y3 : int]: (((plus_plus_int @ (times_times_int @ X3 @ X3) @ (times_times_int @ Y3 @ Y3)) = zero_zero_int) = (((X3 = zero_zero_int)) & ((Y3 = zero_zero_int))))))). % sum_squares_eq_zero_iff
thf(fact_186_div__mult__mult1__if, axiom,
    ((![C : nat, A : nat, B : nat]: (((C = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = zero_zero_nat)) & ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (divide_divide_nat @ A @ B))))))). % div_mult_mult1_if
thf(fact_187_div__mult__mult1__if, axiom,
    ((![C : int, A : int, B : int]: (((C = zero_zero_int) => ((divide_divide_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = zero_zero_int)) & ((~ ((C = zero_zero_int))) => ((divide_divide_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (divide_divide_int @ A @ B))))))). % div_mult_mult1_if
thf(fact_188_div__mult__mult2, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) = (divide_divide_nat @ A @ B)))))). % div_mult_mult2
thf(fact_189_div__mult__mult2, axiom,
    ((![C : int, A : int, B : int]: ((~ ((C = zero_zero_int))) => ((divide_divide_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)) = (divide_divide_int @ A @ B)))))). % div_mult_mult2
thf(fact_190_div__mult__mult1, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (divide_divide_nat @ A @ B)))))). % div_mult_mult1
thf(fact_191_div__mult__mult1, axiom,
    ((![C : int, A : int, B : int]: ((~ ((C = zero_zero_int))) => ((divide_divide_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (divide_divide_int @ A @ B)))))). % div_mult_mult1
thf(fact_192_nonzero__mult__divide__mult__cancel__right2, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right2
thf(fact_193_nonzero__mult__divide__mult__cancel__right, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right
thf(fact_194_nonzero__mult__divide__mult__cancel__left2, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ B @ C)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left2
thf(fact_195_nonzero__mult__divide__mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left
thf(fact_196_mult__divide__mult__cancel__left__if, axiom,
    ((![C : complex, A : complex, B : complex]: (((C = zero_zero_complex) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = zero_zero_complex)) & ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B))))))). % mult_divide_mult_cancel_left_if
thf(fact_197_divide__eq__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = one_one_real) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_198_divide__eq__1__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = one_one_complex) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_199_one__eq__divide__iff, axiom,
    ((![A : real, B : real]: ((one_one_real = (divide_divide_real @ A @ B)) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_200_one__eq__divide__iff, axiom,
    ((![A : complex, B : complex]: ((one_one_complex = (divide1210191872omplex @ A @ B)) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_201_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_202_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_203_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_204_divide__self__if, axiom,
    ((![A : complex]: (((A = zero_zero_complex) => ((divide1210191872omplex @ A @ A) = zero_zero_complex)) & ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex)))))). % divide_self_if
thf(fact_205_divide__eq__eq__1, axiom,
    ((![B : real, A : real]: (((divide_divide_real @ B @ A) = one_one_real) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % divide_eq_eq_1
thf(fact_206_eq__divide__eq__1, axiom,
    ((![B : real, A : real]: ((one_one_real = (divide_divide_real @ B @ A)) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % eq_divide_eq_1
thf(fact_207_one__divide__eq__0__iff, axiom,
    ((![A : real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % one_divide_eq_0_iff
thf(fact_208_zero__eq__1__divide__iff, axiom,
    ((![A : real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real))))). % zero_eq_1_divide_iff
thf(fact_209_distrib__left__numeral, axiom,
    ((![V : num, B : nat, C : nat]: ((times_times_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ V) @ B) @ (times_times_nat @ (numeral_numeral_nat @ V) @ C)))))). % distrib_left_numeral
thf(fact_210_distrib__left__numeral, axiom,
    ((![V : num, B : int, C : int]: ((times_times_int @ (numeral_numeral_int @ V) @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ V) @ B) @ (times_times_int @ (numeral_numeral_int @ V) @ C)))))). % distrib_left_numeral
thf(fact_211_distrib__left__numeral, axiom,
