% 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_900__5376480_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:33:58.772

% Could-be-implicit typings (7)
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__Real__Oreal_J, type,
    poly_real : $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__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (51)
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_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    one_one_poly_complex : poly_complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    one_one_poly_nat : poly_nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    one_one_poly_real : poly_real).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__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_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex, type,
    semiri356525583omplex : nat > complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    semiri1679838999omplex : nat > poly_complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal, type,
    semiri2110766477t_real : nat > real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $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_Oorder_001t__Complex__Ocomplex, type,
    order_complex : complex > poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    order_poly_complex : poly_complex > poly_poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Real__Oreal, type,
    order_real : real > poly_real > 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__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opseudo__mod_001t__Complex__Ocomplex, type,
    pseudo_mod_complex : poly_complex > poly_complex > 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__Real__Oreal_J, type,
    power_2108872382y_real : poly_real > nat > poly_real).
thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal, type,
    power_power_real : real > nat > real).
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__Real__Oreal, type,
    dvd_dvd_real : real > real > $o).
thf(sy_v_a____, type,
    a : complex).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_pa____, type,
    pa : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).
thf(sy_v_qa____, type,
    qa : poly_complex).

% Relevant facts (237)
thf(fact_0_n0, axiom,
    ((~ ((na = zero_zero_nat))))). % n0
thf(fact_1_dpn, axiom,
    (((degree_complex @ pa) = na))). % dpn
thf(fact_2_pne, axiom,
    ((~ ((pa = zero_z1746442943omplex))))). % pne
thf(fact_3_pq0, axiom,
    ((![X : complex]: (((poly_complex2 @ pa @ X) = zero_zero_complex) => ((poly_complex2 @ qa @ X) = zero_zero_complex))))). % pq0
thf(fact_4_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_5_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_6_dvd__power__same, axiom,
    ((![X2 : real, Y : real, N : nat]: ((dvd_dvd_real @ X2 @ Y) => (dvd_dvd_real @ (power_power_real @ X2 @ N) @ (power_power_real @ Y @ N)))))). % dvd_power_same
thf(fact_7_dvd__refl, axiom,
    ((![A : real]: (dvd_dvd_real @ A @ A)))). % dvd_refl
thf(fact_8_dvd__refl, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ A)))). % dvd_refl
thf(fact_9_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_10_dvd__trans, axiom,
    ((![A : real, B : real, C : real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ B @ C) => (dvd_dvd_real @ A @ C)))))). % dvd_trans
thf(fact_11_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_12_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_13_True, axiom,
    ((?[A2 : complex]: ((poly_complex2 @ pa @ A2) = zero_zero_complex)))). % True
thf(fact_14_assms_I3_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(3)
thf(fact_15_that, axiom,
    ((~ (((order_complex @ a @ pa) = zero_zero_nat))))). % that
thf(fact_16_IH, axiom,
    ((![M : nat]: ((ord_less_nat @ M @ na) => (![P : poly_complex, Q : poly_complex]: ((![X3 : complex]: (((poly_complex2 @ P @ X3) = zero_zero_complex) => ((poly_complex2 @ Q @ X3) = zero_zero_complex))) => (((degree_complex @ P) = M) => ((~ ((M = zero_zero_nat))) => (dvd_dvd_poly_complex @ P @ (power_184595776omplex @ Q @ M)))))))))). % IH
thf(fact_17_content__dvd__contentI, axiom,
    ((![P2 : poly_nat, Q2 : poly_nat]: ((dvd_dvd_poly_nat @ P2 @ Q2) => (dvd_dvd_nat @ (content_nat @ P2) @ (content_nat @ Q2)))))). % content_dvd_contentI
thf(fact_18_a, axiom,
    (((poly_complex2 @ pa @ a) = zero_zero_complex))). % a
thf(fact_19_poly__power, axiom,
    ((![P2 : poly_poly_complex, N : nat, X2 : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P2 @ N) @ X2) = (power_184595776omplex @ (poly_poly_complex2 @ P2 @ X2) @ N))))). % poly_power
