% 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/FFT/prob_362__3226076_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:10:42.542

% Could-be-implicit typings (5)
thf(ty_n_t__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $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 (40)
thf(sy_c_FFT__Mirabelle__ulikgskiun_Oroot, type,
    fFT_Mirabelle_root : nat > complex).
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_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_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_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_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__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Complex__Ocomplex, type,
    groups59700922omplex : (nat > complex) > set_nat > complex).
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_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__eq_001t__Int__Oint, type,
    ord_less_eq_int : int > int > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum, type,
    ord_less_eq_num : num > num > $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_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_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat, type,
    set_or562006527an_nat : nat > nat > set_nat).
thf(sy_v_a, type,
    a : nat > complex).
thf(sy_v_i, type,
    i : nat).
thf(sy_v_m, type,
    m : nat).

% Relevant facts (237)
thf(fact_0_mbound, axiom,
    ((ord_less_nat @ zero_zero_nat @ m))). % mbound
thf(fact_1_root0, axiom,
    (((fFT_Mirabelle_root @ zero_zero_nat) = one_one_complex))). % root0
thf(fact_2_ibound, axiom,
    ((ord_less_eq_nat @ m @ i))). % ibound
thf(fact_3_root2, axiom,
    (((fFT_Mirabelle_root @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1204672759omplex @ one_one_complex)))). % root2
thf(fact_4_root__unity, axiom,
    ((![N : nat]: ((power_power_complex @ (fFT_Mirabelle_root @ N) @ N) = one_one_complex)))). % root_unity
thf(fact_5_root__cancel1, axiom,
    ((![M : nat, I : nat, J : nat]: ((power_power_complex @ (fFT_Mirabelle_root @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ M)) @ (times_times_nat @ I @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ J))) = (power_power_complex @ (fFT_Mirabelle_root @ M) @ (times_times_nat @ I @ J)))))). % root_cancel1
thf(fact_6_power__minus1__even, axiom,
    ((![N : nat]: ((power_power_complex @ (uminus1204672759omplex @ one_one_complex) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)) = one_one_complex)))). % power_minus1_even
thf(fact_7_power__minus1__even, axiom,
    ((![N : nat]: ((power_power_int @ (uminus_uminus_int @ one_one_int) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)) = one_one_int)))). % power_minus1_even
thf(fact_8_Power_Oring__1__class_Opower__minus__even, axiom,
    ((![A : complex, N : nat]: ((power_power_complex @ (uminus1204672759omplex @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)) = (power_power_complex @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)))))). % Power.ring_1_class.power_minus_even
thf(fact_9_Power_Oring__1__class_Opower__minus__even, axiom,
    ((![A : int, N : nat]: ((power_power_int @ (uminus_uminus_int @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)) = (power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N)))))). % Power.ring_1_class.power_minus_even
thf(fact_10_sum__power2__eq__zero__iff, axiom,
    ((![X : int, Y : int]: (((plus_plus_int @ (power_power_int @ X @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ Y @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_int) = (((X = zero_zero_int)) & ((Y = zero_zero_int))))))). % sum_power2_eq_zero_iff
thf(fact_11_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_12_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_13_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_14_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_15_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_16_one__div__two__eq__zero, axiom,
    (((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % one_div_two_eq_zero
thf(fact_17_one__div__two__eq__zero, axiom,
    (((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))). % one_div_two_eq_zero
thf(fact_18_add__2__eq__Suc, axiom,
    ((![N : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) = (suc @ (suc @ N)))))). % add_2_eq_Suc
thf(fact_19_add__2__eq__Suc_H, axiom,
    ((![N : nat]: ((plus_plus_nat @ N @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ N)))))). % add_2_eq_Suc'
thf(fact_20_power2__minus, axiom,
    ((![A : complex]: ((power_power_complex @ (uminus1204672759omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))))))). % power2_minus
thf(fact_21_power2__minus, axiom,
    ((![A : int]: ((power_power_int @ (uminus_uminus_int @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))))))). % power2_minus
thf(fact_22_zero__eq__power2, axiom,
    ((![A : complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex) = (A = zero_zero_complex))))). % zero_eq_power2
thf(fact_23_zero__eq__power2, axiom,
    ((![A : nat]: (((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat) = (A = zero_zero_nat))))). % zero_eq_power2
thf(fact_24_zero__eq__power2, axiom,
    ((![A : int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int) = (A = zero_zero_int))))). % zero_eq_power2
