% 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_1043__5377740_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:30.965

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

% Explicit typings (62)
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_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Nat__Onat, type,
    fundam1567013434ze_nat : poly_nat > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1956464160omplex : poly_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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    one_on1331105667omplex : 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_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    zero_z1059985641ly_nat : poly_poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    zero_z1200043727omplex : poly_p1267267526omplex).
thf(sy_c_If_001t__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Complex__Ocomplex, type,
    degree_complex : poly_complex > nat).
thf(sy_c_Polynomial_Odegree_001t__Nat__Onat, type,
    degree_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    degree_poly_complex : poly_poly_complex > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    degree_poly_nat : poly_poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    degree2006505739omplex : poly_p1267267526omplex > nat).
thf(sy_c_Polynomial_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat, type,
    is_zero_nat : poly_nat > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    is_zero_poly_complex : poly_poly_complex > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Complex__Ocomplex, type,
    coeff_complex : poly_complex > nat > complex).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Nat__Onat, type,
    coeff_nat : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    coeff_poly_complex : poly_poly_complex > nat > poly_complex).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    coeff_poly_nat : poly_poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    coeff_1429652124omplex : poly_p1267267526omplex > nat > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Nat__Onat, type,
    poly_cutoff_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_c622223248omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Complex__Ocomplex, type,
    reflect_poly_complex : poly_complex > poly_complex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Nat__Onat, type,
    reflect_poly_nat : poly_nat > poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    reflec309385472omplex : poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    reflec781175074ly_nat : poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    reflec1997789704omplex : poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_c_Polynomial_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > poly_complex).
thf(sy_c_Polynomial_Osynthetic__div_001t__Nat__Onat, type,
    synthetic_div_nat : poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Osynthetic__div_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    synthe1985144195omplex : poly_poly_complex > 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__Nat__Onat_J, type,
    power_power_poly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    power_432682568omplex : poly_poly_complex > nat > poly_poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    power_1336127338ly_nat : poly_poly_nat > nat > poly_poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    power_2001192272omplex : poly_p1267267526omplex > nat > poly_p1267267526omplex).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex, type,
    dvd_dvd_complex : complex > complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    dvd_dvd_poly_complex : poly_complex > poly_complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    dvd_dvd_poly_nat : poly_nat > poly_nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    dvd_dv598755940omplex : poly_poly_complex > poly_poly_complex > $o).
thf(sy_v_n____, type,
    n : nat).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).

% Relevant facts (243)
thf(fact_0_dp_I1_J, axiom,
    ((~ ((p = zero_z1746442943omplex))))). % dp(1)
thf(fact_1_dp_I2_J, axiom,
    (((degree_complex @ p) = (suc @ n)))). % dp(2)
thf(fact_2__092_060open_062_092_060And_062x_O_A_092_060lbrakk_062p_Advd_Aq_A_094_ASuc_An_059_Apoly_Ap_Ax_A_061_A0_059_Apoly_Aq_Ax_A_092_060noteq_062_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((![X : complex]: ((dvd_dvd_poly_complex @ p @ (power_184595776omplex @ q @ (suc @ n))) => (((poly_complex2 @ p @ X) = zero_zero_complex) => ((poly_complex2 @ q @ X) = zero_zero_complex)))))). % \<open>\<And>x. \<lbrakk>p dvd q ^ Suc n; poly p x = 0; poly q x \<noteq> 0\<rbrakk> \<Longrightarrow> False\<close>
thf(fact_3__092_060open_062_092_060lbrakk_062_092_060forall_062x_O_Apoly_Ap_Ax_A_061_A0_A_092_060longrightarrow_062_Apoly_Aq_Ax_A_061_A0_059_Adegree_Ap_A_061_Adegree_Ap_059_Adegree_Ap_A_092_060noteq_062_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Ap_Advd_Aq_A_094_Adegree_Ap_092_060close_062, axiom,
    (((![X2 : complex]: (((poly_complex2 @ p @ X2) = zero_zero_complex) => ((poly_complex2 @ q @ X2) = zero_zero_complex))) => (((degree_complex @ p) = (degree_complex @ p)) => ((~ (((degree_complex @ p) = zero_zero_nat))) => (dvd_dvd_poly_complex @ p @ (power_184595776omplex @ q @ (degree_complex @ p)))))))). % \<open>\<lbrakk>\<forall>x. poly p x = 0 \<longrightarrow> poly q x = 0; degree p = degree p; degree p \<noteq> 0\<rbrakk> \<Longrightarrow> p dvd q ^ degree p\<close>
