% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Fundamental_Theorem_Algebra/prob_885__5376374_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:33:54.404

% Could-be-implicit typings (7)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    poly_p1267267526omplex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    poly_poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (37)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
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__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Polynomial_Ocontent_001t__Nat__Onat, type,
    content_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Complex__Ocomplex, type,
    degree_complex : poly_complex > nat).
thf(sy_c_Polynomial_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Complex__Ocomplex, type,
    reflect_poly_complex : poly_complex > poly_complex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Nat__Onat, type,
    reflect_poly_nat : poly_nat > poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    reflec309385472omplex : poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex, type,
    power_power_complex : complex > nat > complex).
thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat, type,
    power_power_nat : nat > nat > nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    power_184595776omplex : poly_complex > nat > poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    power_power_poly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    power_432682568omplex : poly_poly_complex > nat > poly_poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    power_1336127338ly_nat : poly_poly_nat > nat > poly_poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    power_2001192272omplex : poly_p1267267526omplex > nat > poly_p1267267526omplex).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex, type,
    dvd_dvd_complex : complex > complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    dvd_dvd_poly_complex : poly_complex > poly_complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    dvd_dvd_poly_nat : poly_nat > poly_nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    dvd_dv598755940omplex : poly_poly_complex > poly_poly_complex > $o).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).

% Relevant facts (181)
thf(fact_0_assms_I3_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(3)
thf(fact_1_assms_I2_J, axiom,
    (((degree_complex @ p) = n))). % assms(2)
thf(fact_2_assms_I1_J, axiom,
    ((![X : complex]: (((poly_complex2 @ p @ X) = zero_zero_complex) => ((poly_complex2 @ q @ X) = zero_zero_complex))))). % assms(1)
thf(fact_3_dvd__power__same, axiom,
    ((![X2 : complex, Y : complex, N : nat]: ((dvd_dvd_complex @ X2 @ Y) => (dvd_dvd_complex @ (power_power_complex @ X2 @ N) @ (power_power_complex @ Y @ N)))))). % dvd_power_same
thf(fact_4_dvd__power__same, axiom,
    ((![X2 : poly_nat, Y : poly_nat, N : nat]: ((dvd_dvd_poly_nat @ X2 @ Y) => (dvd_dvd_poly_nat @ (power_power_poly_nat @ X2 @ N) @ (power_power_poly_nat @ Y @ N)))))). % dvd_power_same
thf(fact_5_dvd__power__same, axiom,
    ((![X2 : poly_poly_complex, Y : poly_poly_complex, N : nat]: ((dvd_dv598755940omplex @ X2 @ Y) => (dvd_dv598755940omplex @ (power_432682568omplex @ X2 @ N) @ (power_432682568omplex @ Y @ N)))))). % dvd_power_same
thf(fact_6_dvd__power__same, axiom,
    ((![X2 : poly_complex, Y : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X2 @ Y) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X2 @ N) @ (power_184595776omplex @ Y @ N)))))). % dvd_power_same
thf(fact_7_dvd__power__same, axiom,
    ((![X2 : nat, Y : nat, N : nat]: ((dvd_dvd_nat @ X2 @ Y) => (dvd_dvd_nat @ (power_power_nat @ X2 @ N) @ (power_power_nat @ Y @ N)))))). % dvd_power_same
thf(fact_8_poly__power, axiom,
    ((![P : poly_poly_nat, N : nat, X2 : poly_nat]: ((poly_poly_nat2 @ (power_1336127338ly_nat @ P @ N) @ X2) = (power_power_poly_nat @ (poly_poly_nat2 @ P @ X2) @ N))))). % poly_power
thf(fact_9_poly__power, axiom,
    ((![P : poly_p1267267526omplex, N : nat, X2 : poly_poly_complex]: ((poly_p282434315omplex @ (power_2001192272omplex @ P @ N) @ X2) = (power_432682568omplex @ (poly_p282434315omplex @ P @ X2) @ N))))). % poly_power