thf(fact_20_poly__power, axiom,
    ((![P2 : poly_nat, N : nat, X2 : nat]: ((poly_nat2 @ (power_power_poly_nat @ P2 @ N) @ X2) = (power_power_nat @ (poly_nat2 @ P2 @ X2) @ N))))). % poly_power
thf(fact_21_poly__power, axiom,
    ((![P2 : poly_real, N : nat, X2 : real]: ((poly_real2 @ (power_2108872382y_real @ P2 @ N) @ X2) = (power_power_real @ (poly_real2 @ P2 @ X2) @ N))))). % poly_power
thf(fact_22_poly__power, axiom,
    ((![P2 : poly_complex, N : nat, X2 : complex]: ((poly_complex2 @ (power_184595776omplex @ P2 @ N) @ X2) = (power_power_complex @ (poly_complex2 @ P2 @ X2) @ N))))). % poly_power
thf(fact_23_assms_I1_J, axiom,
    ((![X : complex]: (((poly_complex2 @ p @ X) = zero_zero_complex) => ((poly_complex2 @ q @ X) = zero_zero_complex))))). % assms(1)
thf(fact_24_assms_I2_J, axiom,
    (((degree_complex @ p) = n))). % assms(2)
thf(fact_25__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062a_O_Apoly_Ap_Aa_A_061_A0_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![A2 : complex]: (~ (((poly_complex2 @ pa @ A2) = zero_zero_complex)))))))). % \<open>\<And>thesis. (\<And>a. poly p a = 0 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_26_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_27_dvd__0__left__iff, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) = (A = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_28_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_29_dvd__0__left__iff, axiom,
    ((![A : real]: ((dvd_dvd_real @ zero_zero_real @ A) = (A = zero_zero_real))))). % dvd_0_left_iff
thf(fact_30_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_31_dvd__0__right, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_32_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_33_dvd__0__right, axiom,
    ((![A : real]: (dvd_dvd_real @ A @ zero_zero_real)))). % dvd_0_right
thf(fact_34_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_35_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_36_poly__0, axiom,
    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
thf(fact_37_poly__0, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
thf(fact_38_poly__0, axiom,
    ((![X2 : real]: ((poly_real2 @ zero_zero_poly_real @ X2) = zero_zero_real)))). % poly_0
thf(fact_39_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_40_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_41_content__eq__zero__iff, axiom,
    ((![P2 : poly_nat]: (((content_nat @ P2) = zero_zero_nat) = (P2 = zero_zero_poly_nat))))). % content_eq_zero_iff
thf(fact_42_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_43_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_44_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_45_power__eq__0__iff, axiom,
    ((![A : real, N : nat]: (((power_power_real @ A @ N) = zero_zero_real) = (((A = zero_zero_real)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_46_order__0I, axiom,
    ((![P2 : poly_poly_complex, A : poly_complex]: ((~ (((poly_poly_complex2 @ P2 @ A) = zero_z1746442943omplex))) => ((order_poly_complex @ A @ P2) = zero_zero_nat))))). % order_0I
thf(fact_47_order__0I, axiom,
    ((![P2 : poly_complex, A : complex]: ((~ (((poly_complex2 @ P2 @ A) = zero_zero_complex))) => ((order_complex @ A @ P2) = zero_zero_nat))))). % order_0I
thf(fact_48_order__0I, axiom,
    ((![P2 : poly_real, A : real]: ((~ (((poly_real2 @ P2 @ A) = zero_zero_real))) => ((order_real @ A @ P2) = zero_zero_nat))))). % order_0I
thf(fact_49_order__root, axiom,
    ((![P2 : poly_poly_complex, A : poly_complex]: (((poly_poly_complex2 @ P2 @ A) = zero_z1746442943omplex) = (((P2 = zero_z1040703943omplex)) | ((~ (((order_poly_complex @ A @ P2) = zero_zero_nat))))))))). % order_root
thf(fact_50_order__root, axiom,
    ((![P2 : poly_complex, A : complex]: (((poly_complex2 @ P2 @ A) = zero_zero_complex) = (((P2 = zero_z1746442943omplex)) | ((~ (((order_complex @ A @ P2) = zero_zero_nat))))))))). % order_root
thf(fact_51_order__root, axiom,
    ((![P2 : poly_real, A : real]: (((poly_real2 @ P2 @ A) = zero_zero_real) = (((P2 = zero_zero_poly_real)) | ((~ (((order_real @ A @ P2) = zero_zero_nat))))))))). % order_root
thf(fact_52_poly__all__0__iff__0, axiom,
    ((![P2 : poly_poly_complex]: ((![X4 : poly_complex]: ((poly_poly_complex2 @ P2 @ X4) = zero_z1746442943omplex)) = (P2 = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_53_poly__all__0__iff__0, axiom,