thf(fact_4__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062p_A_061_A0_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062p_A_092_060noteq_062_A0_059_Adegree_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060And_062n_O_A_092_060lbrakk_062p_A_092_060noteq_062_A0_059_Adegree_Ap_A_061_ASuc_An_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    (((~ ((p = zero_z1746442943omplex))) => (((~ ((p = zero_z1746442943omplex))) => (~ (((degree_complex @ p) = zero_zero_nat)))) => (~ (((~ ((p = zero_z1746442943omplex))) => (![N : nat]: (~ (((degree_complex @ p) = (suc @ N)))))))))))). % \<open>\<And>thesis. \<lbrakk>p = 0 \<Longrightarrow> thesis; \<lbrakk>p \<noteq> 0; degree p = 0\<rbrakk> \<Longrightarrow> thesis; \<And>n. \<lbrakk>p \<noteq> 0; degree p = Suc n\<rbrakk> \<Longrightarrow> thesis\<rbrakk> \<Longrightarrow> thesis\<close>
thf(fact_5_nullstellensatz__lemma, axiom,
    ((![P : poly_complex, Q : poly_complex, N2 : nat]: ((![X2 : complex]: (((poly_complex2 @ P @ X2) = zero_zero_complex) => ((poly_complex2 @ Q @ X2) = zero_zero_complex))) => (((degree_complex @ P) = N2) => ((~ ((N2 = zero_zero_nat))) => (dvd_dvd_poly_complex @ P @ (power_184595776omplex @ Q @ N2)))))))). % nullstellensatz_lemma
thf(fact_6_poly__power, axiom,
    ((![P : poly_poly_nat, N2 : nat, X : poly_nat]: ((poly_poly_nat2 @ (power_1336127338ly_nat @ P @ N2) @ X) = (power_power_poly_nat @ (poly_poly_nat2 @ P @ X) @ N2))))). % poly_power
thf(fact_7_poly__power, axiom,
    ((![P : poly_p1267267526omplex, N2 : nat, X : poly_poly_complex]: ((poly_p282434315omplex @ (power_2001192272omplex @ P @ N2) @ X) = (power_432682568omplex @ (poly_p282434315omplex @ P @ X) @ N2))))). % poly_power
thf(fact_8_poly__power, axiom,
    ((![P : poly_poly_complex, N2 : nat, X : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P @ N2) @ X) = (power_184595776omplex @ (poly_poly_complex2 @ P @ X) @ N2))))). % poly_power
thf(fact_9_poly__power, axiom,
    ((![P : poly_nat, N2 : nat, X : nat]: ((poly_nat2 @ (power_power_poly_nat @ P @ N2) @ X) = (power_power_nat @ (poly_nat2 @ P @ X) @ N2))))). % poly_power
thf(fact_10_poly__power, axiom,
    ((![P : poly_complex, N2 : nat, X : complex]: ((poly_complex2 @ (power_184595776omplex @ P @ N2) @ X) = (power_power_complex @ (poly_complex2 @ P @ X) @ N2))))). % poly_power
thf(fact_11_poly__0, axiom,
    ((![X : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X) = zero_zero_poly_nat)))). % poly_0
thf(fact_12_poly__0, axiom,
    ((![X : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X) = zero_z1040703943omplex)))). % poly_0
thf(fact_13_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_14_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_15_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_16_dvd__0__right, axiom,
    ((![A : poly_nat]: (dvd_dvd_poly_nat @ A @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_17_dvd__0__right, axiom,
    ((![A : poly_poly_complex]: (dvd_dv598755940omplex @ A @ zero_z1040703943omplex)))). % dvd_0_right
thf(fact_18_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_19_dvd__0__right, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_20_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_21_dvd__0__left__iff, axiom,
    ((![A : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A) = (A = zero_zero_poly_nat))))). % dvd_0_left_iff
thf(fact_22_dvd__0__left__iff, axiom,
    ((![A : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A) = (A = zero_z1040703943omplex))))). % dvd_0_left_iff
thf(fact_23_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_24_dvd__0__left__iff, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) = (A = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_25_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_26_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X3 : complex]: ((poly_complex2 @ P @ X3) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_27_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X3 : poly_complex]: ((poly_poly_complex2 @ P @ X3) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_28_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X3 : poly_poly_complex]: ((poly_p282434315omplex @ P @ X3) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_29_fundamental__theorem__of__algebra, axiom,
    ((![P : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra
thf(fact_30_dvd__power__same, axiom,
    ((![X : poly_complex, Y : poly_complex, N2 : nat]: ((dvd_dvd_poly_complex @ X @ Y) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X @ N2) @ (power_184595776omplex @ Y @ N2)))))). % dvd_power_same
thf(fact_31_dvd__power__same, axiom,
    ((![X : nat, Y : nat, N2 : nat]: ((dvd_dvd_nat @ X @ Y) => (dvd_dvd_nat @ (power_power_nat @ X @ N2) @ (power_power_nat @ Y @ N2)))))). % dvd_power_same
thf(fact_32_dvd__power__same, axiom,
    ((![X : complex, Y : complex, N2 : nat]: ((dvd_dvd_complex @ X @ Y) => (dvd_dvd_complex @ (power_power_complex @ X @ N2) @ (power_power_complex @ Y @ N2)))))). % dvd_power_same
thf(fact_33_dvd__power__same, axiom,
    ((![X : poly_nat, Y : poly_nat, N2 : nat]: ((dvd_dvd_poly_nat @ X @ Y) => (dvd_dvd_poly_nat @ (power_power_poly_nat @ X @ N2) @ (power_power_poly_nat @ Y @ N2)))))). % dvd_power_same
thf(fact_34_dvd__power__same, axiom,
    ((![X : poly_poly_complex, Y : poly_poly_complex, N2 : nat]: ((dvd_dv598755940omplex @ X @ Y) => (dvd_dv598755940omplex @ (power_432682568omplex @ X @ N2) @ (power_432682568omplex @ Y @ N2)))))). % dvd_power_same
thf(fact_35_dvd__field__iff, axiom,
    ((dvd_dvd_complex = (^[A2 : complex]: (^[B : complex]: (((A2 = zero_zero_complex)) => ((B = zero_zero_complex)))))))). % dvd_field_iff
