% 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_1195__5379348_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:36:25.430

% Could-be-implicit typings (6)
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__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 (41)
thf(sy_c_Factorial__Ring_Ocomm__semiring__1__class_Oprime__elem_001t__Complex__Ocomplex, type,
    factor392545715omplex : complex > $o).
thf(sy_c_Factorial__Ring_Ocomm__semiring__1__class_Oprime__elem_001t__Nat__Onat, type,
    factor127820501em_nat : nat > $o).
thf(sy_c_Factorial__Ring_Ocomm__semiring__1__class_Oprime__elem_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    factor477435579omplex : poly_complex > $o).
thf(sy_c_Factorial__Ring_Ocomm__semiring__1__class_Oprime__elem_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    factor1360491971omplex : poly_poly_complex > $o).
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__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    times_1246143675omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    times_times_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    times_1460995011omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
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_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__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    semiri1679838999omplex : nat > poly_complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    semiri1266910751omplex : nat > poly_poly_complex).
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_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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_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__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__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    power_2001192272omplex : poly_p1267267526omplex > nat > poly_p1267267526omplex).
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__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    divide1187762952omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    divide350004240omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
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__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).
thf(sy_v_r, type,
    r : poly_complex).

% Relevant facts (249)
thf(fact_0_h, axiom,
    ((![X : complex]: ((poly_complex2 @ (power_184595776omplex @ q @ n) @ X) = (poly_complex2 @ r @ X))))). % h
thf(fact_1_dvd__power__same, axiom,
    ((![X : complex, Y : complex, N : nat]: ((dvd_dvd_complex @ X @ Y) => (dvd_dvd_complex @ (power_power_complex @ X @ N) @ (power_power_complex @ Y @ N)))))). % dvd_power_same
thf(fact_2_dvd__power__same, axiom,
    ((![X : poly_poly_complex, Y : poly_poly_complex, N : nat]: ((dvd_dv598755940omplex @ X @ Y) => (dvd_dv598755940omplex @ (power_432682568omplex @ X @ N) @ (power_432682568omplex @ Y @ N)))))). % dvd_power_same
thf(fact_3_dvd__power__same, axiom,
    ((![X : poly_complex, Y : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X @ Y) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X @ N) @ (power_184595776omplex @ Y @ N)))))). % dvd_power_same
thf(fact_4_dvd__refl, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ A)))). % dvd_refl
thf(fact_5_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_6_poly__power, axiom,
    ((![P : poly_p1267267526omplex, N : nat, X : poly_poly_complex]: ((poly_p282434315omplex @ (power_2001192272omplex @ P @ N) @ X) = (power_432682568omplex @ (poly_p282434315omplex @ P @ X) @ N))))). % poly_power
thf(fact_7_poly__power, axiom,
    ((![P : poly_poly_complex, N : nat, X : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P @ N) @ X) = (power_184595776omplex @ (poly_poly_complex2 @ P @ X) @ N))))). % poly_power
thf(fact_8_poly__power, axiom,
    ((![P : poly_complex, N : nat, X : complex]: ((poly_complex2 @ (power_184595776omplex @ P @ N) @ X) = (power_power_complex @ (poly_complex2 @ P @ X) @ N))))). % poly_power
thf(fact_9_dvd__power__le, axiom,
    ((![X : complex, Y : complex, N : nat, M : nat]: ((dvd_dvd_complex @ X @ Y) => ((ord_less_eq_nat @ N @ M) => (dvd_dvd_complex @ (power_power_complex @ X @ N) @ (power_power_complex @ Y @ M))))))). % dvd_power_le
thf(fact_10_dvd__power__le, axiom,
    ((![X : poly_poly_complex, Y : poly_poly_complex, N : nat, M : nat]: ((dvd_dv598755940omplex @ X @ Y) => ((ord_less_eq_nat @ N @ M) => (dvd_dv598755940omplex @ (power_432682568omplex @ X @ N) @ (power_432682568omplex @ Y @ M))))))). % dvd_power_le
thf(fact_11_dvd__power__le, axiom,
    ((![X : poly_complex, Y : poly_complex, N : nat, M : nat]: ((dvd_dvd_poly_complex @ X @ Y) => ((ord_less_eq_nat @ N @ M) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X @ N) @ (power_184595776omplex @ Y @ M))))))). % dvd_power_le
thf(fact_12_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_13_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_14_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_15_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_16_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_17_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_18_prime__elem__dvd__power, axiom,
    ((![P : complex, X : complex, N : nat]: ((factor392545715omplex @ P) => ((dvd_dvd_complex @ P @ (power_power_complex @ X @ N)) => (dvd_dvd_complex @ P @ X)))))). % prime_elem_dvd_power
thf(fact_19_prime__elem__dvd__power, axiom,
    ((![P : poly_poly_complex, X : poly_poly_complex, N : nat]: ((factor1360491971omplex @ P) => ((dvd_dv598755940omplex @ P @ (power_432682568omplex @ X @ N)) => (dvd_dv598755940omplex @ P @ X)))))). % prime_elem_dvd_power