    ((![P2 : poly_complex]: ((![X4 : complex]: ((poly_complex2 @ P2 @ X4) = zero_zero_complex)) = (P2 = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_54_poly__all__0__iff__0, axiom,
    ((![P2 : poly_real]: ((![X4 : real]: ((poly_real2 @ P2 @ X4) = zero_zero_real)) = (P2 = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_55_nat__power__less__imp__less, axiom,
    ((![I : nat, M2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ I) => ((ord_less_nat @ (power_power_nat @ I @ M2) @ (power_power_nat @ I @ N)) => (ord_less_nat @ M2 @ N)))))). % nat_power_less_imp_less
thf(fact_56_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_complex, Q2 : poly_complex]: (((poly_complex2 @ P2) = (poly_complex2 @ Q2)) = (P2 = Q2))))). % poly_eq_poly_eq_iff
thf(fact_57_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_real, Q2 : poly_real]: (((poly_real2 @ P2) = (poly_real2 @ Q2)) = (P2 = Q2))))). % poly_eq_poly_eq_iff
thf(fact_58_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex))))). % zero_power
thf(fact_59_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_184595776omplex @ zero_z1746442943omplex @ N) = zero_z1746442943omplex))))). % zero_power
thf(fact_60_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat))))). % zero_power
thf(fact_61_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_real @ zero_zero_real @ N) = zero_zero_real))))). % zero_power
thf(fact_62_zero__less__power, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ N)))))). % zero_less_power
thf(fact_63_zero__less__power, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (power_power_real @ A @ N)))))). % zero_less_power
thf(fact_64_linorder__neqE__linordered__idom, axiom,
    ((![X2 : real, Y : real]: ((~ ((X2 = Y))) => ((~ ((ord_less_real @ X2 @ Y))) => (ord_less_real @ Y @ X2)))))). % linorder_neqE_linordered_idom
thf(fact_65_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_66_power__not__zero, axiom,
    ((![A : poly_complex, N : nat]: ((~ ((A = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_67_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_68_power__not__zero, axiom,
    ((![A : real, N : nat]: ((~ ((A = zero_zero_real))) => (~ (((power_power_real @ A @ N) = zero_zero_real))))))). % power_not_zero
thf(fact_69_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_70_dvd__0__left, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) => (A = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_71_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_72_dvd__0__left, axiom,
    ((![A : real]: ((dvd_dvd_real @ zero_zero_real @ A) => (A = zero_zero_real))))). % dvd_0_left
thf(fact_73_pow__divides__pow__iff, axiom,
    ((![N : nat, A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((dvd_dvd_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N)) = (dvd_dvd_nat @ A @ B)))))). % pow_divides_pow_iff
thf(fact_74_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_75_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_76_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_77_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_78_pseudo__mod_I2_J, axiom,
    ((![G : poly_complex, F : poly_complex]: ((~ ((G = zero_z1746442943omplex))) => (((pseudo_mod_complex @ F @ G) = zero_z1746442943omplex) | (ord_less_nat @ (degree_complex @ (pseudo_mod_complex @ F @ G)) @ (degree_complex @ G))))))). % pseudo_mod(2)
thf(fact_79_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_80_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_81_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_82_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_83_zero__reorient, axiom,
    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) = (X2 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_84_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_85_zero__reorient, axiom,
    ((![X2 : real]: ((zero_zero_real = X2) = (X2 = zero_zero_real))))). % zero_reorient
thf(fact_86_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_87_gcd__nat_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (((dvd_dvd_nat @ A @ zero_zero_nat)) & ((~ ((A = zero_zero_nat))))))))). % gcd_nat.not_eq_extremum
thf(fact_88_gcd__nat_Oextremum__unique, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_89_gcd__nat_Oextremum__strict, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A) & (~ ((zero_zero_nat = A))))))))). % gcd_nat.extremum_strict
thf(fact_90_gcd__nat_Oextremum, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_91_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_92_infinite__descent, axiom,
