% 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_165__3224376_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:37.615

% 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 (40)
thf(sy_c_Complex_Ocis, type,
    cis : real > complex).
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_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint, type,
    times_times_int : int > int > int).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum, type,
    times_times_num : num > num > num).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint, type,
    zero_zero_int : int).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex, type,
    semiri356525583omplex : nat > complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint, type,
    semiri2019852685at_int : nat > int).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal, type,
    semiri2110766477t_real : nat > 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_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_Transcendental_Ocos_001t__Complex__Ocomplex, type,
    cos_complex : complex > complex).
thf(sy_c_Transcendental_Ocos_001t__Real__Oreal, type,
    cos_real : real > real).
thf(sy_c_Transcendental_Opi, type,
    pi : real).
thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex, type,
    sin_complex : complex > complex).
thf(sy_c_Transcendental_Osin_001t__Real__Oreal, type,
    sin_real : real > real).
thf(sy_v_k, type,
    k : nat).
thf(sy_v_n, type,
    n : nat).

% Relevant facts (241)
thf(fact_0_realk, axiom,
    ((ord_less_real @ (divide_divide_real @ (times_times_real @ (semiri2110766477t_real @ k) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) @ (semiri2110766477t_real @ n)) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)))). % realk
thf(fact_1_real0, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ (times_times_real @ (semiri2110766477t_real @ k) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) @ (semiri2110766477t_real @ n))))). % real0
thf(fact_2_sin__cos__between__zero__two__pi, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => ((~ (((sin_real @ X) = zero_zero_real))) | (~ (((cos_real @ X) = one_one_real))))))))). % sin_cos_between_zero_two_pi
thf(fact_3_k_I2_J, axiom,
    ((ord_less_nat @ k @ n))). % k(2)
thf(fact_4_cis__2pi, axiom,
    (((cis @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = one_one_complex))). % cis_2pi
thf(fact_5_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_6_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_real @ N) = one_one_real) = (N = one))))). % numeral_eq_one_iff
thf(fact_7_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_8_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_int @ N) = one_one_int) = (N = one))))). % numeral_eq_one_iff
thf(fact_9_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_10_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_real = (numeral_numeral_real @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_11_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_12_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_int = (numeral_numeral_int @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_13__092_060open_062k_A_060_An_A_092_060Longrightarrow_062_Areal_Ak_A_K_A_I2_A_K_Api_J_A_P_Areal_An_A_060_A2_A_K_Api_092_060close_062, axiom,
    (((ord_less_nat @ k @ n) => (ord_less_real @ (divide_divide_real @ (times_times_real @ (semiri2110766477t_real @ k) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) @ (semiri2110766477t_real @ n)) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))))). % \<open>k < n \<Longrightarrow> real k * (2 * pi) / real n < 2 * pi\<close>
thf(fact_14_FFT__Mirabelle__ulikgskiun_Oroot__def, axiom,
    ((fFT_Mirabelle_root = (^[N2 : nat]: (cis @ (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ (semiri2110766477t_real @ N2))))))). % FFT_Mirabelle_ulikgskiun.root_def
thf(fact_15_real__divide__square__eq, axiom,
    ((![R : real, A : real]: ((divide_divide_real @ (times_times_real @ R @ A) @ (times_times_real @ R @ R)) = (divide_divide_real @ A @ R))))). % real_divide_square_eq
thf(fact_16_pi__half__neq__two, axiom,
    ((~ (((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) = (numeral_numeral_real @ (bit0 @ one))))))). % pi_half_neq_two
thf(fact_17_of__nat__1, axiom,
    (((semiri356525583omplex @ one_one_nat) = one_one_complex))). % of_nat_1