    ((![V : num, B : complex, C : complex]: ((times_times_complex @ (numera632737353omplex @ V) @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ (numera632737353omplex @ V) @ B) @ (times_times_complex @ (numera632737353omplex @ V) @ C)))))). % distrib_left_numeral
thf(fact_212_distrib__right__numeral, axiom,
    ((![A : nat, B : nat, V : num]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ V)) = (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ V)) @ (times_times_nat @ B @ (numeral_numeral_nat @ V))))))). % distrib_right_numeral
thf(fact_213_distrib__right__numeral, axiom,
    ((![A : int, B : int, V : num]: ((times_times_int @ (plus_plus_int @ A @ B) @ (numeral_numeral_int @ V)) = (plus_plus_int @ (times_times_int @ A @ (numeral_numeral_int @ V)) @ (times_times_int @ B @ (numeral_numeral_int @ V))))))). % distrib_right_numeral
thf(fact_214_distrib__right__numeral, axiom,
    ((![A : complex, B : complex, V : num]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ (numera632737353omplex @ V)) = (plus_plus_complex @ (times_times_complex @ A @ (numera632737353omplex @ V)) @ (times_times_complex @ B @ (numera632737353omplex @ V))))))). % distrib_right_numeral
thf(fact_215_left__diff__distrib__numeral, axiom,
    ((![A : int, B : int, V : num]: ((times_times_int @ (minus_minus_int @ A @ B) @ (numeral_numeral_int @ V)) = (minus_minus_int @ (times_times_int @ A @ (numeral_numeral_int @ V)) @ (times_times_int @ B @ (numeral_numeral_int @ V))))))). % left_diff_distrib_numeral
thf(fact_216_left__diff__distrib__numeral, axiom,
    ((![A : complex, B : complex, V : num]: ((times_times_complex @ (minus_minus_complex @ A @ B) @ (numera632737353omplex @ V)) = (minus_minus_complex @ (times_times_complex @ A @ (numera632737353omplex @ V)) @ (times_times_complex @ B @ (numera632737353omplex @ V))))))). % left_diff_distrib_numeral
thf(fact_217_right__diff__distrib__numeral, axiom,
    ((![V : num, B : int, C : int]: ((times_times_int @ (numeral_numeral_int @ V) @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ (numeral_numeral_int @ V) @ B) @ (times_times_int @ (numeral_numeral_int @ V) @ C)))))). % right_diff_distrib_numeral
thf(fact_218_right__diff__distrib__numeral, axiom,
    ((![V : num, B : complex, C : complex]: ((times_times_complex @ (numera632737353omplex @ V) @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (times_times_complex @ (numera632737353omplex @ V) @ B) @ (times_times_complex @ (numera632737353omplex @ V) @ C)))))). % right_diff_distrib_numeral
thf(fact_219_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_220_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_221_power__inject__exp, axiom,
    ((![A : int, M : nat, N : nat]: ((ord_less_int @ one_one_int @ A) => (((power_power_int @ A @ M) = (power_power_int @ A @ N)) = (M = N)))))). % power_inject_exp
thf(fact_222_power__zero__numeral, axiom,
    ((![K : num]: ((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ K)) = zero_zero_int)))). % power_zero_numeral
thf(fact_223_power__zero__numeral, axiom,
    ((![K : num]: ((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ K)) = zero_zero_complex)))). % power_zero_numeral
thf(fact_224_power__zero__numeral, axiom,
    ((![K : num]: ((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ K)) = zero_zero_nat)))). % power_zero_numeral
thf(fact_225_half__negative__int__iff, axiom,
    ((![K : int]: ((ord_less_int @ (divide_divide_int @ K @ (numeral_numeral_int @ (bit0 @ one))) @ zero_zero_int) = (ord_less_int @ K @ zero_zero_int))))). % half_negative_int_iff
thf(fact_226_divide__less__0__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % divide_less_0_1_iff
thf(fact_227_divide__less__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B)))))). % divide_less_eq_1_neg
thf(fact_228_div__mult__self1, axiom,
    ((![B : nat, A : nat, C : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ A @ (times_times_nat @ C @ B)) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self1
thf(fact_229_div__mult__self1, axiom,
    ((![B : int, A : int, C : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ A @ (times_times_int @ C @ B)) @ B) = (plus_plus_int @ C @ (divide_divide_int @ A @ B))))))). % div_mult_self1
thf(fact_230_div__mult__self2, axiom,
    ((![B : nat, A : nat, C : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ A @ (times_times_nat @ B @ C)) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self2
thf(fact_231_div__mult__self2, axiom,
    ((![B : int, A : int, C : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ A @ (times_times_int @ B @ C)) @ B) = (plus_plus_int @ C @ (divide_divide_int @ A @ B))))))). % div_mult_self2
thf(fact_232_div__mult__self3, axiom,