thf(fact_36_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_37_dvd__0__left, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) => (A = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_38_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_39_dvd__0__left, axiom,
    ((![A : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A) => (A = zero_zero_poly_nat))))). % dvd_0_left
thf(fact_40_dvd__0__left, axiom,
    ((![A : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A) => (A = zero_z1040703943omplex))))). % dvd_0_left
thf(fact_41_power__not__zero, axiom,
    ((![A : poly_complex, N2 : nat]: ((~ ((A = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A @ N2) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_42_power__not__zero, axiom,
    ((![A : nat, N2 : nat]: ((~ ((A = zero_zero_nat))) => (~ (((power_power_nat @ A @ N2) = zero_zero_nat))))))). % power_not_zero
thf(fact_43_power__not__zero, axiom,
    ((![A : complex, N2 : nat]: ((~ ((A = zero_zero_complex))) => (~ (((power_power_complex @ A @ N2) = zero_zero_complex))))))). % power_not_zero
thf(fact_44_power__not__zero, axiom,
    ((![A : poly_nat, N2 : nat]: ((~ ((A = zero_zero_poly_nat))) => (~ (((power_power_poly_nat @ A @ N2) = zero_zero_poly_nat))))))). % power_not_zero
thf(fact_45_power__not__zero, axiom,
    ((![A : poly_poly_complex, N2 : nat]: ((~ ((A = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A @ N2) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_46_power__Suc__0, axiom,
    ((![N2 : nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ N2) = (suc @ zero_zero_nat))))). % power_Suc_0
thf(fact_47_nat__power__eq__Suc__0__iff, axiom,
    ((![X : nat, M : nat]: (((power_power_nat @ X @ M) = (suc @ zero_zero_nat)) = (((M = zero_zero_nat)) | ((X = (suc @ zero_zero_nat)))))))). % nat_power_eq_Suc_0_iff
thf(fact_48_power__0__Suc, axiom,
    ((![N2 : nat]: ((power_184595776omplex @ zero_z1746442943omplex @ (suc @ N2)) = zero_z1746442943omplex)))). % power_0_Suc
thf(fact_49_power__0__Suc, axiom,
    ((![N2 : nat]: ((power_power_nat @ zero_zero_nat @ (suc @ N2)) = zero_zero_nat)))). % power_0_Suc
thf(fact_50_power__0__Suc, axiom,
    ((![N2 : nat]: ((power_power_complex @ zero_zero_complex @ (suc @ N2)) = zero_zero_complex)))). % power_0_Suc
thf(fact_51_power__0__Suc, axiom,
    ((![N2 : nat]: ((power_power_poly_nat @ zero_zero_poly_nat @ (suc @ N2)) = zero_zero_poly_nat)))). % power_0_Suc
thf(fact_52_power__0__Suc, axiom,
    ((![N2 : nat]: ((power_432682568omplex @ zero_z1040703943omplex @ (suc @ N2)) = zero_z1040703943omplex)))). % power_0_Suc
thf(fact_53_power__Suc0__right, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_54_power__Suc0__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_55_power__Suc0__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_56_power__Suc0__right, axiom,
    ((![A : poly_nat]: ((power_power_poly_nat @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_57_power__Suc0__right, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_58_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_59_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_60_degree__0, axiom,
    (((degree_poly_complex @ zero_z1040703943omplex) = zero_zero_nat))). % degree_0
thf(fact_61_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y2 : complex]: ((F @ X3) = (F @ Y2)))))))). % constant_def
thf(fact_62_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_63_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_64_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_65_zero__reorient, axiom,
    ((![X : poly_nat]: ((zero_zero_poly_nat = X) = (X = zero_zero_poly_nat))))). % zero_reorient
thf(fact_66_zero__reorient, axiom,
    ((![X : poly_poly_complex]: ((zero_z1040703943omplex = X) = (X = zero_z1040703943omplex))))). % zero_reorient
thf(fact_67_dvd__trans, axiom,
    ((![A : poly_complex, B2 : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ A @ B2) => ((dvd_dvd_poly_complex @ B2 @ C) => (dvd_dvd_poly_complex @ A @ C)))))). % dvd_trans
thf(fact_68_dvd__trans, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ C) => (dvd_dvd_nat @ A @ C)))))). % dvd_trans
thf(fact_69_dvd__trans, axiom,
    ((![A : complex, B2 : complex, C : complex]: ((dvd_dvd_complex @ A @ B2) => ((dvd_dvd_complex @ B2 @ C) => (dvd_dvd_complex @ A @ C)))))). % dvd_trans
thf(fact_70_dvd__refl, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ A)))). % dvd_refl
thf(fact_71_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_72_dvd__refl, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ A)))). % dvd_refl
thf(fact_73_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_74_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_75_dvd__1__left, axiom,
    ((![K : nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ K)))). % dvd_1_left
thf(fact_76_dvd__1__iff__1, axiom,
    ((![M : nat]: ((dvd_dvd_nat @ M @ (suc @ zero_zero_nat)) = (M = (suc @ zero_zero_nat)))))). % dvd_1_iff_1
thf(fact_77_nat_Oinject, axiom,
    ((![X22 : nat, Y22 : nat]: (((suc @ X22) = (suc @ Y22)) = (X22 = Y22))))). % nat.inject
thf(fact_78_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_79_psize__def, axiom,
    ((fundam1709708056omplex = (^[P2 : poly_complex]: (if_nat @ (P2 = zero_z1746442943omplex) @ zero_zero_nat @ (suc @ (degree_complex @ P2))))))). % psize_def
thf(fact_80_psize__def, axiom,
    ((fundam1567013434ze_nat = (^[P2 : poly_nat]: (if_nat @ (P2 = zero_zero_poly_nat) @ zero_zero_nat @ (suc @ (degree_nat @ P2))))))). % psize_def
thf(fact_81_psize__def, axiom,