thf(fact_10_poly__power, axiom,
    ((![P : poly_poly_complex, N : nat, X2 : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P @ N) @ X2) = (power_184595776omplex @ (poly_poly_complex2 @ P @ X2) @ N))))). % poly_power
thf(fact_11_poly__power, axiom,
    ((![P : poly_nat, N : nat, X2 : nat]: ((poly_nat2 @ (power_power_poly_nat @ P @ N) @ X2) = (power_power_nat @ (poly_nat2 @ P @ X2) @ N))))). % poly_power
thf(fact_12_poly__power, axiom,
    ((![P : poly_complex, N : nat, X2 : complex]: ((poly_complex2 @ (power_184595776omplex @ P @ N) @ X2) = (power_power_complex @ (poly_complex2 @ P @ X2) @ N))))). % poly_power
thf(fact_13_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_14_dvd__refl, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ A)))). % dvd_refl
thf(fact_15_dvd__refl, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ A)))). % dvd_refl
thf(fact_16_dvd__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A @ C)))))). % dvd_trans
thf(fact_17_dvd__trans, axiom,
    ((![A : complex, B : complex, C : complex]: ((dvd_dvd_complex @ A @ B) => ((dvd_dvd_complex @ B @ C) => (dvd_dvd_complex @ A @ C)))))). % dvd_trans
thf(fact_18_dvd__trans, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((dvd_dvd_poly_complex @ B @ C) => (dvd_dvd_poly_complex @ A @ C)))))). % dvd_trans
thf(fact_19_dvd__0__right, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_20_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_21_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_22_dvd__0__left__iff, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) = (A = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_23_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_24_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_25_content__dvd__contentI, axiom,
    ((![P : poly_nat, Q : poly_nat]: ((dvd_dvd_poly_nat @ P @ Q) => (dvd_dvd_nat @ (content_nat @ P) @ (content_nat @ Q)))))). % content_dvd_contentI
thf(fact_26_dvd__field__iff, axiom,
    ((dvd_dvd_complex = (^[A2 : complex]: (^[B2 : complex]: (((A2 = zero_zero_complex)) => ((B2 = zero_zero_complex)))))))). % dvd_field_iff
thf(fact_27_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_28_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_29_dvd__0__left, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) => (A = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_30_power__not__zero, axiom,
    ((![A : poly_complex, N : nat]: ((~ ((A = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_31_power__not__zero, axiom,
    ((![A : nat, N : nat]: ((~ ((A = zero_zero_nat))) => (~ (((power_power_nat @ A @ N) = zero_zero_nat))))))). % power_not_zero
thf(fact_32_power__not__zero, axiom,
    ((![A : complex, N : nat]: ((~ ((A = zero_zero_complex))) => (~ (((power_power_complex @ A @ N) = zero_zero_complex))))))). % power_not_zero
thf(fact_33_power__not__zero, axiom,
    ((![A : poly_nat, N : nat]: ((~ ((A = zero_zero_poly_nat))) => (~ (((power_power_poly_nat @ A @ N) = zero_zero_poly_nat))))))). % power_not_zero
thf(fact_34_power__not__zero, axiom,
    ((![A : poly_poly_complex, N : nat]: ((~ ((A = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A @ N) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_35_dvd__power__le, axiom,
    ((![X2 : poly_complex, Y : poly_complex, N : nat, M : nat]: ((dvd_dvd_poly_complex @ X2 @ Y) => ((ord_less_eq_nat @ N @ M) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X2 @ N) @ (power_184595776omplex @ Y @ M))))))). % dvd_power_le
thf(fact_36_dvd__power__le, axiom,
    ((![X2 : nat, Y : nat, N : nat, M : nat]: ((dvd_dvd_nat @ X2 @ Y) => ((ord_less_eq_nat @ N @ M) => (dvd_dvd_nat @ (power_power_nat @ X2 @ N) @ (power_power_nat @ Y @ M))))))). % dvd_power_le
thf(fact_37_dvd__power__le, axiom,
    ((![X2 : complex, Y : complex, N : nat, M : nat]: ((dvd_dvd_complex @ X2 @ Y) => ((ord_less_eq_nat @ N @ M) => (dvd_dvd_complex @ (power_power_complex @ X2 @ N) @ (power_power_complex @ Y @ M))))))). % dvd_power_le
thf(fact_38_dvd__power__le, axiom,
    ((![X2 : poly_nat, Y : poly_nat, N : nat, M : nat]: ((dvd_dvd_poly_nat @ X2 @ Y) => ((ord_less_eq_nat @ N @ M) => (dvd_dvd_poly_nat @ (power_power_poly_nat @ X2 @ N) @ (power_power_poly_nat @ Y @ M))))))). % dvd_power_le