thf(fact_18_of__nat__1, axiom,
    (((semiri1382578993at_nat @ one_one_nat) = one_one_nat))). % of_nat_1
thf(fact_19_of__nat__1, axiom,
    (((semiri2019852685at_int @ one_one_nat) = one_one_int))). % of_nat_1
thf(fact_20_of__nat__1, axiom,
    (((semiri2110766477t_real @ one_one_nat) = one_one_real))). % of_nat_1
thf(fact_21_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_complex = (semiri356525583omplex @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_22_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_nat = (semiri1382578993at_nat @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_23_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_int = (semiri2019852685at_int @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_24_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_real = (semiri2110766477t_real @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_25_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri356525583omplex @ N) = one_one_complex) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_26_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri1382578993at_nat @ N) = one_one_nat) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_27_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri2019852685at_int @ N) = one_one_int) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_28_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri2110766477t_real @ N) = one_one_real) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_29_of__nat__numeral, axiom,
    ((![N : num]: ((semiri1382578993at_nat @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ N))))). % of_nat_numeral
thf(fact_30_of__nat__numeral, axiom,
    ((![N : num]: ((semiri2019852685at_int @ (numeral_numeral_nat @ N)) = (numeral_numeral_int @ N))))). % of_nat_numeral
thf(fact_31_of__nat__numeral, axiom,
    ((![N : num]: ((semiri356525583omplex @ (numeral_numeral_nat @ N)) = (numera632737353omplex @ N))))). % of_nat_numeral
thf(fact_32_of__nat__numeral, axiom,
    ((![N : num]: ((semiri2110766477t_real @ (numeral_numeral_nat @ N)) = (numeral_numeral_real @ N))))). % of_nat_numeral
thf(fact_33_of__nat__mult, axiom,
    ((![M : nat, N : nat]: ((semiri1382578993at_nat @ (times_times_nat @ M @ N)) = (times_times_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)))))). % of_nat_mult
thf(fact_34_of__nat__mult, axiom,
    ((![M : nat, N : nat]: ((semiri2110766477t_real @ (times_times_nat @ M @ N)) = (times_times_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)))))). % of_nat_mult
thf(fact_35_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_36_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_37_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_38_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_39_of__nat__eq__iff, axiom,
    ((![M : nat, N : nat]: (((semiri2110766477t_real @ M) = (semiri2110766477t_real @ N)) = (M = N))))). % of_nat_eq_iff
thf(fact_40_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_41_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_42_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_43_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_44_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_45_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_46_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_47_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (times_times_real @ (numeral_numeral_real @ W) @ Z)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ V @ W)) @ Z))))). % mult_numeral_left_semiring_numeral
thf(fact_48_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_49_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_50_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_51_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri1382578993at_nat @ M) = zero_zero_nat) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_52_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri2019852685at_int @ M) = zero_zero_int) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_53_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri2110766477t_real @ M) = zero_zero_real) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_54_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_nat = (semiri1382578993at_nat @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_55_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_int = (semiri2019852685at_int @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_56_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_real = (semiri2110766477t_real @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_57_of__nat__0, axiom,
