% 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_833__5375992_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:33:32.476

% 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 (72)
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_Ooffset__poly_001t__Complex__Ocomplex, type,
    fundam1201687030omplex : poly_complex > complex > poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Nat__Onat, type,
    fundam170929432ly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1307691262omplex : poly_poly_complex > poly_complex > poly_poly_complex).
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_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    uminus1138659839omplex : poly_complex > poly_complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    uminus1762810119omplex : poly_poly_complex > poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_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_Polynomial_Ocontent_001t__Nat__Onat, type,
    content_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Complex__Ocomplex, type,
    divide23485933omplex : complex > poly_complex > poly_complex > poly_complex > nat > nat > poly_complex).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    divide219992821omplex : poly_complex > poly_poly_complex > poly_poly_complex > poly_poly_complex > nat > nat > poly_poly_complex).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    divide713971197omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex > poly_p1267267526omplex > nat > nat > poly_p1267267526omplex).
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_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__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    order_1735763309omplex : poly_poly_complex > poly_p1267267526omplex > nat).
thf(sy_c_Polynomial_OpCons_001t__Complex__Ocomplex, type,
    pCons_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Nat__Onat, type,
    pCons_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    pCons_poly_complex : poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    pCons_poly_nat : poly_nat > poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    pCons_1087637536omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex).
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_Opoly__shift_001t__Complex__Ocomplex, type,
    poly_shift_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly__shift_001t__Nat__Onat, type,
    poly_shift_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__shift_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_s558570093omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Oprimitive__part_001t__Nat__Onat, type,
    primitive_part_nat : poly_nat > poly_nat).
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_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_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    dvd_dv1870147948omplex : poly_p1267267526omplex > poly_p1267267526omplex > $o).
thf(sy_c_Rings_Onormalization__semidom__class_Onormalize_001t__Nat__Onat, type,
    normal728885956ze_nat : nat > nat).
thf(sy_v_c____, type,
    c : complex).
thf(sy_v_cs____, type,
    cs : poly_complex).
thf(sy_v_p, type,
    p : poly_complex).

% Relevant facts (247)
thf(fact_0_False, axiom,
    ((~ ((c = zero_zero_complex))))). % False
thf(fact_1__C0_Oprems_C, axiom,
    ((![W : complex]: ((~ ((W = zero_zero_complex))) => ((poly_complex2 @ zero_z1746442943omplex @ W) = zero_zero_complex))))). % "0.prems"
thf(fact_2_assms, axiom,
    ((~ ((?[A : complex, L : poly_complex]: ((~ ((A = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (p = (pCons_complex @ A @ L))))))))). % assms
thf(fact_3_poly__0, axiom,
    ((![X : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X) = zero_zero_poly_nat)))). % poly_0
thf(fact_4_poly__0, axiom,
    ((![X : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X) = zero_z1040703943omplex)))). % poly_0
thf(fact_5_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_6_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_7_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_8_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_complex))) | (~ ((cs = zero_z1746442943omplex)))))). % pCons.hyps(1)
thf(fact_9_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ P @ X2) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_10_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X2 : poly_complex]: ((poly_poly_complex2 @ P @ X2) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_11_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X2 : complex]: ((poly_complex2 @ P @ X2) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_12_zero__reorient, axiom,
    ((![X : poly_nat]: ((zero_zero_poly_nat = X) = (X = zero_zero_poly_nat))))). % zero_reorient
thf(fact_13_zero__reorient, axiom,
    ((![X : poly_poly_complex]: ((zero_z1040703943omplex = X) = (X = zero_z1040703943omplex))))). % zero_reorient
thf(fact_14_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_15_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_16_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_17_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_18_offset__poly__0, axiom,
    ((![H : poly_complex]: ((fundam1307691262omplex @ zero_z1040703943omplex @ H) = zero_z1040703943omplex)))). % offset_poly_0