thf(fact_20_prime__elem__dvd__power, axiom,
    ((![P : poly_complex, X : poly_complex, N : nat]: ((factor477435579omplex @ P) => ((dvd_dvd_poly_complex @ P @ (power_184595776omplex @ X @ N)) => (dvd_dvd_poly_complex @ P @ X)))))). % prime_elem_dvd_power
thf(fact_21_div__power, axiom,
    ((![B : poly_complex, A : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ B @ A) => ((power_184595776omplex @ (divide1187762952omplex @ A @ B) @ N) = (divide1187762952omplex @ (power_184595776omplex @ A @ N) @ (power_184595776omplex @ B @ N))))))). % div_power
thf(fact_22_div__power, axiom,
    ((![B : poly_poly_complex, A : poly_poly_complex, N : nat]: ((dvd_dv598755940omplex @ B @ A) => ((power_432682568omplex @ (divide350004240omplex @ A @ B) @ N) = (divide350004240omplex @ (power_432682568omplex @ A @ N) @ (power_432682568omplex @ B @ N))))))). % div_power
thf(fact_23_div__dvd__div, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((dvd_dvd_poly_complex @ A @ C) => ((dvd_dvd_poly_complex @ (divide1187762952omplex @ B @ A) @ (divide1187762952omplex @ C @ A)) = (dvd_dvd_poly_complex @ B @ C))))))). % div_dvd_div
thf(fact_24_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_25_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_26_power__divide, axiom,
    ((![A : complex, B : complex, N : nat]: ((power_power_complex @ (divide1210191872omplex @ A @ B) @ N) = (divide1210191872omplex @ (power_power_complex @ A @ N) @ (power_power_complex @ B @ N)))))). % power_divide
thf(fact_27_div__div__div__same, axiom,
    ((![D : poly_complex, B : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ D @ B) => ((dvd_dvd_poly_complex @ B @ A) => ((divide1187762952omplex @ (divide1187762952omplex @ A @ D) @ (divide1187762952omplex @ B @ D)) = (divide1187762952omplex @ A @ B))))))). % div_div_div_same
thf(fact_28_dvd__div__eq__cancel, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: (((divide1187762952omplex @ A @ C) = (divide1187762952omplex @ B @ C)) => ((dvd_dvd_poly_complex @ C @ A) => ((dvd_dvd_poly_complex @ C @ B) => (A = B))))))). % dvd_div_eq_cancel
thf(fact_29_dvd__div__eq__iff, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ C @ A) => ((dvd_dvd_poly_complex @ C @ B) => (((divide1187762952omplex @ A @ C) = (divide1187762952omplex @ B @ C)) = (A = B))))))). % dvd_div_eq_iff
thf(fact_30_order__refl, axiom,
    ((![X : nat]: (ord_less_eq_nat @ X @ X)))). % order_refl
thf(fact_31_of__nat__le__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: ((ord_less_eq_nat @ (power_power_nat @ (semiri1382578993at_nat @ B) @ W) @ (semiri1382578993at_nat @ X)) = (ord_less_eq_nat @ (power_power_nat @ B @ W) @ X))))). % of_nat_le_of_nat_power_cancel_iff
thf(fact_32_of__nat__power__le__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: ((ord_less_eq_nat @ (semiri1382578993at_nat @ X) @ (power_power_nat @ (semiri1382578993at_nat @ B) @ W)) = (ord_less_eq_nat @ X @ (power_power_nat @ B @ W)))))). % of_nat_power_le_of_nat_cancel_iff
thf(fact_33_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_34_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_35_eq__imp__le, axiom,
    ((![M : nat, N : nat]: ((M = N) => (ord_less_eq_nat @ M @ N))))). % eq_imp_le
thf(fact_36_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_37_bot__nat__0_Oextremum, axiom,
    ((![A : nat]: (ord_less_eq_nat @ zero_zero_nat @ A)))). % bot_nat_0.extremum
thf(fact_38_le0, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % le0
thf(fact_39_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_40_mult__zero__left, axiom,
    ((![A : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ A) = zero_z1746442943omplex)))). % mult_zero_left
thf(fact_41_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_42_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_43_mult__zero__right, axiom,
    ((![A : poly_complex]: ((times_1246143675omplex @ A @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % mult_zero_right
thf(fact_44_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_45_mult__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_46_mult__eq__0__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex) = (((A = zero_z1746442943omplex)) | ((B = zero_z1746442943omplex))))))). % mult_eq_0_iff
thf(fact_47_mult__eq__0__iff, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = (((A = zero_zero_nat)) | ((B = zero_zero_nat))))))). % mult_eq_0_iff
thf(fact_48_mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_left
thf(fact_49_mult__cancel__left, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: (((times_1246143675omplex @ C @ A) = (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((A = B))))))). % mult_cancel_left
thf(fact_50_mult__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_left
thf(fact_51_mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_right
thf(fact_52_mult__cancel__right, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A @ C) = (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((A = B))))))). % mult_cancel_right
thf(fact_53_mult__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_right
thf(fact_54_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_55_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_56_div__by__0, axiom,
    ((![A : poly_complex]: ((divide1187762952omplex @ A @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % div_by_0
thf(fact_57_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_58_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_59_div__0, axiom,
    ((![A : poly_complex]: ((divide1187762952omplex @ zero_z1746442943omplex @ A) = zero_z1746442943omplex)))). % div_0