    ((fundam1956464160omplex = (^[P2 : poly_poly_complex]: (if_nat @ (P2 = zero_z1040703943omplex) @ zero_zero_nat @ (suc @ (degree_poly_complex @ P2))))))). % psize_def
thf(fact_82_nat_Odistinct_I1_J, axiom,
    ((![X22 : nat]: (~ ((zero_zero_nat = (suc @ X22))))))). % nat.distinct(1)
thf(fact_83_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_84_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_85_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_86_psize__eq__0__iff, axiom,
    ((![P : poly_nat]: (((fundam1567013434ze_nat @ P) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % psize_eq_0_iff
thf(fact_87_psize__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((fundam1956464160omplex @ P) = zero_zero_nat) = (P = zero_z1040703943omplex))))). % psize_eq_0_iff
thf(fact_88_dvd__antisym, axiom,
    ((![M : nat, N2 : nat]: ((dvd_dvd_nat @ M @ N2) => ((dvd_dvd_nat @ N2 @ M) => (M = N2)))))). % dvd_antisym
thf(fact_89_n__not__Suc__n, axiom,
    ((![N2 : nat]: (~ ((N2 = (suc @ N2))))))). % n_not_Suc_n
thf(fact_90_Suc__inject, axiom,
    ((![X : nat, Y : nat]: (((suc @ X) = (suc @ Y)) => (X = Y))))). % Suc_inject
thf(fact_91_not0__implies__Suc, axiom,
    ((![N2 : nat]: ((~ ((N2 = zero_zero_nat))) => (?[M2 : nat]: (N2 = (suc @ M2))))))). % not0_implies_Suc
thf(fact_92_old_Onat_Oinducts, axiom,
    ((![P3 : nat > $o, Nat : nat]: ((P3 @ zero_zero_nat) => ((![Nat3 : nat]: ((P3 @ Nat3) => (P3 @ (suc @ Nat3)))) => (P3 @ Nat)))))). % old.nat.inducts
thf(fact_93_old_Onat_Oexhaust, axiom,
    ((![Y : nat]: ((~ ((Y = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_94_Zero__not__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_not_Suc
thf(fact_95_Zero__neq__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_neq_Suc
thf(fact_96_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_97_zero__induct, axiom,
    ((![P3 : nat > $o, K : nat]: ((P3 @ K) => ((![N : nat]: ((P3 @ (suc @ N)) => (P3 @ N))) => (P3 @ zero_zero_nat)))))). % zero_induct
thf(fact_98_diff__induct, axiom,
    ((![P3 : nat > nat > $o, M : nat, N2 : nat]: ((![X2 : nat]: (P3 @ X2 @ zero_zero_nat)) => ((![Y3 : nat]: (P3 @ zero_zero_nat @ (suc @ Y3))) => ((![X2 : nat, Y3 : nat]: ((P3 @ X2 @ Y3) => (P3 @ (suc @ X2) @ (suc @ Y3)))) => (P3 @ M @ N2))))))). % diff_induct
thf(fact_99_nat__induct, axiom,
    ((![P3 : nat > $o, N2 : nat]: ((P3 @ zero_zero_nat) => ((![N : nat]: ((P3 @ N) => (P3 @ (suc @ N)))) => (P3 @ N2)))))). % nat_induct
thf(fact_100_nat_OdiscI, axiom,
    ((![Nat : nat, X22 : nat]: ((Nat = (suc @ X22)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_101_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_102_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_103_gcd__nat_Oextremum__unique, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_104_gcd__nat_Oextremum__strict, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A) & (~ ((zero_zero_nat = A))))))))). % gcd_nat.extremum_strict
thf(fact_105_gcd__nat_Oextremum, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_106_exists__least__lemma, axiom,
    ((![P3 : nat > $o]: ((~ ((P3 @ zero_zero_nat))) => ((?[X_1 : nat]: (P3 @ X_1)) => (?[N : nat]: ((~ ((P3 @ N))) & (P3 @ (suc @ N))))))))). % exists_least_lemma
thf(fact_107_gcd__nat_Onot__eq__order__implies__strict, axiom,
    ((![A : nat, B2 : nat]: ((~ ((A = B2))) => ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ A @ B2) & (~ ((A = B2))))))))). % gcd_nat.not_eq_order_implies_strict
thf(fact_108_gcd__nat_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B2 : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => (~ ((A = B2))))))). % gcd_nat.strict_implies_not_eq
thf(fact_109_gcd__nat_Ostrict__implies__order, axiom,
    ((![A : nat, B2 : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => (dvd_dvd_nat @ A @ B2))))). % gcd_nat.strict_implies_order
thf(fact_110_gcd__nat_Ostrict__iff__order, axiom,
    ((![A : nat, B2 : nat]: ((((dvd_dvd_nat @ A @ B2)) & ((~ ((A = B2))))) = (((dvd_dvd_nat @ A @ B2)) & ((~ ((A = B2))))))))). % gcd_nat.strict_iff_order
thf(fact_111_gcd__nat_Oorder__iff__strict, axiom,
    ((dvd_dvd_nat = (^[A2 : nat]: (^[B : nat]: (((((dvd_dvd_nat @ A2 @ B)) & ((~ ((A2 = B)))))) | ((A2 = B)))))))). % gcd_nat.order_iff_strict
thf(fact_112_gcd__nat_Ostrict__trans2, axiom,
    ((![A : nat, B2 : nat, C : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => ((dvd_dvd_nat @ B2 @ C) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans2
thf(fact_113_gcd__nat_Ostrict__trans1, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((dvd_dvd_nat @ A @ B2) => (((dvd_dvd_nat @ B2 @ C) & (~ ((B2 = C)))) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans1
thf(fact_114_gcd__nat_Ostrict__trans, axiom,
    ((![A : nat, B2 : nat, C : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => (((dvd_dvd_nat @ B2 @ C) & (~ ((B2 = C)))) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans
thf(fact_115_gcd__nat_Oantisym, axiom,
    ((![A : nat, B2 : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ A) => (A = B2)))))). % gcd_nat.antisym
thf(fact_116_gcd__nat_Oirrefl, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ A @ A) & (~ ((A = A))))))))). % gcd_nat.irrefl
thf(fact_117_gcd__nat_Oeq__iff, axiom,
    (((^[Y4 : nat]: (^[Z2 : nat]: (Y4 = Z2))) = (^[A2 : nat]: (^[B : nat]: (((dvd_dvd_nat @ A2 @ B)) & ((dvd_dvd_nat @ B @ A2)))))))). % gcd_nat.eq_iff
thf(fact_118_gcd__nat_Otrans, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ C) => (dvd_dvd_nat @ A @ C)))))). % gcd_nat.trans
thf(fact_119_gcd__nat_Orefl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % gcd_nat.refl
thf(fact_120_gcd__nat_Oasym, axiom,