thf(fact_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_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_29_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_30_power__one__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_31_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_32_power__one__right, axiom,
    ((![A : int]: ((power_power_int @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_33_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_34_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_35_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_36_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_37_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_38_bits__div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % bits_div_by_0
thf(fact_39_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_40_bits__div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % bits_div_0
thf(fact_41_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_42_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_43_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_44_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z : complex]: ((times_times_complex @ (numera632737353omplex @ V) @ (times_times_complex @ (numera632737353omplex @ W) @ Z)) = (times_times_complex @ (numera632737353omplex @ (times_times_num @ V @ W)) @ Z))))). % mult_numeral_left_semiring_numeral
thf(fact_45_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z : nat]: ((times_times_nat @ (numeral_numeral_nat @ V) @ (times_times_nat @ (numeral_numeral_nat @ W) @ Z)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ V @ W)) @ Z))))). % mult_numeral_left_semiring_numeral
thf(fact_46_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z : int]: ((times_times_int @ (numeral_numeral_int @ V) @ (times_times_int @ (numeral_numeral_int @ W) @ Z)) = (times_times_int @ (numeral_numeral_int @ (times_times_num @ V @ W)) @ Z))))). % mult_numeral_left_semiring_numeral
thf(fact_47_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_48_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_49_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_50_add__numeral__left, axiom,
    ((![V : num, W : num, Z : complex]: ((plus_plus_complex @ (numera632737353omplex @ V) @ (plus_plus_complex @ (numera632737353omplex @ W) @ Z)) = (plus_plus_complex @ (numera632737353omplex @ (plus_plus_num @ V @ W)) @ Z))))). % add_numeral_left
thf(fact_51_add__numeral__left, axiom,
    ((![V : num, W : num, Z : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ (numeral_numeral_nat @ W) @ Z)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ V @ W)) @ Z))))). % add_numeral_left
thf(fact_52_add__numeral__left, axiom,
    ((![V : num, W : num, Z : int]: ((plus_plus_int @ (numeral_numeral_int @ V) @ (plus_plus_int @ (numeral_numeral_int @ W) @ Z)) = (plus_plus_int @ (numeral_numeral_int @ (plus_plus_num @ V @ W)) @ Z))))). % add_numeral_left
thf(fact_53_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_54_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_55_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_56_bits__div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % bits_div_by_1
thf(fact_57_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_58_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_59_power__one, axiom,
    ((![N : nat]: ((power_power_int @ one_one_int @ N) = one_one_int)))). % power_one
thf(fact_60_div__minus__minus, axiom,
    ((![A : int, B : int]: ((divide_divide_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (divide_divide_int @ A @ B))))). % div_minus_minus
thf(fact_61_nat__power__eq__Suc__0__iff, axiom,
    ((![X : nat, M : nat]: (((power_power_nat @ X @ M) = (suc @ zero_zero_nat)) = (((M = zero_zero_nat)) | ((X = (suc @ zero_zero_nat)))))))). % nat_power_eq_Suc_0_iff
thf(fact_62_power__Suc__0, axiom,
    ((![N : nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ N) = (suc @ zero_zero_nat))))). % power_Suc_0
thf(fact_63_div__by__Suc__0, axiom,
    ((![M : nat]: ((divide_divide_nat @ M @ (suc @ zero_zero_nat)) = M)))). % div_by_Suc_0
thf(fact_64_div__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => ((divide_divide_nat @ M @ N) = zero_zero_nat))))). % div_less
thf(fact_65_nat__zero__less__power__iff, axiom,
    ((![X : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ X @ N)) = (((ord_less_nat @ zero_zero_nat @ X)) | ((N = zero_zero_nat))))))). % nat_zero_less_power_iff
thf(fact_66_root1, axiom,
    (((fFT_Mirabelle_root @ one_one_nat) = one_one_complex))). % root1
thf(fact_67_sum__squares__eq__zero__iff, axiom,
    ((![X : int, Y : int]: (((plus_plus_int @ (times_times_int @ X @ X) @ (times_times_int @ Y @ Y)) = zero_zero_int) = (((X = zero_zero_int)) & ((Y = zero_zero_int))))))). % sum_squares_eq_zero_iff
thf(fact_68_div__mult__mult1__if, axiom,
    ((![C : nat, A : nat, B : nat]: (((C = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = zero_zero_nat)) & ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (divide_divide_nat @ A @ B))))))). % div_mult_mult1_if
thf(fact_69_div__mult__mult1__if, axiom,
    ((![C : int, A : int, B : int]: (((C = zero_zero_int) => ((divide_divide_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = zero_zero_int)) & ((~ ((C = zero_zero_int))) => ((divide_divide_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (divide_divide_int @ A @ B))))))). % div_mult_mult1_if