thf(fact_60_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_61_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_62_dvd__0__right, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_63_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_64_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_65_dvd__0__left__iff, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) = (A = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_66_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri1382578993at_nat @ M) = zero_zero_nat) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_67_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri356525583omplex @ M) = zero_zero_complex) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_68_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri1679838999omplex @ M) = zero_z1746442943omplex) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_69_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_nat = (semiri1382578993at_nat @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_70_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_complex = (semiri356525583omplex @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_71_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_z1746442943omplex = (semiri1679838999omplex @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_72_of__nat__0, axiom,
    (((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat))). % of_nat_0
thf(fact_73_of__nat__0, axiom,
    (((semiri356525583omplex @ zero_zero_nat) = zero_zero_complex))). % of_nat_0
thf(fact_74_of__nat__0, axiom,
    (((semiri1679838999omplex @ zero_zero_nat) = zero_z1746442943omplex))). % of_nat_0
thf(fact_75_of__nat__mult, axiom,
    ((![M : nat, N : nat]: ((semiri1382578993at_nat @ (times_times_nat @ M @ N)) = (times_times_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)))))). % of_nat_mult
thf(fact_76_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_77_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_78_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_79_poly__mult, axiom,
    ((![P : poly_complex, Q : poly_complex, X : complex]: ((poly_complex2 @ (times_1246143675omplex @ P @ Q) @ X) = (times_times_complex @ (poly_complex2 @ P @ X) @ (poly_complex2 @ Q @ X)))))). % poly_mult
thf(fact_80_poly__mult, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (times_1460995011omplex @ P @ Q) @ X) = (times_1246143675omplex @ (poly_poly_complex2 @ P @ X) @ (poly_poly_complex2 @ Q @ X)))))). % poly_mult
thf(fact_81_poly__mult, axiom,
    ((![P : poly_nat, Q : poly_nat, X : nat]: ((poly_nat2 @ (times_times_poly_nat @ P @ Q) @ X) = (times_times_nat @ (poly_nat2 @ P @ X) @ (poly_nat2 @ Q @ X)))))). % poly_mult
thf(fact_82_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_83_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_84_nonzero__mult__div__cancel__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_85_nonzero__mult__div__cancel__right, axiom,
    ((![B : poly_complex, A : poly_complex]: ((~ ((B = zero_z1746442943omplex))) => ((divide1187762952omplex @ (times_1246143675omplex @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_86_nonzero__mult__div__cancel__right, axiom,
    ((![B : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_87_nonzero__mult__div__cancel__left, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_88_nonzero__mult__div__cancel__left, axiom,
    ((![A : poly_complex, B : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((divide1187762952omplex @ (times_1246143675omplex @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_89_nonzero__mult__div__cancel__left, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_90_of__nat__le__0__iff, axiom,
    ((![M : nat]: ((ord_less_eq_nat @ (semiri1382578993at_nat @ M) @ zero_zero_nat) = (M = zero_zero_nat))))). % of_nat_le_0_iff
thf(fact_91_dvd__times__right__cancel__iff, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((dvd_dvd_poly_complex @ (times_1246143675omplex @ B @ A) @ (times_1246143675omplex @ C @ A)) = (dvd_dvd_poly_complex @ B @ C)))))). % dvd_times_right_cancel_iff
thf(fact_92_dvd__times__right__cancel__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((~ ((A = zero_zero_nat))) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)))))). % dvd_times_right_cancel_iff
thf(fact_93_dvd__times__left__cancel__iff, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((dvd_dvd_poly_complex @ (times_1246143675omplex @ A @ B) @ (times_1246143675omplex @ A @ C)) = (dvd_dvd_poly_complex @ B @ C)))))). % dvd_times_left_cancel_iff
thf(fact_94_dvd__times__left__cancel__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((~ ((A = zero_zero_nat))) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C)))))). % dvd_times_left_cancel_iff
thf(fact_95_dvd__mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((dvd_dvd_complex @ A @ B))))))). % dvd_mult_cancel_right
thf(fact_96_dvd__mult__cancel__right, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ A @ C) @ (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((dvd_dvd_poly_complex @ A @ B))))))). % dvd_mult_cancel_right
thf(fact_97_dvd__mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((dvd_dvd_complex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((dvd_dvd_complex @ A @ B))))))). % dvd_mult_cancel_left
thf(fact_98_dvd__mult__cancel__left, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ C @ A) @ (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((dvd_dvd_poly_complex @ A @ B))))))). % dvd_mult_cancel_left
thf(fact_99_dvd__mult__div__cancel, axiom,