    ((![P3 : nat > $o, N : nat]: ((![N2 : nat]: ((~ ((P3 @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P3 @ M))))))) => (P3 @ N))))). % infinite_descent
thf(fact_93_nat__less__induct, axiom,
    ((![P3 : nat > $o, N : nat]: ((![N2 : nat]: ((![M : nat]: ((ord_less_nat @ M @ N2) => (P3 @ M))) => (P3 @ N2))) => (P3 @ N))))). % nat_less_induct
thf(fact_94_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_95_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_96_less__not__refl2, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ N @ M2) => (~ ((M2 = N))))))). % less_not_refl2
thf(fact_97_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_98_nat__neq__iff, axiom,
    ((![M2 : nat, N : nat]: ((~ ((M2 = N))) = (((ord_less_nat @ M2 @ N)) | ((ord_less_nat @ N @ M2))))))). % nat_neq_iff
thf(fact_99_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_100_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_101_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_102_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_103_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_104_infinite__descent0, axiom,
    ((![P3 : nat > $o, N : nat]: ((P3 @ zero_zero_nat) => ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((~ ((P3 @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P3 @ M)))))))) => (P3 @ N)))))). % infinite_descent0
thf(fact_105_nat__dvd__not__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ M2) => ((ord_less_nat @ M2 @ N) => (~ ((dvd_dvd_nat @ N @ M2)))))))). % nat_dvd_not_less
thf(fact_106_gr__implies__not0, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_107_dvd__pos__nat, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((dvd_dvd_nat @ M2 @ N) => (ord_less_nat @ zero_zero_nat @ M2)))))). % dvd_pos_nat
thf(fact_108_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_109_realpow__pos__nth__unique, axiom,
    ((![N : nat, A : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ zero_zero_real @ A) => (?[X3 : real]: (((ord_less_real @ zero_zero_real @ X3) & ((power_power_real @ X3 @ N) = A)) & (![Y2 : real]: (((ord_less_real @ zero_zero_real @ Y2) & ((power_power_real @ Y2 @ N) = A)) => (Y2 = X3)))))))))). % realpow_pos_nth_unique
thf(fact_110_realpow__pos__nth, axiom,
    ((![N : nat, A : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ zero_zero_real @ A) => (?[R : real]: ((ord_less_real @ zero_zero_real @ R) & ((power_power_real @ R @ N) = A)))))))). % realpow_pos_nth
thf(fact_111_fundamental__theorem__of__algebra, axiom,
    ((![P2 : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P2)))) => (?[Z : complex]: ((poly_complex2 @ P2 @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra
thf(fact_112_dvd__field__iff, axiom,
    ((dvd_dvd_complex = (^[A3 : complex]: (^[B2 : complex]: (((A3 = zero_zero_complex)) => ((B2 = zero_zero_complex)))))))). % dvd_field_iff
thf(fact_113_dvd__field__iff, axiom,
    ((dvd_dvd_real = (^[A3 : real]: (^[B2 : real]: (((A3 = zero_zero_real)) => ((B2 = zero_zero_real)))))))). % dvd_field_iff
thf(fact_114_field__lbound__gt__zero, axiom,
    ((![D1 : real, D2 : real]: ((ord_less_real @ zero_zero_real @ D1) => ((ord_less_real @ zero_zero_real @ D2) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ D1) & (ord_less_real @ E @ D2))))))))). % field_lbound_gt_zero
thf(fact_115_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_116_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_117_dvd__antisym, axiom,
    ((![M2 : nat, N : nat]: ((dvd_dvd_nat @ M2 @ N) => ((dvd_dvd_nat @ N @ M2) => (M2 = N)))))). % dvd_antisym
thf(fact_118_gcd__nat_Oasym, axiom,
    ((![A : nat, B : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => (~ (((dvd_dvd_nat @ B @ A) & (~ ((B = A)))))))))). % gcd_nat.asym
thf(fact_119_gcd__nat_Orefl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % gcd_nat.refl
thf(fact_120_gcd__nat_Otrans, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A @ C)))))). % gcd_nat.trans
thf(fact_121_gcd__nat_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z2 : nat]: (Y3 = Z2))) = (^[A3 : nat]: (^[B2 : nat]: (((dvd_dvd_nat @ A3 @ B2)) & ((dvd_dvd_nat @ B2 @ A3)))))))). % gcd_nat.eq_iff
thf(fact_122_gcd__nat_Oirrefl, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ A @ A) & (~ ((A = A))))))))). % gcd_nat.irrefl
thf(fact_123_gcd__nat_Oantisym, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ A) => (A = B)))))). % gcd_nat.antisym