thf(fact_39_dvd__power__le, axiom,
    ((![X2 : poly_poly_complex, Y : poly_poly_complex, N : nat, M : nat]: ((dvd_dv598755940omplex @ X2 @ Y) => ((ord_less_eq_nat @ N @ M) => (dvd_dv598755940omplex @ (power_432682568omplex @ X2 @ N) @ (power_432682568omplex @ Y @ M))))))). % dvd_power_le
thf(fact_40_power__le__dvd, axiom,
    ((![A : poly_complex, N : nat, B : poly_complex, M : nat]: ((dvd_dvd_poly_complex @ (power_184595776omplex @ A @ N) @ B) => ((ord_less_eq_nat @ M @ N) => (dvd_dvd_poly_complex @ (power_184595776omplex @ A @ M) @ B)))))). % power_le_dvd
thf(fact_41_power__le__dvd, axiom,
    ((![A : nat, N : nat, B : nat, M : nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ N) @ B) => ((ord_less_eq_nat @ M @ N) => (dvd_dvd_nat @ (power_power_nat @ A @ M) @ B)))))). % power_le_dvd
thf(fact_42_power__le__dvd, axiom,
    ((![A : complex, N : nat, B : complex, M : nat]: ((dvd_dvd_complex @ (power_power_complex @ A @ N) @ B) => ((ord_less_eq_nat @ M @ N) => (dvd_dvd_complex @ (power_power_complex @ A @ M) @ B)))))). % power_le_dvd
thf(fact_43_power__le__dvd, axiom,
    ((![A : poly_nat, N : nat, B : poly_nat, M : nat]: ((dvd_dvd_poly_nat @ (power_power_poly_nat @ A @ N) @ B) => ((ord_less_eq_nat @ M @ N) => (dvd_dvd_poly_nat @ (power_power_poly_nat @ A @ M) @ B)))))). % power_le_dvd
thf(fact_44_power__le__dvd, axiom,
    ((![A : poly_poly_complex, N : nat, B : poly_poly_complex, M : nat]: ((dvd_dv598755940omplex @ (power_432682568omplex @ A @ N) @ B) => ((ord_less_eq_nat @ M @ N) => (dvd_dv598755940omplex @ (power_432682568omplex @ A @ M) @ B)))))). % power_le_dvd
thf(fact_45_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_46_poly__0, axiom,
    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
thf(fact_47_poly__0, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
thf(fact_48_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_49_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_50_content__eq__zero__iff, axiom,
    ((![P : poly_nat]: (((content_nat @ P) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % content_eq_zero_iff
thf(fact_51_divides__degree, axiom,
    ((![P : poly_complex, Q : poly_complex]: ((dvd_dvd_poly_complex @ P @ Q) => ((ord_less_eq_nat @ (degree_complex @ P) @ (degree_complex @ Q)) | (Q = zero_z1746442943omplex)))))). % divides_degree
thf(fact_52_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X3 : complex]: ((poly_complex2 @ P @ X3) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_53_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X3 : poly_complex]: ((poly_poly_complex2 @ P @ X3) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_54_dvd__imp__degree__le, axiom,
    ((![P : poly_complex, Q : poly_complex]: ((dvd_dvd_poly_complex @ P @ Q) => ((~ ((Q = zero_z1746442943omplex))) => (ord_less_eq_nat @ (degree_complex @ P) @ (degree_complex @ Q))))))). % dvd_imp_degree_le
thf(fact_55_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_56_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex]: (((poly_poly_complex2 @ P) = (poly_poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_57_zero__le__power, axiom,
    ((![A : nat, N : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (power_power_nat @ A @ N)))))). % zero_le_power
thf(fact_58_power__mono, axiom,
    ((![A : nat, B : nat, N : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N))))))). % power_mono
thf(fact_59_le__imp__power__dvd, axiom,
    ((![M : nat, N : nat, A : poly_complex]: ((ord_less_eq_nat @ M @ N) => (dvd_dvd_poly_complex @ (power_184595776omplex @ A @ M) @ (power_184595776omplex @ A @ N)))))). % le_imp_power_dvd
thf(fact_60_le__imp__power__dvd, axiom,
    ((![M : nat, N : nat, A : nat]: ((ord_less_eq_nat @ M @ N) => (dvd_dvd_nat @ (power_power_nat @ A @ M) @ (power_power_nat @ A @ N)))))). % le_imp_power_dvd
thf(fact_61_le__imp__power__dvd, axiom,
    ((![M : nat, N : nat, A : complex]: ((ord_less_eq_nat @ M @ N) => (dvd_dvd_complex @ (power_power_complex @ A @ M) @ (power_power_complex @ A @ N)))))). % le_imp_power_dvd
thf(fact_62_le__imp__power__dvd, axiom,
    ((![M : nat, N : nat, A : poly_nat]: ((ord_less_eq_nat @ M @ N) => (dvd_dvd_poly_nat @ (power_power_poly_nat @ A @ M) @ (power_power_poly_nat @ A @ N)))))). % le_imp_power_dvd