thf(fact_70_div__mult__mult2, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) = (divide_divide_nat @ A @ B)))))). % div_mult_mult2
thf(fact_71_div__mult__mult2, axiom,
    ((![C : int, A : int, B : int]: ((~ ((C = zero_zero_int))) => ((divide_divide_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)) = (divide_divide_int @ A @ B)))))). % div_mult_mult2
thf(fact_72_div__mult__mult1, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (divide_divide_nat @ A @ B)))))). % div_mult_mult1
thf(fact_73_div__mult__mult1, axiom,
    ((![C : int, A : int, B : int]: ((~ ((C = zero_zero_int))) => ((divide_divide_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (divide_divide_int @ A @ B)))))). % div_mult_mult1
thf(fact_74_neg__numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (ord_less_eq_num @ N @ M))))). % neg_numeral_le_iff
thf(fact_75_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_76_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_77_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_78_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_79_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_80_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_81_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_82_power__inject__exp, axiom,
    ((![A : int, M : nat, N : nat]: ((ord_less_int @ one_one_int @ A) => (((power_power_int @ A @ M) = (power_power_int @ A @ N)) = (M = N)))))). % power_inject_exp
thf(fact_83_power__inject__exp, axiom,
    ((![A : nat, M : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => (((power_power_nat @ A @ M) = (power_power_nat @ A @ N)) = (M = N)))))). % power_inject_exp
thf(fact_84_mult__neg__numeral__simps_I1_J, axiom,
    ((![M : num, N : num]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (numera632737353omplex @ (times_times_num @ M @ N)))))). % mult_neg_numeral_simps(1)
thf(fact_85_mult__neg__numeral__simps_I1_J, axiom,
    ((![M : num, N : num]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (numeral_numeral_int @ (times_times_num @ M @ N)))))). % mult_neg_numeral_simps(1)
thf(fact_86_mult__neg__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ (numera632737353omplex @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(2)
thf(fact_87_mult__neg__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (numeral_numeral_int @ N)) = (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(2)
thf(fact_88_mult__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((times_times_complex @ (numera632737353omplex @ M) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (uminus1204672759omplex @ (numera632737353omplex @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(3)
thf(fact_89_mult__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((times_times_int @ (numeral_numeral_int @ M) @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(3)
thf(fact_90_mult__minus1__right, axiom,
    ((![Z : complex]: ((times_times_complex @ Z @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ Z))))). % mult_minus1_right
thf(fact_91_mult__minus1__right, axiom,
    ((![Z : int]: ((times_times_int @ Z @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ Z))))). % mult_minus1_right
thf(fact_92_mult__minus1, axiom,
    ((![Z : complex]: ((times_times_complex @ (uminus1204672759omplex @ one_one_complex) @ Z) = (uminus1204672759omplex @ Z))))). % mult_minus1
thf(fact_93_mult__minus1, axiom,
    ((![Z : int]: ((times_times_int @ (uminus_uminus_int @ one_one_int) @ Z) = (uminus_uminus_int @ Z))))). % mult_minus1
thf(fact_94_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_95_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_96_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_int = (numeral_numeral_int @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_97_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_98_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_99_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_int @ N) = one_one_int) = (N = one))))). % numeral_eq_one_iff
thf(fact_100_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_101_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_102_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_complex @ zero_zero_complex @ (suc @ N)) = zero_zero_complex)))). % power_0_Suc
thf(fact_103_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_nat @ zero_zero_nat @ (suc @ N)) = zero_zero_nat)))). % power_0_Suc
thf(fact_104_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_int @ zero_zero_int @ (suc @ N)) = zero_zero_int)))). % power_0_Suc
thf(fact_105_div__minus1__right, axiom,
    ((![A : int]: ((divide_divide_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ A))))). % div_minus1_right
thf(fact_106_power__zero__numeral, axiom,
    ((![K : num]: ((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ K)) = zero_zero_complex)))). % power_zero_numeral
thf(fact_107_power__zero__numeral, axiom,
    ((![K : num]: ((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ K)) = zero_zero_nat)))). % power_zero_numeral
thf(fact_108_power__zero__numeral, axiom,
    ((![K : num]: ((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ K)) = zero_zero_int)))). % power_zero_numeral
thf(fact_109_power__add__numeral2, axiom,
    ((![A : int, M : num, N : num, B : int]: ((times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ M)) @ (times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ N)) @ B)) = (times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ (plus_plus_num @ M @ N))) @ B))))). % power_add_numeral2