thf(fact_19_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_20_offset__poly__eq__0__iff, axiom,
    ((![P : poly_nat, H : nat]: (((fundam170929432ly_nat @ P @ H) = zero_zero_poly_nat) = (P = zero_zero_poly_nat))))). % offset_poly_eq_0_iff
thf(fact_21_offset__poly__eq__0__iff, axiom,
    ((![P : poly_poly_complex, H : poly_complex]: (((fundam1307691262omplex @ P @ H) = zero_z1040703943omplex) = (P = zero_z1040703943omplex))))). % offset_poly_eq_0_iff
thf(fact_22_offset__poly__eq__0__iff, axiom,
    ((![P : poly_complex, H : complex]: (((fundam1201687030omplex @ P @ H) = zero_z1746442943omplex) = (P = zero_z1746442943omplex))))). % offset_poly_eq_0_iff
thf(fact_23_divide__poly__main__0, axiom,
    ((![R : poly_poly_complex, D : poly_poly_complex, Dr : nat, N : nat]: ((divide219992821omplex @ zero_z1746442943omplex @ zero_z1040703943omplex @ R @ D @ Dr @ N) = zero_z1040703943omplex)))). % divide_poly_main_0
thf(fact_24_divide__poly__main__0, axiom,
    ((![R : poly_complex, D : poly_complex, Dr : nat, N : nat]: ((divide23485933omplex @ zero_zero_complex @ zero_z1746442943omplex @ R @ D @ Dr @ N) = zero_z1746442943omplex)))). % divide_poly_main_0
thf(fact_25_divide__poly__main__0, axiom,
    ((![R : poly_p1267267526omplex, D : poly_p1267267526omplex, Dr : nat, N : nat]: ((divide713971197omplex @ zero_z1040703943omplex @ zero_z1200043727omplex @ R @ D @ Dr @ N) = zero_z1200043727omplex)))). % divide_poly_main_0
thf(fact_26_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_27_pCons_Ohyps_I2_J, axiom,
    (((~ ((?[A2 : complex, L2 : poly_complex]: ((~ ((A2 = zero_zero_complex))) & ((L2 = zero_z1746442943omplex) & (cs = (pCons_complex @ A2 @ L2))))))) => (?[Z : complex]: ((poly_complex2 @ cs @ Z) = zero_zero_complex))))). % pCons.hyps(2)
thf(fact_28_pCons_Oprems, axiom,
    ((~ ((?[A : complex, L : poly_complex]: ((~ ((A = zero_zero_complex))) & ((L = zero_z1746442943omplex) & ((pCons_complex @ c @ cs) = (pCons_complex @ A @ L))))))))). % pCons.prems
thf(fact_29__092_060open_062_092_060forall_062w_O_Aw_A_092_060noteq_062_A0_A_092_060longrightarrow_062_Apoly_Acs_Aw_A_061_A0_092_060close_062, axiom,
    ((![W : complex]: ((~ ((W = zero_zero_complex))) => ((poly_complex2 @ cs @ W) = zero_zero_complex))))). % \<open>\<forall>w. w \<noteq> 0 \<longrightarrow> poly cs w = 0\<close>
thf(fact_30_pCons__eq__iff, axiom,
    ((![A3 : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A3 @ P) = (pCons_complex @ B @ Q)) = (((A3 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_31_nc, axiom,
    ((fundam1158420650omplex @ (poly_complex2 @ (pCons_complex @ c @ cs))))). % nc
thf(fact_32__092_060open_062_092_060And_062y_O_Apoly_A_IpCons_Ac_Acs_J_A0_A_061_Apoly_A_IpCons_Ac_Acs_J_Ay_092_060close_062, axiom,
    ((![Y : complex]: ((poly_complex2 @ (pCons_complex @ c @ cs) @ zero_zero_complex) = (poly_complex2 @ (pCons_complex @ c @ cs) @ Y))))). % \<open>\<And>y. poly (pCons c cs) 0 = poly (pCons c cs) y\<close>
thf(fact_33_pCons__eq__0__iff, axiom,
    ((![A3 : poly_nat, P : poly_poly_nat]: (((pCons_poly_nat @ A3 @ P) = zero_z1059985641ly_nat) = (((A3 = zero_zero_poly_nat)) & ((P = zero_z1059985641ly_nat))))))). % pCons_eq_0_iff
thf(fact_34_pCons__eq__0__iff, axiom,
    ((![A3 : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A3 @ P) = zero_z1200043727omplex) = (((A3 = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_35_pCons__eq__0__iff, axiom,
    ((![A3 : complex, P : poly_complex]: (((pCons_complex @ A3 @ P) = zero_z1746442943omplex) = (((A3 = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_36_pCons__eq__0__iff, axiom,
    ((![A3 : nat, P : poly_nat]: (((pCons_nat @ A3 @ P) = zero_zero_poly_nat) = (((A3 = zero_zero_nat)) & ((P = zero_zero_poly_nat))))))). % pCons_eq_0_iff
thf(fact_37_pCons__eq__0__iff, axiom,
    ((![A3 : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A3 @ P) = zero_z1040703943omplex) = (((A3 = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_38_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_39_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_40_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_41_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_42_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_43_content__eq__zero__iff, axiom,
    ((![P : poly_nat]: (((content_nat @ P) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % content_eq_zero_iff
thf(fact_44_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A2 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_45_pderiv_Ocases, axiom,
    ((![X : poly_complex]: (~ ((![A2 : complex, P2 : poly_complex]: (~ ((X = (pCons_complex @ A2 @ P2)))))))))). % pderiv.cases
thf(fact_46_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_47_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_48_pderiv_Oinduct, axiom,
    ((![P3 : poly_complex > $o, A0 : poly_complex]: ((![A2 : complex, P2 : poly_complex]: (((~ ((P2 = zero_z1746442943omplex))) => (P3 @ P2)) => (P3 @ (pCons_complex @ A2 @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_49_pderiv_Oinduct, axiom,
    ((![P3 : poly_nat > $o, A0 : poly_nat]: ((![A2 : nat, P2 : poly_nat]: (((~ ((P2 = zero_zero_poly_nat))) => (P3 @ P2)) => (P3 @ (pCons_nat @ A2 @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_50_pderiv_Oinduct, axiom,
