% 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_194__3224594_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:50.481

% Could-be-implicit typings (4)
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).

% Explicit typings (32)
thf(sy_c_Complex_Ocis, type,
    cis : real > complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
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__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_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_real : real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__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__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__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__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__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__Real__Oreal, type,
    cos_real : real > real).
thf(sy_c_Transcendental_Opi, type,
    pi : real).
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 (213)
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_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_6_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_7_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ one_one_real)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_8_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ one_one_complex)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_9_divide__minus1, axiom,
    ((![X : real]: ((divide_divide_real @ X @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ X))))). % divide_minus1
thf(fact_10_divide__minus1, axiom,
    ((![X : complex]: ((divide1210191872omplex @ X @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ X))))). % divide_minus1
thf(fact_11_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_real @ N) = one_one_real) = (N = one))))). % numeral_eq_one_iff
thf(fact_12_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_13_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_14_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_real = (numeral_numeral_real @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_15_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_16_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_17_mult__minus1, axiom,
    ((![Z : real]: ((times_times_real @ (uminus_uminus_real @ one_one_real) @ Z) = (uminus_uminus_real @ Z))))). % mult_minus1
thf(fact_18_mult__minus1, axiom,
    ((![Z : complex]: ((times_times_complex @ (uminus1204672759omplex @ one_one_complex) @ Z) = (uminus1204672759omplex @ Z))))). % mult_minus1
thf(fact_19_mult__minus1__right, axiom,
    ((![Z : real]: ((times_times_real @ Z @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ Z))))). % mult_minus1_right
thf(fact_20_mult__minus1__right, axiom,
    ((![Z : complex]: ((times_times_complex @ Z @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ Z))))). % mult_minus1_right
thf(fact_21_semiring__norm_I172_J, axiom,
    ((![V : num, W : num, Y : real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ V)) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ W)) @ Y)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ V @ W)) @ Y))))). % semiring_norm(172)
thf(fact_22_semiring__norm_I172_J, axiom,
    ((![V : num, W : num, Y : complex]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ V)) @ (times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ W)) @ Y)) = (times_times_complex @ (numera632737353omplex @ (times_times_num @ V @ W)) @ Y))))). % semiring_norm(172)
thf(fact_23_semiring__norm_I171_J, axiom,
    ((![V : num, W : num, Y : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ W)) @ Y)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ V @ W))) @ Y))))). % semiring_norm(171)
thf(fact_24_semiring__norm_I171_J, axiom,
    ((![V : num, W : num, Y : complex]: ((times_times_complex @ (numera632737353omplex @ V) @ (times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ W)) @ Y)) = (times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ (times_times_num @ V @ W))) @ Y))))). % semiring_norm(171)
thf(fact_25_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_26_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_27_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_28_semiring__norm_I87_J, axiom,
    ((![M : num, N : num]: (((bit0 @ M) = (bit0 @ N)) = (M = N))))). % semiring_norm(87)
thf(fact_29_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_30_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_31_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_32_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_33_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_34_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_35_divide__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_right
thf(fact_36_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_37_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_38_divide__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((divide1210191872omplex @ C @ A) = (divide1210191872omplex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_left
thf(fact_39_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_40_divide__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % divide_eq_0_iff
thf(fact_41_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_42_times__divide__eq__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ A @ (divide1210191872omplex @ B @ C)) = (divide1210191872omplex @ (times_times_complex @ A @ B) @ C))))). % times_divide_eq_right
thf(fact_43_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_44_divide__divide__eq__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ A @ (divide1210191872omplex @ B @ C)) = (divide1210191872omplex @ (times_times_complex @ A @ C) @ B))))). % divide_divide_eq_right