    ((![A : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((times_1246143675omplex @ A @ (divide1187762952omplex @ B @ A)) = B))))). % dvd_mult_div_cancel
thf(fact_100_dvd__mult__div__cancel, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ A @ (divide_divide_nat @ B @ A)) = B))))). % dvd_mult_div_cancel
thf(fact_101_dvd__div__mult__self, axiom,
    ((![A : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((times_1246143675omplex @ (divide1187762952omplex @ B @ A) @ A) = B))))). % dvd_div_mult_self
thf(fact_102_dvd__div__mult__self, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B))))). % dvd_div_mult_self
thf(fact_103_of__nat__le__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)) = (ord_less_eq_nat @ M @ N))))). % of_nat_le_iff
thf(fact_104_of__nat__power, axiom,
    ((![M : nat, N : nat]: ((semiri1679838999omplex @ (power_power_nat @ M @ N)) = (power_184595776omplex @ (semiri1679838999omplex @ M) @ N))))). % of_nat_power
thf(fact_105_of__nat__power, axiom,
    ((![M : nat, N : nat]: ((semiri356525583omplex @ (power_power_nat @ M @ N)) = (power_power_complex @ (semiri356525583omplex @ M) @ N))))). % of_nat_power
thf(fact_106_of__nat__power, axiom,
    ((![M : nat, N : nat]: ((semiri1266910751omplex @ (power_power_nat @ M @ N)) = (power_432682568omplex @ (semiri1266910751omplex @ M) @ N))))). % of_nat_power
thf(fact_107_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: (((power_184595776omplex @ (semiri1679838999omplex @ B) @ W) = (semiri1679838999omplex @ X)) = ((power_power_nat @ B @ W) = X))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_108_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: (((power_power_complex @ (semiri356525583omplex @ B) @ W) = (semiri356525583omplex @ X)) = ((power_power_nat @ B @ W) = X))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_109_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: (((power_432682568omplex @ (semiri1266910751omplex @ B) @ W) = (semiri1266910751omplex @ X)) = ((power_power_nat @ B @ W) = X))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_110_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: (((semiri1679838999omplex @ X) = (power_184595776omplex @ (semiri1679838999omplex @ B) @ W)) = (X = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_111_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: (((semiri356525583omplex @ X) = (power_power_complex @ (semiri356525583omplex @ B) @ W)) = (X = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_112_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: (((semiri1266910751omplex @ X) = (power_432682568omplex @ (semiri1266910751omplex @ B) @ W)) = (X = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_113_mult__not__zero, axiom,
    ((![A : complex, B : complex]: ((~ (((times_times_complex @ A @ B) = zero_zero_complex))) => ((~ ((A = zero_zero_complex))) & (~ ((B = zero_zero_complex)))))))). % mult_not_zero
thf(fact_114_mult__not__zero, axiom,
    ((![A : poly_complex, B : poly_complex]: ((~ (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex))) => ((~ ((A = zero_z1746442943omplex))) & (~ ((B = zero_z1746442943omplex)))))))). % mult_not_zero
thf(fact_115_mult__not__zero, axiom,
    ((![A : nat, B : nat]: ((~ (((times_times_nat @ A @ B) = zero_zero_nat))) => ((~ ((A = zero_zero_nat))) & (~ ((B = zero_zero_nat)))))))). % mult_not_zero
thf(fact_116_mult__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))))). % mult_mono
thf(fact_117_mult__mono_H, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))))). % mult_mono'
thf(fact_118_mult__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % mult_left_mono
thf(fact_119_mult__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))))). % mult_right_mono
thf(fact_120_split__mult__neg__le, axiom,
    ((![A : nat, B : nat]: ((((ord_less_eq_nat @ zero_zero_nat @ A) & (ord_less_eq_nat @ B @ zero_zero_nat)) | ((ord_less_eq_nat @ A @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ B))) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))). % split_mult_neg_le
thf(fact_121_mult__nonneg__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))))). % mult_nonneg_nonneg
thf(fact_122_mult__nonneg__nonpos, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))))). % mult_nonneg_nonpos
thf(fact_123_mult__nonpos__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))))). % mult_nonpos_nonneg
thf(fact_124_mult__nonneg__nonpos2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)))))). % mult_nonneg_nonpos2
thf(fact_125_divisors__zero, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) => ((A = zero_zero_complex) | (B = zero_zero_complex)))))). % divisors_zero
thf(fact_126_divisors__zero, axiom,
    ((![A : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex) => ((A = zero_z1746442943omplex) | (B = zero_z1746442943omplex)))))). % divisors_zero
thf(fact_127_divisors__zero, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((A = zero_zero_nat) | (B = zero_zero_nat)))))). % divisors_zero
thf(fact_128_of__nat__0__le__iff, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1382578993at_nat @ N))))). % of_nat_0_le_iff
thf(fact_129_ordered__comm__semiring__class_Ocomm__mult__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % ordered_comm_semiring_class.comm_mult_left_mono
thf(fact_130_no__zero__divisors, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (~ (((times_times_complex @ A @ B) = zero_zero_complex)))))))). % no_zero_divisors
thf(fact_131_no__zero__divisors, axiom,
    ((![A : poly_complex, B : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((~ ((B = zero_z1746442943omplex))) => (~ (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex)))))))). % no_zero_divisors