thf(fact_110_power__add__numeral2, axiom,
    ((![A : nat, M : num, N : num, B : nat]: ((times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ M)) @ (times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ N)) @ B)) = (times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (plus_plus_num @ M @ N))) @ B))))). % power_add_numeral2
thf(fact_111_power__add__numeral2, axiom,
    ((![A : complex, M : num, N : num, B : complex]: ((times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ M)) @ (times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ N)) @ B)) = (times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ (plus_plus_num @ M @ N))) @ B))))). % power_add_numeral2
thf(fact_112_power__add__numeral, axiom,
    ((![A : int, M : num, N : num]: ((times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ M)) @ (power_power_int @ A @ (numeral_numeral_nat @ N))) = (power_power_int @ A @ (numeral_numeral_nat @ (plus_plus_num @ M @ N))))))). % power_add_numeral
thf(fact_113_power__add__numeral, axiom,
    ((![A : nat, M : num, N : num]: ((times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ M)) @ (power_power_nat @ A @ (numeral_numeral_nat @ N))) = (power_power_nat @ A @ (numeral_numeral_nat @ (plus_plus_num @ M @ N))))))). % power_add_numeral
thf(fact_114_power__add__numeral, axiom,
    ((![A : complex, M : num, N : num]: ((times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ M)) @ (power_power_complex @ A @ (numeral_numeral_nat @ N))) = (power_power_complex @ A @ (numeral_numeral_nat @ (plus_plus_num @ M @ N))))))). % power_add_numeral
thf(fact_115_power__Suc0__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_116_power__Suc0__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_117_power__Suc0__right, axiom,
    ((![A : int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_118_Suc__numeral, axiom,
    ((![N : num]: ((suc @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ N @ one)))))). % Suc_numeral
thf(fact_119_div__mult__self1__is__m, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((divide_divide_nat @ (times_times_nat @ N @ M) @ N) = M))))). % div_mult_self1_is_m
thf(fact_120_div__mult__self__is__m, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((divide_divide_nat @ (times_times_nat @ M @ N) @ N) = M))))). % div_mult_self_is_m
thf(fact_121_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_122_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_123_div__mult__self4, axiom,
    ((![B : nat, C : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ A) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self4
thf(fact_124_div__mult__self4, axiom,
    ((![B : int, C : int, A : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ (times_times_int @ B @ C) @ A) @ B) = (plus_plus_int @ C @ (divide_divide_int @ A @ B))))))). % div_mult_self4
thf(fact_125_div__mult__self3, axiom,
    ((![B : nat, C : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ C @ B) @ A) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self3
thf(fact_126_div__mult__self3, axiom,
    ((![B : int, C : int, A : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ (times_times_int @ C @ B) @ A) @ B) = (plus_plus_int @ C @ (divide_divide_int @ A @ B))))))). % div_mult_self3
thf(fact_127_div__mult__self2, axiom,
    ((![B : nat, A : nat, C : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ A @ (times_times_nat @ B @ C)) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self2
thf(fact_128_div__mult__self2, axiom,
    ((![B : int, A : int, C : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ A @ (times_times_int @ B @ C)) @ B) = (plus_plus_int @ C @ (divide_divide_int @ A @ B))))))). % div_mult_self2
thf(fact_129_div__mult__self1, axiom,
    ((![B : nat, A : nat, C : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ A @ (times_times_nat @ C @ B)) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self1
thf(fact_130_div__mult__self1, axiom,
    ((![B : int, A : int, C : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ A @ (times_times_int @ C @ B)) @ B) = (plus_plus_int @ C @ (divide_divide_int @ A @ B))))))). % div_mult_self1
thf(fact_131_numeral__le__one__iff, axiom,
    ((![N : num]: ((ord_less_eq_int @ (numeral_numeral_int @ N) @ one_one_int) = (ord_less_eq_num @ N @ one))))). % numeral_le_one_iff
thf(fact_132_numeral__le__one__iff, axiom,
    ((![N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ N) @ one_one_nat) = (ord_less_eq_num @ N @ one))))). % numeral_le_one_iff
thf(fact_133_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_134_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_135_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_136_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_137_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_138_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_139_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_140_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_141_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_142_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_143_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_144_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_145_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ one_one_complex)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_146_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_147_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_148_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_149_left__minus__one__mult__self, axiom,