thf(fact_124_poly__IVT__neg, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ A)) => ((ord_less_real @ (poly_real2 @ P2 @ B) @ zero_zero_real) => (?[X3 : real]: ((ord_less_real @ A @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P2 @ X3) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_125_poly__IVT__pos, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P2 @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ B)) => (?[X3 : real]: ((ord_less_real @ A @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P2 @ X3) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_126_gcd__nat_Ostrict__trans, axiom,
    ((![A : nat, B : nat, C : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => (((dvd_dvd_nat @ B @ C) & (~ ((B = C)))) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans
thf(fact_127_gcd__nat_Ostrict__trans1, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => (((dvd_dvd_nat @ B @ C) & (~ ((B = C)))) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans1
thf(fact_128_gcd__nat_Ostrict__trans2, axiom,
    ((![A : nat, B : nat, C : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => ((dvd_dvd_nat @ B @ C) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans2
thf(fact_129_gcd__nat_Oorder__iff__strict, axiom,
    ((dvd_dvd_nat = (^[A3 : nat]: (^[B2 : nat]: (((((dvd_dvd_nat @ A3 @ B2)) & ((~ ((A3 = B2)))))) | ((A3 = B2)))))))). % gcd_nat.order_iff_strict
thf(fact_130_gcd__nat_Ostrict__iff__order, axiom,
    ((![A : nat, B : nat]: ((((dvd_dvd_nat @ A @ B)) & ((~ ((A = B))))) = (((dvd_dvd_nat @ A @ B)) & ((~ ((A = B))))))))). % gcd_nat.strict_iff_order
thf(fact_131_gcd__nat_Ostrict__implies__order, axiom,
    ((![A : nat, B : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => (dvd_dvd_nat @ A @ B))))). % gcd_nat.strict_implies_order
thf(fact_132_gcd__nat_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => (~ ((A = B))))))). % gcd_nat.strict_implies_not_eq
thf(fact_133_gcd__nat_Onot__eq__order__implies__strict, axiom,
    ((![A : nat, B : nat]: ((~ ((A = B))) => ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ B) & (~ ((A = B))))))))). % gcd_nat.not_eq_order_implies_strict
thf(fact_134_real__sup__exists, axiom,
    ((![P3 : real > $o]: ((?[X_1 : real]: (P3 @ X_1)) => ((?[Z3 : real]: (![X3 : real]: ((P3 @ X3) => (ord_less_real @ X3 @ Z3)))) => (?[S2 : real]: (![Y2 : real]: ((?[X4 : real]: (((P3 @ X4)) & ((ord_less_real @ Y2 @ X4)))) = (ord_less_real @ Y2 @ S2))))))))). % real_sup_exists
thf(fact_135_constant__def, axiom,
    ((fundam1158420650omplex = (^[F2 : complex > complex]: (![X4 : complex]: (![Y4 : complex]: ((F2 @ X4) = (F2 @ Y4)))))))). % constant_def
thf(fact_136_linordered__field__no__lb, axiom,
    ((![X : real]: (?[Y5 : real]: (ord_less_real @ Y5 @ X))))). % linordered_field_no_lb
thf(fact_137_linordered__field__no__ub, axiom,
    ((![X : real]: (?[X_12 : real]: (ord_less_real @ X @ X_12))))). % linordered_field_no_ub
thf(fact_138_psize__eq__0__iff, axiom,
    ((![P2 : poly_complex]: (((fundam1709708056omplex @ P2) = zero_zero_nat) = (P2 = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_139_of__nat__zero__less__power__iff, axiom,
    ((![X2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ (semiri1382578993at_nat @ X2) @ N)) = (((ord_less_nat @ zero_zero_nat @ X2)) | ((N = zero_zero_nat))))))). % of_nat_zero_less_power_iff
thf(fact_140_of__nat__zero__less__power__iff, axiom,
    ((![X2 : nat, N : nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ (semiri2110766477t_real @ X2) @ N)) = (((ord_less_nat @ zero_zero_nat @ X2)) | ((N = zero_zero_nat))))))). % of_nat_zero_less_power_iff
thf(fact_141_synthetic__div__eq__0__iff, axiom,
    ((![P2 : poly_complex, C : complex]: (((synthe151143547omplex @ P2 @ C) = zero_z1746442943omplex) = ((degree_complex @ P2) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_142_power__strict__decreasing__iff, axiom,
    ((![B : nat, M2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ B @ one_one_nat) => ((ord_less_nat @ (power_power_nat @ B @ M2) @ (power_power_nat @ B @ N)) = (ord_less_nat @ N @ M2))))))). % power_strict_decreasing_iff
thf(fact_143_power__strict__decreasing__iff, axiom,
    ((![B : real, M2 : nat, N : nat]: ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ B @ one_one_real) => ((ord_less_real @ (power_power_real @ B @ M2) @ (power_power_real @ B @ N)) = (ord_less_nat @ N @ M2))))))). % power_strict_decreasing_iff
thf(fact_144_power__one__right, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_145_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_146_power__one__right, axiom,
    ((![A : real]: ((power_power_real @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_147_nat__dvd__1__iff__1, axiom,