thf(fact_132_no__zero__divisors, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((~ ((B = zero_zero_nat))) => (~ (((times_times_nat @ A @ B) = zero_zero_nat)))))))). % no_zero_divisors
thf(fact_133_mult__left__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_134_mult__left__cancel, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => (((times_1246143675omplex @ C @ A) = (times_1246143675omplex @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_135_mult__left__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_136_mult__right__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_137_mult__right__cancel, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => (((times_1246143675omplex @ A @ C) = (times_1246143675omplex @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_138_mult__right__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_139_mult__of__nat__commute, axiom,
    ((![X : nat, Y : nat]: ((times_times_nat @ (semiri1382578993at_nat @ X) @ Y) = (times_times_nat @ Y @ (semiri1382578993at_nat @ X)))))). % mult_of_nat_commute
thf(fact_140_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X2 : complex]: ((poly_complex2 @ P @ X2) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_141_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X2 : poly_complex]: ((poly_poly_complex2 @ P @ X2) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_142_mpoly__base__conv_I1_J, axiom,
    ((![X : complex]: (zero_zero_complex = (poly_complex2 @ zero_z1746442943omplex @ X))))). % mpoly_base_conv(1)
thf(fact_143_mpoly__base__conv_I1_J, axiom,
    ((![X : poly_complex]: (zero_z1746442943omplex = (poly_poly_complex2 @ zero_z1040703943omplex @ X))))). % mpoly_base_conv(1)
thf(fact_144_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_nat]: (~ ((?[X3 : nat]: (((poly_nat2 @ P @ X3) = zero_zero_nat) & (~ (((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))))))))). % basic_cqe_conv1(1)
thf(fact_145_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_complex]: (~ ((?[X3 : complex]: (((poly_complex2 @ P @ X3) = zero_zero_complex) & (~ (((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))))))))). % basic_cqe_conv1(1)
thf(fact_146_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_poly_complex]: (~ ((?[X3 : poly_complex]: (((poly_poly_complex2 @ P @ X3) = zero_z1746442943omplex) & (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))))))))). % basic_cqe_conv1(1)
thf(fact_147_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : nat]: (~ (((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))))))). % basic_cqe_conv1(2)
thf(fact_148_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_complex]: (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))))))). % basic_cqe_conv1(2)
thf(fact_149_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : complex]: (~ (((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))))))). % basic_cqe_conv1(2)
thf(fact_150_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X4) = zero_zero_nat)))). % basic_cqe_conv1(4)
thf(fact_151_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X4) = zero_z1746442943omplex)))). % basic_cqe_conv1(4)
thf(fact_152_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X4) = zero_zero_complex)))). % basic_cqe_conv1(4)
thf(fact_153_mult__le__mono2, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (times_times_nat @ K @ I) @ (times_times_nat @ K @ J)))))). % mult_le_mono2
thf(fact_154_mult__le__mono1, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (times_times_nat @ I @ K) @ (times_times_nat @ J @ K)))))). % mult_le_mono1
thf(fact_155_mult__le__mono, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ K @ L) => (ord_less_eq_nat @ (times_times_nat @ I @ K) @ (times_times_nat @ J @ L))))))). % mult_le_mono
thf(fact_156_le__square, axiom,
    ((![M : nat]: (ord_less_eq_nat @ M @ (times_times_nat @ M @ M))))). % le_square
thf(fact_157_le__cube, axiom,
    ((![M : nat]: (ord_less_eq_nat @ M @ (times_times_nat @ M @ (times_times_nat @ M @ M)))))). % le_cube
thf(fact_158_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_159_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_160_le__0__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_0_eq
thf(fact_161_less__eq__nat_Osimps_I1_J, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % less_eq_nat.simps(1)
thf(fact_162_basic__cqe__conv__2b, axiom,
    ((![P : poly_complex]: ((?[X2 : complex]: (~ (((poly_complex2 @ P @ X2) = zero_zero_complex)))) = (~ ((P = zero_z1746442943omplex))))))). % basic_cqe_conv_2b
thf(fact_163_dvd__div__div__eq__mult, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex, D : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((~ ((C = zero_z1746442943omplex))) => ((dvd_dvd_poly_complex @ A @ B) => ((dvd_dvd_poly_complex @ C @ D) => (((divide1187762952omplex @ B @ A) = (divide1187762952omplex @ D @ C)) = ((times_1246143675omplex @ B @ C) = (times_1246143675omplex @ A @ D)))))))))). % dvd_div_div_eq_mult
thf(fact_164_dvd__div__div__eq__mult, axiom,
    ((![A : nat, C : nat, B : nat, D : nat]: ((~ ((A = zero_zero_nat))) => ((~ ((C = zero_zero_nat))) => ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ D) => (((divide_divide_nat @ B @ A) = (divide_divide_nat @ D @ C)) = ((times_times_nat @ B @ C) = (times_times_nat @ A @ D)))))))))). % dvd_div_div_eq_mult
thf(fact_165_dvd__div__iff__mult, axiom,
    ((![C : poly_complex, B : poly_complex, A : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => ((dvd_dvd_poly_complex @ C @ B) => ((dvd_dvd_poly_complex @ A @ (divide1187762952omplex @ B @ C)) = (dvd_dvd_poly_complex @ (times_1246143675omplex @ A @ C) @ B))))))). % dvd_div_iff_mult