    ((![A : nat, B2 : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => (~ (((dvd_dvd_nat @ B2 @ A) & (~ ((B2 = A)))))))))). % gcd_nat.asym
thf(fact_121_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_complex, C : complex]: (((synthe151143547omplex @ P @ C) = zero_z1746442943omplex) = ((degree_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_122_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_nat, C : nat]: (((synthetic_div_nat @ P @ C) = zero_zero_poly_nat) = ((degree_nat @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_123_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_poly_complex, C : poly_complex]: (((synthe1985144195omplex @ P @ C) = zero_z1040703943omplex) = ((degree_poly_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_124_is__zero__null, axiom,
    ((is_zero_complex = (^[P2 : poly_complex]: (P2 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_125_is__zero__null, axiom,
    ((is_zero_nat = (^[P2 : poly_nat]: (P2 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_126_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P2 : poly_poly_complex]: (P2 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_127_poly__cutoff__0, axiom,
    ((![N2 : nat]: ((poly_cutoff_complex @ N2 @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_128_poly__cutoff__0, axiom,
    ((![N2 : nat]: ((poly_cutoff_nat @ N2 @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_129_poly__cutoff__0, axiom,
    ((![N2 : nat]: ((poly_c622223248omplex @ N2 @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_130_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_complex]: (((poly_complex2 @ (reflect_poly_complex @ P) @ zero_zero_complex) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_131_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((poly_poly_complex2 @ (reflec309385472omplex @ P) @ zero_z1746442943omplex) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_132_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_nat]: (((poly_nat2 @ (reflect_poly_nat @ P) @ zero_zero_nat) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_133_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_nat]: (((poly_poly_nat2 @ (reflec781175074ly_nat @ P) @ zero_zero_poly_nat) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_134_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((poly_p282434315omplex @ (reflec1997789704omplex @ P) @ zero_z1040703943omplex) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_135_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_136_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_137_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_138_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_139_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_140_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_141_reflect__poly__power, axiom,
    ((![P : poly_complex, N2 : nat]: ((reflect_poly_complex @ (power_184595776omplex @ P @ N2)) = (power_184595776omplex @ (reflect_poly_complex @ P) @ N2))))). % reflect_poly_power
thf(fact_142_reflect__poly__power, axiom,
    ((![P : poly_nat, N2 : nat]: ((reflect_poly_nat @ (power_power_poly_nat @ P @ N2)) = (power_power_poly_nat @ (reflect_poly_nat @ P) @ N2))))). % reflect_poly_power
thf(fact_143_reflect__poly__power, axiom,
    ((![P : poly_poly_complex, N2 : nat]: ((reflec309385472omplex @ (power_432682568omplex @ P @ N2)) = (power_432682568omplex @ (reflec309385472omplex @ P) @ N2))))). % reflect_poly_power
thf(fact_144_poly__reflect__poly__0, axiom,
    ((![P : poly_complex]: ((poly_complex2 @ (reflect_poly_complex @ P) @ zero_zero_complex) = (coeff_complex @ P @ (degree_complex @ P)))))). % poly_reflect_poly_0
thf(fact_145_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_complex]: ((poly_poly_complex2 @ (reflec309385472omplex @ P) @ zero_z1746442943omplex) = (coeff_poly_complex @ P @ (degree_poly_complex @ P)))))). % poly_reflect_poly_0
thf(fact_146_poly__reflect__poly__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ (reflect_poly_nat @ P) @ zero_zero_nat) = (coeff_nat @ P @ (degree_nat @ P)))))). % poly_reflect_poly_0
thf(fact_147_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_nat]: ((poly_poly_nat2 @ (reflec781175074ly_nat @ P) @ zero_zero_poly_nat) = (coeff_poly_nat @ P @ (degree_poly_nat @ P)))))). % poly_reflect_poly_0
thf(fact_148_poly__reflect__poly__0, axiom,
    ((![P : poly_p1267267526omplex]: ((poly_p282434315omplex @ (reflec1997789704omplex @ P) @ zero_z1040703943omplex) = (coeff_1429652124omplex @ P @ (degree2006505739omplex @ P)))))). % poly_reflect_poly_0
thf(fact_149_poly__cutoff__1, axiom,
    ((![N2 : nat]: (((N2 = zero_zero_nat) => ((poly_cutoff_complex @ N2 @ one_one_poly_complex) = zero_z1746442943omplex)) & ((~ ((N2 = zero_zero_nat))) => ((poly_cutoff_complex @ N2 @ one_one_poly_complex) = one_one_poly_complex)))))). % poly_cutoff_1
thf(fact_150_poly__cutoff__1, axiom,
    ((![N2 : nat]: (((N2 = zero_zero_nat) => ((poly_cutoff_nat @ N2 @ one_one_poly_nat) = zero_zero_poly_nat)) & ((~ ((N2 = zero_zero_nat))) => ((poly_cutoff_nat @ N2 @ one_one_poly_nat) = one_one_poly_nat)))))). % poly_cutoff_1
thf(fact_151_poly__cutoff__1, axiom,
    ((![N2 : nat]: (((N2 = zero_zero_nat) => ((poly_c622223248omplex @ N2 @ one_on1331105667omplex) = zero_z1040703943omplex)) & ((~ ((N2 = zero_zero_nat))) => ((poly_c622223248omplex @ N2 @ one_on1331105667omplex) = one_on1331105667omplex)))))). % poly_cutoff_1
thf(fact_152_degree__reflect__poly__eq, axiom,