    (((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat))). % of_nat_0
thf(fact_58_of__nat__0, axiom,
    (((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int))). % of_nat_0
thf(fact_59_of__nat__0, axiom,
    (((semiri2110766477t_real @ zero_zero_nat) = zero_zero_real))). % of_nat_0
thf(fact_60_num__double, axiom,
    ((![N : num]: ((times_times_num @ (bit0 @ one) @ N) = (bit0 @ N))))). % num_double
thf(fact_61_sin__zero, axiom,
    (((sin_real @ zero_zero_real) = zero_zero_real))). % sin_zero
thf(fact_62_nat__1__eq__mult__iff, axiom,
    ((![M : nat, N : nat]: ((one_one_nat = (times_times_nat @ M @ N)) = (((M = one_one_nat)) & ((N = one_one_nat))))))). % nat_1_eq_mult_iff
thf(fact_63_nat__mult__eq__1__iff, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = one_one_nat) = (((M = one_one_nat)) & ((N = one_one_nat))))))). % nat_mult_eq_1_iff
thf(fact_64_k_I1_J, axiom,
    ((ord_less_nat @ zero_zero_nat @ k))). % k(1)
thf(fact_65_of__nat__less__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)) = (ord_less_nat @ M @ N))))). % of_nat_less_iff
thf(fact_66_of__nat__less__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N)) = (ord_less_nat @ M @ N))))). % of_nat_less_iff
thf(fact_67_of__nat__less__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)) = (ord_less_nat @ M @ N))))). % of_nat_less_iff
thf(fact_68_cos__zero, axiom,
    (((cos_complex @ zero_zero_complex) = one_one_complex))). % cos_zero
thf(fact_69_cos__zero, axiom,
    (((cos_real @ zero_zero_real) = one_one_real))). % cos_zero
thf(fact_70_not__real__square__gt__zero, axiom,
    ((![X : real]: ((~ ((ord_less_real @ zero_zero_real @ (times_times_real @ X @ X)))) = (X = zero_zero_real))))). % not_real_square_gt_zero
thf(fact_71_sin__pi, axiom,
    (((sin_real @ pi) = zero_zero_real))). % sin_pi
thf(fact_72_cis__zero, axiom,
    (((cis @ zero_zero_real) = one_one_complex))). % cis_zero
thf(fact_73_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_74_eq__divide__eq__numeral1_I1_J, axiom,
    ((![A : real, B : real, W : num]: ((A = (divide_divide_real @ B @ (numeral_numeral_real @ W))) = (((((~ (((numeral_numeral_real @ W) = zero_zero_real)))) => (((times_times_real @ A @ (numeral_numeral_real @ W)) = B)))) & (((((numeral_numeral_real @ W) = zero_zero_real)) => ((A = zero_zero_real))))))))). % eq_divide_eq_numeral1(1)
thf(fact_75_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_76_divide__eq__eq__numeral1_I1_J, axiom,
    ((![B : real, W : num, A : real]: (((divide_divide_real @ B @ (numeral_numeral_real @ W)) = A) = (((((~ (((numeral_numeral_real @ W) = zero_zero_real)))) => ((B = (times_times_real @ A @ (numeral_numeral_real @ W)))))) & (((((numeral_numeral_real @ W) = zero_zero_real)) => ((A = zero_zero_real))))))))). % divide_eq_eq_numeral1(1)
thf(fact_77_less__divide__eq__numeral1_I1_J, axiom,
    ((![A : real, B : real, W : num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ W))) = (ord_less_real @ (times_times_real @ A @ (numeral_numeral_real @ W)) @ B))))). % less_divide_eq_numeral1(1)
thf(fact_78_divide__less__eq__numeral1_I1_J, axiom,
    ((![B : real, W : num, A : real]: ((ord_less_real @ (divide_divide_real @ B @ (numeral_numeral_real @ W)) @ A) = (ord_less_real @ B @ (times_times_real @ A @ (numeral_numeral_real @ W))))))). % divide_less_eq_numeral1(1)
thf(fact_79_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_80_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_81_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_82_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1382578993at_nat @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_83_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_int @ zero_zero_int @ (semiri2019852685at_int @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_84_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_real @ zero_zero_real @ (semiri2110766477t_real @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_85_sin__npi2, axiom,
    ((![N : nat]: ((sin_real @ (times_times_real @ pi @ (semiri2110766477t_real @ N))) = zero_zero_real)))). % sin_npi2
thf(fact_86_sin__npi, axiom,