thf(fact_45_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_46_divide__divide__eq__left, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ A @ B) @ C) = (divide1210191872omplex @ A @ (times_times_complex @ B @ C)))))). % divide_divide_eq_left
thf(fact_47_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_48_times__divide__eq__left, axiom,
    ((![B : complex, C : complex, A : complex]: ((times_times_complex @ (divide1210191872omplex @ B @ C) @ A) = (divide1210191872omplex @ (times_times_complex @ B @ A) @ C))))). % times_divide_eq_left
thf(fact_49_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_50_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_51_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_52_semiring__norm_I83_J, axiom,
    ((![N : num]: (~ ((one = (bit0 @ N))))))). % semiring_norm(83)
thf(fact_53_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_54_of__nat__numeral, axiom,
    ((![N : num]: ((semiri1382578993at_nat @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ N))))). % of_nat_numeral
thf(fact_55_of__nat__numeral, axiom,
    ((![N : num]: ((semiri356525583omplex @ (numeral_numeral_nat @ N)) = (numera632737353omplex @ N))))). % of_nat_numeral
thf(fact_56_of__nat__numeral, axiom,
    ((![N : num]: ((semiri2110766477t_real @ (numeral_numeral_nat @ N)) = (numeral_numeral_real @ N))))). % of_nat_numeral
thf(fact_57_k_I1_J, axiom,
    ((ord_less_nat @ zero_zero_nat @ k))). % k(1)
thf(fact_58_semiring__norm_I13_J, axiom,
    ((![M : num, N : num]: ((times_times_num @ (bit0 @ M) @ (bit0 @ N)) = (bit0 @ (bit0 @ (times_times_num @ M @ N))))))). % semiring_norm(13)
thf(fact_59_semiring__norm_I11_J, axiom,
    ((![M : num]: ((times_times_num @ M @ one) = M)))). % semiring_norm(11)
thf(fact_60_semiring__norm_I12_J, axiom,
    ((![N : num]: ((times_times_num @ one @ N) = N)))). % semiring_norm(12)
thf(fact_61_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_62_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_63_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_64_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_65_nonzero__mult__divide__mult__cancel__right2, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right2
thf(fact_66_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_67_nonzero__mult__divide__mult__cancel__right, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right
thf(fact_68_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_69_nonzero__mult__divide__mult__cancel__left2, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ B @ C)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left2
thf(fact_70_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_71_nonzero__mult__divide__mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left
thf(fact_72_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_73_mult__divide__mult__cancel__left__if, axiom,
    ((![C : complex, A : complex, B : complex]: (((C = zero_zero_complex) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = zero_zero_complex)) & ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B))))))). % mult_divide_mult_cancel_left_if
thf(fact_74_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_75_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_76_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_77_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_78_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_79_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_80_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_81_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_82_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_83_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_84_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_85_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_86_neg__numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (ord_less_num @ N @ M))))). % neg_numeral_less_iff
thf(fact_87_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_88_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_89_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_90_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_91_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_92_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_93_num__double, axiom,
    ((![N : num]: ((times_times_num @ (bit0 @ one) @ N) = (bit0 @ N))))). % num_double
thf(fact_94_cis__zero, axiom,
    (((cis @ zero_zero_real) = one_one_complex))). % cis_zero
thf(fact_95_cis__pi, axiom,
    (((cis @ pi) = (uminus1204672759omplex @ one_one_complex)))). % cis_pi
thf(fact_96__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_97_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_98_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_99_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_100_divide__less__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)))))). % divide_less_eq_1_pos
thf(fact_101_divide__less__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B)))))). % divide_less_eq_1_neg
thf(fact_102_divide__less__0__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % divide_less_0_1_iff
thf(fact_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_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_111_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_112_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_113_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_114_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_115_mult__neg__numeral__simps_I1_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ (times_times_num @ M @ N)))))). % mult_neg_numeral_simps(1)