    ((![P : poly_complex]: ((~ (((coeff_complex @ P @ zero_zero_nat) = zero_zero_complex))) => ((degree_complex @ (reflect_poly_complex @ P)) = (degree_complex @ P)))))). % degree_reflect_poly_eq
thf(fact_153_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_complex]: ((~ (((coeff_poly_complex @ P @ zero_zero_nat) = zero_z1746442943omplex))) => ((degree_poly_complex @ (reflec309385472omplex @ P)) = (degree_poly_complex @ P)))))). % degree_reflect_poly_eq
thf(fact_154_degree__reflect__poly__eq, axiom,
    ((![P : poly_nat]: ((~ (((coeff_nat @ P @ zero_zero_nat) = zero_zero_nat))) => ((degree_nat @ (reflect_poly_nat @ P)) = (degree_nat @ P)))))). % degree_reflect_poly_eq
thf(fact_155_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_nat]: ((~ (((coeff_poly_nat @ P @ zero_zero_nat) = zero_zero_poly_nat))) => ((degree_poly_nat @ (reflec781175074ly_nat @ P)) = (degree_poly_nat @ P)))))). % degree_reflect_poly_eq
thf(fact_156_degree__reflect__poly__eq, axiom,
    ((![P : poly_p1267267526omplex]: ((~ (((coeff_1429652124omplex @ P @ zero_zero_nat) = zero_z1040703943omplex))) => ((degree2006505739omplex @ (reflec1997789704omplex @ P)) = (degree2006505739omplex @ P)))))). % degree_reflect_poly_eq
thf(fact_157_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_complex]: (((coeff_complex @ (reflect_poly_complex @ P) @ zero_zero_nat) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_158_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_complex]: (((coeff_poly_complex @ (reflec309385472omplex @ P) @ zero_zero_nat) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_159_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_nat]: (((coeff_nat @ (reflect_poly_nat @ P) @ zero_zero_nat) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_160_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_nat]: (((coeff_poly_nat @ (reflec781175074ly_nat @ P) @ zero_zero_nat) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_161_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((coeff_1429652124omplex @ (reflec1997789704omplex @ P) @ zero_zero_nat) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_162_power__one, axiom,
    ((![N2 : nat]: ((power_184595776omplex @ one_one_poly_complex @ N2) = one_one_poly_complex)))). % power_one
thf(fact_163_power__one, axiom,
    ((![N2 : nat]: ((power_power_nat @ one_one_nat @ N2) = one_one_nat)))). % power_one
thf(fact_164_power__one, axiom,
    ((![N2 : nat]: ((power_power_complex @ one_one_complex @ N2) = one_one_complex)))). % power_one
thf(fact_165_power__one, axiom,
    ((![N2 : nat]: ((power_power_poly_nat @ one_one_poly_nat @ N2) = one_one_poly_nat)))). % power_one
thf(fact_166_power__one, axiom,
    ((![N2 : nat]: ((power_432682568omplex @ one_on1331105667omplex @ N2) = one_on1331105667omplex)))). % power_one
thf(fact_167_coeff__0, axiom,
    ((![N2 : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N2) = zero_zero_poly_nat)))). % coeff_0
thf(fact_168_coeff__0, axiom,
    ((![N2 : nat]: ((coeff_1429652124omplex @ zero_z1200043727omplex @ N2) = zero_z1040703943omplex)))). % coeff_0
thf(fact_169_coeff__0, axiom,
    ((![N2 : nat]: ((coeff_complex @ zero_z1746442943omplex @ N2) = zero_zero_complex)))). % coeff_0
thf(fact_170_coeff__0, axiom,
    ((![N2 : nat]: ((coeff_nat @ zero_zero_poly_nat @ N2) = zero_zero_nat)))). % coeff_0
thf(fact_171_coeff__0, axiom,
    ((![N2 : nat]: ((coeff_poly_complex @ zero_z1040703943omplex @ N2) = zero_z1746442943omplex)))). % coeff_0
thf(fact_172_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_173_poly__1, axiom,
    ((![X : complex]: ((poly_complex2 @ one_one_poly_complex @ X) = one_one_complex)))). % poly_1
thf(fact_174_poly__1, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ one_on1331105667omplex @ X) = one_one_poly_complex)))). % poly_1
thf(fact_175_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_176_leading__coeff__0__iff, axiom,
    ((![P : poly_complex]: (((coeff_complex @ P @ (degree_complex @ P)) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % leading_coeff_0_iff
thf(fact_177_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_complex]: (((coeff_poly_complex @ P @ (degree_poly_complex @ P)) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % leading_coeff_0_iff
thf(fact_178_leading__coeff__0__iff, axiom,
    ((![P : poly_nat]: (((coeff_nat @ P @ (degree_nat @ P)) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % leading_coeff_0_iff
thf(fact_179_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_nat]: (((coeff_poly_nat @ P @ (degree_poly_nat @ P)) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % leading_coeff_0_iff
thf(fact_180_leading__coeff__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((coeff_1429652124omplex @ P @ (degree2006505739omplex @ P)) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % leading_coeff_0_iff
thf(fact_181_reflect__poly__reflect__poly, axiom,
    ((![P : poly_complex]: ((~ (((coeff_complex @ P @ zero_zero_nat) = zero_zero_complex))) => ((reflect_poly_complex @ (reflect_poly_complex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_182_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_complex]: ((~ (((coeff_poly_complex @ P @ zero_zero_nat) = zero_z1746442943omplex))) => ((reflec309385472omplex @ (reflec309385472omplex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_183_reflect__poly__reflect__poly, axiom,
    ((![P : poly_nat]: ((~ (((coeff_nat @ P @ zero_zero_nat) = zero_zero_nat))) => ((reflect_poly_nat @ (reflect_poly_nat @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_184_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_nat]: ((~ (((coeff_poly_nat @ P @ zero_zero_nat) = zero_zero_poly_nat))) => ((reflec781175074ly_nat @ (reflec781175074ly_nat @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_185_reflect__poly__reflect__poly, axiom,
