% 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_206__5369586_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:14.020

% 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 (51)
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_Nat_OSuc, type,
    suc : nat > nat).
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__Complex__Ocomplex, type,
    dvd_dvd_complex : complex > complex > $o).
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_m____, type,
    m : nat).
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_th0, axiom,
    (((real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) = one_one_real))). % th0
thf(fact_3__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_4_assms_I2_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(2)
thf(fact_5_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_6_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_7_odd__two__times__div__two__succ, axiom,
    ((![A : int]: ((~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) => ((plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) @ one_one_int) = A))))). % odd_two_times_div_two_succ
thf(fact_8_odd__two__times__div__two__succ, axiom,
    ((![A : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) => ((plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_nat) = A))))). % odd_two_times_div_two_succ
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_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_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_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_13_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_14_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_15_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_16_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_17_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_18_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_19_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_20_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_21_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_22_even__mult__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ A @ B)) = (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))). % even_mult_iff
thf(fact_23_even__mult__iff, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (times_times_int @ A @ B)) = (((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) | ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))))). % even_mult_iff
thf(fact_24_one__add__one, axiom,
    (((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one))))). % one_add_one
thf(fact_25_one__add__one, axiom,
    (((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % one_add_one
thf(fact_26_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_27_one__add__one, axiom,
    (((plus_plus_int @ one_one_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one))))). % one_add_one
thf(fact_28_unit__mult__div__div, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((times_times_nat @ B @ (divide_divide_nat @ one_one_nat @ A)) = (divide_divide_nat @ B @ A)))))). % unit_mult_div_div
thf(fact_29_unit__mult__div__div, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ B @ (divide_divide_int @ one_one_int @ A)) = (divide_divide_int @ B @ A)))))). % unit_mult_div_div
thf(fact_30_unit__div__mult__self, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B))))). % unit_div_mult_self
thf(fact_31_unit__div__mult__self, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ (divide_divide_int @ B @ A) @ A) = B))))). % unit_div_mult_self
thf(fact_32_n, axiom,
    ((~ ((na = zero_zero_nat))))). % n
thf(fact_33_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_34_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_35_mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_right
thf(fact_36_mult__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_right
thf(fact_37_mult__cancel__right, axiom,
    ((![A : int, C : int, B : int]: (((times_times_int @ A @ C) = (times_times_int @ B @ C)) = (((C = zero_zero_int)) | ((A = B))))))). % mult_cancel_right
thf(fact_38_mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_left
thf(fact_39_mult__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_left
thf(fact_40_mult__cancel__left, axiom,
    ((![C : int, A : int, B : int]: (((times_times_int @ C @ A) = (times_times_int @ C @ B)) = (((C = zero_zero_int)) | ((A = B))))))). % mult_cancel_left
thf(fact_41_mult__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_42_mult__eq__0__iff, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = (((A = zero_zero_nat)) | ((B = zero_zero_nat))))))). % mult_eq_0_iff
thf(fact_43_mult__eq__0__iff, axiom,
    ((![A : int, B : int]: (((times_times_int @ A @ B) = zero_zero_int) = (((A = zero_zero_int)) | ((B = zero_zero_int))))))). % mult_eq_0_iff
thf(fact_44_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_45_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_46_mult__zero__right, axiom,
    ((![A : int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int)))). % mult_zero_right
thf(fact_47_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_48_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_49_mult__zero__left, axiom,
    ((![A : int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int)))). % mult_zero_left
thf(fact_50_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_51_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_52_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_53_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_54_bits__div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % bits_div_by_0
thf(fact_55_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_56_bits__div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % bits_div_0
