% 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_200__5369530_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:05.535

% 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 (47)
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_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint, type,
    uminus_uminus_int : int > int).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_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_m____, type,
    m : nat).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).

% Relevant facts (248)
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_power2__i, axiom,
    (((power_power_complex @ imaginary_unit @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1204672759omplex @ one_one_complex)))). % power2_i
thf(fact_9_neg__one__odd__power, axiom,
    ((![N : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N))) => ((power_power_real @ (uminus_uminus_real @ one_one_real) @ N) = (uminus_uminus_real @ one_one_real)))))). % neg_one_odd_power
thf(fact_10_neg__one__odd__power, axiom,
    ((![N : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N))) => ((power_power_complex @ (uminus1204672759omplex @ one_one_complex) @ N) = (uminus1204672759omplex @ one_one_complex)))))). % neg_one_odd_power
thf(fact_11_neg__one__odd__power, axiom,
    ((![N : nat]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N))) => ((power_power_int @ (uminus_uminus_int @ one_one_int) @ N) = (uminus_uminus_int @ one_one_int)))))). % neg_one_odd_power
thf(fact_12_neg__one__even__power, axiom,
    ((![N : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) => ((power_power_complex @ (uminus1204672759omplex @ one_one_complex) @ N) = one_one_complex))))). % neg_one_even_power
thf(fact_13_neg__one__even__power, axiom,
    ((![N : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) => ((power_power_int @ (uminus_uminus_int @ one_one_int) @ N) = one_one_int))))). % neg_one_even_power
thf(fact_14_neg__one__even__power, axiom,
    ((![N : nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) => ((power_power_real @ (uminus_uminus_real @ one_one_real) @ N) = one_one_real))))). % neg_one_even_power
thf(fact_15_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_16_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_17_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_18_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_19_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_20_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_21_power__minus__odd, axiom,
    ((![N : nat, A : complex]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N))) => ((power_power_complex @ (uminus1204672759omplex @ A) @ N) = (uminus1204672759omplex @ (power_power_complex @ A @ N))))))). % power_minus_odd
thf(fact_22_power__minus__odd, axiom,
    ((![N : nat, A : int]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N))) => ((power_power_int @ (uminus_uminus_int @ A) @ N) = (uminus_uminus_int @ (power_power_int @ A @ N))))))). % power_minus_odd
thf(fact_23_power__minus__odd, axiom,
    ((![N : nat, A : real]: ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N))) => ((power_power_real @ (uminus_uminus_real @ A) @ N) = (uminus_uminus_real @ (power_power_real @ A @ N))))))). % power_minus_odd
thf(fact_24_Parity_Oring__1__class_Opower__minus__even, axiom,
    ((![N : nat, A : complex]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) => ((power_power_complex @ (uminus1204672759omplex @ A) @ N) = (power_power_complex @ A @ N)))))). % Parity.ring_1_class.power_minus_even
thf(fact_25_Parity_Oring__1__class_Opower__minus__even, axiom,
    ((![N : nat, A : int]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) => ((power_power_int @ (uminus_uminus_int @ A) @ N) = (power_power_int @ A @ N)))))). % Parity.ring_1_class.power_minus_even
thf(fact_26_Parity_Oring__1__class_Opower__minus__even, axiom,
    ((![N : nat, A : real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) => ((power_power_real @ (uminus_uminus_real @ A) @ N) = (power_power_real @ A @ N)))))). % Parity.ring_1_class.power_minus_even
thf(fact_27_minus__1__div__2__eq, axiom,
    (((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (uminus_uminus_int @ one_one_int)))). % minus_1_div_2_eq
thf(fact_28_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_29_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_30_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_31_diff__numeral__special_I11_J, axiom,
    (((minus_minus_complex @ one_one_complex @ (uminus1204672759omplex @ one_one_complex)) = (numera632737353omplex @ (bit0 @ one))))). % diff_numeral_special(11)
thf(fact_32_diff__numeral__special_I11_J, axiom,
    (((minus_minus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = (numeral_numeral_int @ (bit0 @ one))))). % diff_numeral_special(11)
thf(fact_33_diff__numeral__special_I11_J, axiom,
    (((minus_minus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = (numeral_numeral_real @ (bit0 @ one))))). % diff_numeral_special(11)
thf(fact_34_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_35_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_36_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_37_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_38_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_39_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_40_bits__div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % bits_div_by_0
thf(fact_41_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_42_bits__div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % bits_div_0
thf(fact_43_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_44_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_45_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_46_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_47_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_48_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_49_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_50_bits__div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % bits_div_by_1