    ((![N : nat]: ((sin_real @ (times_times_real @ (semiri2110766477t_real @ N) @ pi)) = zero_zero_real)))). % sin_npi
thf(fact_87_cos__pi__half, axiom,
    (((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real))). % cos_pi_half
thf(fact_88_sin__two__pi, axiom,
    (((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = zero_zero_real))). % sin_two_pi
thf(fact_89_sin__pi__half, axiom,
    (((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = one_one_real))). % sin_pi_half
thf(fact_90_cos__two__pi, axiom,
    (((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = one_one_real))). % cos_two_pi
thf(fact_91_sin__2npi, axiom,
    ((![N : nat]: ((sin_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri2110766477t_real @ N)) @ pi)) = zero_zero_real)))). % sin_2npi
thf(fact_92_cos__2npi, axiom,
    ((![N : nat]: ((cos_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri2110766477t_real @ N)) @ pi)) = one_one_real)))). % cos_2npi
thf(fact_93_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_94_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_95_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_96_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_numeral_extra(3)
thf(fact_97_nat__mult__1, axiom,
    ((![N : nat]: ((times_times_nat @ one_one_nat @ N) = N)))). % nat_mult_1
thf(fact_98_nat__neq__iff, axiom,
    ((![M : nat, N : nat]: ((~ ((M = N))) = (((ord_less_nat @ M @ N)) | ((ord_less_nat @ N @ M))))))). % nat_neq_iff
thf(fact_99_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_100_less__not__refl2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ N @ M) => (~ ((M = N))))))). % less_not_refl2
thf(fact_101_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_102_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_103_nat__less__induct, axiom,
    ((![P : nat > $o, N : nat]: ((![N3 : nat]: ((![M2 : nat]: ((ord_less_nat @ M2 @ N3) => (P @ M2))) => (P @ N3))) => (P @ N))))). % nat_less_induct
thf(fact_104_infinite__descent, axiom,
    ((![P : nat > $o, N : nat]: ((![N3 : nat]: ((~ ((P @ N3))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N3) & (~ ((P @ M2))))))) => (P @ N))))). % infinite_descent
thf(fact_105_nat__mult__1__right, axiom,
    ((![N : nat]: ((times_times_nat @ N @ one_one_nat) = N)))). % nat_mult_1_right
thf(fact_106_linorder__neqE__nat, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % linorder_neqE_nat
thf(fact_107_of__nat__less__imp__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)) => (ord_less_nat @ M @ N))))). % of_nat_less_imp_less
thf(fact_108_of__nat__less__imp__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N)) => (ord_less_nat @ M @ N))))). % of_nat_less_imp_less
thf(fact_109_of__nat__less__imp__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)) => (ord_less_nat @ M @ N))))). % of_nat_less_imp_less
thf(fact_110_less__imp__of__nat__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (ord_less_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)))))). % less_imp_of_nat_less
thf(fact_111_less__imp__of__nat__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (ord_less_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N)))))). % less_imp_of_nat_less
thf(fact_112_less__imp__of__nat__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)))))). % less_imp_of_nat_less
thf(fact_113_cos__one__sin__zero, axiom,
    ((![X : complex]: (((cos_complex @ X) = one_one_complex) => ((sin_complex @ X) = zero_zero_complex))))). % cos_one_sin_zero
thf(fact_114_cos__one__sin__zero, axiom,
    ((![X : real]: (((cos_real @ X) = one_one_real) => ((sin_real @ X) = zero_zero_real))))). % cos_one_sin_zero
thf(fact_115_sin__gt__zero, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ pi) => (ord_less_real @ zero_zero_real @ (sin_real @ X))))))). % sin_gt_zero
thf(fact_116_polar__Ex, axiom,
    ((![X : real, Y : real]: (?[R2 : real, A2 : real]: ((X = (times_times_real @ R2 @ (cos_real @ A2))) & (Y = (times_times_real @ R2 @ (sin_real @ A2)))))))). % polar_Ex
thf(fact_117_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ zero_zero_real)))))). % not_numeral_less_zero
thf(fact_118_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ zero_zero_nat)))))). % not_numeral_less_zero
thf(fact_119_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N) @ zero_zero_int)))))). % not_numeral_less_zero
thf(fact_120_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ N))))). % zero_less_numeral