    ((![N : nat, A : complex]: ((times_times_complex @ (power_power_complex @ (uminus1204672759omplex @ one_one_complex) @ N) @ (times_times_complex @ (power_power_complex @ (uminus1204672759omplex @ one_one_complex) @ N) @ A)) = A)))). % left_minus_one_mult_self
thf(fact_150_left__minus__one__mult__self, axiom,
    ((![N : nat, A : int]: ((times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ N) @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ N) @ A)) = A)))). % left_minus_one_mult_self
thf(fact_151_minus__one__mult__self, axiom,
    ((![N : nat]: ((times_times_complex @ (power_power_complex @ (uminus1204672759omplex @ one_one_complex) @ N) @ (power_power_complex @ (uminus1204672759omplex @ one_one_complex) @ N)) = one_one_complex)))). % minus_one_mult_self
thf(fact_152_minus__one__mult__self, axiom,
    ((![N : nat]: ((times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ N) @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ N)) = one_one_int)))). % minus_one_mult_self
thf(fact_153_power__strict__increasing__iff, axiom,
    ((![B : int, X : nat, Y : nat]: ((ord_less_int @ one_one_int @ B) => ((ord_less_int @ (power_power_int @ B @ X) @ (power_power_int @ B @ Y)) = (ord_less_nat @ X @ Y)))))). % power_strict_increasing_iff
thf(fact_154_power__strict__increasing__iff, axiom,
    ((![B : nat, X : nat, Y : nat]: ((ord_less_nat @ one_one_nat @ B) => ((ord_less_nat @ (power_power_nat @ B @ X) @ (power_power_nat @ B @ Y)) = (ord_less_nat @ X @ Y)))))). % power_strict_increasing_iff
thf(fact_155_power__eq__0__iff, axiom,
    ((![A : complex, N : nat]: (((power_power_complex @ A @ N) = zero_zero_complex) = (((A = zero_zero_complex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_156_power__eq__0__iff, axiom,
    ((![A : nat, N : nat]: (((power_power_nat @ A @ N) = zero_zero_nat) = (((A = zero_zero_nat)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_157_power__eq__0__iff, axiom,
    ((![A : int, N : nat]: (((power_power_int @ A @ N) = zero_zero_int) = (((A = zero_zero_int)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_158_div2__Suc__Suc, axiom,
    ((![M : nat]: ((divide_divide_nat @ (suc @ (suc @ M)) @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (divide_divide_nat @ M @ (numeral_numeral_nat @ (bit0 @ one)))))))). % div2_Suc_Suc
thf(fact_159_Suc__1, axiom,
    (((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % Suc_1
thf(fact_160_add__self__div__2, axiom,
    ((![M : nat]: ((divide_divide_nat @ (plus_plus_nat @ M @ M) @ (numeral_numeral_nat @ (bit0 @ one))) = M)))). % add_self_div_2
thf(fact_161_eq__divide__eq__numeral1_I2_J, axiom,
    ((![A : complex, B : complex, W : num]: ((A = (divide1210191872omplex @ B @ (uminus1204672759omplex @ (numera632737353omplex @ W)))) = (((((~ (((uminus1204672759omplex @ (numera632737353omplex @ W)) = zero_zero_complex)))) => (((times_times_complex @ A @ (uminus1204672759omplex @ (numera632737353omplex @ W))) = B)))) & (((((uminus1204672759omplex @ (numera632737353omplex @ W)) = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % eq_divide_eq_numeral1(2)
thf(fact_162_divide__eq__eq__numeral1_I2_J, axiom,
    ((![B : complex, W : num, A : complex]: (((divide1210191872omplex @ B @ (uminus1204672759omplex @ (numera632737353omplex @ W))) = A) = (((((~ (((uminus1204672759omplex @ (numera632737353omplex @ W)) = zero_zero_complex)))) => ((B = (times_times_complex @ A @ (uminus1204672759omplex @ (numera632737353omplex @ W))))))) & (((((uminus1204672759omplex @ (numera632737353omplex @ W)) = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % divide_eq_eq_numeral1(2)
thf(fact_163_not__neg__one__le__neg__numeral__iff, axiom,
    ((![M : num]: ((~ ((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ M))))) = (~ ((M = one))))))). % not_neg_one_le_neg_numeral_iff
thf(fact_164_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_165_power__strict__decreasing__iff, axiom,
    ((![B : int, M : nat, N : nat]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_int @ B @ one_one_int) => ((ord_less_int @ (power_power_int @ B @ M) @ (power_power_int @ B @ N)) = (ord_less_nat @ N @ M))))))). % power_strict_decreasing_iff
thf(fact_166_power__strict__decreasing__iff, axiom,
    ((![B : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ B @ one_one_nat) => ((ord_less_nat @ (power_power_nat @ B @ M) @ (power_power_nat @ B @ N)) = (ord_less_nat @ N @ M))))))). % power_strict_decreasing_iff
thf(fact_167_power__increasing__iff, axiom,
    ((![B : int, X : nat, Y : nat]: ((ord_less_int @ one_one_int @ B) => ((ord_less_eq_int @ (power_power_int @ B @ X) @ (power_power_int @ B @ Y)) = (ord_less_eq_nat @ X @ Y)))))). % power_increasing_iff
thf(fact_168_power__increasing__iff, axiom,
    ((![B : nat, X : nat, Y : nat]: ((ord_less_nat @ one_one_nat @ B) => ((ord_less_eq_nat @ (power_power_nat @ B @ X) @ (power_power_nat @ B @ Y)) = (ord_less_eq_nat @ X @ Y)))))). % power_increasing_iff
thf(fact_169_power__mono__iff, axiom,
    ((![A : int, B : int, N : nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_eq_int @ (power_power_int @ A @ N) @ (power_power_int @ B @ N)) = (ord_less_eq_int @ A @ B)))))))). % power_mono_iff