thf(fact_166_dvd__div__iff__mult, axiom,
    ((![C : nat, B : nat, A : nat]: ((~ ((C = zero_zero_nat))) => ((dvd_dvd_nat @ C @ B) => ((dvd_dvd_nat @ A @ (divide_divide_nat @ B @ C)) = (dvd_dvd_nat @ (times_times_nat @ A @ C) @ B))))))). % dvd_div_iff_mult
thf(fact_167_div__dvd__iff__mult, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: ((~ ((B = zero_z1746442943omplex))) => ((dvd_dvd_poly_complex @ B @ A) => ((dvd_dvd_poly_complex @ (divide1187762952omplex @ A @ B) @ C) = (dvd_dvd_poly_complex @ A @ (times_1246143675omplex @ C @ B)))))))). % div_dvd_iff_mult
thf(fact_168_div__dvd__iff__mult, axiom,
    ((![B : nat, A : nat, C : nat]: ((~ ((B = zero_zero_nat))) => ((dvd_dvd_nat @ B @ A) => ((dvd_dvd_nat @ (divide_divide_nat @ A @ B) @ C) = (dvd_dvd_nat @ A @ (times_times_nat @ C @ B)))))))). % div_dvd_iff_mult
thf(fact_169_dvd__div__eq__mult, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((dvd_dvd_poly_complex @ A @ B) => (((divide1187762952omplex @ B @ A) = C) = (B = (times_1246143675omplex @ C @ A)))))))). % dvd_div_eq_mult
thf(fact_170_dvd__div__eq__mult, axiom,
    ((![A : nat, B : nat, C : nat]: ((~ ((A = zero_zero_nat))) => ((dvd_dvd_nat @ A @ B) => (((divide_divide_nat @ B @ A) = C) = (B = (times_times_nat @ C @ A)))))))). % dvd_div_eq_mult
thf(fact_171_power__commutes, axiom,
    ((![A : poly_complex, N : nat]: ((times_1246143675omplex @ (power_184595776omplex @ A @ N) @ A) = (times_1246143675omplex @ A @ (power_184595776omplex @ A @ N)))))). % power_commutes
thf(fact_172_power__commutes, axiom,
    ((![A : complex, N : nat]: ((times_times_complex @ (power_power_complex @ A @ N) @ A) = (times_times_complex @ A @ (power_power_complex @ A @ N)))))). % power_commutes
thf(fact_173_power__commutes, axiom,
    ((![A : poly_poly_complex, N : nat]: ((times_1460995011omplex @ (power_432682568omplex @ A @ N) @ A) = (times_1460995011omplex @ A @ (power_432682568omplex @ A @ N)))))). % power_commutes
thf(fact_174_power__commutes, axiom,
    ((![A : nat, N : nat]: ((times_times_nat @ (power_power_nat @ A @ N) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ N)))))). % power_commutes
thf(fact_175_power__mult__distrib, axiom,
    ((![A : poly_complex, B : poly_complex, N : nat]: ((power_184595776omplex @ (times_1246143675omplex @ A @ B) @ N) = (times_1246143675omplex @ (power_184595776omplex @ A @ N) @ (power_184595776omplex @ B @ N)))))). % power_mult_distrib
thf(fact_176_power__mult__distrib, axiom,
    ((![A : complex, B : complex, N : nat]: ((power_power_complex @ (times_times_complex @ A @ B) @ N) = (times_times_complex @ (power_power_complex @ A @ N) @ (power_power_complex @ B @ N)))))). % power_mult_distrib
thf(fact_177_power__mult__distrib, axiom,
    ((![A : poly_poly_complex, B : poly_poly_complex, N : nat]: ((power_432682568omplex @ (times_1460995011omplex @ A @ B) @ N) = (times_1460995011omplex @ (power_432682568omplex @ A @ N) @ (power_432682568omplex @ B @ N)))))). % power_mult_distrib
thf(fact_178_power__mult__distrib, axiom,
    ((![A : nat, B : nat, N : nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ N) = (times_times_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N)))))). % power_mult_distrib
thf(fact_179_power__commuting__commutes, axiom,
    ((![X : poly_complex, Y : poly_complex, N : nat]: (((times_1246143675omplex @ X @ Y) = (times_1246143675omplex @ Y @ X)) => ((times_1246143675omplex @ (power_184595776omplex @ X @ N) @ Y) = (times_1246143675omplex @ Y @ (power_184595776omplex @ X @ N))))))). % power_commuting_commutes
thf(fact_180_power__commuting__commutes, axiom,
    ((![X : complex, Y : complex, N : nat]: (((times_times_complex @ X @ Y) = (times_times_complex @ Y @ X)) => ((times_times_complex @ (power_power_complex @ X @ N) @ Y) = (times_times_complex @ Y @ (power_power_complex @ X @ N))))))). % power_commuting_commutes
thf(fact_181_power__commuting__commutes, axiom,
    ((![X : poly_poly_complex, Y : poly_poly_complex, N : nat]: (((times_1460995011omplex @ X @ Y) = (times_1460995011omplex @ Y @ X)) => ((times_1460995011omplex @ (power_432682568omplex @ X @ N) @ Y) = (times_1460995011omplex @ Y @ (power_432682568omplex @ X @ N))))))). % power_commuting_commutes
thf(fact_182_power__commuting__commutes, axiom,
    ((![X : nat, Y : nat, N : nat]: (((times_times_nat @ X @ Y) = (times_times_nat @ Y @ X)) => ((times_times_nat @ (power_power_nat @ X @ N) @ Y) = (times_times_nat @ Y @ (power_power_nat @ X @ N))))))). % power_commuting_commutes
thf(fact_183_dvdE, axiom,
    ((![B : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ B @ A) => (~ ((![K2 : poly_complex]: (~ ((A = (times_1246143675omplex @ B @ K2))))))))))). % dvdE
thf(fact_184_dvdE, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ A) => (~ ((![K2 : nat]: (~ ((A = (times_times_nat @ B @ K2))))))))))). % dvdE
thf(fact_185_dvdI, axiom,
    ((![A : poly_complex, B : poly_complex, K : poly_complex]: ((A = (times_1246143675omplex @ B @ K)) => (dvd_dvd_poly_complex @ B @ A))))). % dvdI
thf(fact_186_dvdI, axiom,
    ((![A : nat, B : nat, K : nat]: ((A = (times_times_nat @ B @ K)) => (dvd_dvd_nat @ B @ A))))). % dvdI
thf(fact_187_dvd__def, axiom,
    ((dvd_dvd_poly_complex = (^[B2 : poly_complex]: (^[A2 : poly_complex]: (?[K3 : poly_complex]: (A2 = (times_1246143675omplex @ B2 @ K3)))))))). % dvd_def
thf(fact_188_dvd__def, axiom,
    ((dvd_dvd_nat = (^[B2 : nat]: (^[A2 : nat]: (?[K3 : nat]: (A2 = (times_times_nat @ B2 @ K3)))))))). % dvd_def
thf(fact_189_dvd__mult, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ A @ C) => (dvd_dvd_poly_complex @ A @ (times_1246143675omplex @ B @ C)))))). % dvd_mult