thf(fact_63_le__imp__power__dvd, axiom,
    ((![M : nat, N : nat, A : poly_poly_complex]: ((ord_less_eq_nat @ M @ N) => (dvd_dv598755940omplex @ (power_432682568omplex @ A @ M) @ (power_432682568omplex @ A @ N)))))). % le_imp_power_dvd
thf(fact_64_le0, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % le0
thf(fact_65_bot__nat__0_Oextremum, axiom,
    ((![A : nat]: (ord_less_eq_nat @ zero_zero_nat @ A)))). % bot_nat_0.extremum
thf(fact_66_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_67_order__refl, axiom,
    ((![X2 : nat]: (ord_less_eq_nat @ X2 @ X2)))). % order_refl
thf(fact_68_fundamental__theorem__of__algebra, axiom,
    ((![P : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra
thf(fact_69_less__eq__nat_Osimps_I1_J, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % less_eq_nat.simps(1)
thf(fact_70_le__0__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_0_eq
thf(fact_71_bot__nat__0_Oextremum__unique, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat))))). % bot_nat_0.extremum_unique
thf(fact_72_bot__nat__0_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat))))). % bot_nat_0.extremum_uniqueI
thf(fact_73_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y2 : complex]: ((F @ X3) = (F @ Y2)))))))). % constant_def
thf(fact_74_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_75_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_76_zero__reorient, axiom,
    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) = (X2 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_77_dual__order_Oantisym, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_78_dual__order_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z2 : nat]: (Y3 = Z2))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A2)) & ((ord_less_eq_nat @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_79_dual__order_Otrans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))))). % dual_order.trans
thf(fact_80_linorder__wlog, axiom,
    ((![P2 : nat > nat > $o, A : nat, B : nat]: ((![A3 : nat, B3 : nat]: ((ord_less_eq_nat @ A3 @ B3) => (P2 @ A3 @ B3))) => ((![A3 : nat, B3 : nat]: ((P2 @ B3 @ A3) => (P2 @ A3 @ B3))) => (P2 @ A @ B)))))). % linorder_wlog
thf(fact_81_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_82_order__trans, axiom,
    ((![X2 : nat, Y : nat, Z3 : nat]: ((ord_less_eq_nat @ X2 @ Y) => ((ord_less_eq_nat @ Y @ Z3) => (ord_less_eq_nat @ X2 @ Z3)))))). % order_trans
thf(fact_83_order__class_Oorder_Oantisym, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_84_ord__le__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C)))))). % ord_le_eq_trans
thf(fact_85_ord__eq__le__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % ord_eq_le_trans
thf(fact_86_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z2 : nat]: (Y3 = Z2))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A2 @ B2)) & ((ord_less_eq_nat @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_87_antisym__conv, axiom,
    ((![Y : nat, X2 : nat]: ((ord_less_eq_nat @ Y @ X2) => ((ord_less_eq_nat @ X2 @ Y) = (X2 = Y)))))). % antisym_conv
thf(fact_88_le__cases3, axiom,
    ((![X2 : nat, Y : nat, Z3 : nat]: (((ord_less_eq_nat @ X2 @ Y) => (~ ((ord_less_eq_nat @ Y @ Z3)))) => (((ord_less_eq_nat @ Y @ X2) => (~ ((ord_less_eq_nat @ X2 @ Z3)))) => (((ord_less_eq_nat @ X2 @ Z3) => (~ ((ord_less_eq_nat @ Z3 @ Y)))) => (((ord_less_eq_nat @ Z3 @ Y) => (~ ((ord_less_eq_nat @ Y @ X2)))) => (((ord_less_eq_nat @ Y @ Z3) => (~ ((ord_less_eq_nat @ Z3 @ X2)))) => (~ (((ord_less_eq_nat @ Z3 @ X2) => (~ ((ord_less_eq_nat @ X2 @ Y)))))))))))))). % le_cases3
thf(fact_89_order_Otrans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % order.trans
thf(fact_90_le__cases, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_eq_nat @ X2 @ Y))) => (ord_less_eq_nat @ Y @ X2))))). % le_cases
thf(fact_91_eq__refl, axiom,
    ((![X2 : nat, Y : nat]: ((X2 = Y) => (ord_less_eq_nat @ X2 @ Y))))). % eq_refl
thf(fact_92_linear, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) | (ord_less_eq_nat @ Y @ X2))))). % linear
thf(fact_93_antisym, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) => ((ord_less_eq_nat @ Y @ X2) => (X2 = Y)))))). % antisym