thf(fact_170_power__mono__iff, axiom,
    ((![A : nat, B : nat, N : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_eq_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N)) = (ord_less_eq_nat @ A @ B)))))))). % power_mono_iff
thf(fact_171_calculation, axiom,
    (((groups59700922omplex @ (^[J2 : nat]: (divide1210191872omplex @ (a @ J2) @ (power_power_complex @ (fFT_Mirabelle_root @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) @ (times_times_nat @ i @ J2)))) @ (set_or562006527an_nat @ zero_zero_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))) = (plus_plus_complex @ (groups59700922omplex @ (^[J2 : nat]: (divide1210191872omplex @ (a @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ J2)) @ (power_power_complex @ (fFT_Mirabelle_root @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) @ (times_times_nat @ i @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ J2))))) @ (set_or562006527an_nat @ zero_zero_nat @ m)) @ (groups59700922omplex @ (^[J2 : nat]: (divide1210191872omplex @ (a @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ J2) @ one_one_nat)) @ (power_power_complex @ (fFT_Mirabelle_root @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) @ (times_times_nat @ i @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ J2) @ one_one_nat))))) @ (set_or562006527an_nat @ zero_zero_nat @ m)))))). % calculation
thf(fact_172_power__decreasing__iff, axiom,
    ((![B : int, M : nat, N : nat]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_int @ B @ one_one_int) => ((ord_less_eq_int @ (power_power_int @ B @ M) @ (power_power_int @ B @ N)) = (ord_less_eq_nat @ N @ M))))))). % power_decreasing_iff
thf(fact_173_power__decreasing__iff, axiom,
    ((![B : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ B @ one_one_nat) => ((ord_less_eq_nat @ (power_power_nat @ B @ M) @ (power_power_nat @ B @ N)) = (ord_less_eq_nat @ N @ M))))))). % power_decreasing_iff
thf(fact_174_power2__eq__iff__nonneg, axiom,
    ((![X : int, Y : int]: ((ord_less_eq_int @ zero_zero_int @ X) => ((ord_less_eq_int @ zero_zero_int @ Y) => (((power_power_int @ X @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ Y @ (numeral_numeral_nat @ (bit0 @ one)))) = (X = Y))))))). % power2_eq_iff_nonneg
thf(fact_175_power2__eq__iff__nonneg, axiom,
    ((![X : nat, Y : nat]: ((ord_less_eq_nat @ zero_zero_nat @ X) => ((ord_less_eq_nat @ zero_zero_nat @ Y) => (((power_power_nat @ X @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_nat @ Y @ (numeral_numeral_nat @ (bit0 @ one)))) = (X = Y))))))). % power2_eq_iff_nonneg
thf(fact_176_power2__less__eq__zero__iff, axiom,
    ((![A : int]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_int) = (A = zero_zero_int))))). % power2_less_eq_zero_iff
thf(fact_177_zero__less__power2, axiom,
    ((![A : int]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (~ ((A = zero_zero_int))))))). % zero_less_power2
thf(fact_178_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_179_nat__power__less__imp__less, axiom,
    ((![I : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ I) => ((ord_less_nat @ (power_power_nat @ I @ M) @ (power_power_nat @ I @ N)) => (ord_less_nat @ M @ N)))))). % nat_power_less_imp_less
thf(fact_180_div__le__mono, axiom,
    ((![M : nat, N : nat, K : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ (divide_divide_nat @ M @ K) @ (divide_divide_nat @ N @ K)))))). % div_le_mono
thf(fact_181_Euclidean__Division_Odiv__eq__0__iff, axiom,
    ((![M : nat, N : nat]: (((divide_divide_nat @ M @ N) = zero_zero_nat) = (((ord_less_nat @ M @ N)) | ((N = zero_zero_nat))))))). % Euclidean_Division.div_eq_0_iff
thf(fact_182_div__le__mono2, axiom,
    ((![M : nat, N : nat, K : nat]: ((ord_less_nat @ zero_zero_nat @ M) => ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ (divide_divide_nat @ K @ N) @ (divide_divide_nat @ K @ M))))))). % div_le_mono2
thf(fact_183_Suc__div__le__mono, axiom,
    ((![M : nat, N : nat]: (ord_less_eq_nat @ (divide_divide_nat @ M @ N) @ (divide_divide_nat @ (suc @ M) @ N))))). % Suc_div_le_mono
thf(fact_184_div__le__dividend, axiom,
    ((![M : nat, N : nat]: (ord_less_eq_nat @ (divide_divide_nat @ M @ N) @ M)))). % div_le_dividend
thf(fact_185_div__less__dividend, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ one_one_nat @ N) => ((ord_less_nat @ zero_zero_nat @ M) => (ord_less_nat @ (divide_divide_nat @ M @ N) @ M)))))). % div_less_dividend
thf(fact_186_div__eq__dividend__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ M) => (((divide_divide_nat @ M @ N) = M) = (N = one_one_nat)))))). % div_eq_dividend_iff
thf(fact_187_div__greater__zero__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ M @ N)) = (((ord_less_eq_nat @ N @ M)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % div_greater_zero_iff
thf(fact_188_less__mult__imp__div__less, axiom,
    ((![M : nat, I : nat, N : nat]: ((ord_less_nat @ M @ (times_times_nat @ I @ N)) => (ord_less_nat @ (divide_divide_nat @ M @ N) @ I))))). % less_mult_imp_div_less
thf(fact_189_div__times__less__eq__dividend, axiom,
    ((![M : nat, N : nat]: (ord_less_eq_nat @ (times_times_nat @ (divide_divide_nat @ M @ N) @ N) @ M)))). % div_times_less_eq_dividend
thf(fact_190_times__div__less__eq__dividend, axiom,
    ((![N : nat, M : nat]: (ord_less_eq_nat @ (times_times_nat @ N @ (divide_divide_nat @ M @ N)) @ M)))). % times_div_less_eq_dividend