    ((![P3 : poly_poly_complex > $o, A0 : poly_poly_complex]: ((![A2 : poly_complex, P2 : poly_poly_complex]: (((~ ((P2 = zero_z1040703943omplex))) => (P3 @ P2)) => (P3 @ (pCons_poly_complex @ A2 @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_51_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_complex > $o, P : poly_complex, Q : poly_complex]: ((P3 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A2 : complex, P2 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A2 @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_52_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_nat > $o, P : poly_complex, Q : poly_nat]: ((P3 @ zero_z1746442943omplex @ zero_zero_poly_nat) => ((![A2 : complex, P2 : poly_complex, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A2 @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_53_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_poly_complex > $o, P : poly_complex, Q : poly_poly_complex]: ((P3 @ zero_z1746442943omplex @ zero_z1040703943omplex) => ((![A2 : complex, P2 : poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A2 @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_54_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_complex > $o, P : poly_nat, Q : poly_complex]: ((P3 @ zero_zero_poly_nat @ zero_z1746442943omplex) => ((![A2 : nat, P2 : poly_nat, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A2 @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_55_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_nat > $o, P : poly_nat, Q : poly_nat]: ((P3 @ zero_zero_poly_nat @ zero_zero_poly_nat) => ((![A2 : nat, P2 : poly_nat, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A2 @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_56_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_poly_complex > $o, P : poly_nat, Q : poly_poly_complex]: ((P3 @ zero_zero_poly_nat @ zero_z1040703943omplex) => ((![A2 : nat, P2 : poly_nat, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A2 @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_57_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_complex > $o, P : poly_poly_complex, Q : poly_complex]: ((P3 @ zero_z1040703943omplex @ zero_z1746442943omplex) => ((![A2 : poly_complex, P2 : poly_poly_complex, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A2 @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_58_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_nat > $o, P : poly_poly_complex, Q : poly_nat]: ((P3 @ zero_z1040703943omplex @ zero_zero_poly_nat) => ((![A2 : poly_complex, P2 : poly_poly_complex, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A2 @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_59_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_poly_complex > $o, P : poly_poly_complex, Q : poly_poly_complex]: ((P3 @ zero_z1040703943omplex @ zero_z1040703943omplex) => ((![A2 : poly_complex, P2 : poly_poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A2 @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_60_offset__poly__single, axiom,
    ((![A3 : nat, H : nat]: ((fundam170929432ly_nat @ (pCons_nat @ A3 @ zero_zero_poly_nat) @ H) = (pCons_nat @ A3 @ zero_zero_poly_nat))))). % offset_poly_single
thf(fact_61_offset__poly__single, axiom,
    ((![A3 : poly_complex, H : poly_complex]: ((fundam1307691262omplex @ (pCons_poly_complex @ A3 @ zero_z1040703943omplex) @ H) = (pCons_poly_complex @ A3 @ zero_z1040703943omplex))))). % offset_poly_single
thf(fact_62_offset__poly__single, axiom,
    ((![A3 : complex, H : complex]: ((fundam1201687030omplex @ (pCons_complex @ A3 @ zero_z1746442943omplex) @ H) = (pCons_complex @ A3 @ zero_z1746442943omplex))))). % offset_poly_single
thf(fact_63_pCons__induct, axiom,
    ((![P3 : poly_poly_nat > $o, P : poly_poly_nat]: ((P3 @ zero_z1059985641ly_nat) => ((![A2 : poly_nat, P2 : poly_poly_nat]: (((~ ((A2 = zero_zero_poly_nat))) | (~ ((P2 = zero_z1059985641ly_nat)))) => ((P3 @ P2) => (P3 @ (pCons_poly_nat @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_64_pCons__induct, axiom,
    ((![P3 : poly_p1267267526omplex > $o, P : poly_p1267267526omplex]: ((P3 @ zero_z1200043727omplex) => ((![A2 : poly_poly_complex, P2 : poly_p1267267526omplex]: (((~ ((A2 = zero_z1040703943omplex))) | (~ ((P2 = zero_z1200043727omplex)))) => ((P3 @ P2) => (P3 @ (pCons_1087637536omplex @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_65_pCons__induct, axiom,
    ((![P3 : poly_complex > $o, P : poly_complex]: ((P3 @ zero_z1746442943omplex) => ((![A2 : complex, P2 : poly_complex]: (((~ ((A2 = zero_zero_complex))) | (~ ((P2 = zero_z1746442943omplex)))) => ((P3 @ P2) => (P3 @ (pCons_complex @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_66_pCons__induct, axiom,
    ((![P3 : poly_nat > $o, P : poly_nat]: ((P3 @ zero_zero_poly_nat) => ((![A2 : nat, P2 : poly_nat]: (((~ ((A2 = zero_zero_nat))) | (~ ((P2 = zero_zero_poly_nat)))) => ((P3 @ P2) => (P3 @ (pCons_nat @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_67_pCons__induct, axiom,
    ((![P3 : poly_poly_complex > $o, P : poly_poly_complex]: ((P3 @ zero_z1040703943omplex) => ((![A2 : poly_complex, P2 : poly_poly_complex]: (((~ ((A2 = zero_z1746442943omplex))) | (~ ((P2 = zero_z1040703943omplex)))) => ((P3 @ P2) => (P3 @ (pCons_poly_complex @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_68_fundamental__theorem__of__algebra, axiom,