thf(fact_57_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_58_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_59_div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % div_by_0
thf(fact_60_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_61_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_62_div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % div_0
thf(fact_63_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_64_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_65_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_66_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_67_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_68_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_69_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_70_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_71_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_72_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_73_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_74_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_75_dvd__0__left__iff, axiom,
    ((![A : int]: ((dvd_dvd_int @ zero_zero_int @ A) = (A = zero_zero_int))))). % dvd_0_left_iff
thf(fact_76_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_77_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_78_dvd__0__right, axiom,
    ((![A : int]: (dvd_dvd_int @ A @ zero_zero_int)))). % dvd_0_right
thf(fact_79_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_80_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_81_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_82_bits__div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % bits_div_by_1
thf(fact_83_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_84_div__by__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ one_one_complex) = A)))). % div_by_1
thf(fact_85_div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % div_by_1
thf(fact_86_div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % div_by_1
thf(fact_87_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_88_dvd__add__triv__right__iff, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ A)) = (dvd_dvd_int @ A @ B))))). % dvd_add_triv_right_iff
thf(fact_89_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_90_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_91_dvd__add__triv__left__iff, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ (plus_plus_int @ A @ B)) = (dvd_dvd_int @ A @ B))))). % dvd_add_triv_left_iff
thf(fact_92_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_93_num__double, axiom,
    ((![N : num]: ((times_times_num @ (bit0 @ one) @ N) = (bit0 @ N))))). % num_double
thf(fact_94_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_95_div__dvd__div, axiom,
    ((![A : int, B : int, C : int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ C) => ((dvd_dvd_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A)) = (dvd_dvd_int @ B @ C))))))). % div_dvd_div
thf(fact_96_mult__cancel__right2, axiom,
    ((![A : real, C : real]: (((times_times_real @ A @ C) = C) = (((C = zero_zero_real)) | ((A = one_one_real))))))). % mult_cancel_right2
thf(fact_97_mult__cancel__right2, axiom,
    ((![A : complex, C : complex]: (((times_times_complex @ A @ C) = C) = (((C = zero_zero_complex)) | ((A = one_one_complex))))))). % mult_cancel_right2
thf(fact_98_mult__cancel__right2, axiom,
    ((![A : int, C : int]: (((times_times_int @ A @ C) = C) = (((C = zero_zero_int)) | ((A = one_one_int))))))). % mult_cancel_right2
thf(fact_99_mult__cancel__right1, axiom,
    ((![C : real, B : real]: ((C = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((B = one_one_real))))))). % mult_cancel_right1
thf(fact_100_mult__cancel__right1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_right1
thf(fact_101_mult__cancel__right1, axiom,
    ((![C : int, B : int]: ((C = (times_times_int @ B @ C)) = (((C = zero_zero_int)) | ((B = one_one_int))))))). % mult_cancel_right1
thf(fact_102_mult__cancel__left2, axiom,
    ((![C : real, A : real]: (((times_times_real @ C @ A) = C) = (((C = zero_zero_real)) | ((A = one_one_real))))))). % mult_cancel_left2
thf(fact_103_mult__cancel__left2, axiom,
    ((![C : complex, A : complex]: (((times_times_complex @ C @ A) = C) = (((C = zero_zero_complex)) | ((A = one_one_complex))))))). % mult_cancel_left2
thf(fact_104_mult__cancel__left2, axiom,
    ((![C : int, A : int]: (((times_times_int @ C @ A) = C) = (((C = zero_zero_int)) | ((A = one_one_int))))))). % mult_cancel_left2
thf(fact_105_mult__cancel__left1, axiom,
    ((![C : real, B : real]: ((C = (times_times_real @ C @ B)) = (((C = zero_zero_real)) | ((B = one_one_real))))))). % mult_cancel_left1
thf(fact_106_mult__cancel__left1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_left1
thf(fact_107_mult__cancel__left1, axiom,
    ((![C : int, B : int]: ((C = (times_times_int @ C @ B)) = (((C = zero_zero_int)) | ((B = one_one_int))))))). % mult_cancel_left1
thf(fact_108_diff__numeral__special_I9_J, axiom,
    (((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real))). % diff_numeral_special(9)
thf(fact_109_diff__numeral__special_I9_J, axiom,
    (((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex))). % diff_numeral_special(9)
thf(fact_110_diff__numeral__special_I9_J, axiom,
    (((minus_minus_int @ one_one_int @ one_one_int) = zero_zero_int))). % diff_numeral_special(9)
thf(fact_111_nonzero__mult__div__cancel__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_112_nonzero__mult__div__cancel__right, axiom,
    ((![B : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_113_nonzero__mult__div__cancel__right, axiom,
    ((![B : int, A : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (times_times_int @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_114_nonzero__mult__div__cancel__left, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_115_nonzero__mult__div__cancel__left, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_116_nonzero__mult__div__cancel__left, axiom,