thf(fact_94_eq__iff, axiom,
    (((^[Y3 : nat]: (^[Z2 : nat]: (Y3 = Z2))) = (^[X3 : nat]: (^[Y2 : nat]: (((ord_less_eq_nat @ X3 @ Y2)) & ((ord_less_eq_nat @ Y2 @ X3)))))))). % eq_iff
thf(fact_95_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (((F2 @ B) = C) => ((![X4 : nat, Y4 : nat]: ((ord_less_eq_nat @ X4 @ Y4) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_96_ord__eq__le__subst, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((A = (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_eq_nat @ X4 @ Y4) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_97_order__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_eq_nat @ X4 @ Y4) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_98_order__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_eq_nat @ X4 @ Y4) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_99_Nat_Oex__has__greatest__nat, axiom,
    ((![P2 : nat > $o, K : nat, B : nat]: ((P2 @ K) => ((![Y4 : nat]: ((P2 @ Y4) => (ord_less_eq_nat @ Y4 @ B))) => (?[X4 : nat]: ((P2 @ X4) & (![Y5 : nat]: ((P2 @ Y5) => (ord_less_eq_nat @ Y5 @ X4)))))))))). % Nat.ex_has_greatest_nat
thf(fact_100_nat__le__linear, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) | (ord_less_eq_nat @ N @ M))))). % nat_le_linear
thf(fact_101_le__antisym, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => ((ord_less_eq_nat @ N @ M) => (M = N)))))). % le_antisym
thf(fact_102_eq__imp__le, axiom,
    ((![M : nat, N : nat]: ((M = N) => (ord_less_eq_nat @ M @ N))))). % eq_imp_le
thf(fact_103_le__trans, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ J @ K) => (ord_less_eq_nat @ I @ K)))))). % le_trans
thf(fact_104_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_105_zero__le, axiom,
    ((![X2 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X2)))). % zero_le
thf(fact_106_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat))). % le_numeral_extra(3)
thf(fact_107_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_108_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_complex, C : complex]: (((synthe151143547omplex @ P @ C) = zero_z1746442943omplex) = ((degree_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_109_is__zero__null, axiom,
    ((is_zero_complex = (^[P3 : poly_complex]: (P3 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_110_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_111_power__mono__iff, axiom,
    ((![A : nat, B : nat, N : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_eq_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N)) = (ord_less_eq_nat @ A @ B)))))))). % power_mono_iff
thf(fact_112_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_nat]: (((poly_nat2 @ (reflect_poly_nat @ P) @ zero_zero_nat) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_113_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_complex]: (((poly_complex2 @ (reflect_poly_complex @ P) @ zero_zero_complex) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_114_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((poly_poly_complex2 @ (reflec309385472omplex @ P) @ zero_z1746442943omplex) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_115_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_116_nat__zero__less__power__iff, axiom,
    ((![X2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ X2 @ N)) = (((ord_less_nat @ zero_zero_nat @ X2)) | ((N = zero_zero_nat))))))). % nat_zero_less_power_iff
thf(fact_117_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_118_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_119_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_120_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_121_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_122_power__eq__0__iff, axiom,
    ((![A : poly_complex, N : nat]: (((power_184595776omplex @ A @ N) = zero_z1746442943omplex) = (((A = zero_z1746442943omplex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_123_power__eq__0__iff, axiom,
    ((![A : nat, N : nat]: (((power_power_nat @ A @ N) = zero_zero_nat) = (((A = zero_zero_nat)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_124_power__eq__0__iff, axiom,
    ((![A : complex, N : nat]: (((power_power_complex @ A @ N) = zero_zero_complex) = (((A = zero_zero_complex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_125_power__eq__0__iff, axiom,