    ((![M2 : nat]: ((dvd_dvd_nat @ M2 @ one_one_nat) = (M2 = one_one_nat))))). % nat_dvd_1_iff_1
thf(fact_148_power__one, axiom,
    ((![N : nat]: ((power_184595776omplex @ one_one_poly_complex @ N) = one_one_poly_complex)))). % power_one
thf(fact_149_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_150_power__one, axiom,
    ((![N : nat]: ((power_power_real @ one_one_real @ N) = one_one_real)))). % power_one
thf(fact_151_of__nat__1, axiom,
    (((semiri1382578993at_nat @ one_one_nat) = one_one_nat))). % of_nat_1
thf(fact_152_of__nat__1, axiom,
    (((semiri2110766477t_real @ one_one_nat) = one_one_real))). % of_nat_1
thf(fact_153_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_nat = (semiri1382578993at_nat @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_154_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_real = (semiri2110766477t_real @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_155_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri1382578993at_nat @ N) = one_one_nat) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_156_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri2110766477t_real @ N) = one_one_real) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_157_less__one, axiom,
    ((![N : nat]: ((ord_less_nat @ N @ one_one_nat) = (N = zero_zero_nat))))). % less_one
thf(fact_158_degree__of__nat, axiom,
    ((![N : nat]: ((degree_complex @ (semiri1679838999omplex @ N)) = zero_zero_nat)))). % degree_of_nat
thf(fact_159_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_160_poly__1, axiom,
    ((![X2 : complex]: ((poly_complex2 @ one_one_poly_complex @ X2) = one_one_complex)))). % poly_1
thf(fact_161_poly__1, axiom,
    ((![X2 : nat]: ((poly_nat2 @ one_one_poly_nat @ X2) = one_one_nat)))). % poly_1
thf(fact_162_poly__1, axiom,
    ((![X2 : real]: ((poly_real2 @ one_one_poly_real @ X2) = one_one_real)))). % poly_1
thf(fact_163_content__1, axiom,
    (((content_nat @ one_one_poly_nat) = one_one_nat))). % content_1
thf(fact_164_order__1__eq__0, axiom,
    ((![X2 : complex]: ((order_complex @ X2 @ one_one_poly_complex) = zero_zero_nat)))). % order_1_eq_0
thf(fact_165_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_166_power__inject__exp, axiom,
    ((![A : nat, M2 : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => (((power_power_nat @ A @ M2) = (power_power_nat @ A @ N)) = (M2 = N)))))). % power_inject_exp
thf(fact_167_power__inject__exp, axiom,
    ((![A : real, M2 : nat, N : nat]: ((ord_less_real @ one_one_real @ A) => (((power_power_real @ A @ M2) = (power_power_real @ A @ N)) = (M2 = N)))))). % power_inject_exp
thf(fact_168_of__nat__eq__0__iff, axiom,
    ((![M2 : nat]: (((semiri1382578993at_nat @ M2) = zero_zero_nat) = (M2 = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_169_of__nat__eq__0__iff, axiom,
    ((![M2 : nat]: (((semiri1679838999omplex @ M2) = zero_z1746442943omplex) = (M2 = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_170_of__nat__eq__0__iff, axiom,
    ((![M2 : nat]: (((semiri356525583omplex @ M2) = zero_zero_complex) = (M2 = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_171_of__nat__eq__0__iff, axiom,
    ((![M2 : nat]: (((semiri2110766477t_real @ M2) = zero_zero_real) = (M2 = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_172_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_173_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_z1746442943omplex = (semiri1679838999omplex @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_174_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_complex = (semiri356525583omplex @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_175_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_real = (semiri2110766477t_real @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_176_of__nat__0, axiom,
    (((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat))). % of_nat_0
thf(fact_177_of__nat__0, axiom,
    (((semiri1679838999omplex @ zero_zero_nat) = zero_z1746442943omplex))). % of_nat_0
thf(fact_178_of__nat__0, axiom,
    (((semiri356525583omplex @ zero_zero_nat) = zero_zero_complex))). % of_nat_0
thf(fact_179_of__nat__0, axiom,
    (((semiri2110766477t_real @ zero_zero_nat) = zero_zero_real))). % of_nat_0
thf(fact_180_of__nat__less__iff, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)) = (ord_less_nat @ M2 @ N))))). % of_nat_less_iff
thf(fact_181_of__nat__less__iff, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_real @ (semiri2110766477t_real @ M2) @ (semiri2110766477t_real @ N)) = (ord_less_nat @ M2 @ N))))). % of_nat_less_iff