    ((![P : poly_p1267267526omplex]: ((~ (((coeff_1429652124omplex @ P @ zero_zero_nat) = zero_z1040703943omplex))) => ((reflec1997789704omplex @ (reflec1997789704omplex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_186_lead__coeff__1, axiom,
    (((coeff_complex @ one_one_poly_complex @ (degree_complex @ one_one_poly_complex)) = one_one_complex))). % lead_coeff_1
thf(fact_187_lead__coeff__1, axiom,
    (((coeff_nat @ one_one_poly_nat @ (degree_nat @ one_one_poly_nat)) = one_one_nat))). % lead_coeff_1
thf(fact_188_coeff__0__reflect__poly, axiom,
    ((![P : poly_complex]: ((coeff_complex @ (reflect_poly_complex @ P) @ zero_zero_nat) = (coeff_complex @ P @ (degree_complex @ P)))))). % coeff_0_reflect_poly
thf(fact_189_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_190_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_191_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_192_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_193_zero__neq__one, axiom,
    ((~ ((zero_z1040703943omplex = one_on1331105667omplex))))). % zero_neq_one
thf(fact_194_one__dvd, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ one_one_poly_complex @ A)))). % one_dvd
thf(fact_195_one__dvd, axiom,
    ((![A : complex]: (dvd_dvd_complex @ one_one_complex @ A)))). % one_dvd
thf(fact_196_one__dvd, axiom,
    ((![A : nat]: (dvd_dvd_nat @ one_one_nat @ A)))). % one_dvd
thf(fact_197_unit__imp__dvd, axiom,
    ((![B2 : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ B2 @ one_one_poly_complex) => (dvd_dvd_poly_complex @ B2 @ A))))). % unit_imp_dvd
thf(fact_198_unit__imp__dvd, axiom,
    ((![B2 : nat, A : nat]: ((dvd_dvd_nat @ B2 @ one_one_nat) => (dvd_dvd_nat @ B2 @ A))))). % unit_imp_dvd
thf(fact_199_dvd__unit__imp__unit, axiom,
    ((![A : poly_complex, B2 : poly_complex]: ((dvd_dvd_poly_complex @ A @ B2) => ((dvd_dvd_poly_complex @ B2 @ one_one_poly_complex) => (dvd_dvd_poly_complex @ A @ one_one_poly_complex)))))). % dvd_unit_imp_unit
thf(fact_200_dvd__unit__imp__unit, axiom,
    ((![A : nat, B2 : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)))))). % dvd_unit_imp_unit
thf(fact_201_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_202_zero__poly_Orep__eq, axiom,
    (((coeff_poly_nat @ zero_z1059985641ly_nat) = (^[Uu : nat]: zero_zero_poly_nat)))). % zero_poly.rep_eq
thf(fact_203_zero__poly_Orep__eq, axiom,
    (((coeff_1429652124omplex @ zero_z1200043727omplex) = (^[Uu : nat]: zero_z1040703943omplex)))). % zero_poly.rep_eq
thf(fact_204_zero__poly_Orep__eq, axiom,
    (((coeff_complex @ zero_z1746442943omplex) = (^[Uu : nat]: zero_zero_complex)))). % zero_poly.rep_eq
thf(fact_205_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_206_zero__poly_Orep__eq, axiom,
    (((coeff_poly_complex @ zero_z1040703943omplex) = (^[Uu : nat]: zero_z1746442943omplex)))). % zero_poly.rep_eq
thf(fact_207_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ one_one_poly_complex))))). % not_is_unit_0
thf(fact_208_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_209_not__is__unit__0, axiom,
    ((~ ((dvd_dv598755940omplex @ zero_z1040703943omplex @ one_on1331105667omplex))))). % not_is_unit_0
thf(fact_210_power__0, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ zero_zero_nat) = one_one_poly_complex)))). % power_0
thf(fact_211_power__0, axiom,
    ((![A : nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat)))). % power_0
thf(fact_212_power__0, axiom,
    ((![A : complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex)))). % power_0
thf(fact_213_power__0, axiom,
    ((![A : poly_nat]: ((power_power_poly_nat @ A @ zero_zero_nat) = one_one_poly_nat)))). % power_0
thf(fact_214_power__0, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ zero_zero_nat) = one_on1331105667omplex)))). % power_0
thf(fact_215_poly__0__coeff__0, axiom,
    ((![P : poly_complex]: ((poly_complex2 @ P @ zero_zero_complex) = (coeff_complex @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_216_poly__0__coeff__0, axiom,
    ((![P : poly_poly_complex]: ((poly_poly_complex2 @ P @ zero_z1746442943omplex) = (coeff_poly_complex @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_217_poly__0__coeff__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ P @ zero_zero_nat) = (coeff_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_218_poly__0__coeff__0, axiom,
    ((![P : poly_poly_nat]: ((poly_poly_nat2 @ P @ zero_zero_poly_nat) = (coeff_poly_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_219_poly__0__coeff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((poly_p282434315omplex @ P @ zero_z1040703943omplex) = (coeff_1429652124omplex @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_220_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_nat]: ((~ ((P = zero_z1059985641ly_nat))) => (~ (((coeff_poly_nat @ P @ (degree_poly_nat @ P)) = zero_zero_poly_nat))))))). % leading_coeff_neq_0
thf(fact_221_leading__coeff__neq__0, axiom,
    ((![P : poly_p1267267526omplex]: ((~ ((P = zero_z1200043727omplex))) => (~ (((coeff_1429652124omplex @ P @ (degree2006505739omplex @ P)) = zero_z1040703943omplex))))))). % leading_coeff_neq_0
thf(fact_222_leading__coeff__neq__0, axiom,
    ((![P : poly_complex]: ((~ ((P = zero_z1746442943omplex))) => (~ (((coeff_complex @ P @ (degree_complex @ P)) = zero_zero_complex))))))). % leading_coeff_neq_0
thf(fact_223_leading__coeff__neq__0, axiom,
    ((![P : poly_nat]: ((~ ((P = zero_zero_poly_nat))) => (~ (((coeff_nat @ P @ (degree_nat @ P)) = zero_zero_nat))))))). % leading_coeff_neq_0