    ((![A : int, B : int]: ((~ ((A = zero_zero_int))) => ((divide_divide_int @ (times_times_int @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_117_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_118_div__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % div_self
thf(fact_119_div__self, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ A @ A) = one_one_nat))))). % div_self
thf(fact_120_div__self, axiom,
    ((![A : int]: ((~ ((A = zero_zero_int))) => ((divide_divide_int @ A @ A) = one_one_int))))). % div_self
thf(fact_121_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_122_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_123_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_124_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_125_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_126_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_127_dvd__times__right__cancel__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((~ ((A = zero_zero_nat))) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)))))). % dvd_times_right_cancel_iff
thf(fact_128_dvd__times__right__cancel__iff, axiom,
    ((![A : int, B : int, C : int]: ((~ ((A = zero_zero_int))) => ((dvd_dvd_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C)))))). % dvd_times_right_cancel_iff
thf(fact_129_dvd__times__left__cancel__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((~ ((A = zero_zero_nat))) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C)))))). % dvd_times_left_cancel_iff
thf(fact_130_dvd__times__left__cancel__iff, axiom,
    ((![A : int, B : int, C : int]: ((~ ((A = zero_zero_int))) => ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (dvd_dvd_int @ B @ C)))))). % dvd_times_left_cancel_iff
thf(fact_131_dvd__mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((dvd_dvd_complex @ A @ B))))))). % dvd_mult_cancel_right
thf(fact_132_dvd__mult__cancel__right, axiom,
    ((![A : int, C : int, B : int]: ((dvd_dvd_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)) = (((C = zero_zero_int)) | ((dvd_dvd_int @ A @ B))))))). % dvd_mult_cancel_right
thf(fact_133_dvd__mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((dvd_dvd_complex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((dvd_dvd_complex @ A @ B))))))). % dvd_mult_cancel_left
thf(fact_134_dvd__mult__cancel__left, axiom,
    ((![C : int, A : int, B : int]: ((dvd_dvd_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (((C = zero_zero_int)) | ((dvd_dvd_int @ A @ B))))))). % dvd_mult_cancel_left
thf(fact_135_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_136_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_137_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_138_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_139_dvd__add__times__triv__right__iff, axiom,
    ((![A : complex, B : complex, C : complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ (times_times_complex @ C @ A))) = (dvd_dvd_complex @ A @ B))))). % dvd_add_times_triv_right_iff
thf(fact_140_dvd__add__times__triv__right__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ (times_times_nat @ C @ A))) = (dvd_dvd_nat @ A @ B))))). % dvd_add_times_triv_right_iff
thf(fact_141_dvd__add__times__triv__right__iff, axiom,
    ((![A : int, B : int, C : int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ (times_times_int @ C @ A))) = (dvd_dvd_int @ A @ B))))). % dvd_add_times_triv_right_iff
thf(fact_142_dvd__add__times__triv__left__iff, axiom,
    ((![A : complex, C : complex, B : complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ (times_times_complex @ C @ A) @ B)) = (dvd_dvd_complex @ A @ B))))). % dvd_add_times_triv_left_iff
thf(fact_143_dvd__add__times__triv__left__iff, axiom,
    ((![A : nat, C : nat, B : nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ (times_times_nat @ C @ A) @ B)) = (dvd_dvd_nat @ A @ B))))). % dvd_add_times_triv_left_iff
thf(fact_144_dvd__add__times__triv__left__iff, axiom,
    ((![A : int, C : int, B : int]: ((dvd_dvd_int @ A @ (plus_plus_int @ (times_times_int @ C @ A) @ B)) = (dvd_dvd_int @ A @ B))))). % dvd_add_times_triv_left_iff
thf(fact_145_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_real = (numeral_numeral_real @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_146_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_147_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_148_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_int = (numeral_numeral_int @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_149_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_real @ N) = one_one_real) = (N = one))))). % numeral_eq_one_iff
thf(fact_150_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_151_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_152_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_int @ N) = one_one_int) = (N = one))))). % numeral_eq_one_iff
thf(fact_153_unit__prod, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat)))))). % unit_prod
thf(fact_154_unit__prod, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int)))))). % unit_prod
thf(fact_155_dvd__mult__div__cancel, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ A @ (divide_divide_nat @ B @ A)) = B))))). % dvd_mult_div_cancel
thf(fact_156_dvd__mult__div__cancel, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ A @ (divide_divide_int @ B @ A)) = B))))). % dvd_mult_div_cancel
thf(fact_157_dvd__div__mult__self, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B))))). % dvd_div_mult_self
thf(fact_158_dvd__div__mult__self, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ (divide_divide_int @ B @ A) @ A) = B))))). % dvd_div_mult_self