    ((![P : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra
thf(fact_69_synthetic__div__pCons, axiom,
    ((![A3 : nat, P : poly_nat, C : nat]: ((synthetic_div_nat @ (pCons_nat @ A3 @ P) @ C) = (pCons_nat @ (poly_nat2 @ P @ C) @ (synthetic_div_nat @ P @ C)))))). % synthetic_div_pCons
thf(fact_70_synthetic__div__pCons, axiom,
    ((![A3 : poly_complex, P : poly_poly_complex, C : poly_complex]: ((synthe1985144195omplex @ (pCons_poly_complex @ A3 @ P) @ C) = (pCons_poly_complex @ (poly_poly_complex2 @ P @ C) @ (synthe1985144195omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_71_synthetic__div__pCons, axiom,
    ((![A3 : complex, P : poly_complex, C : complex]: ((synthe151143547omplex @ (pCons_complex @ A3 @ P) @ C) = (pCons_complex @ (poly_complex2 @ P @ C) @ (synthe151143547omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_72_is__zero__null, axiom,
    ((is_zero_complex = (^[P4 : poly_complex]: (P4 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_73_is__zero__null, axiom,
    ((is_zero_nat = (^[P4 : poly_nat]: (P4 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_74_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P4 : poly_poly_complex]: (P4 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_75_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_76_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_77_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_c622223248omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_78_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_79_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_80_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_81_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_82_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_83_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_84_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_85_poly__shift__0, axiom,
    ((![N : nat]: ((poly_s558570093omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_shift_0
thf(fact_86_content__const, axiom,
    ((![C : nat]: ((content_nat @ (pCons_nat @ C @ zero_zero_poly_nat)) = (normal728885956ze_nat @ C))))). % content_const
thf(fact_87_order__root, axiom,
    ((![P : poly_poly_complex, A3 : poly_complex]: (((poly_poly_complex2 @ P @ A3) = zero_z1746442943omplex) = (((P = zero_z1040703943omplex)) | ((~ (((order_poly_complex @ A3 @ P) = zero_zero_nat))))))))). % order_root
thf(fact_88_order__root, axiom,
    ((![P : poly_complex, A3 : complex]: (((poly_complex2 @ P @ A3) = zero_zero_complex) = (((P = zero_z1746442943omplex)) | ((~ (((order_complex @ A3 @ P) = zero_zero_nat))))))))). % order_root
thf(fact_89_order__root, axiom,
    ((![P : poly_p1267267526omplex, A3 : poly_poly_complex]: (((poly_p282434315omplex @ P @ A3) = zero_z1040703943omplex) = (((P = zero_z1200043727omplex)) | ((~ (((order_1735763309omplex @ A3 @ P) = zero_zero_nat))))))))). % order_root
thf(fact_90_reflect__poly__const, axiom,
    ((![A3 : complex]: ((reflect_poly_complex @ (pCons_complex @ A3 @ zero_z1746442943omplex)) = (pCons_complex @ A3 @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_91_reflect__poly__const, axiom,
    ((![A3 : nat]: ((reflect_poly_nat @ (pCons_nat @ A3 @ zero_zero_poly_nat)) = (pCons_nat @ A3 @ zero_zero_poly_nat))))). % reflect_poly_const
thf(fact_92_reflect__poly__const, axiom,
    ((![A3 : poly_complex]: ((reflec309385472omplex @ (pCons_poly_complex @ A3 @ zero_z1040703943omplex)) = (pCons_poly_complex @ A3 @ zero_z1040703943omplex))))). % reflect_poly_const
thf(fact_93_content__dvd, axiom,
    ((![P : poly_nat]: (dvd_dvd_poly_nat @ (pCons_nat @ (content_nat @ P) @ zero_zero_poly_nat) @ P)))). % content_dvd
thf(fact_94_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_95_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_96_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_97_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_98_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_99_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_100_content__dvd__contentI, axiom,
    ((![P : poly_nat, Q : poly_nat]: ((dvd_dvd_poly_nat @ P @ Q) => (dvd_dvd_nat @ (content_nat @ P) @ (content_nat @ Q)))))). % content_dvd_contentI
thf(fact_101_const__poly__dvd__const__poly__iff, axiom,
    ((![A3 : complex, B : complex]: ((dvd_dvd_poly_complex @ (pCons_complex @ A3 @ zero_z1746442943omplex) @ (pCons_complex @ B @ zero_z1746442943omplex)) = (dvd_dvd_complex @ A3 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_102_const__poly__dvd__const__poly__iff, axiom,
    ((![A3 : nat, B : nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ A3 @ zero_zero_poly_nat) @ (pCons_nat @ B @ zero_zero_poly_nat)) = (dvd_dvd_nat @ A3 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_103_const__poly__dvd__const__poly__iff, axiom,
    ((![A3 : poly_complex, B : poly_complex]: ((dvd_dv598755940omplex @ (pCons_poly_complex @ A3 @ zero_z1040703943omplex) @ (pCons_poly_complex @ B @ zero_z1040703943omplex)) = (dvd_dvd_poly_complex @ A3 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_104_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X2 : complex]: (![Y2 : complex]: ((F @ X2) = (F @ Y2)))))))). % constant_def
thf(fact_105_const__poly__dvd__iff__dvd__content, axiom,