thf(fact_224_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_complex]: ((~ ((P = zero_z1040703943omplex))) => (~ (((coeff_poly_complex @ P @ (degree_poly_complex @ P)) = zero_z1746442943omplex))))))). % leading_coeff_neq_0
thf(fact_225_coeff__0__power, axiom,
    ((![P : poly_poly_nat, N2 : nat]: ((coeff_poly_nat @ (power_1336127338ly_nat @ P @ N2) @ zero_zero_nat) = (power_power_poly_nat @ (coeff_poly_nat @ P @ zero_zero_nat) @ N2))))). % coeff_0_power
thf(fact_226_coeff__0__power, axiom,
    ((![P : poly_p1267267526omplex, N2 : nat]: ((coeff_1429652124omplex @ (power_2001192272omplex @ P @ N2) @ zero_zero_nat) = (power_432682568omplex @ (coeff_1429652124omplex @ P @ zero_zero_nat) @ N2))))). % coeff_0_power
thf(fact_227_coeff__0__power, axiom,
    ((![P : poly_complex, N2 : nat]: ((coeff_complex @ (power_184595776omplex @ P @ N2) @ zero_zero_nat) = (power_power_complex @ (coeff_complex @ P @ zero_zero_nat) @ N2))))). % coeff_0_power
thf(fact_228_coeff__0__power, axiom,
    ((![P : poly_nat, N2 : nat]: ((coeff_nat @ (power_power_poly_nat @ P @ N2) @ zero_zero_nat) = (power_power_nat @ (coeff_nat @ P @ zero_zero_nat) @ N2))))). % coeff_0_power
thf(fact_229_coeff__0__power, axiom,
    ((![P : poly_poly_complex, N2 : nat]: ((coeff_poly_complex @ (power_432682568omplex @ P @ N2) @ zero_zero_nat) = (power_184595776omplex @ (coeff_poly_complex @ P @ zero_zero_nat) @ N2))))). % coeff_0_power
thf(fact_230_lead__coeff__power, axiom,
    ((![P : poly_poly_nat, N2 : nat]: ((coeff_poly_nat @ (power_1336127338ly_nat @ P @ N2) @ (degree_poly_nat @ (power_1336127338ly_nat @ P @ N2))) = (power_power_poly_nat @ (coeff_poly_nat @ P @ (degree_poly_nat @ P)) @ N2))))). % lead_coeff_power
thf(fact_231_lead__coeff__power, axiom,
    ((![P : poly_p1267267526omplex, N2 : nat]: ((coeff_1429652124omplex @ (power_2001192272omplex @ P @ N2) @ (degree2006505739omplex @ (power_2001192272omplex @ P @ N2))) = (power_432682568omplex @ (coeff_1429652124omplex @ P @ (degree2006505739omplex @ P)) @ N2))))). % lead_coeff_power
thf(fact_232_lead__coeff__power, axiom,
    ((![P : poly_complex, N2 : nat]: ((coeff_complex @ (power_184595776omplex @ P @ N2) @ (degree_complex @ (power_184595776omplex @ P @ N2))) = (power_power_complex @ (coeff_complex @ P @ (degree_complex @ P)) @ N2))))). % lead_coeff_power
thf(fact_233_lead__coeff__power, axiom,
    ((![P : poly_nat, N2 : nat]: ((coeff_nat @ (power_power_poly_nat @ P @ N2) @ (degree_nat @ (power_power_poly_nat @ P @ N2))) = (power_power_nat @ (coeff_nat @ P @ (degree_nat @ P)) @ N2))))). % lead_coeff_power
thf(fact_234_lead__coeff__power, axiom,
    ((![P : poly_poly_complex, N2 : nat]: ((coeff_poly_complex @ (power_432682568omplex @ P @ N2) @ (degree_poly_complex @ (power_432682568omplex @ P @ N2))) = (power_184595776omplex @ (coeff_poly_complex @ P @ (degree_poly_complex @ P)) @ N2))))). % lead_coeff_power
thf(fact_235_power__0__left, axiom,
    ((![N2 : nat]: (((N2 = zero_zero_nat) => ((power_184595776omplex @ zero_z1746442943omplex @ N2) = one_one_poly_complex)) & ((~ ((N2 = zero_zero_nat))) => ((power_184595776omplex @ zero_z1746442943omplex @ N2) = zero_z1746442943omplex)))))). % power_0_left
thf(fact_236_power__0__left, axiom,
    ((![N2 : nat]: (((N2 = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ N2) = one_one_nat)) & ((~ ((N2 = zero_zero_nat))) => ((power_power_nat @ zero_zero_nat @ N2) = zero_zero_nat)))))). % power_0_left
thf(fact_237_power__0__left, axiom,
    ((![N2 : nat]: (((N2 = zero_zero_nat) => ((power_power_complex @ zero_zero_complex @ N2) = one_one_complex)) & ((~ ((N2 = zero_zero_nat))) => ((power_power_complex @ zero_zero_complex @ N2) = zero_zero_complex)))))). % power_0_left
thf(fact_238_power__0__left, axiom,
    ((![N2 : nat]: (((N2 = zero_zero_nat) => ((power_power_poly_nat @ zero_zero_poly_nat @ N2) = one_one_poly_nat)) & ((~ ((N2 = zero_zero_nat))) => ((power_power_poly_nat @ zero_zero_poly_nat @ N2) = zero_zero_poly_nat)))))). % power_0_left
thf(fact_239_power__0__left, axiom,
    ((![N2 : nat]: (((N2 = zero_zero_nat) => ((power_432682568omplex @ zero_z1040703943omplex @ N2) = one_on1331105667omplex)) & ((~ ((N2 = zero_zero_nat))) => ((power_432682568omplex @ zero_z1040703943omplex @ N2) = zero_z1040703943omplex)))))). % power_0_left
thf(fact_240_is__unit__power__iff, axiom,
    ((![A : nat, N2 : nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ N2) @ one_one_nat) = (((dvd_dvd_nat @ A @ one_one_nat)) | ((N2 = zero_zero_nat))))))). % is_unit_power_iff
thf(fact_241_is__unit__power__iff, axiom,
    ((![A : poly_poly_complex, N2 : nat]: ((dvd_dv598755940omplex @ (power_432682568omplex @ A @ N2) @ one_on1331105667omplex) = (((dvd_dv598755940omplex @ A @ one_on1331105667omplex)) | ((N2 = zero_zero_nat))))))). % is_unit_power_iff
thf(fact_242_nat__dvd__1__iff__1, axiom,
    ((![M : nat]: ((dvd_dvd_nat @ M @ one_one_nat) = (M = one_one_nat))))). % nat_dvd_1_iff_1

% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T, axiom,
    ((![P3 : $o]: ((P3 = $true) | (P3 = $false))))).
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X : nat, Y : nat]: ((if_nat @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X : nat, Y : nat]: ((if_nat @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    (((![X3 : complex]: ((((poly_complex2 @ p @ X3) = zero_zero_complex)) => (((poly_complex2 @ q @ X3) = zero_zero_complex)))) = (((dvd_dvd_poly_complex @ p @ (power_184595776omplex @ q @ (degree_complex @ p)))) | ((((p = zero_z1746442943omplex)) & ((q = zero_z1746442943omplex)))))))).