thf(fact_159_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_160_div__add, axiom,
    ((![C : int, A : int, B : int]: ((dvd_dvd_int @ C @ A) => ((dvd_dvd_int @ C @ B) => ((divide_divide_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (divide_divide_int @ A @ C) @ (divide_divide_int @ B @ C)))))))). % div_add
thf(fact_161_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_162_unit__div__1__div__1, axiom,
    ((![A : int]: ((dvd_dvd_int @ A @ one_one_int) => ((divide_divide_int @ one_one_int @ (divide_divide_int @ one_one_int @ A)) = A))))). % unit_div_1_div_1
thf(fact_163_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_164_unit__div__1__unit, axiom,
    ((![A : int]: ((dvd_dvd_int @ A @ one_one_int) => (dvd_dvd_int @ (divide_divide_int @ one_one_int @ A) @ one_one_int))))). % unit_div_1_unit
thf(fact_165_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_166_unit__div, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ (divide_divide_int @ A @ B) @ one_one_int)))))). % unit_div
thf(fact_167_div__diff, axiom,
    ((![C : int, A : int, B : int]: ((dvd_dvd_int @ C @ A) => ((dvd_dvd_int @ C @ B) => ((divide_divide_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (divide_divide_int @ A @ C) @ (divide_divide_int @ B @ C)))))))). % div_diff
thf(fact_168_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_169_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_170_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_171_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_172_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_173_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_174_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_175_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_176_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_177_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_178_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_179_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_180_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_181_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_182_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_183_odd__two__times__div__two__nat, axiom,
    ((![N : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N))) => ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ N @ (numeral_numeral_nat @ (bit0 @ one)))) = (minus_minus_nat @ N @ one_one_nat)))))). % odd_two_times_div_two_nat
thf(fact_184_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_185_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_186_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_187_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_188_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_189_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_190_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_191_m, axiom,
    ((na = (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))). % m
thf(fact_192_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_193_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_194_add__One__commute, axiom,
    ((![N : num]: ((plus_plus_num @ one @ N) = (plus_plus_num @ N @ one))))). % add_One_commute
thf(fact_195_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_196_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_197_mult__right__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_198_mult__right__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_199_mult__right__cancel, axiom,
    ((![C : int, A : int, B : int]: ((~ ((C = zero_zero_int))) => (((times_times_int @ A @ C) = (times_times_int @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_200_mult__left__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_201_mult__left__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_202_mult__left__cancel, axiom,
    ((![C : int, A : int, B : int]: ((~ ((C = zero_zero_int))) => (((times_times_int @ C @ A) = (times_times_int @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_203_no__zero__divisors, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (~ (((times_times_complex @ A @ B) = zero_zero_complex)))))))). % no_zero_divisors
thf(fact_204_no__zero__divisors, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((~ ((B = zero_zero_nat))) => (~ (((times_times_nat @ A @ B) = zero_zero_nat)))))))). % no_zero_divisors
thf(fact_205_no__zero__divisors, axiom,
    ((![A : int, B : int]: ((~ ((A = zero_zero_int))) => ((~ ((B = zero_zero_int))) => (~ (((times_times_int @ A @ B) = zero_zero_int)))))))). % no_zero_divisors
thf(fact_206_divisors__zero, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) => ((A = zero_zero_complex) | (B = zero_zero_complex)))))). % divisors_zero
thf(fact_207_divisors__zero, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((A = zero_zero_nat) | (B = zero_zero_nat)))))). % divisors_zero
thf(fact_208_divisors__zero, axiom,
    ((![A : int, B : int]: (((times_times_int @ A @ B) = zero_zero_int) => ((A = zero_zero_int) | (B = zero_zero_int)))))). % divisors_zero
thf(fact_209_mult__not__zero, axiom,
    ((![A : complex, B : complex]: ((~ (((times_times_complex @ A @ B) = zero_zero_complex))) => ((~ ((A = zero_zero_complex))) & (~ ((B = zero_zero_complex)))))))). % mult_not_zero
thf(fact_210_mult__not__zero, axiom,
    ((![A : nat, B : nat]: ((~ (((times_times_nat @ A @ B) = zero_zero_nat))) => ((~ ((A = zero_zero_nat))) & (~ ((B = zero_zero_nat)))))))). % mult_not_zero
thf(fact_211_mult__not__zero, axiom,
    ((![A : int, B : int]: ((~ (((times_times_int @ A @ B) = zero_zero_int))) => ((~ ((A = zero_zero_int))) & (~ ((B = zero_zero_int)))))))). % mult_not_zero
thf(fact_212_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_213_zero__neq__one, axiom,