thf(fact_51_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_52_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_53_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus_uminus_int @ (numeral_numeral_int @ M)) = (uminus_uminus_int @ (numeral_numeral_int @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_54_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_55_diff__numeral__special_I9_J, axiom,
    (((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real))). % diff_numeral_special(9)
thf(fact_56_diff__numeral__special_I9_J, axiom,
    (((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex))). % diff_numeral_special(9)
thf(fact_57_diff__numeral__special_I9_J, axiom,
    (((minus_minus_int @ one_one_int @ one_one_int) = zero_zero_int))). % diff_numeral_special(9)
thf(fact_58_neg__numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (ord_less_num @ N @ M))))). % neg_numeral_less_iff
thf(fact_59_neg__numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (ord_less_num @ N @ M))))). % neg_numeral_less_iff
thf(fact_60_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((plus_plus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (uminus1204672759omplex @ (plus_plus_complex @ (numera632737353omplex @ M) @ (numera632737353omplex @ N))))))). % add_neg_numeral_simps(3)
thf(fact_61_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (uminus_uminus_int @ (plus_plus_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N))))))). % add_neg_numeral_simps(3)
thf(fact_62_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_real @ (plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N))))))). % add_neg_numeral_simps(3)
thf(fact_63_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_real = (numeral_numeral_real @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_64_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_65_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_int = (numeral_numeral_int @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_66_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_67_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_real @ N) = one_one_real) = (N = one))))). % numeral_eq_one_iff
thf(fact_68_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_69_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_int @ N) = one_one_int) = (N = one))))). % numeral_eq_one_iff
thf(fact_70_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_71_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((minus_minus_complex @ (numera632737353omplex @ M) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (numera632737353omplex @ (plus_plus_num @ M @ N)))))). % diff_numeral_simps(2)
thf(fact_72_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((minus_minus_int @ (numeral_numeral_int @ M) @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (numeral_numeral_int @ (plus_plus_num @ M @ N)))))). % diff_numeral_simps(2)
thf(fact_73_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((minus_minus_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ (plus_plus_num @ M @ N)))))). % diff_numeral_simps(2)
thf(fact_74_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((minus_minus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ M @ N))))))). % diff_numeral_simps(3)
thf(fact_75_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (numeral_numeral_int @ N)) = (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ M @ N))))))). % diff_numeral_simps(3)
thf(fact_76_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ M @ N))))))). % diff_numeral_simps(3)
thf(fact_77_norm__ii, axiom,
    (((real_V638595069omplex @ imaginary_unit) = one_one_real))). % norm_ii
thf(fact_78_add__neg__numeral__special_I7_J, axiom,
    (((plus_plus_complex @ one_one_complex @ (uminus1204672759omplex @ one_one_complex)) = zero_zero_complex))). % add_neg_numeral_special(7)
thf(fact_79_add__neg__numeral__special_I7_J, axiom,
    (((plus_plus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = zero_zero_int))). % add_neg_numeral_special(7)
thf(fact_80_add__neg__numeral__special_I7_J, axiom,
    (((plus_plus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = zero_zero_real))). % add_neg_numeral_special(7)
thf(fact_81_add__neg__numeral__special_I8_J, axiom,
    (((plus_plus_complex @ (uminus1204672759omplex @ one_one_complex) @ one_one_complex) = zero_zero_complex))). % add_neg_numeral_special(8)
thf(fact_82_add__neg__numeral__special_I8_J, axiom,
    (((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = zero_zero_int))). % add_neg_numeral_special(8)
thf(fact_83_add__neg__numeral__special_I8_J, axiom,
    (((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = zero_zero_real))). % add_neg_numeral_special(8)
thf(fact_84_diff__numeral__special_I12_J, axiom,
    (((minus_minus_complex @ (uminus1204672759omplex @ one_one_complex) @ (uminus1204672759omplex @ one_one_complex)) = zero_zero_complex))). % diff_numeral_special(12)
thf(fact_85_diff__numeral__special_I12_J, axiom,
    (((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ one_one_int)) = zero_zero_int))). % diff_numeral_special(12)
thf(fact_86_diff__numeral__special_I12_J, axiom,
    (((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = zero_zero_real))). % diff_numeral_special(12)