    ((![C : nat, P : poly_nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ C @ zero_zero_poly_nat) @ P) = (dvd_dvd_nat @ C @ (content_nat @ P)))))). % const_poly_dvd_iff_dvd_content
thf(fact_106_order__0I, axiom,
    ((![P : poly_poly_complex, A3 : poly_complex]: ((~ (((poly_poly_complex2 @ P @ A3) = zero_z1746442943omplex))) => ((order_poly_complex @ A3 @ P) = zero_zero_nat))))). % order_0I
thf(fact_107_order__0I, axiom,
    ((![P : poly_complex, A3 : complex]: ((~ (((poly_complex2 @ P @ A3) = zero_zero_complex))) => ((order_complex @ A3 @ P) = zero_zero_nat))))). % order_0I
thf(fact_108_order__0I, axiom,
    ((![P : poly_p1267267526omplex, A3 : poly_poly_complex]: ((~ (((poly_p282434315omplex @ P @ A3) = zero_z1040703943omplex))) => ((order_1735763309omplex @ A3 @ P) = zero_zero_nat))))). % order_0I
thf(fact_109_normalize__dvd__iff, axiom,
    ((![A3 : nat, B : nat]: ((dvd_dvd_nat @ (normal728885956ze_nat @ A3) @ B) = (dvd_dvd_nat @ A3 @ B))))). % normalize_dvd_iff
thf(fact_110_dvd__normalize__iff, axiom,
    ((![A3 : nat, B : nat]: ((dvd_dvd_nat @ A3 @ (normal728885956ze_nat @ B)) = (dvd_dvd_nat @ A3 @ B))))). % dvd_normalize_iff
thf(fact_111_lcm_Onormalize__bottom, axiom,
    (((normal728885956ze_nat @ zero_zero_nat) = zero_zero_nat))). % lcm.normalize_bottom
thf(fact_112_normalize__0, axiom,
    (((normal728885956ze_nat @ zero_zero_nat) = zero_zero_nat))). % normalize_0
thf(fact_113_normalize__eq__0__iff, axiom,
    ((![A3 : nat]: (((normal728885956ze_nat @ A3) = zero_zero_nat) = (A3 = zero_zero_nat))))). % normalize_eq_0_iff
thf(fact_114_dvd__0__right, axiom,
    ((![A3 : poly_complex]: (dvd_dvd_poly_complex @ A3 @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_115_dvd__0__right, axiom,
    ((![A3 : complex]: (dvd_dvd_complex @ A3 @ zero_zero_complex)))). % dvd_0_right
thf(fact_116_dvd__0__right, axiom,
    ((![A3 : nat]: (dvd_dvd_nat @ A3 @ zero_zero_nat)))). % dvd_0_right
thf(fact_117_dvd__0__right, axiom,
    ((![A3 : poly_nat]: (dvd_dvd_poly_nat @ A3 @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_118_dvd__0__right, axiom,
    ((![A3 : poly_poly_complex]: (dvd_dv598755940omplex @ A3 @ zero_z1040703943omplex)))). % dvd_0_right
thf(fact_119_dvd__0__left__iff, axiom,
    ((![A3 : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A3) = (A3 = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_120_dvd__0__left__iff, axiom,
    ((![A3 : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A3) = (A3 = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_121_dvd__0__left__iff, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) = (A3 = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_122_dvd__0__left__iff, axiom,
    ((![A3 : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A3) = (A3 = zero_zero_poly_nat))))). % dvd_0_left_iff
thf(fact_123_dvd__0__left__iff, axiom,
    ((![A3 : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A3) = (A3 = zero_z1040703943omplex))))). % dvd_0_left_iff
thf(fact_124_gcd__nat_Oextremum, axiom,
    ((![A3 : nat]: (dvd_dvd_nat @ A3 @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_125_gcd__nat_Oextremum__strict, axiom,
    ((![A3 : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A3) & (~ ((zero_zero_nat = A3))))))))). % gcd_nat.extremum_strict
thf(fact_126_gcd__nat_Oextremum__unique, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) = (A3 = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_127_gcd__nat_Onot__eq__extremum, axiom,
    ((![A3 : nat]: ((~ ((A3 = zero_zero_nat))) = (((dvd_dvd_nat @ A3 @ zero_zero_nat)) & ((~ ((A3 = zero_zero_nat))))))))). % gcd_nat.not_eq_extremum
thf(fact_128_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) => (A3 = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_129_dvd__refl, axiom,
    ((![A3 : nat]: (dvd_dvd_nat @ A3 @ A3)))). % dvd_refl
thf(fact_130_dvd__trans, axiom,
    ((![A3 : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A3 @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A3 @ C)))))). % dvd_trans
thf(fact_131_dvd__0__left, axiom,
    ((![A3 : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A3) => (A3 = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_132_dvd__0__left, axiom,
    ((![A3 : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A3) => (A3 = zero_zero_complex))))). % dvd_0_left
thf(fact_133_dvd__0__left, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) => (A3 = zero_zero_nat))))). % dvd_0_left
thf(fact_134_dvd__0__left, axiom,
    ((![A3 : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A3) => (A3 = zero_zero_poly_nat))))). % dvd_0_left
thf(fact_135_dvd__0__left, axiom,
    ((![A3 : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A3) => (A3 = zero_z1040703943omplex))))). % dvd_0_left
thf(fact_136_associatedI, axiom,
    ((![A3 : nat, B : nat]: ((dvd_dvd_nat @ A3 @ B) => ((dvd_dvd_nat @ B @ A3) => ((normal728885956ze_nat @ A3) = (normal728885956ze_nat @ B))))))). % associatedI
thf(fact_137_associatedD1, axiom,
    ((![A3 : nat, B : nat]: (((normal728885956ze_nat @ A3) = (normal728885956ze_nat @ B)) => (dvd_dvd_nat @ A3 @ B))))). % associatedD1
thf(fact_138_associatedD2, axiom,
    ((![A3 : nat, B : nat]: (((normal728885956ze_nat @ A3) = (normal728885956ze_nat @ B)) => (dvd_dvd_nat @ B @ A3))))). % associatedD2
thf(fact_139_associated__eqI, axiom,
    ((![A3 : nat, B : nat]: ((dvd_dvd_nat @ A3 @ B) => ((dvd_dvd_nat @ B @ A3) => (((normal728885956ze_nat @ A3) = A3) => (((normal728885956ze_nat @ B) = B) => (A3 = B)))))))). % associated_eqI