thf(fact_121_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ N))))). % zero_less_numeral
thf(fact_122_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ N))))). % zero_less_numeral
thf(fact_123_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_124_less__numeral__extra_I1_J, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % less_numeral_extra(1)
thf(fact_125_less__numeral__extra_I1_J, axiom,
    ((ord_less_int @ zero_zero_int @ one_one_int))). % less_numeral_extra(1)
thf(fact_126_of__nat__less__0__iff, axiom,
    ((![M : nat]: (~ ((ord_less_nat @ (semiri1382578993at_nat @ M) @ zero_zero_nat)))))). % of_nat_less_0_iff
thf(fact_127_of__nat__less__0__iff, axiom,
    ((![M : nat]: (~ ((ord_less_int @ (semiri2019852685at_int @ M) @ zero_zero_int)))))). % of_nat_less_0_iff
thf(fact_128_of__nat__less__0__iff, axiom,
    ((![M : nat]: (~ ((ord_less_real @ (semiri2110766477t_real @ M) @ zero_zero_real)))))). % of_nat_less_0_iff
thf(fact_129_pi__not__less__zero, axiom,
    ((~ ((ord_less_real @ pi @ zero_zero_real))))). % pi_not_less_zero
thf(fact_130_pi__gt__zero, axiom,
    ((ord_less_real @ zero_zero_real @ pi))). % pi_gt_zero
thf(fact_131_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_132_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ one_one_nat))))). % less_numeral_extra(4)
thf(fact_133_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_int @ one_one_int @ one_one_int))))). % less_numeral_extra(4)
thf(fact_134_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_real = (numeral_numeral_real @ N))))))). % zero_neq_numeral
thf(fact_135_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_136_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N))))))). % zero_neq_numeral
thf(fact_137_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N))))))). % zero_neq_numeral
thf(fact_138_pi__neq__zero, axiom,
    ((~ ((pi = zero_zero_real))))). % pi_neq_zero
thf(fact_139_sin__gt__zero__02, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ (numeral_numeral_real @ (bit0 @ one))) => (ord_less_real @ zero_zero_real @ (sin_real @ X))))))). % sin_gt_zero_02
thf(fact_140_cos__two__less__zero, axiom,
    ((ord_less_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real))). % cos_two_less_zero
thf(fact_141_cos__double__less__one, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ (numeral_numeral_real @ (bit0 @ one))) => (ord_less_real @ (cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ X)) @ one_one_real)))))). % cos_double_less_one
thf(fact_142_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ one_one_real)))))). % not_numeral_less_one
thf(fact_143_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ one_one_nat)))))). % not_numeral_less_one
thf(fact_144_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N) @ one_one_int)))))). % not_numeral_less_one
thf(fact_145_less__divide__eq__numeral_I1_J, axiom,
    ((![W : num, B : real, C : real]: ((ord_less_real @ (numeral_numeral_real @ W) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ (times_times_real @ (numeral_numeral_real @ W) @ C) @ B)))) & ((((~ ((ord_less_real @ zero_zero_real @ C)))) => ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ (times_times_real @ (numeral_numeral_real @ W) @ C))))) & ((((~ ((ord_less_real @ C @ zero_zero_real)))) => ((ord_less_real @ (numeral_numeral_real @ W) @ zero_zero_real))))))))))))). % less_divide_eq_numeral(1)
thf(fact_146_divide__less__eq__numeral_I1_J, axiom,
    ((![B : real, C : real, W : num]: ((ord_less_real @ (divide_divide_real @ B @ C) @ (numeral_numeral_real @ W)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ B @ (times_times_real @ (numeral_numeral_real @ W) @ C))))) & ((((~ ((ord_less_real @ zero_zero_real @ C)))) => ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ (times_times_real @ (numeral_numeral_real @ W) @ C) @ B)))) & ((((~ ((ord_less_real @ C @ zero_zero_real)))) => ((ord_less_real @ zero_zero_real @ (numeral_numeral_real @ W)))))))))))))). % divide_less_eq_numeral(1)
thf(fact_147_cos__two__neq__zero, axiom,
    ((~ (((cos_real @ (numeral_numeral_real @ (bit0 @ one))) = zero_zero_real))))). % cos_two_neq_zero
thf(fact_148_sin__double, axiom,
    ((![X : real]: ((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ X)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ X)) @ (cos_real @ X)))))). % sin_double