thf(fact_87_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_88_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_89_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_90_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_91_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_92_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_93_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_94_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_95_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_96_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_97_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_98_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ one_one_complex)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_99_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus_uminus_int @ (numeral_numeral_int @ N)) = (uminus_uminus_int @ one_one_int)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_100_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ one_one_real)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_101_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_102_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus_uminus_int @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_103_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_104_neg__numeral__less__neg__one__iff, axiom,
    ((![M : num]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (uminus_uminus_int @ one_one_int)) = (~ ((M = one))))))). % neg_numeral_less_neg_one_iff
thf(fact_105_neg__numeral__less__neg__one__iff, axiom,
    ((![M : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ one_one_real)) = (~ ((M = one))))))). % neg_numeral_less_neg_one_iff
thf(fact_106_one__add__one, axiom,
    (((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one))))). % one_add_one
thf(fact_107_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_108_one__add__one, axiom,
    (((plus_plus_int @ one_one_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one))))). % one_add_one
thf(fact_109_one__add__one, axiom,
    (((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % one_add_one
thf(fact_110_diff__numeral__special_I3_J, axiom,
    ((![N : num]: ((minus_minus_complex @ one_one_complex @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (numera632737353omplex @ (plus_plus_num @ one @ N)))))). % diff_numeral_special(3)
thf(fact_111_diff__numeral__special_I3_J, axiom,
    ((![N : num]: ((minus_minus_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (numeral_numeral_int @ (plus_plus_num @ one @ N)))))). % diff_numeral_special(3)
thf(fact_112_diff__numeral__special_I3_J, axiom,
    ((![N : num]: ((minus_minus_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ (plus_plus_num @ one @ N)))))). % diff_numeral_special(3)
thf(fact_113_diff__numeral__special_I4_J, axiom,
    ((![M : num]: ((minus_minus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ M @ one))))))). % diff_numeral_special(4)
thf(fact_114_diff__numeral__special_I4_J, axiom,
    ((![M : num]: ((minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ M @ one))))))). % diff_numeral_special(4)
thf(fact_115_diff__numeral__special_I4_J, axiom,
    ((![M : num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ M @ one))))))). % diff_numeral_special(4)
thf(fact_116_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_117_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_118_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_119_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_120_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_121_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_122_add__neg__numeral__special_I9_J, axiom,
    (((plus_plus_complex @ (uminus1204672759omplex @ one_one_complex) @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ (numera632737353omplex @ (bit0 @ one)))))). % add_neg_numeral_special(9)
thf(fact_123_add__neg__numeral__special_I9_J, axiom,
    (((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one)))))). % add_neg_numeral_special(9)
thf(fact_124_add__neg__numeral__special_I9_J, axiom,
    (((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one)))))). % add_neg_numeral_special(9)
thf(fact_125_diff__numeral__special_I10_J, axiom,
    (((minus_minus_complex @ (uminus1204672759omplex @ one_one_complex) @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ (bit0 @ one)))))). % diff_numeral_special(10)
thf(fact_126_diff__numeral__special_I10_J, axiom,
    (((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one)))))). % diff_numeral_special(10)
thf(fact_127_diff__numeral__special_I10_J, axiom,
    (((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one)))))). % diff_numeral_special(10)
thf(fact_128_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_129_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_130_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_131_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_132_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_133_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_134_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_135_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_136_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_137_minus__1__div__exp__eq__int, axiom,
    ((![N : nat]: ((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ N)) = (uminus_uminus_int @ one_one_int))))). % minus_1_div_exp_eq_int
thf(fact_138_add__One__commute, axiom,
    ((![N : num]: ((plus_plus_num @ one @ N) = (plus_plus_num @ N @ one))))). % add_One_commute
thf(fact_139_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_140_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_141_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_142_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N))))))). % zero_neq_numeral
thf(fact_143_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N))))))). % zero_neq_numeral
thf(fact_144_complex__i__not__numeral, axiom,
    ((![W : num]: (~ ((imaginary_unit = (numera632737353omplex @ W))))))). % complex_i_not_numeral
thf(fact_145_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_146_complex__i__not__zero, axiom,
    ((~ ((imaginary_unit = zero_zero_complex))))). % complex_i_not_zero
thf(fact_147_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_148_less__numeral__extra_I1_J, axiom,
    ((ord_less_int @ zero_zero_int @ one_one_int))). % less_numeral_extra(1)
thf(fact_149_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_150_less__numeral__extra_I1_J, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % less_numeral_extra(1)
thf(fact_151_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ zero_zero_real)))))). % not_numeral_less_zero