thf(fact_140_associated__iff__dvd, axiom,
    ((![A3 : nat, B : nat]: (((normal728885956ze_nat @ A3) = (normal728885956ze_nat @ B)) = (((dvd_dvd_nat @ A3 @ B)) & ((dvd_dvd_nat @ B @ A3))))))). % associated_iff_dvd
thf(fact_141_dvd__field__iff, axiom,
    ((dvd_dvd_complex = (^[A4 : complex]: (^[B3 : complex]: (((A4 = zero_zero_complex)) => ((B3 = zero_zero_complex)))))))). % dvd_field_iff
thf(fact_142_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_143_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_144_psize__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((fundam1956464160omplex @ P) = zero_zero_nat) = (P = zero_z1040703943omplex))))). % psize_eq_0_iff
thf(fact_145_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_complex @ N @ one_one_poly_complex) = zero_z1746442943omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_complex @ N @ one_one_poly_complex) = one_one_poly_complex)))))). % poly_cutoff_1
thf(fact_146_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_nat @ N @ one_one_poly_nat) = zero_zero_poly_nat)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_nat @ N @ one_one_poly_nat) = one_one_poly_nat)))))). % poly_cutoff_1
thf(fact_147_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_c622223248omplex @ N @ one_on1331105667omplex) = zero_z1040703943omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_c622223248omplex @ N @ one_on1331105667omplex) = one_on1331105667omplex)))))). % poly_cutoff_1
thf(fact_148_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_149_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_150_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_151_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_152_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_153_is__unit__pCons__iff, axiom,
    ((![A3 : complex, P : poly_complex]: ((dvd_dvd_poly_complex @ (pCons_complex @ A3 @ P) @ one_one_poly_complex) = (((P = zero_z1746442943omplex)) & ((~ ((A3 = zero_zero_complex))))))))). % is_unit_pCons_iff
thf(fact_154_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_155_coeff__0, axiom,
    ((![N : nat]: ((coeff_1429652124omplex @ zero_z1200043727omplex @ N) = zero_z1040703943omplex)))). % coeff_0
thf(fact_156_coeff__0, axiom,
    ((![N : nat]: ((coeff_complex @ zero_z1746442943omplex @ N) = zero_zero_complex)))). % coeff_0
thf(fact_157_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_158_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_complex @ zero_z1040703943omplex @ N) = zero_z1746442943omplex)))). % coeff_0
thf(fact_159_coeff__pCons__0, axiom,
    ((![A3 : complex, P : poly_complex]: ((coeff_complex @ (pCons_complex @ A3 @ P) @ zero_zero_nat) = A3)))). % coeff_pCons_0
thf(fact_160_is__unit__content__iff, axiom,
    ((![P : poly_nat]: ((dvd_dvd_nat @ (content_nat @ P) @ one_one_nat) = ((content_nat @ P) = one_one_nat))))). % is_unit_content_iff
thf(fact_161_poly__1, axiom,
    ((![X : complex]: ((poly_complex2 @ one_one_poly_complex @ X) = one_one_complex)))). % poly_1
thf(fact_162_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_163_poly__1, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ one_on1331105667omplex @ X) = one_one_poly_complex)))). % poly_1
thf(fact_164_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_165_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_166_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_167_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_168_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_169_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_complex = (pCons_complex @ one_one_complex @ zero_z1746442943omplex)))). % one_poly_eq_simps(1)
thf(fact_170_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_nat = (pCons_nat @ one_one_nat @ zero_zero_poly_nat)))). % one_poly_eq_simps(1)
thf(fact_171_one__poly__eq__simps_I1_J, axiom,
    ((one_on1331105667omplex = (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex)))). % one_poly_eq_simps(1)
thf(fact_172_one__poly__eq__simps_I2_J, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % one_poly_eq_simps(2)
thf(fact_173_one__poly__eq__simps_I2_J, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % one_poly_eq_simps(2)
thf(fact_174_one__poly__eq__simps_I2_J, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % one_poly_eq_simps(2)
thf(fact_175_gcd__nat_Onot__eq__order__implies__strict, axiom,
    ((![A3 : nat, B : nat]: ((~ ((A3 = B))) => ((dvd_dvd_nat @ A3 @ B) => ((dvd_dvd_nat @ A3 @ B) & (~ ((A3 = B))))))))). % gcd_nat.not_eq_order_implies_strict
thf(fact_176_gcd__nat_Ostrict__implies__not__eq, axiom,
    ((![A3 : nat, B : nat]: (((dvd_dvd_nat @ A3 @ B) & (~ ((A3 = B)))) => (~ ((A3 = B))))))). % gcd_nat.strict_implies_not_eq
thf(fact_177_gcd__nat_Ostrict__implies__order, axiom,
    ((![A3 : nat, B : nat]: (((dvd_dvd_nat @ A3 @ B) & (~ ((A3 = B)))) => (dvd_dvd_nat @ A3 @ B))))). % gcd_nat.strict_implies_order
thf(fact_178_gcd__nat_Ostrict__iff__order, axiom,
    ((![A3 : nat, B : nat]: ((((dvd_dvd_nat @ A3 @ B)) & ((~ ((A3 = B))))) = (((dvd_dvd_nat @ A3 @ B)) & ((~ ((A3 = B))))))))). % gcd_nat.strict_iff_order
thf(fact_179_gcd__nat_Oorder__iff__strict, axiom,
    ((dvd_dvd_nat = (^[A4 : nat]: (^[B3 : nat]: (((((dvd_dvd_nat @ A4 @ B3)) & ((~ ((A4 = B3)))))) | ((A4 = B3)))))))). % gcd_nat.order_iff_strict