thf(fact_116_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_117_mult__neg__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(2)
thf(fact_118_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_119_mult__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(3)
thf(fact_120_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_121_semiring__norm_I170_J, axiom,
    ((![V : num, W : num, Y : real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ V)) @ (times_times_real @ (numeral_numeral_real @ W) @ Y)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ V @ W))) @ Y))))). % semiring_norm(170)
thf(fact_122_semiring__norm_I170_J, axiom,
    ((![V : num, W : num, Y : complex]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ V)) @ (times_times_complex @ (numera632737353omplex @ W) @ Y)) = (times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ (times_times_num @ V @ W))) @ Y))))). % semiring_norm(170)
thf(fact_123_eq__divide__eq__numeral1_I2_J, axiom,
    ((![A : real, B : real, W : num]: ((A = (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W)))) = (((((~ (((uminus_uminus_real @ (numeral_numeral_real @ W)) = zero_zero_real)))) => (((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W))) = B)))) & (((((uminus_uminus_real @ (numeral_numeral_real @ W)) = zero_zero_real)) => ((A = zero_zero_real))))))))). % eq_divide_eq_numeral1(2)
thf(fact_124_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_125_divide__eq__eq__numeral1_I2_J, axiom,
    ((![B : real, W : num, A : real]: (((divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W))) = A) = (((((~ (((uminus_uminus_real @ (numeral_numeral_real @ W)) = zero_zero_real)))) => ((B = (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W))))))) & (((((uminus_uminus_real @ (numeral_numeral_real @ W)) = zero_zero_real)) => ((A = zero_zero_real))))))))). % divide_eq_eq_numeral1(2)
thf(fact_126_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_127_less__divide__eq__numeral1_I2_J, axiom,
    ((![A : real, B : real, W : num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W)))) = (ord_less_real @ B @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W)))))))). % less_divide_eq_numeral1(2)
thf(fact_128_divide__less__eq__numeral1_I2_J, axiom,
    ((![B : real, W : num, A : real]: ((ord_less_real @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W))) @ A) = (ord_less_real @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W))) @ B))))). % divide_less_eq_numeral1(2)
thf(fact_129_neg__numeral__less__neg__one__iff, axiom,
    ((![M : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ one_one_real)) = (~ ((M = one))))))). % neg_numeral_less_neg_one_iff
thf(fact_130_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_131_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_132_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_133_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_134_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_135_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_136_linordered__field__no__lb, axiom,
    ((![X2 : real]: (?[Y2 : real]: (ord_less_real @ Y2 @ X2))))). % linordered_field_no_lb
thf(fact_137_linordered__field__no__ub, axiom,
    ((![X2 : real]: (?[X_1 : real]: (ord_less_real @ X2 @ X_1))))). % linordered_field_no_ub
thf(fact_138_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ zero_zero_real)))))). % not_numeral_less_zero
thf(fact_139_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ zero_zero_nat)))))). % not_numeral_less_zero
thf(fact_140_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ N))))). % zero_less_numeral
thf(fact_141_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ N))))). % zero_less_numeral
thf(fact_142_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_143_less__numeral__extra_I1_J, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % less_numeral_extra(1)
thf(fact_144_divide__strict__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono_neg
thf(fact_145_divide__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono
thf(fact_146_zero__less__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ zero_zero_real @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real))))))))). % zero_less_divide_iff
thf(fact_147_divide__less__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A)))) & ((~ ((C = zero_zero_real))))))))))). % divide_less_cancel
thf(fact_148_divide__less__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ zero_zero_real)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B))))))))). % divide_less_0_iff
thf(fact_149_divide__pos__pos, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ zero_zero_real @ Y) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X @ Y))))))). % divide_pos_pos
thf(fact_150_divide__pos__neg, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ Y @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X @ Y) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_151_divide__neg__pos, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y) => (ord_less_real @ (divide_divide_real @ X @ Y) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_152_divide__neg__neg, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ zero_zero_real) => ((ord_less_real @ Y @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X @ Y))))))). % divide_neg_neg
thf(fact_153_div__mult2__numeral__eq, axiom,
    ((![A : nat, K : num, L : num]: ((divide_divide_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ K)) @ (numeral_numeral_nat @ L)) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (times_times_num @ K @ L))))))). % div_mult2_numeral_eq