thf(fact_182_of__nat__power, axiom,
    ((![M2 : nat, N : nat]: ((semiri1679838999omplex @ (power_power_nat @ M2 @ N)) = (power_184595776omplex @ (semiri1679838999omplex @ M2) @ N))))). % of_nat_power
thf(fact_183_of__nat__power, axiom,
    ((![M2 : nat, N : nat]: ((semiri1382578993at_nat @ (power_power_nat @ M2 @ N)) = (power_power_nat @ (semiri1382578993at_nat @ M2) @ N))))). % of_nat_power
thf(fact_184_of__nat__power, axiom,
    ((![M2 : nat, N : nat]: ((semiri2110766477t_real @ (power_power_nat @ M2 @ N)) = (power_power_real @ (semiri2110766477t_real @ M2) @ N))))). % of_nat_power
thf(fact_185_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X2 : nat]: (((power_184595776omplex @ (semiri1679838999omplex @ B) @ W) = (semiri1679838999omplex @ X2)) = ((power_power_nat @ B @ W) = X2))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_186_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X2 : nat]: (((power_power_nat @ (semiri1382578993at_nat @ B) @ W) = (semiri1382578993at_nat @ X2)) = ((power_power_nat @ B @ W) = X2))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_187_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X2 : nat]: (((power_power_real @ (semiri2110766477t_real @ B) @ W) = (semiri2110766477t_real @ X2)) = ((power_power_nat @ B @ W) = X2))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_188_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X2 : nat, B : nat, W : nat]: (((semiri1679838999omplex @ X2) = (power_184595776omplex @ (semiri1679838999omplex @ B) @ W)) = (X2 = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_189_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X2 : nat, B : nat, W : nat]: (((semiri1382578993at_nat @ X2) = (power_power_nat @ (semiri1382578993at_nat @ B) @ W)) = (X2 = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_190_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X2 : nat, B : nat, W : nat]: (((semiri2110766477t_real @ X2) = (power_power_real @ (semiri2110766477t_real @ B) @ W)) = (X2 = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_191_is__unit__content__iff, axiom,
    ((![P2 : poly_nat]: ((dvd_dvd_nat @ (content_nat @ P2) @ one_one_nat) = ((content_nat @ P2) = one_one_nat))))). % is_unit_content_iff
thf(fact_192_power__strict__increasing__iff, axiom,
    ((![B : nat, X2 : nat, Y : nat]: ((ord_less_nat @ one_one_nat @ B) => ((ord_less_nat @ (power_power_nat @ B @ X2) @ (power_power_nat @ B @ Y)) = (ord_less_nat @ X2 @ Y)))))). % power_strict_increasing_iff
thf(fact_193_power__strict__increasing__iff, axiom,
    ((![B : real, X2 : nat, Y : nat]: ((ord_less_real @ one_one_real @ B) => ((ord_less_real @ (power_power_real @ B @ X2) @ (power_power_real @ B @ Y)) = (ord_less_nat @ X2 @ Y)))))). % power_strict_increasing_iff
thf(fact_194_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1382578993at_nat @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_195_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_real @ zero_zero_real @ (semiri2110766477t_real @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_196_of__nat__power__less__of__nat__cancel__iff, axiom,
    ((![X2 : nat, B : nat, W : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ X2) @ (power_power_nat @ (semiri1382578993at_nat @ B) @ W)) = (ord_less_nat @ X2 @ (power_power_nat @ B @ W)))))). % of_nat_power_less_of_nat_cancel_iff
thf(fact_197_of__nat__power__less__of__nat__cancel__iff, axiom,
    ((![X2 : nat, B : nat, W : nat]: ((ord_less_real @ (semiri2110766477t_real @ X2) @ (power_power_real @ (semiri2110766477t_real @ B) @ W)) = (ord_less_nat @ X2 @ (power_power_nat @ B @ W)))))). % of_nat_power_less_of_nat_cancel_iff
thf(fact_198_of__nat__less__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X2 : nat]: ((ord_less_nat @ (power_power_nat @ (semiri1382578993at_nat @ B) @ W) @ (semiri1382578993at_nat @ X2)) = (ord_less_nat @ (power_power_nat @ B @ W) @ X2))))). % of_nat_less_of_nat_power_cancel_iff
thf(fact_199_of__nat__less__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X2 : nat]: ((ord_less_real @ (power_power_real @ (semiri2110766477t_real @ B) @ W) @ (semiri2110766477t_real @ X2)) = (ord_less_nat @ (power_power_nat @ B @ W) @ X2))))). % of_nat_less_of_nat_power_cancel_iff
thf(fact_200_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ one_one_nat))))). % less_numeral_extra(4)
thf(fact_201_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_202_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_203_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_204_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_205_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_206_dvd__unit__imp__unit, axiom,