thf(fact_191_power__le__imp__le__exp, axiom,
    ((![A : int, M : nat, N : nat]: ((ord_less_int @ one_one_int @ A) => ((ord_less_eq_int @ (power_power_int @ A @ M) @ (power_power_int @ A @ N)) => (ord_less_eq_nat @ M @ N)))))). % power_le_imp_le_exp
thf(fact_192_power__le__imp__le__exp, axiom,
    ((![A : nat, M : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ (power_power_nat @ A @ M) @ (power_power_nat @ A @ N)) => (ord_less_eq_nat @ M @ N)))))). % power_le_imp_le_exp
thf(fact_193_div__nat__eqI, axiom,
    ((![N : nat, Q : nat, M : nat]: ((ord_less_eq_nat @ (times_times_nat @ N @ Q) @ M) => ((ord_less_nat @ M @ (times_times_nat @ N @ (suc @ Q))) => ((divide_divide_nat @ M @ N) = Q)))))). % div_nat_eqI
thf(fact_194_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_numeral_extra(3)
thf(fact_195_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_196_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_int @ zero_zero_int @ zero_zero_int))). % le_numeral_extra(3)
thf(fact_197_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat))). % le_numeral_extra(3)
thf(fact_198_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_int @ one_one_int @ one_one_int))))). % less_numeral_extra(4)
thf(fact_199_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ one_one_nat))))). % less_numeral_extra(4)
thf(fact_200_add__One__commute, axiom,
    ((![N : num]: ((plus_plus_num @ one @ N) = (plus_plus_num @ N @ one))))). % add_One_commute
thf(fact_201_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_int @ one_one_int @ one_one_int))). % le_numeral_extra(4)
thf(fact_202_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_nat @ one_one_nat @ one_one_nat))). % le_numeral_extra(4)
thf(fact_203_div__mult2__eq, axiom,
    ((![M : nat, N : nat, Q : nat]: ((divide_divide_nat @ M @ (times_times_nat @ N @ Q)) = (divide_divide_nat @ (divide_divide_nat @ M @ N) @ Q))))). % div_mult2_eq
thf(fact_204_power__less__imp__less__base, axiom,
    ((![A : int, N : nat, B : int]: ((ord_less_int @ (power_power_int @ A @ N) @ (power_power_int @ B @ N)) => ((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_int @ A @ B)))))). % power_less_imp_less_base
thf(fact_205_power__less__imp__less__base, axiom,
    ((![A : nat, N : nat, B : nat]: ((ord_less_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N)) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ A @ B)))))). % power_less_imp_less_base
thf(fact_206_power__strict__increasing, axiom,
    ((![N : nat, N2 : nat, A : int]: ((ord_less_nat @ N @ N2) => ((ord_less_int @ one_one_int @ A) => (ord_less_int @ (power_power_int @ A @ N) @ (power_power_int @ A @ N2))))))). % power_strict_increasing
thf(fact_207_power__strict__increasing, axiom,
    ((![N : nat, N2 : nat, A : nat]: ((ord_less_nat @ N @ N2) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ A @ N2))))))). % power_strict_increasing
thf(fact_208_power__less__imp__less__exp, axiom,
    ((![A : int, M : nat, N : nat]: ((ord_less_int @ one_one_int @ A) => ((ord_less_int @ (power_power_int @ A @ M) @ (power_power_int @ A @ N)) => (ord_less_nat @ M @ N)))))). % power_less_imp_less_exp
thf(fact_209_power__less__imp__less__exp, axiom,
    ((![A : nat, M : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ M) @ (power_power_nat @ A @ N)) => (ord_less_nat @ M @ N)))))). % power_less_imp_less_exp
thf(fact_210_power__increasing, axiom,
    ((![N : nat, N2 : nat, A : int]: ((ord_less_eq_nat @ N @ N2) => ((ord_less_eq_int @ one_one_int @ A) => (ord_less_eq_int @ (power_power_int @ A @ N) @ (power_power_int @ A @ N2))))))). % power_increasing
thf(fact_211_power__increasing, axiom,
    ((![N : nat, N2 : nat, A : nat]: ((ord_less_eq_nat @ N @ N2) => ((ord_less_eq_nat @ one_one_nat @ A) => (ord_less_eq_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ A @ N2))))))). % power_increasing
thf(fact_212_power__gt__expt, axiom,
    ((![N : nat, K : nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ N) => (ord_less_nat @ K @ (power_power_nat @ N @ K)))))). % power_gt_expt
thf(fact_213_nat__one__le__power, axiom,
    ((![I : nat, N : nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ I) => (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (power_power_nat @ I @ N)))))). % nat_one_le_power
thf(fact_214_power__strict__mono, axiom,
    ((![A : int, B : int, N : nat]: ((ord_less_int @ A @ B) => ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_int @ (power_power_int @ A @ N) @ (power_power_int @ B @ N)))))))). % power_strict_mono
thf(fact_215_power__strict__mono, axiom,
    ((![A : nat, B : nat, N : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N)))))))). % power_strict_mono
thf(fact_216_split__div_H, axiom,
    ((![P : nat > $o, M : nat, N : nat]: ((P @ (divide_divide_nat @ M @ N)) = (((((N = zero_zero_nat)) & ((P @ zero_zero_nat)))) | ((?[Q2 : nat]: (((((ord_less_eq_nat @ (times_times_nat @ N @ Q2) @ M)) & ((ord_less_nat @ M @ (times_times_nat @ N @ (suc @ Q2)))))) & ((P @ Q2)))))))))). % split_div'
thf(fact_217_ex__power__ivl2, axiom,
    ((![B : nat, K : nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ K) => (?[N3 : nat]: ((ord_less_nat @ (power_power_nat @ B @ N3) @ K) & (ord_less_eq_nat @ K @ (power_power_nat @ B @ (plus_plus_nat @ N3 @ one_one_nat)))))))))). % ex_power_ivl2
thf(fact_218_ex__power__ivl1, axiom,