thf(fact_154_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_155_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ one_one_nat))))). % less_numeral_extra(4)
thf(fact_156_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_real = (numeral_numeral_real @ N))))))). % zero_neq_numeral
thf(fact_157_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_158_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N))))))). % zero_neq_numeral
thf(fact_159_divide__strict__left__mono__neg, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => (ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B)))))))). % divide_strict_left_mono_neg
thf(fact_160_divide__strict__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => (ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B)))))))). % divide_strict_left_mono
thf(fact_161_mult__imp__less__div__pos, axiom,
    ((![Y : real, Z : real, X : real]: ((ord_less_real @ zero_zero_real @ Y) => ((ord_less_real @ (times_times_real @ Z @ Y) @ X) => (ord_less_real @ Z @ (divide_divide_real @ X @ Y))))))). % mult_imp_less_div_pos
thf(fact_162_mult__imp__div__pos__less, axiom,
    ((![Y : real, X : real, Z : real]: ((ord_less_real @ zero_zero_real @ Y) => ((ord_less_real @ X @ (times_times_real @ Z @ Y)) => (ord_less_real @ (divide_divide_real @ X @ Y) @ Z)))))). % mult_imp_div_pos_less
thf(fact_163_pos__less__divide__eq, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (ord_less_real @ (times_times_real @ A @ C) @ B)))))). % pos_less_divide_eq
thf(fact_164_pos__divide__less__eq, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (divide_divide_real @ B @ C) @ A) = (ord_less_real @ B @ (times_times_real @ A @ C))))))). % pos_divide_less_eq
thf(fact_165_neg__less__divide__eq, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (ord_less_real @ B @ (times_times_real @ A @ C))))))). % neg_less_divide_eq
thf(fact_166_neg__divide__less__eq, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ C) @ A) = (ord_less_real @ (times_times_real @ A @ C) @ B)))))). % neg_divide_less_eq
thf(fact_167_less__divide__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ (times_times_real @ A @ C) @ B)))) & ((((~ ((ord_less_real @ zero_zero_real @ C)))) => ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ (times_times_real @ A @ C))))) & ((((~ ((ord_less_real @ C @ zero_zero_real)))) => ((ord_less_real @ A @ zero_zero_real))))))))))))). % less_divide_eq
thf(fact_168_divide__less__eq, axiom,
    ((![B : real, C : real, A : real]: ((ord_less_real @ (divide_divide_real @ B @ C) @ A) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ B @ (times_times_real @ A @ C))))) & ((((~ ((ord_less_real @ zero_zero_real @ C)))) => ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ (times_times_real @ A @ C) @ B)))) & ((((~ ((ord_less_real @ C @ zero_zero_real)))) => ((ord_less_real @ zero_zero_real @ A))))))))))))). % divide_less_eq
thf(fact_169_not__zero__less__neg__numeral, axiom,
    ((![N : num]: (~ ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % not_zero_less_neg_numeral
thf(fact_170_neg__numeral__less__zero, axiom,
    ((![N : num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ N)) @ zero_zero_real)))). % neg_numeral_less_zero
thf(fact_171_less__divide__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ A @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ A))))))))). % less_divide_eq_1
thf(fact_172_divide__less__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ A)))) | ((((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ A @ B)))) | ((A = zero_zero_real))))))))). % divide_less_eq_1
thf(fact_173_less__minus__one__simps_I1_J, axiom,
    ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real))). % less_minus_one_simps(1)
thf(fact_174_less__minus__one__simps_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))))). % less_minus_one_simps(3)
thf(fact_175_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ one_one_real)))))). % not_numeral_less_one
thf(fact_176_not__numeral__less__one, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ one_one_nat)))))). % not_numeral_less_one
thf(fact_177_not__numeral__less__neg__numeral, axiom,
    ((![M : num, N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % not_numeral_less_neg_numeral
thf(fact_178_neg__numeral__less__numeral, axiom,
    ((![M : num, N : num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N))))). % neg_numeral_less_numeral
thf(fact_179_less__minus__one__simps_I2_J, axiom,
    ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ one_one_real))). % less_minus_one_simps(2)
thf(fact_180_less__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))))). % less_minus_one_simps(4)
thf(fact_181_nonzero__eq__divide__eq, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((A = (divide_divide_real @ B @ C)) = ((times_times_real @ A @ C) = B)))))). % nonzero_eq_divide_eq
thf(fact_182_nonzero__eq__divide__eq, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((A = (divide1210191872omplex @ B @ C)) = ((times_times_complex @ A @ C) = B)))))). % nonzero_eq_divide_eq
thf(fact_183_nonzero__divide__eq__eq, axiom,
    ((![C : real, B : real, A : real]: ((~ ((C = zero_zero_real))) => (((divide_divide_real @ B @ C) = A) = (B = (times_times_real @ A @ C))))))). % nonzero_divide_eq_eq
thf(fact_184_nonzero__divide__eq__eq, axiom,
    ((![C : complex, B : complex, A : complex]: ((~ ((C = zero_zero_complex))) => (((divide1210191872omplex @ B @ C) = A) = (B = (times_times_complex @ A @ C))))))). % nonzero_divide_eq_eq
thf(fact_185_eq__divide__imp, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => (((times_times_real @ A @ C) = B) => (A = (divide_divide_real @ B @ C))))))). % eq_divide_imp
thf(fact_186_eq__divide__imp, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A @ C) = B) => (A = (divide1210191872omplex @ B @ C))))))). % eq_divide_imp