    ((![B : nat, C : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ C @ B) @ A) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self3
thf(fact_233_div__mult__self3, axiom,
    ((![B : int, C : int, A : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ (times_times_int @ C @ B) @ A) @ B) = (plus_plus_int @ C @ (divide_divide_int @ A @ B))))))). % div_mult_self3
thf(fact_234_div__mult__self4, axiom,
    ((![B : nat, C : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ A) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self4
thf(fact_235_div__mult__self4, axiom,
    ((![B : int, C : int, A : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ (times_times_int @ B @ C) @ A) @ B) = (plus_plus_int @ C @ (divide_divide_int @ A @ B))))))). % div_mult_self4
thf(fact_236_nonzero__divide__mult__cancel__left, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ B)))))). % nonzero_divide_mult_cancel_left
thf(fact_237_nonzero__divide__mult__cancel__left, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ (times_times_complex @ A @ B)) = (divide1210191872omplex @ one_one_complex @ B)))))). % nonzero_divide_mult_cancel_left
thf(fact_238_nonzero__divide__mult__cancel__right, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((divide_divide_real @ B @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ A)))))). % nonzero_divide_mult_cancel_right
thf(fact_239_nonzero__divide__mult__cancel__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ B @ (times_times_complex @ A @ B)) = (divide1210191872omplex @ one_one_complex @ A)))))). % nonzero_divide_mult_cancel_right
thf(fact_240_divide__eq__eq__numeral1_I1_J, axiom,
    ((![B : complex, W : num, A : complex]: (((divide1210191872omplex @ B @ (numera632737353omplex @ W)) = A) = (((((~ (((numera632737353omplex @ W) = zero_zero_complex)))) => ((B = (times_times_complex @ A @ (numera632737353omplex @ W)))))) & (((((numera632737353omplex @ W) = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % divide_eq_eq_numeral1(1)
thf(fact_241_eq__divide__eq__numeral1_I1_J, axiom,
    ((![A : complex, B : complex, W : num]: ((A = (divide1210191872omplex @ B @ (numera632737353omplex @ W))) = (((((~ (((numera632737353omplex @ W) = zero_zero_complex)))) => (((times_times_complex @ A @ (numera632737353omplex @ W)) = B)))) & (((((numera632737353omplex @ W) = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % eq_divide_eq_numeral1(1)
thf(fact_242_divide__less__eq__numeral1_I1_J, axiom,
    ((![B : real, W : num, A : real]: ((ord_less_real @ (divide_divide_real @ B @ (numeral_numeral_real @ W)) @ A) = (ord_less_real @ B @ (times_times_real @ A @ (numeral_numeral_real @ W))))))). % divide_less_eq_numeral1(1)
thf(fact_243_less__divide__eq__numeral1_I1_J, axiom,
    ((![A : real, B : real, W : num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ W))) = (ord_less_real @ (times_times_real @ A @ (numeral_numeral_real @ W)) @ B))))). % less_divide_eq_numeral1(1)
thf(fact_244_power__strict__increasing__iff, axiom,
    ((![B : real, X3 : nat, Y3 : nat]: ((ord_less_real @ one_one_real @ B) => ((ord_less_real @ (power_power_real @ B @ X3) @ (power_power_real @ B @ Y3)) = (ord_less_nat @ X3 @ Y3)))))). % power_strict_increasing_iff
thf(fact_245_power__strict__increasing__iff, axiom,
    ((![B : nat, X3 : nat, Y3 : nat]: ((ord_less_nat @ one_one_nat @ B) => ((ord_less_nat @ (power_power_nat @ B @ X3) @ (power_power_nat @ B @ Y3)) = (ord_less_nat @ X3 @ Y3)))))). % power_strict_increasing_iff
thf(fact_246_power__strict__increasing__iff, axiom,
    ((![B : int, X3 : nat, Y3 : nat]: ((ord_less_int @ one_one_int @ B) => ((ord_less_int @ (power_power_int @ B @ X3) @ (power_power_int @ B @ Y3)) = (ord_less_nat @ X3 @ Y3)))))). % power_strict_increasing_iff
thf(fact_247_add__self__div__2, axiom,
    ((![M : nat]: ((divide_divide_nat @ (plus_plus_nat @ M @ M) @ (numeral_numeral_nat @ (bit0 @ one))) = M)))). % add_self_div_2
thf(fact_248_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

% Conjectures (6)
thf(conj_0, hypothesis,
    ($true)).
thf(conj_1, hypothesis,
    ($true)).
thf(conj_2, hypothesis,
    ((~ ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ one_one_complex)) @ one_one_real))))).
thf(conj_3, hypothesis,
    ((~ ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ one_one_complex)) @ one_one_real))))).
thf(conj_4, hypothesis,
    ((~ ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ imaginary_unit)) @ one_one_real))))).
thf(conj_5, conjecture,
    ((?[V2 : complex]: (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ (power_power_complex @ V2 @ na))) @ one_one_real)))).