    ((![A : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((dvd_dvd_poly_complex @ B @ one_one_poly_complex) => (dvd_dvd_poly_complex @ A @ one_one_poly_complex)))))). % dvd_unit_imp_unit
thf(fact_207_dvd__unit__imp__unit, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)))))). % dvd_unit_imp_unit
thf(fact_208_unit__imp__dvd, axiom,
    ((![B : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ B @ one_one_poly_complex) => (dvd_dvd_poly_complex @ B @ A))))). % unit_imp_dvd
thf(fact_209_unit__imp__dvd, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ B @ A))))). % unit_imp_dvd
thf(fact_210_one__dvd, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ one_one_poly_complex @ A)))). % one_dvd
thf(fact_211_one__dvd, axiom,
    ((![A : nat]: (dvd_dvd_nat @ one_one_nat @ A)))). % one_dvd
thf(fact_212_one__dvd, axiom,
    ((![A : real]: (dvd_dvd_real @ one_one_real @ A)))). % one_dvd
thf(fact_213_one__reorient, axiom,
    ((![X2 : nat]: ((one_one_nat = X2) = (X2 = one_one_nat))))). % one_reorient
thf(fact_214_one__reorient, axiom,
    ((![X2 : real]: ((one_one_real = X2) = (X2 = one_one_real))))). % one_reorient
thf(fact_215_of__nat__less__0__iff, axiom,
    ((![M2 : nat]: (~ ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ zero_zero_nat)))))). % of_nat_less_0_iff
thf(fact_216_of__nat__less__0__iff, axiom,
    ((![M2 : nat]: (~ ((ord_less_real @ (semiri2110766477t_real @ M2) @ zero_zero_real)))))). % of_nat_less_0_iff
thf(fact_217_of__nat__less__imp__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)) => (ord_less_nat @ M2 @ N))))). % of_nat_less_imp_less
thf(fact_218_of__nat__less__imp__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_real @ (semiri2110766477t_real @ M2) @ (semiri2110766477t_real @ N)) => (ord_less_nat @ M2 @ N))))). % of_nat_less_imp_less
thf(fact_219_less__imp__of__nat__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)))))). % less_imp_of_nat_less
thf(fact_220_less__imp__of__nat__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_real @ (semiri2110766477t_real @ M2) @ (semiri2110766477t_real @ N)))))). % less_imp_of_nat_less
thf(fact_221_not__one__less__zero, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ zero_zero_nat))))). % not_one_less_zero
thf(fact_222_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_223_zero__less__one, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % zero_less_one
thf(fact_224_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_225_less__numeral__extra_I1_J, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % less_numeral_extra(1)
thf(fact_226_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_227_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_228_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ one_one_poly_complex))))). % not_is_unit_0
thf(fact_229_power__0, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ zero_zero_nat) = one_one_poly_complex)))). % power_0
thf(fact_230_power__0, axiom,
    ((![A : nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat)))). % power_0
thf(fact_231_power__0, axiom,
    ((![A : real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real)))). % power_0
thf(fact_232_real__arch__pow, axiom,
    ((![X2 : real, Y : real]: ((ord_less_real @ one_one_real @ X2) => (?[N2 : nat]: (ord_less_real @ Y @ (power_power_real @ X2 @ N2))))))). % real_arch_pow
thf(fact_233_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_complex @ zero_zero_complex @ N) = one_one_complex)) & ((~ ((N = zero_zero_nat))) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex)))))). % power_0_left
thf(fact_234_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_184595776omplex @ zero_z1746442943omplex @ N) = one_one_poly_complex)) & ((~ ((N = zero_zero_nat))) => ((power_184595776omplex @ zero_z1746442943omplex @ N) = zero_z1746442943omplex)))))). % power_0_left
thf(fact_235_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ N) = one_one_nat)) & ((~ ((N = zero_zero_nat))) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat)))))). % power_0_left
thf(fact_236_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_real @ zero_zero_real @ N) = one_one_real)) & ((~ ((N = zero_zero_nat))) => ((power_power_real @ zero_zero_real @ N) = zero_zero_real)))))). % power_0_left

% Conjectures (1)
thf(conj_0, conjecture,
    ((dvd_dvd_poly_complex @ pa @ (power_184595776omplex @ qa @ na)))).