thf(fact_149_sin__double, axiom,
    ((![X : complex]: ((sin_complex @ (times_times_complex @ (numera632737353omplex @ (bit0 @ one)) @ X)) = (times_times_complex @ (times_times_complex @ (numera632737353omplex @ (bit0 @ one)) @ (sin_complex @ X)) @ (cos_complex @ X)))))). % sin_double
thf(fact_150_sin__gt__zero2, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ zero_zero_real @ (sin_real @ X))))))). % sin_gt_zero2
thf(fact_151_sin__lt__zero, axiom,
    ((![X : real]: ((ord_less_real @ pi @ X) => ((ord_less_real @ X @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => (ord_less_real @ (sin_real @ X) @ zero_zero_real)))))). % sin_lt_zero
thf(fact_152_cos__gt__zero, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ zero_zero_real @ (cos_real @ X))))))). % cos_gt_zero
thf(fact_153_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_154_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_155_eq__divide__eq__numeral_I1_J, axiom,
    ((![W : num, B : complex, C : complex]: (((numera632737353omplex @ W) = (divide1210191872omplex @ B @ C)) = (((((~ ((C = zero_zero_complex)))) => (((times_times_complex @ (numera632737353omplex @ W) @ C) = B)))) & ((((C = zero_zero_complex)) => (((numera632737353omplex @ W) = zero_zero_complex))))))))). % eq_divide_eq_numeral(1)
thf(fact_156_eq__divide__eq__numeral_I1_J, axiom,
    ((![W : num, B : real, C : real]: (((numeral_numeral_real @ W) = (divide_divide_real @ B @ C)) = (((((~ ((C = zero_zero_real)))) => (((times_times_real @ (numeral_numeral_real @ W) @ C) = B)))) & ((((C = zero_zero_real)) => (((numeral_numeral_real @ W) = zero_zero_real))))))))). % eq_divide_eq_numeral(1)
thf(fact_157_divide__eq__eq__numeral_I1_J, axiom,
    ((![B : complex, C : complex, W : num]: (((divide1210191872omplex @ B @ C) = (numera632737353omplex @ W)) = (((((~ ((C = zero_zero_complex)))) => ((B = (times_times_complex @ (numera632737353omplex @ W) @ C))))) & ((((C = zero_zero_complex)) => (((numera632737353omplex @ W) = zero_zero_complex))))))))). % divide_eq_eq_numeral(1)
thf(fact_158_divide__eq__eq__numeral_I1_J, axiom,
    ((![B : real, C : real, W : num]: (((divide_divide_real @ B @ C) = (numeral_numeral_real @ W)) = (((((~ ((C = zero_zero_real)))) => ((B = (times_times_real @ (numeral_numeral_real @ W) @ C))))) & ((((C = zero_zero_real)) => (((numeral_numeral_real @ W) = zero_zero_real))))))))). % divide_eq_eq_numeral(1)
thf(fact_159_pi__half__gt__zero, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))). % pi_half_gt_zero
thf(fact_160_mult__of__nat__commute, axiom,
    ((![X : nat, Y : nat]: ((times_times_nat @ (semiri1382578993at_nat @ X) @ Y) = (times_times_nat @ Y @ (semiri1382578993at_nat @ X)))))). % mult_of_nat_commute
thf(fact_161_mult__of__nat__commute, axiom,
    ((![X : nat, Y : real]: ((times_times_real @ (semiri2110766477t_real @ X) @ Y) = (times_times_real @ Y @ (semiri2110766477t_real @ X)))))). % mult_of_nat_commute
thf(fact_162_pi__less__4, axiom,
    ((ord_less_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))). % pi_less_4
thf(fact_163_pi__half__less__two, axiom,
    ((ord_less_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))). % pi_half_less_two
thf(fact_164_pi__half__neq__zero, axiom,
    ((~ (((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) = zero_zero_real))))). % pi_half_neq_zero
thf(fact_165_mult__numeral__1__right, axiom,
    ((![A : real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A)))). % mult_numeral_1_right
thf(fact_166_mult__numeral__1__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A)))). % mult_numeral_1_right
thf(fact_167_mult__numeral__1__right, axiom,
    ((![A : int]: ((times_times_int @ A @ (numeral_numeral_int @ one)) = A)))). % mult_numeral_1_right
thf(fact_168_mult__numeral__1__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ (numera632737353omplex @ one)) = A)))). % mult_numeral_1_right
thf(fact_169_mult__numeral__1, axiom,
    ((![A : real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A)))). % mult_numeral_1
thf(fact_170_mult__numeral__1, axiom,
    ((![A : nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A)))). % mult_numeral_1
thf(fact_171_mult__numeral__1, axiom,
    ((![A : int]: ((times_times_int @ (numeral_numeral_int @ one) @ A) = A)))). % mult_numeral_1
thf(fact_172_mult__numeral__1, axiom,
    ((![A : complex]: ((times_times_complex @ (numera632737353omplex @ one) @ A) = A)))). % mult_numeral_1