thf(fact_190_dvd__mult, axiom,
    ((![A : nat, C : nat, B : nat]: ((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (times_times_nat @ B @ C)))))). % dvd_mult
thf(fact_191_dvd__mult2, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => (dvd_dvd_poly_complex @ A @ (times_1246143675omplex @ B @ C)))))). % dvd_mult2
thf(fact_192_dvd__mult2, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ A @ (times_times_nat @ B @ C)))))). % dvd_mult2
thf(fact_193_dvd__mult__left, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ A @ B) @ C) => (dvd_dvd_poly_complex @ A @ C))))). % dvd_mult_left
thf(fact_194_dvd__mult__left, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) => (dvd_dvd_nat @ A @ C))))). % dvd_mult_left
thf(fact_195_dvd__triv__left, axiom,
    ((![A : poly_complex, B : poly_complex]: (dvd_dvd_poly_complex @ A @ (times_1246143675omplex @ A @ B))))). % dvd_triv_left
thf(fact_196_dvd__triv__left, axiom,
    ((![A : nat, B : nat]: (dvd_dvd_nat @ A @ (times_times_nat @ A @ B))))). % dvd_triv_left
thf(fact_197_mult__dvd__mono, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex, D : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((dvd_dvd_poly_complex @ C @ D) => (dvd_dvd_poly_complex @ (times_1246143675omplex @ A @ C) @ (times_1246143675omplex @ B @ D))))))). % mult_dvd_mono
thf(fact_198_mult__dvd__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ D) => (dvd_dvd_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))). % mult_dvd_mono
thf(fact_199_dvd__mult__right, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ A @ B) @ C) => (dvd_dvd_poly_complex @ B @ C))))). % dvd_mult_right
thf(fact_200_dvd__mult__right, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) => (dvd_dvd_nat @ B @ C))))). % dvd_mult_right
thf(fact_201_dvd__triv__right, axiom,
    ((![A : poly_complex, B : poly_complex]: (dvd_dvd_poly_complex @ A @ (times_1246143675omplex @ B @ A))))). % dvd_triv_right
thf(fact_202_dvd__triv__right, axiom,
    ((![A : nat, B : nat]: (dvd_dvd_nat @ A @ (times_times_nat @ B @ A))))). % dvd_triv_right
thf(fact_203_power__mult, axiom,
    ((![A : poly_complex, M : nat, N : nat]: ((power_184595776omplex @ A @ (times_times_nat @ M @ N)) = (power_184595776omplex @ (power_184595776omplex @ A @ M) @ N))))). % power_mult
thf(fact_204_power__mult, axiom,
    ((![A : complex, M : nat, N : nat]: ((power_power_complex @ A @ (times_times_nat @ M @ N)) = (power_power_complex @ (power_power_complex @ A @ M) @ N))))). % power_mult
thf(fact_205_power__mult, axiom,
    ((![A : poly_poly_complex, M : nat, N : nat]: ((power_432682568omplex @ A @ (times_times_nat @ M @ N)) = (power_432682568omplex @ (power_432682568omplex @ A @ M) @ N))))). % power_mult
thf(fact_206_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_207_power__not__zero, axiom,
    ((![A : poly_complex, N : nat]: ((~ ((A = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_208_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_209_power__not__zero, axiom,
    ((![A : poly_poly_complex, N : nat]: ((~ ((A = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A @ N) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_210_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_211_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_212_dvd__0__left, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) => (A = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_213_of__nat__mono, axiom,
    ((![I : nat, J : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (semiri1382578993at_nat @ I) @ (semiri1382578993at_nat @ J)))))). % of_nat_mono
thf(fact_214_prime__elem__not__zeroI, axiom,
    ((![P : nat]: ((factor127820501em_nat @ P) => (~ ((P = zero_zero_nat))))))). % prime_elem_not_zeroI
thf(fact_215_prime__elem__not__zeroI, axiom,
    ((![P : complex]: ((factor392545715omplex @ P) => (~ ((P = zero_zero_complex))))))). % prime_elem_not_zeroI
thf(fact_216_prime__elem__not__zeroI, axiom,
    ((![P : poly_complex]: ((factor477435579omplex @ P) => (~ ((P = zero_z1746442943omplex))))))). % prime_elem_not_zeroI
thf(fact_217_not__prime__elem__zero, axiom,
    ((~ ((factor127820501em_nat @ zero_zero_nat))))). % not_prime_elem_zero
thf(fact_218_not__prime__elem__zero, axiom,
    ((~ ((factor392545715omplex @ zero_zero_complex))))). % not_prime_elem_zero
thf(fact_219_not__prime__elem__zero, axiom,
    ((~ ((factor477435579omplex @ zero_z1746442943omplex))))). % not_prime_elem_zero
thf(fact_220_div__mult__div__if__dvd, axiom,
    ((![B : poly_complex, A : poly_complex, D : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ B @ A) => ((dvd_dvd_poly_complex @ D @ C) => ((times_1246143675omplex @ (divide1187762952omplex @ A @ B) @ (divide1187762952omplex @ C @ D)) = (divide1187762952omplex @ (times_1246143675omplex @ A @ C) @ (times_1246143675omplex @ B @ D)))))))). % div_mult_div_if_dvd
thf(fact_221_div__mult__div__if__dvd, axiom,
    ((![B : nat, A : nat, D : nat, C : nat]: ((dvd_dvd_nat @ B @ A) => ((dvd_dvd_nat @ D @ C) => ((times_times_nat @ (divide_divide_nat @ A @ B) @ (divide_divide_nat @ C @ D)) = (divide_divide_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)))))))). % div_mult_div_if_dvd
thf(fact_222_dvd__mult__imp__div, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ A @ C) @ B) => (dvd_dvd_poly_complex @ A @ (divide1187762952omplex @ B @ C)))))). % dvd_mult_imp_div
thf(fact_223_dvd__mult__imp__div, axiom,
    ((![A : nat, C : nat, B : nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ C) @ B) => (dvd_dvd_nat @ A @ (divide_divide_nat @ B @ C)))))). % dvd_mult_imp_div
thf(fact_224_dvd__div__mult2__eq, axiom,