thf(fact_187_divide__eq__imp, axiom,
    ((![C : real, B : real, A : real]: ((~ ((C = zero_zero_real))) => ((B = (times_times_real @ A @ C)) => ((divide_divide_real @ B @ C) = A)))))). % divide_eq_imp
thf(fact_188_divide__eq__imp, axiom,
    ((![C : complex, B : complex, A : complex]: ((~ ((C = zero_zero_complex))) => ((B = (times_times_complex @ A @ C)) => ((divide1210191872omplex @ B @ C) = A)))))). % divide_eq_imp
thf(fact_189_eq__divide__eq, axiom,
    ((![A : real, B : real, C : real]: ((A = (divide_divide_real @ B @ C)) = (((((~ ((C = zero_zero_real)))) => (((times_times_real @ A @ C) = B)))) & ((((C = zero_zero_real)) => ((A = zero_zero_real))))))))). % eq_divide_eq
thf(fact_190_eq__divide__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((A = (divide1210191872omplex @ B @ C)) = (((((~ ((C = zero_zero_complex)))) => (((times_times_complex @ A @ C) = B)))) & ((((C = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % eq_divide_eq
thf(fact_191_divide__eq__eq, axiom,
    ((![B : real, C : real, A : real]: (((divide_divide_real @ B @ C) = A) = (((((~ ((C = zero_zero_real)))) => ((B = (times_times_real @ A @ C))))) & ((((C = zero_zero_real)) => ((A = zero_zero_real))))))))). % divide_eq_eq
thf(fact_192_divide__eq__eq, axiom,
    ((![B : complex, C : complex, A : complex]: (((divide1210191872omplex @ B @ C) = A) = (((((~ ((C = zero_zero_complex)))) => ((B = (times_times_complex @ A @ C))))) & ((((C = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % divide_eq_eq
thf(fact_193_frac__eq__eq, axiom,
    ((![Y : real, Z : real, X : real, W : real]: ((~ ((Y = zero_zero_real))) => ((~ ((Z = zero_zero_real))) => (((divide_divide_real @ X @ Y) = (divide_divide_real @ W @ Z)) = ((times_times_real @ X @ Z) = (times_times_real @ W @ Y)))))))). % frac_eq_eq
thf(fact_194_frac__eq__eq, axiom,
    ((![Y : complex, Z : complex, X : complex, W : complex]: ((~ ((Y = zero_zero_complex))) => ((~ ((Z = zero_zero_complex))) => (((divide1210191872omplex @ X @ Y) = (divide1210191872omplex @ W @ Z)) = ((times_times_complex @ X @ Z) = (times_times_complex @ W @ Y)))))))). % frac_eq_eq
thf(fact_195_zero__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_real = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % zero_neq_neg_numeral
thf(fact_196_zero__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % zero_neq_neg_numeral
thf(fact_197_right__inverse__eq, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => (((divide_divide_real @ A @ B) = one_one_real) = (A = B)))))). % right_inverse_eq
thf(fact_198_right__inverse__eq, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => (((divide1210191872omplex @ A @ B) = one_one_complex) = (A = B)))))). % right_inverse_eq
thf(fact_199_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_real = (uminus_uminus_real @ one_one_real)))))). % zero_neq_neg_one
thf(fact_200_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_complex = (uminus1204672759omplex @ one_one_complex)))))). % zero_neq_neg_one
thf(fact_201_nonzero__minus__divide__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((divide_divide_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (divide_divide_real @ A @ B)))))). % nonzero_minus_divide_divide
thf(fact_202_nonzero__minus__divide__divide, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ (uminus1204672759omplex @ A) @ (uminus1204672759omplex @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_minus_divide_divide
thf(fact_203_nonzero__minus__divide__right, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ A @ (uminus_uminus_real @ B))))))). % nonzero_minus_divide_right
thf(fact_204_nonzero__minus__divide__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((uminus1204672759omplex @ (divide1210191872omplex @ A @ B)) = (divide1210191872omplex @ A @ (uminus1204672759omplex @ B))))))). % nonzero_minus_divide_right
thf(fact_205_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_206_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_207_pos__minus__divide__less__eq, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ C)) @ A) = (ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C))))))). % pos_minus_divide_less_eq
thf(fact_208_pos__less__minus__divide__eq, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ A @ (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (ord_less_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B))))))). % pos_less_minus_divide_eq
thf(fact_209_neg__minus__divide__less__eq, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ C)) @ A) = (ord_less_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B))))))). % neg_minus_divide_less_eq
thf(fact_210_neg__less__minus__divide__eq, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ A @ (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C))))))). % neg_less_minus_divide_eq
thf(fact_211_minus__divide__less__eq, axiom,
    ((![B : real, C : real, A : real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ C)) @ A) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C))))) & ((((~ ((ord_less_real @ zero_zero_real @ C)))) => ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B))))) & ((((~ ((ord_less_real @ C @ zero_zero_real)))) => ((ord_less_real @ zero_zero_real @ A))))))))))))). % minus_divide_less_eq
thf(fact_212_less__minus__divide__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B))))) & ((((~ ((ord_less_real @ zero_zero_real @ C)))) => ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C))))) & ((((~ ((ord_less_real @ C @ zero_zero_real)))) => ((ord_less_real @ A @ zero_zero_real))))))))))))). % less_minus_divide_eq

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