thf(fact_173_numeral__One, axiom,
    (((numeral_numeral_real @ one) = one_one_real))). % numeral_One
thf(fact_174_numeral__One, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numeral_One
thf(fact_175_numeral__One, axiom,
    (((numeral_numeral_int @ one) = one_one_int))). % numeral_One
thf(fact_176_numeral__One, axiom,
    (((numera632737353omplex @ one) = one_one_complex))). % numeral_One
thf(fact_177_divide__numeral__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ (numera632737353omplex @ one)) = A)))). % divide_numeral_1
thf(fact_178_divide__numeral__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A)))). % divide_numeral_1
thf(fact_179_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_180_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_181_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_182_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_183_real__of__nat__less__numeral__iff, axiom,
    ((![N : nat, W : num]: ((ord_less_real @ (semiri2110766477t_real @ N) @ (numeral_numeral_real @ W)) = (ord_less_nat @ N @ (numeral_numeral_nat @ W)))))). % real_of_nat_less_numeral_iff
thf(fact_184_numeral__less__real__of__nat__iff, axiom,
    ((![W : num, N : nat]: ((ord_less_real @ (numeral_numeral_real @ W) @ (semiri2110766477t_real @ N)) = (ord_less_nat @ (numeral_numeral_nat @ W) @ N))))). % numeral_less_real_of_nat_iff
thf(fact_185_nonzero__divide__mult__cancel__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ B @ (times_times_complex @ A @ B)) = (divide1210191872omplex @ one_one_complex @ A)))))). % nonzero_divide_mult_cancel_right
thf(fact_186_nonzero__divide__mult__cancel__right, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((divide_divide_real @ B @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ A)))))). % nonzero_divide_mult_cancel_right
thf(fact_187_nonzero__divide__mult__cancel__left, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ (times_times_complex @ A @ B)) = (divide1210191872omplex @ one_one_complex @ B)))))). % nonzero_divide_mult_cancel_left
thf(fact_188_nonzero__divide__mult__cancel__left, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ B)))))). % nonzero_divide_mult_cancel_left
thf(fact_189_zero__less__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_divide_1_iff
thf(fact_190_less__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)))))). % less_divide_eq_1_pos
thf(fact_191_less__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)))))). % less_divide_eq_1_neg
thf(fact_192_divide__eq__0__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % divide_eq_0_iff
thf(fact_193_divide__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((divide_divide_real @ C @ A) = (divide_divide_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_left
thf(fact_194_bits__div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % bits_div_0
thf(fact_195_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_196_divide__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((divide_divide_real @ A @ C) = (divide_divide_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_right
thf(fact_197_bits__div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % bits_div_by_0
thf(fact_198_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_199_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_200_times__divide__eq__left, axiom,
    ((![B : real, C : real, A : real]: ((times_times_real @ (divide_divide_real @ B @ C) @ A) = (divide_divide_real @ (times_times_real @ B @ A) @ C))))). % times_divide_eq_left
thf(fact_201_divide__divide__eq__left, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ B @ C)))))). % divide_divide_eq_left
thf(fact_202_divide__divide__eq__right, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ C) @ B))))). % divide_divide_eq_right
thf(fact_203_times__divide__eq__right, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ B) @ C))))). % times_divide_eq_right
thf(fact_204_bits__div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % bits_div_by_1
thf(fact_205_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_206_half__negative__int__iff, axiom,
    ((![K : int]: ((ord_less_int @ (divide_divide_int @ K @ (numeral_numeral_int @ (bit0 @ one))) @ zero_zero_int) = (ord_less_int @ K @ zero_zero_int))))). % half_negative_int_iff