    ((![A : poly_nat, N : nat]: (((power_power_poly_nat @ A @ N) = zero_zero_poly_nat) = (((A = zero_zero_poly_nat)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_126_power__eq__0__iff, axiom,
    ((![A : poly_poly_complex, N : nat]: (((power_432682568omplex @ A @ N) = zero_z1040703943omplex) = (((A = zero_z1040703943omplex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_127_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_128_order_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_129_not__less__iff__gr__or__eq, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_nat @ X2 @ Y))) = (((ord_less_nat @ Y @ X2)) | ((X2 = Y))))))). % not_less_iff_gr_or_eq
thf(fact_130_dual__order_Ostrict__trans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_nat @ B @ A) => ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))))). % dual_order.strict_trans
thf(fact_131_linorder__less__wlog, axiom,
    ((![P2 : nat > nat > $o, A : nat, B : nat]: ((![A3 : nat, B3 : nat]: ((ord_less_nat @ A3 @ B3) => (P2 @ A3 @ B3))) => ((![A3 : nat]: (P2 @ A3 @ A3)) => ((![A3 : nat, B3 : nat]: ((P2 @ B3 @ A3) => (P2 @ A3 @ B3))) => (P2 @ A @ B))))))). % linorder_less_wlog
thf(fact_132_exists__least__iff, axiom,
    (((^[P4 : nat > $o]: (?[X5 : nat]: (P4 @ X5))) = (^[P5 : nat > $o]: (?[N2 : nat]: (((P5 @ N2)) & ((![M2 : nat]: (((ord_less_nat @ M2 @ N2)) => ((~ ((P5 @ M2))))))))))))). % exists_least_iff
thf(fact_133_less__imp__not__less, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (~ ((ord_less_nat @ Y @ X2))))))). % less_imp_not_less
thf(fact_134_order_Ostrict__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))))). % order.strict_trans
thf(fact_135_dual__order_Oirrefl, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ A)))))). % dual_order.irrefl
thf(fact_136_linorder__cases, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_nat @ X2 @ Y))) => ((~ ((X2 = Y))) => (ord_less_nat @ Y @ X2)))))). % linorder_cases
thf(fact_137_less__imp__triv, axiom,
    ((![X2 : nat, Y : nat, P2 : $o]: ((ord_less_nat @ X2 @ Y) => ((ord_less_nat @ Y @ X2) => P2))))). % less_imp_triv
thf(fact_138_less__imp__not__eq2, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (~ ((Y = X2))))))). % less_imp_not_eq2
thf(fact_139_antisym__conv3, axiom,
    ((![Y : nat, X2 : nat]: ((~ ((ord_less_nat @ Y @ X2))) => ((~ ((ord_less_nat @ X2 @ Y))) = (X2 = Y)))))). % antisym_conv3
thf(fact_140_less__induct, axiom,
    ((![P2 : nat > $o, A : nat]: ((![X4 : nat]: ((![Y5 : nat]: ((ord_less_nat @ Y5 @ X4) => (P2 @ Y5))) => (P2 @ X4))) => (P2 @ A))))). % less_induct
thf(fact_141_less__not__sym, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (~ ((ord_less_nat @ Y @ X2))))))). % less_not_sym
thf(fact_142_less__imp__not__eq, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (~ ((X2 = Y))))))). % less_imp_not_eq
thf(fact_143_dual__order_Oasym, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((ord_less_nat @ A @ B))))))). % dual_order.asym
thf(fact_144_ord__less__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C)))))). % ord_less_eq_trans
thf(fact_145_ord__eq__less__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))))). % ord_eq_less_trans
thf(fact_146_less__irrefl, axiom,
    ((![X2 : nat]: (~ ((ord_less_nat @ X2 @ X2)))))). % less_irrefl
thf(fact_147_less__linear, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) | ((X2 = Y) | (ord_less_nat @ Y @ X2)))))). % less_linear
thf(fact_148_less__trans, axiom,
    ((![X2 : nat, Y : nat, Z3 : nat]: ((ord_less_nat @ X2 @ Y) => ((ord_less_nat @ Y @ Z3) => (ord_less_nat @ X2 @ Z3)))))). % less_trans
thf(fact_149_less__asym_H, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % less_asym'
thf(fact_150_less__asym, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (~ ((ord_less_nat @ Y @ X2))))))). % less_asym
thf(fact_151_less__imp__neq, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (~ ((X2 = Y))))))). % less_imp_neq
thf(fact_152_order_Oasym, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % order.asym
thf(fact_153_neq__iff, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((X2 = Y))) = (((ord_less_nat @ X2 @ Y)) | ((ord_less_nat @ Y @ X2))))))). % neq_iff