thf(fact_180_gcd__nat_Ostrict__trans2, axiom,
    ((![A3 : nat, B : nat, C : nat]: (((dvd_dvd_nat @ A3 @ B) & (~ ((A3 = B)))) => ((dvd_dvd_nat @ B @ C) => ((dvd_dvd_nat @ A3 @ C) & (~ ((A3 = C))))))))). % gcd_nat.strict_trans2
thf(fact_181_gcd__nat_Ostrict__trans1, axiom,
    ((![A3 : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A3 @ B) => (((dvd_dvd_nat @ B @ C) & (~ ((B = C)))) => ((dvd_dvd_nat @ A3 @ C) & (~ ((A3 = C))))))))). % gcd_nat.strict_trans1
thf(fact_182_gcd__nat_Ostrict__trans, axiom,
    ((![A3 : nat, B : nat, C : nat]: (((dvd_dvd_nat @ A3 @ B) & (~ ((A3 = B)))) => (((dvd_dvd_nat @ B @ C) & (~ ((B = C)))) => ((dvd_dvd_nat @ A3 @ C) & (~ ((A3 = C))))))))). % gcd_nat.strict_trans
thf(fact_183_gcd__nat_Oantisym, axiom,
    ((![A3 : nat, B : nat]: ((dvd_dvd_nat @ A3 @ B) => ((dvd_dvd_nat @ B @ A3) => (A3 = B)))))). % gcd_nat.antisym
thf(fact_184_gcd__nat_Oirrefl, axiom,
    ((![A3 : nat]: (~ (((dvd_dvd_nat @ A3 @ A3) & (~ ((A3 = A3))))))))). % gcd_nat.irrefl
thf(fact_185_gcd__nat_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z2 : nat]: (Y3 = Z2))) = (^[A4 : nat]: (^[B3 : nat]: (((dvd_dvd_nat @ A4 @ B3)) & ((dvd_dvd_nat @ B3 @ A4)))))))). % gcd_nat.eq_iff
thf(fact_186_gcd__nat_Otrans, axiom,
    ((![A3 : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A3 @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A3 @ C)))))). % gcd_nat.trans
thf(fact_187_gcd__nat_Orefl, axiom,
    ((![A3 : nat]: (dvd_dvd_nat @ A3 @ A3)))). % gcd_nat.refl
thf(fact_188_gcd__nat_Oasym, axiom,
    ((![A3 : nat, B : nat]: (((dvd_dvd_nat @ A3 @ B) & (~ ((A3 = B)))) => (~ (((dvd_dvd_nat @ B @ A3) & (~ ((B = A3)))))))))). % gcd_nat.asym
thf(fact_189_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_190_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_191_pCons__one, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % pCons_one
thf(fact_192_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_193_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_194_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_195_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_196_zero__neq__one, axiom,
    ((~ ((zero_z1040703943omplex = one_on1331105667omplex))))). % zero_neq_one
thf(fact_197_one__dvd, axiom,
    ((![A3 : nat]: (dvd_dvd_nat @ one_one_nat @ A3)))). % one_dvd
thf(fact_198_unit__imp__dvd, axiom,
    ((![B : nat, A3 : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ B @ A3))))). % unit_imp_dvd
thf(fact_199_dvd__unit__imp__unit, axiom,
    ((![A3 : nat, B : nat]: ((dvd_dvd_nat @ A3 @ B) => ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ A3 @ one_one_nat)))))). % dvd_unit_imp_unit
thf(fact_200_zero__poly_Orep__eq, axiom,
    (((coeff_poly_nat @ zero_z1059985641ly_nat) = (^[Uu : nat]: zero_zero_poly_nat)))). % zero_poly.rep_eq
thf(fact_201_zero__poly_Orep__eq, axiom,
    (((coeff_1429652124omplex @ zero_z1200043727omplex) = (^[Uu : nat]: zero_z1040703943omplex)))). % zero_poly.rep_eq
thf(fact_202_zero__poly_Orep__eq, axiom,
    (((coeff_complex @ zero_z1746442943omplex) = (^[Uu : nat]: zero_zero_complex)))). % zero_poly.rep_eq
thf(fact_203_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_204_zero__poly_Orep__eq, axiom,
    (((coeff_poly_complex @ zero_z1040703943omplex) = (^[Uu : nat]: zero_z1746442943omplex)))). % zero_poly.rep_eq
thf(fact_205_content__dvd__coeff, axiom,
    ((![P : poly_nat, N : nat]: (dvd_dvd_nat @ (content_nat @ P) @ (coeff_nat @ P @ N))))). % content_dvd_coeff
thf(fact_206_is__unit__polyE, axiom,
    ((![P : poly_complex]: ((dvd_dvd_poly_complex @ P @ one_one_poly_complex) => (~ ((![C2 : complex]: ((P = (pCons_complex @ C2 @ zero_z1746442943omplex)) => (~ ((dvd_dvd_complex @ C2 @ one_one_complex))))))))))). % is_unit_polyE
thf(fact_207_is__unit__polyE, axiom,
    ((![P : poly_nat]: ((dvd_dvd_poly_nat @ P @ one_one_poly_nat) => (~ ((![C2 : nat]: ((P = (pCons_nat @ C2 @ zero_zero_poly_nat)) => (~ ((dvd_dvd_nat @ C2 @ one_one_nat))))))))))). % is_unit_polyE
thf(fact_208_is__unit__polyE, axiom,
    ((![P : poly_poly_complex]: ((dvd_dv598755940omplex @ P @ one_on1331105667omplex) => (~ ((![C2 : poly_complex]: ((P = (pCons_poly_complex @ C2 @ zero_z1040703943omplex)) => (~ ((dvd_dvd_poly_complex @ C2 @ one_one_poly_complex))))))))))). % is_unit_polyE
thf(fact_209_is__unit__poly__iff, axiom,
    ((![P : poly_complex]: ((dvd_dvd_poly_complex @ P @ one_one_poly_complex) = (?[C3 : complex]: (((P = (pCons_complex @ C3 @ zero_z1746442943omplex))) & ((dvd_dvd_complex @ C3 @ one_one_complex)))))))). % is_unit_poly_iff
thf(fact_210_is__unit__poly__iff, axiom,
    ((![P : poly_nat]: ((dvd_dvd_poly_nat @ P @ one_one_poly_nat) = (?[C3 : nat]: (((P = (pCons_nat @ C3 @ zero_zero_poly_nat))) & ((dvd_dvd_nat @ C3 @ one_one_nat)))))))). % is_unit_poly_iff
thf(fact_211_is__unit__poly__iff, axiom,
    ((![P : poly_poly_complex]: ((dvd_dv598755940omplex @ P @ one_on1331105667omplex) = (?[C3 : poly_complex]: (((P = (pCons_poly_complex @ C3 @ zero_z1040703943omplex))) & ((dvd_dvd_poly_complex @ C3 @ one_one_poly_complex)))))))). % is_unit_poly_iff
thf(fact_212_is__unit__const__poly__iff, axiom,
    ((![C : complex]: ((dvd_dvd_poly_complex @ (pCons_complex @ C @ zero_z1746442943omplex) @ one_one_poly_complex) = (dvd_dvd_complex @ C @ one_one_complex))))). % is_unit_const_poly_iff