thf(fact_152_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ zero_zero_nat)))))). % not_numeral_less_zero
thf(fact_153_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N) @ zero_zero_int)))))). % not_numeral_less_zero
thf(fact_154_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ N))))). % zero_less_numeral
thf(fact_155_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ N))))). % zero_less_numeral
thf(fact_156_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ N))))). % zero_less_numeral
thf(fact_157_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_complex = (uminus1204672759omplex @ one_one_complex)))))). % zero_neq_neg_one
thf(fact_158_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_int = (uminus_uminus_int @ one_one_int)))))). % zero_neq_neg_one
thf(fact_159_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_real = (uminus_uminus_real @ one_one_real)))))). % zero_neq_neg_one
thf(fact_160_zero__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % zero_neq_neg_numeral
thf(fact_161_zero__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % zero_neq_neg_numeral
thf(fact_162_zero__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_real = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % zero_neq_neg_numeral
thf(fact_163_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_164_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_165_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_166_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_167_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_168_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_169_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_170_complex__i__not__neg__numeral, axiom,
    ((![W : num]: (~ ((imaginary_unit = (uminus1204672759omplex @ (numera632737353omplex @ W)))))))). % complex_i_not_neg_numeral
thf(fact_171_less__minus__one__simps_I1_J, axiom,
    ((ord_less_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int))). % less_minus_one_simps(1)
thf(fact_172_less__minus__one__simps_I1_J, axiom,
    ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real))). % less_minus_one_simps(1)
thf(fact_173_less__minus__one__simps_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))))). % less_minus_one_simps(3)
thf(fact_174_less__minus__one__simps_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))))). % less_minus_one_simps(3)
thf(fact_175_not__zero__less__neg__numeral, axiom,
    ((![N : num]: (~ ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % not_zero_less_neg_numeral
thf(fact_176_not__zero__less__neg__numeral, axiom,
    ((![N : num]: (~ ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % not_zero_less_neg_numeral
thf(fact_177_neg__numeral__less__zero, axiom,
    ((![N : num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ N)) @ zero_zero_int)))). % neg_numeral_less_zero
thf(fact_178_neg__numeral__less__zero, axiom,
    ((![N : num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ N)) @ zero_zero_real)))). % neg_numeral_less_zero
thf(fact_179_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_180_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_181_even__zero, axiom,
    ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ zero_zero_nat))). % even_zero
thf(fact_182_even__zero, axiom,
    ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ zero_zero_int))). % even_zero
thf(fact_183_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_184_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_185_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_186_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_187_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_188_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_189_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_int @ one_one_int @ one_one_int))))). % less_numeral_extra(4)
thf(fact_190_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_191_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ one_one_nat))))). % less_numeral_extra(4)
thf(fact_192_is__num__normalize_I8_J, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1204672759omplex @ B) @ (uminus1204672759omplex @ A)))))). % is_num_normalize(8)
thf(fact_193_is__num__normalize_I8_J, axiom,
    ((![A : int, B : int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)))))). % is_num_normalize(8)
thf(fact_194_is__num__normalize_I8_J, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % is_num_normalize(8)
thf(fact_195_one__neq__neg__one, axiom,
    ((~ ((one_one_complex = (uminus1204672759omplex @ one_one_complex)))))). % one_neq_neg_one
thf(fact_196_one__neq__neg__one, axiom,
    ((~ ((one_one_int = (uminus_uminus_int @ one_one_int)))))). % one_neq_neg_one
thf(fact_197_one__neq__neg__one, axiom,
    ((~ ((one_one_real = (uminus_uminus_real @ one_one_real)))))). % one_neq_neg_one
thf(fact_198_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numera632737353omplex @ M) = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % numeral_neq_neg_numeral
thf(fact_199_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numeral_numeral_int @ M) = (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % numeral_neq_neg_numeral
thf(fact_200_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numeral_numeral_real @ M) = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % numeral_neq_neg_numeral
thf(fact_201_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (numera632737353omplex @ N))))))). % neg_numeral_neq_numeral
thf(fact_202_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus_uminus_int @ (numeral_numeral_int @ M)) = (numeral_numeral_int @ N))))))). % neg_numeral_neq_numeral
thf(fact_203_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (numeral_numeral_real @ N))))))). % neg_numeral_neq_numeral
thf(fact_204_complex__i__not__one, axiom,
    ((~ ((imaginary_unit = one_one_complex))))). % complex_i_not_one
thf(fact_205_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ one_one_real)))))). % not_numeral_less_one