thf(fact_207_div__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => ((divide_divide_nat @ M @ N) = zero_zero_nat))))). % div_less
thf(fact_208_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_209_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_210_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_211_mult__cancel2, axiom,
    ((![M : nat, K : nat, N : nat]: (((times_times_nat @ M @ K) = (times_times_nat @ N @ K)) = (((M = N)) | ((K = zero_zero_nat))))))). % mult_cancel2
thf(fact_212_mult__cancel1, axiom,
    ((![K : nat, M : nat, N : nat]: (((times_times_nat @ K @ M) = (times_times_nat @ K @ N)) = (((M = N)) | ((K = zero_zero_nat))))))). % mult_cancel1
thf(fact_213_mult__0__right, axiom,
    ((![M : nat]: ((times_times_nat @ M @ zero_zero_nat) = zero_zero_nat)))). % mult_0_right
thf(fact_214_mult__is__0, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = zero_zero_nat) = (((M = zero_zero_nat)) | ((N = zero_zero_nat))))))). % mult_is_0
thf(fact_215_mult__divide__mult__cancel__left__if, axiom,
    ((![C : real, A : real, B : real]: (((C = zero_zero_real) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = zero_zero_real)) & ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B))))))). % mult_divide_mult_cancel_left_if
thf(fact_216_nonzero__mult__divide__mult__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left
thf(fact_217_nonzero__mult__divide__mult__cancel__left2, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ B @ C)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left2
thf(fact_218_nonzero__mult__divide__mult__cancel__right, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right
thf(fact_219_nonzero__mult__divide__mult__cancel__right2, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ A @ C) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right2
thf(fact_220_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_221_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_222_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_223_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_224_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_225_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_226_divide__eq__1__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = one_one_complex) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_227_divide__eq__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = one_one_real) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_228_one__eq__divide__iff, axiom,
    ((![A : complex, B : complex]: ((one_one_complex = (divide1210191872omplex @ A @ B)) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_229_one__eq__divide__iff, axiom,
    ((![A : real, B : real]: ((one_one_real = (divide_divide_real @ A @ B)) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_230_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_231_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_232_divide__self__if, axiom,
    ((![A : complex]: (((A = zero_zero_complex) => ((divide1210191872omplex @ A @ A) = zero_zero_complex)) & ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex)))))). % divide_self_if
thf(fact_233_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_234_divide__eq__eq__1, axiom,
    ((![B : real, A : real]: (((divide_divide_real @ B @ A) = one_one_real) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % divide_eq_eq_1
thf(fact_235_eq__divide__eq__1, axiom,
    ((![B : real, A : real]: ((one_one_real = (divide_divide_real @ B @ A)) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % eq_divide_eq_1
thf(fact_236_one__divide__eq__0__iff, axiom,
    ((![A : real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % one_divide_eq_0_iff
thf(fact_237_zero__eq__1__divide__iff, axiom,
    ((![A : real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real))))). % zero_eq_1_divide_iff
thf(fact_238_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_239_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_240_nat__0__less__mult__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ M @ N)) = (((ord_less_nat @ zero_zero_nat @ M)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % nat_0_less_mult_iff

% Conjectures (1)
thf(conj_0, conjecture,
    ((~ (((cis @ (divide_divide_real @ (times_times_real @ (semiri2110766477t_real @ k) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) @ (semiri2110766477t_real @ n))) = one_one_complex))))).