thf(fact_154_neqE, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((X2 = Y))) => ((~ ((ord_less_nat @ X2 @ Y))) => (ord_less_nat @ Y @ X2)))))). % neqE
thf(fact_155_gt__ex, axiom,
    ((![X2 : nat]: (?[X_1 : nat]: (ord_less_nat @ X2 @ X_1))))). % gt_ex
thf(fact_156_order__less__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (F2 @ B) @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_nat @ X4 @ Y4) => (ord_less_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % order_less_subst2
thf(fact_157_order__less__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_nat @ A @ (F2 @ B)) => ((ord_less_nat @ B @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_nat @ X4 @ Y4) => (ord_less_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % order_less_subst1
thf(fact_158_ord__less__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_nat @ A @ B) => (((F2 @ B) = C) => ((![X4 : nat, Y4 : nat]: ((ord_less_nat @ X4 @ Y4) => (ord_less_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % ord_less_eq_subst
thf(fact_159_ord__eq__less__subst, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((A = (F2 @ B)) => ((ord_less_nat @ B @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_nat @ X4 @ Y4) => (ord_less_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % ord_eq_less_subst
thf(fact_160_linorder__neqE__nat, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((X2 = Y))) => ((~ ((ord_less_nat @ X2 @ Y))) => (ord_less_nat @ Y @ X2)))))). % linorder_neqE_nat
thf(fact_161_infinite__descent, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N3 : nat]: ((~ ((P2 @ N3))) => (?[M3 : nat]: ((ord_less_nat @ M3 @ N3) & (~ ((P2 @ M3))))))) => (P2 @ N))))). % infinite_descent
thf(fact_162_nat__less__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N3 : nat]: ((![M3 : nat]: ((ord_less_nat @ M3 @ N3) => (P2 @ M3))) => (P2 @ N3))) => (P2 @ N))))). % nat_less_induct
thf(fact_163_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_164_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_165_less__not__refl2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ N @ M) => (~ ((M = N))))))). % less_not_refl2
thf(fact_166_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_167_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_168_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_169_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_170_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_171_gr__implies__not__zero, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_172_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_173_leD, axiom,
    ((![Y : nat, X2 : nat]: ((ord_less_eq_nat @ Y @ X2) => (~ ((ord_less_nat @ X2 @ Y))))))). % leD
thf(fact_174_leI, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_nat @ X2 @ Y))) => (ord_less_eq_nat @ Y @ X2))))). % leI
thf(fact_175_le__less, axiom,
    ((ord_less_eq_nat = (^[X3 : nat]: (^[Y2 : nat]: (((ord_less_nat @ X3 @ Y2)) | ((X3 = Y2)))))))). % le_less
thf(fact_176_less__le, axiom,
    ((ord_less_nat = (^[X3 : nat]: (^[Y2 : nat]: (((ord_less_eq_nat @ X3 @ Y2)) & ((~ ((X3 = Y2)))))))))). % less_le
thf(fact_177_order__le__less__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_nat @ B @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_nat @ X4 @ Y4) => (ord_less_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % order_le_less_subst1
thf(fact_178_order__le__less__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (F2 @ B) @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_eq_nat @ X4 @ Y4) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % order_le_less_subst2
thf(fact_179_order__less__le__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_nat @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_eq_nat @ X4 @ Y4) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % order_less_le_subst1
thf(fact_180_order__less__le__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X4 : nat, Y4 : nat]: ((ord_less_nat @ X4 @ Y4) => (ord_less_nat @ (F2 @ X4) @ (F2 @ Y4)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % order_less_le_subst2

% Conjectures (1)
thf(conj_0, conjecture,
    ((dvd_dvd_poly_complex @ p @ (power_184595776omplex @ q @ n)))).