thf(fact_206_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ one_one_nat)))))). % not_numeral_less_one
thf(fact_207_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N) @ one_one_int)))))). % not_numeral_less_one
thf(fact_208_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_209_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_210_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_211_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_212_less__minus__one__simps_I2_J, axiom,
    ((ord_less_int @ (uminus_uminus_int @ one_one_int) @ one_one_int))). % less_minus_one_simps(2)
thf(fact_213_less__minus__one__simps_I2_J, axiom,
    ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ one_one_real))). % less_minus_one_simps(2)
thf(fact_214_less__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))))). % less_minus_one_simps(4)
thf(fact_215_less__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))))). % less_minus_one_simps(4)
thf(fact_216_not__numeral__less__neg__numeral, axiom,
    ((![M : num, N : num]: (~ ((ord_less_int @ (numeral_numeral_int @ M) @ (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % not_numeral_less_neg_numeral
thf(fact_217_not__numeral__less__neg__numeral, axiom,
    ((![M : num, N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % not_numeral_less_neg_numeral
thf(fact_218_neg__numeral__less__numeral, axiom,
    ((![M : num, N : num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (numeral_numeral_int @ N))))). % neg_numeral_less_numeral
thf(fact_219_neg__numeral__less__numeral, axiom,
    ((![M : num, N : num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N))))). % neg_numeral_less_numeral
thf(fact_220_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_221_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_222_numeral__Bit0, axiom,
    ((![N : num]: ((numera632737353omplex @ (bit0 @ N)) = (plus_plus_complex @ (numera632737353omplex @ N) @ (numera632737353omplex @ N)))))). % numeral_Bit0
thf(fact_223_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_complex = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % one_neq_neg_numeral
thf(fact_224_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_int = (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % one_neq_neg_numeral
thf(fact_225_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_real = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % one_neq_neg_numeral
thf(fact_226_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numera632737353omplex @ N) = (uminus1204672759omplex @ one_one_complex))))))). % numeral_neq_neg_one
thf(fact_227_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numeral_numeral_int @ N) = (uminus_uminus_int @ one_one_int))))))). % numeral_neq_neg_one
thf(fact_228_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numeral_numeral_real @ N) = (uminus_uminus_real @ one_one_real))))))). % numeral_neq_neg_one
thf(fact_229_numeral__One, axiom,
    (((numeral_numeral_real @ one) = one_one_real))). % numeral_One
thf(fact_230_numeral__One, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numeral_One
thf(fact_231_numeral__One, axiom,
    (((numeral_numeral_int @ one) = one_one_int))). % numeral_One
thf(fact_232_numeral__One, axiom,
    (((numera632737353omplex @ one) = one_one_complex))). % numeral_One
thf(fact_233_divide__numeral__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ (numera632737353omplex @ one)) = A)))). % divide_numeral_1
thf(fact_234_not__neg__one__less__neg__numeral, axiom,
    ((![M : num]: (~ ((ord_less_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ M)))))))). % not_neg_one_less_neg_numeral
thf(fact_235_not__neg__one__less__neg__numeral, axiom,
    ((![M : num]: (~ ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ M)))))))). % not_neg_one_less_neg_numeral
thf(fact_236_not__one__less__neg__numeral, axiom,
    ((![M : num]: (~ ((ord_less_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)))))))). % not_one_less_neg_numeral
thf(fact_237_not__one__less__neg__numeral, axiom,
    ((![M : num]: (~ ((ord_less_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)))))))). % not_one_less_neg_numeral
thf(fact_238_not__numeral__less__neg__one, axiom,
    ((![M : num]: (~ ((ord_less_int @ (numeral_numeral_int @ M) @ (uminus_uminus_int @ one_one_int))))))). % not_numeral_less_neg_one
thf(fact_239_not__numeral__less__neg__one, axiom,
    ((![M : num]: (~ ((ord_less_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ one_one_real))))))). % not_numeral_less_neg_one
thf(fact_240_neg__one__less__numeral, axiom,
    ((![M : num]: (ord_less_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ M))))). % neg_one_less_numeral
thf(fact_241_neg__one__less__numeral, axiom,
    ((![M : num]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ M))))). % neg_one_less_numeral
thf(fact_242_neg__numeral__less__one, axiom,
    ((![M : num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ one_one_int)))). % neg_numeral_less_one
thf(fact_243_neg__numeral__less__one, axiom,
    ((![M : num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ one_one_real)))). % neg_numeral_less_one
thf(fact_244_uminus__numeral__One, axiom,
    (((uminus_uminus_int @ (numeral_numeral_int @ one)) = (uminus_uminus_int @ one_one_int)))). % uminus_numeral_One
thf(fact_245_uminus__numeral__One, axiom,
    (((uminus_uminus_real @ (numeral_numeral_real @ one)) = (uminus_uminus_real @ one_one_real)))). % uminus_numeral_One
thf(fact_246_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_247_div__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => ((divide_divide_nat @ M @ N) = zero_zero_nat))))). % div_less

% Conjectures (7)
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, hypothesis,
    ((~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))).
thf(conj_6, conjecture,
    ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ (power_power_complex @ (uminus1204672759omplex @ imaginary_unit) @ na))) @ one_one_real))).