    ((~ ((zero_zero_int = one_one_int))))). % zero_neq_one
thf(fact_214_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_215_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_216_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N))))))). % zero_neq_numeral
thf(fact_217_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_218_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N))))))). % zero_neq_numeral
thf(fact_219_dvd__0__left, axiom,
    ((![A : int]: ((dvd_dvd_int @ zero_zero_int @ A) => (A = zero_zero_int))))). % dvd_0_left
thf(fact_220_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_221_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_222_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_223_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_224_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_int @ A @ B) => ((ord_less_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_225_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_226_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_227_mult__less__cancel__right__disj, axiom,
    ((![A : int, C : int, B : int]: ((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)) = (((((ord_less_int @ zero_zero_int @ C)) & ((ord_less_int @ A @ B)))) | ((((ord_less_int @ C @ zero_zero_int)) & ((ord_less_int @ B @ A))))))))). % mult_less_cancel_right_disj
thf(fact_228_mult__less__cancel__right__disj, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ A @ B)))) | ((((ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ B @ A))))))))). % mult_less_cancel_right_disj
thf(fact_229_mult__strict__right__mono, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_int @ A @ B) => ((ord_less_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))))). % mult_strict_right_mono
thf(fact_230_mult__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono
thf(fact_231_mult__strict__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))))). % mult_strict_right_mono
thf(fact_232_mult__strict__right__mono__neg, axiom,
    ((![B : int, A : int, C : int]: ((ord_less_int @ B @ A) => ((ord_less_int @ C @ zero_zero_int) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))))). % mult_strict_right_mono_neg
thf(fact_233_mult__strict__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono_neg
thf(fact_234_mult__less__cancel__left__disj, axiom,
    ((![C : int, A : int, B : int]: ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (((((ord_less_int @ zero_zero_int @ C)) & ((ord_less_int @ A @ B)))) | ((((ord_less_int @ C @ zero_zero_int)) & ((ord_less_int @ B @ A))))))))). % mult_less_cancel_left_disj
thf(fact_235_mult__less__cancel__left__disj, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (((((ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ A @ B)))) | ((((ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ B @ A))))))))). % mult_less_cancel_left_disj
thf(fact_236_mult__strict__left__mono, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_int @ A @ B) => ((ord_less_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))))))). % mult_strict_left_mono
thf(fact_237_mult__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_strict_left_mono
thf(fact_238_mult__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % mult_strict_left_mono
thf(fact_239_mult__strict__left__mono__neg, axiom,
    ((![B : int, A : int, C : int]: ((ord_less_int @ B @ A) => ((ord_less_int @ C @ zero_zero_int) => (ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))))))). % mult_strict_left_mono_neg
thf(fact_240_mult__strict__left__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_strict_left_mono_neg
thf(fact_241_mult__less__cancel__left__pos, axiom,
    ((![C : int, A : int, B : int]: ((ord_less_int @ zero_zero_int @ C) => ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (ord_less_int @ A @ B)))))). % mult_less_cancel_left_pos
thf(fact_242_mult__less__cancel__left__pos, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ A @ B)))))). % mult_less_cancel_left_pos
thf(fact_243_mult__less__cancel__left__neg, axiom,
    ((![C : int, A : int, B : int]: ((ord_less_int @ C @ zero_zero_int) => ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (ord_less_int @ B @ A)))))). % mult_less_cancel_left_neg
thf(fact_244_mult__less__cancel__left__neg, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ B @ A)))))). % mult_less_cancel_left_neg
thf(fact_245_zero__less__mult__pos2, axiom,
    ((![B : int, A : int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ B @ A)) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ B)))))). % zero_less_mult_pos2
thf(fact_246_zero__less__mult__pos2, axiom,
    ((![B : real, A : real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B)))))). % zero_less_mult_pos2
thf(fact_247_zero__less__mult__pos2, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ B @ A)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ B)))))). % zero_less_mult_pos2
thf(fact_248_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)

% Conjectures (6)
thf(conj_0, hypothesis,
    ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ imaginary_unit)) @ one_one_real))).
thf(conj_1, hypothesis,
    ((~ ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ one_one_complex)) @ one_one_real))))).
thf(conj_2, hypothesis,
    ((~ ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ one_one_complex)) @ one_one_real))))).
thf(conj_3, hypothesis,
    ((~ ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ imaginary_unit)) @ one_one_real))))).
thf(conj_4, hypothesis,
    ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))).
thf(conj_5, conjecture,
    ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ (times_times_complex @ imaginary_unit @ (power_power_complex @ (power_power_complex @ imaginary_unit @ (numeral_numeral_nat @ (bit0 @ one))) @ m)))) @ one_one_real))).