    ((![B : nat, K : nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) => ((ord_less_eq_nat @ one_one_nat @ K) => (?[N3 : nat]: ((ord_less_eq_nat @ (power_power_nat @ B @ N3) @ K) & (ord_less_nat @ K @ (power_power_nat @ B @ (plus_plus_nat @ N3 @ one_one_nat)))))))))). % ex_power_ivl1
thf(fact_219_power__strict__decreasing, axiom,
    ((![N : nat, N2 : nat, A : int]: ((ord_less_nat @ N @ N2) => ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ one_one_int) => (ord_less_int @ (power_power_int @ A @ N2) @ (power_power_int @ A @ N)))))))). % power_strict_decreasing
thf(fact_220_power__strict__decreasing, axiom,
    ((![N : nat, N2 : nat, A : nat]: ((ord_less_nat @ N @ N2) => ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (power_power_nat @ A @ N2) @ (power_power_nat @ A @ N)))))))). % power_strict_decreasing
thf(fact_221_power__decreasing, axiom,
    ((![N : nat, N2 : nat, A : int]: ((ord_less_eq_nat @ N @ N2) => ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ N2) @ (power_power_int @ A @ N)))))))). % power_decreasing
thf(fact_222_power__decreasing, axiom,
    ((![N : nat, N2 : nat, A : nat]: ((ord_less_eq_nat @ N @ N2) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ A @ N2) @ (power_power_nat @ A @ N)))))))). % power_decreasing
thf(fact_223_power__eq__imp__eq__base, axiom,
    ((![A : int, N : nat, B : int]: (((power_power_int @ A @ N) = (power_power_int @ B @ N)) => ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((ord_less_nat @ zero_zero_nat @ N) => (A = B)))))))). % power_eq_imp_eq_base
thf(fact_224_power__eq__imp__eq__base, axiom,
    ((![A : nat, N : nat, B : nat]: (((power_power_nat @ A @ N) = (power_power_nat @ B @ N)) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ N) => (A = B)))))))). % power_eq_imp_eq_base
thf(fact_225_power__eq__iff__eq__base, axiom,
    ((![N : nat, A : int, B : int]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => (((power_power_int @ A @ N) = (power_power_int @ B @ N)) = (A = B)))))))). % power_eq_iff_eq_base
thf(fact_226_power__eq__iff__eq__base, axiom,
    ((![N : nat, A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (((power_power_nat @ A @ N) = (power_power_nat @ B @ N)) = (A = B)))))))). % power_eq_iff_eq_base
thf(fact_227_power2__nat__le__imp__le, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ (power_power_nat @ M @ (numeral_numeral_nat @ (bit0 @ one))) @ N) => (ord_less_eq_nat @ M @ N))))). % power2_nat_le_imp_le
thf(fact_228_power2__nat__le__eq__le, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ (power_power_nat @ M @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ N @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_nat @ M @ N))))). % power2_nat_le_eq_le
thf(fact_229_self__le__ge2__pow, axiom,
    ((![K : nat, M : nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ K) => (ord_less_eq_nat @ M @ (power_power_nat @ K @ M)))))). % self_le_ge2_pow
thf(fact_230_one__less__power, axiom,
    ((![A : int, N : nat]: ((ord_less_int @ one_one_int @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_int @ one_one_int @ (power_power_int @ A @ N))))))). % one_less_power
thf(fact_231_one__less__power, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ one_one_nat @ (power_power_nat @ A @ N))))))). % one_less_power
thf(fact_232_self__le__power, axiom,
    ((![A : int, N : nat]: ((ord_less_eq_int @ one_one_int @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_eq_int @ A @ (power_power_int @ A @ N))))))). % self_le_power
thf(fact_233_self__le__power, axiom,
    ((![A : nat, N : nat]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_eq_nat @ A @ (power_power_nat @ A @ N))))))). % self_le_power
thf(fact_234_dividend__less__times__div, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ M @ (plus_plus_nat @ N @ (times_times_nat @ N @ (divide_divide_nat @ M @ N)))))))). % dividend_less_times_div
thf(fact_235_dividend__less__div__times, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ M @ (plus_plus_nat @ N @ (times_times_nat @ (divide_divide_nat @ M @ N) @ N))))))). % dividend_less_div_times
thf(fact_236_split__div, axiom,
    ((![P : nat > $o, M : nat, N : nat]: ((P @ (divide_divide_nat @ M @ N)) = (((((N = zero_zero_nat)) => ((P @ zero_zero_nat)))) & ((((~ ((N = zero_zero_nat)))) => ((![I2 : nat]: (![J2 : nat]: (((ord_less_nat @ J2 @ N)) => ((((M = (plus_plus_nat @ (times_times_nat @ N @ I2) @ J2))) => ((P @ I2))))))))))))))). % split_div

% Conjectures (1)
thf(conj_0, conjecture,
    (((groups59700922omplex @ (^[J2 : nat]: (divide1210191872omplex @ (a @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ J2))) @ (power_power_complex @ (fFT_Mirabelle_root @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) @ (plus_plus_nat @ i @ (times_times_nat @ i @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ J2)))))) @ (set_or562006527an_nat @ zero_zero_nat @ m)) = (uminus1204672759omplex @ (divide1210191872omplex @ (times_times_complex @ (power_power_complex @ (divide1210191872omplex @ one_one_complex @ (fFT_Mirabelle_root @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))) @ i) @ (groups59700922omplex @ (^[J2 : nat]: (divide1210191872omplex @ (a @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ J2))) @ (power_power_complex @ (power_power_complex @ (fFT_Mirabelle_root @ m) @ i) @ J2))) @ (set_or562006527an_nat @ zero_zero_nat @ m))) @ (power_power_complex @ (divide1210191872omplex @ one_one_complex @ (fFT_Mirabelle_root @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))) @ m)))))).