    ((![B : poly_complex, C : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ B @ C) @ A) => ((divide1187762952omplex @ A @ (times_1246143675omplex @ B @ C)) = (divide1187762952omplex @ (divide1187762952omplex @ A @ B) @ C)))))). % dvd_div_mult2_eq
thf(fact_225_dvd__div__mult2__eq, axiom,
    ((![B : nat, C : nat, A : nat]: ((dvd_dvd_nat @ (times_times_nat @ B @ C) @ A) => ((divide_divide_nat @ A @ (times_times_nat @ B @ C)) = (divide_divide_nat @ (divide_divide_nat @ A @ B) @ C)))))). % dvd_div_mult2_eq
thf(fact_226_div__div__eq__right, axiom,
    ((![C : poly_complex, B : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ C @ B) => ((dvd_dvd_poly_complex @ B @ A) => ((divide1187762952omplex @ A @ (divide1187762952omplex @ B @ C)) = (times_1246143675omplex @ (divide1187762952omplex @ A @ B) @ C))))))). % div_div_eq_right
thf(fact_227_div__div__eq__right, axiom,
    ((![C : nat, B : nat, A : nat]: ((dvd_dvd_nat @ C @ B) => ((dvd_dvd_nat @ B @ A) => ((divide_divide_nat @ A @ (divide_divide_nat @ B @ C)) = (times_times_nat @ (divide_divide_nat @ A @ B) @ C))))))). % div_div_eq_right
thf(fact_228_div__mult__swap, axiom,
    ((![C : poly_complex, B : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ C @ B) => ((times_1246143675omplex @ A @ (divide1187762952omplex @ B @ C)) = (divide1187762952omplex @ (times_1246143675omplex @ A @ B) @ C)))))). % div_mult_swap
thf(fact_229_div__mult__swap, axiom,
    ((![C : nat, B : nat, A : nat]: ((dvd_dvd_nat @ C @ B) => ((times_times_nat @ A @ (divide_divide_nat @ B @ C)) = (divide_divide_nat @ (times_times_nat @ A @ B) @ C)))))). % div_mult_swap
thf(fact_230_dvd__div__mult, axiom,
    ((![C : poly_complex, B : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ C @ B) => ((times_1246143675omplex @ (divide1187762952omplex @ B @ C) @ A) = (divide1187762952omplex @ (times_1246143675omplex @ B @ A) @ C)))))). % dvd_div_mult
thf(fact_231_dvd__div__mult, axiom,
    ((![C : nat, B : nat, A : nat]: ((dvd_dvd_nat @ C @ B) => ((times_times_nat @ (divide_divide_nat @ B @ C) @ A) = (divide_divide_nat @ (times_times_nat @ B @ A) @ C)))))). % dvd_div_mult
thf(fact_232_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_233_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_234_dvd__div__eq__0__iff, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ A) => (((divide_divide_nat @ A @ B) = zero_zero_nat) = (A = zero_zero_nat)))))). % dvd_div_eq_0_iff
thf(fact_235_dvd__div__eq__0__iff, axiom,
    ((![B : complex, A : complex]: ((dvd_dvd_complex @ B @ A) => (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (A = zero_zero_complex)))))). % dvd_div_eq_0_iff
thf(fact_236_dvd__div__eq__0__iff, axiom,
    ((![B : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ B @ A) => (((divide1187762952omplex @ A @ B) = zero_z1746442943omplex) = (A = zero_z1746442943omplex)))))). % dvd_div_eq_0_iff
thf(fact_237_prime__elem__dvd__mult__iff, axiom,
    ((![P : nat, A : nat, B : nat]: ((factor127820501em_nat @ P) => ((dvd_dvd_nat @ P @ (times_times_nat @ A @ B)) = (((dvd_dvd_nat @ P @ A)) | ((dvd_dvd_nat @ P @ B)))))))). % prime_elem_dvd_mult_iff
thf(fact_238_prime__elem__dvd__mult__iff, axiom,
    ((![P : poly_complex, A : poly_complex, B : poly_complex]: ((factor477435579omplex @ P) => ((dvd_dvd_poly_complex @ P @ (times_1246143675omplex @ A @ B)) = (((dvd_dvd_poly_complex @ P @ A)) | ((dvd_dvd_poly_complex @ P @ B)))))))). % prime_elem_dvd_mult_iff
thf(fact_239_prime__elem__dvd__cases, axiom,
    ((![P : nat, K : nat, M : nat, N : nat]: ((dvd_dvd_nat @ (times_times_nat @ P @ K) @ (times_times_nat @ M @ N)) => ((factor127820501em_nat @ P) => ((?[X4 : nat]: ((dvd_dvd_nat @ K @ (times_times_nat @ X4 @ N)) & (M = (times_times_nat @ P @ X4)))) | (?[Y2 : nat]: ((dvd_dvd_nat @ K @ (times_times_nat @ M @ Y2)) & (N = (times_times_nat @ P @ Y2)))))))))). % prime_elem_dvd_cases
thf(fact_240_prime__elem__dvd__cases, axiom,
    ((![P : poly_complex, K : poly_complex, M : poly_complex, N : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ P @ K) @ (times_1246143675omplex @ M @ N)) => ((factor477435579omplex @ P) => ((?[X4 : poly_complex]: ((dvd_dvd_poly_complex @ K @ (times_1246143675omplex @ X4 @ N)) & (M = (times_1246143675omplex @ P @ X4)))) | (?[Y2 : poly_complex]: ((dvd_dvd_poly_complex @ K @ (times_1246143675omplex @ M @ Y2)) & (N = (times_1246143675omplex @ P @ Y2)))))))))). % prime_elem_dvd_cases
thf(fact_241_prime__elem__dvd__multD, axiom,
    ((![P : nat, A : nat, B : nat]: ((factor127820501em_nat @ P) => ((dvd_dvd_nat @ P @ (times_times_nat @ A @ B)) => ((dvd_dvd_nat @ P @ A) | (dvd_dvd_nat @ P @ B))))))). % prime_elem_dvd_multD
thf(fact_242_prime__elem__dvd__multD, axiom,
    ((![P : poly_complex, A : poly_complex, B : poly_complex]: ((factor477435579omplex @ P) => ((dvd_dvd_poly_complex @ P @ (times_1246143675omplex @ A @ B)) => ((dvd_dvd_poly_complex @ P @ A) | (dvd_dvd_poly_complex @ P @ B))))))). % prime_elem_dvd_multD
thf(fact_243_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_244_dual__order_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z : nat]: (Y3 = Z))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A2)) & ((ord_less_eq_nat @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_245_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_246_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_247_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_248_order__trans, axiom,
    ((![X : nat, Y : nat, Z2 : nat]: ((ord_less_eq_nat @ X @ Y) => ((ord_less_eq_nat @ Y @ Z2) => (ord_less_eq_nat @ X @ Z2)))))). % order_trans

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