thf(fact_213_is__unit__const__poly__iff, axiom,
    ((![C : nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ C @ zero_zero_poly_nat) @ one_one_poly_nat) = (dvd_dvd_nat @ C @ one_one_nat))))). % is_unit_const_poly_iff
thf(fact_214_is__unit__const__poly__iff, axiom,
    ((![C : poly_complex]: ((dvd_dv598755940omplex @ (pCons_poly_complex @ C @ zero_z1040703943omplex) @ one_on1331105667omplex) = (dvd_dvd_poly_complex @ C @ one_one_poly_complex))))). % is_unit_const_poly_iff
thf(fact_215_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ one_one_poly_complex))))). % not_is_unit_0
thf(fact_216_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_217_not__is__unit__0, axiom,
    ((~ ((dvd_dv598755940omplex @ zero_z1040703943omplex @ one_on1331105667omplex))))). % not_is_unit_0
thf(fact_218_normalize__idem__imp__is__unit__iff, axiom,
    ((![A3 : nat]: (((normal728885956ze_nat @ A3) = A3) => ((dvd_dvd_nat @ A3 @ one_one_nat) = (A3 = one_one_nat)))))). % normalize_idem_imp_is_unit_iff
thf(fact_219_is__unit__normalize, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ A3 @ one_one_nat) => ((normal728885956ze_nat @ A3) = one_one_nat))))). % is_unit_normalize
thf(fact_220_normalize__1__iff, axiom,
    ((![A3 : nat]: (((normal728885956ze_nat @ A3) = one_one_nat) = (dvd_dvd_nat @ A3 @ one_one_nat))))). % normalize_1_iff
thf(fact_221_associated__unit, axiom,
    ((![A3 : nat, B : nat]: (((normal728885956ze_nat @ A3) = (normal728885956ze_nat @ B)) => ((dvd_dvd_nat @ A3 @ one_one_nat) => (dvd_dvd_nat @ B @ one_one_nat)))))). % associated_unit
thf(fact_222_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_223_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_224_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_225_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_226_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_227_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_complex @ N @ one_one_poly_complex) = one_one_poly_complex)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_complex @ N @ one_one_poly_complex) = zero_z1746442943omplex)))))). % poly_shift_1
thf(fact_228_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_nat @ N @ one_one_poly_nat) = one_one_poly_nat)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_nat @ N @ one_one_poly_nat) = zero_zero_poly_nat)))))). % poly_shift_1
thf(fact_229_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_s558570093omplex @ N @ one_on1331105667omplex) = one_on1331105667omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_s558570093omplex @ N @ one_on1331105667omplex) = zero_z1040703943omplex)))))). % poly_shift_1
thf(fact_230_const__poly__dvd__iff, axiom,
    ((![C : complex, P : poly_complex]: ((dvd_dvd_poly_complex @ (pCons_complex @ C @ zero_z1746442943omplex) @ P) = (![N2 : nat]: (dvd_dvd_complex @ C @ (coeff_complex @ P @ N2))))))). % const_poly_dvd_iff
thf(fact_231_const__poly__dvd__iff, axiom,
    ((![C : nat, P : poly_nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ C @ zero_zero_poly_nat) @ P) = (![N2 : nat]: (dvd_dvd_nat @ C @ (coeff_nat @ P @ N2))))))). % const_poly_dvd_iff
thf(fact_232_const__poly__dvd__iff, axiom,
    ((![C : poly_complex, P : poly_poly_complex]: ((dvd_dv598755940omplex @ (pCons_poly_complex @ C @ zero_z1040703943omplex) @ P) = (![N2 : nat]: (dvd_dvd_poly_complex @ C @ (coeff_poly_complex @ P @ N2))))))). % const_poly_dvd_iff
thf(fact_233_is__unit__triv, axiom,
    ((![A3 : complex]: ((~ ((A3 = zero_zero_complex))) => (dvd_dvd_poly_complex @ (pCons_complex @ A3 @ zero_z1746442943omplex) @ one_one_poly_complex))))). % is_unit_triv
thf(fact_234_content__primitive__part, axiom,
    ((![P : poly_nat]: ((~ ((P = zero_zero_poly_nat))) => ((content_nat @ (primitive_part_nat @ P)) = one_one_nat))))). % content_primitive_part
thf(fact_235_poly__eq__0__iff__dvd, axiom,
    ((![P : poly_poly_complex, C : poly_complex]: (((poly_poly_complex2 @ P @ C) = zero_z1746442943omplex) = (dvd_dv598755940omplex @ (pCons_poly_complex @ (uminus1138659839omplex @ C) @ (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex)) @ P))))). % poly_eq_0_iff_dvd
thf(fact_236_poly__eq__0__iff__dvd, axiom,
    ((![P : poly_complex, C : complex]: (((poly_complex2 @ P @ C) = zero_zero_complex) = (dvd_dvd_poly_complex @ (pCons_complex @ (uminus1204672759omplex @ C) @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ P))))). % poly_eq_0_iff_dvd
thf(fact_237_poly__eq__0__iff__dvd, axiom,
    ((![P : poly_p1267267526omplex, C : poly_poly_complex]: (((poly_p282434315omplex @ P @ C) = zero_z1040703943omplex) = (dvd_dv1870147948omplex @ (pCons_1087637536omplex @ (uminus1762810119omplex @ C) @ (pCons_1087637536omplex @ one_on1331105667omplex @ zero_z1200043727omplex)) @ P))))). % poly_eq_0_iff_dvd
thf(fact_238_add_Oinverse__neutral, axiom,
    (((uminus1138659839omplex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % add.inverse_neutral
thf(fact_239_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_240_add_Oinverse__neutral, axiom,
    (((uminus1762810119omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % add.inverse_neutral
thf(fact_241_neg__0__equal__iff__equal, axiom,
    ((![A3 : poly_complex]: ((zero_z1746442943omplex = (uminus1138659839omplex @ A3)) = (zero_z1746442943omplex = A3))))). % neg_0_equal_iff_equal
thf(fact_242_neg__0__equal__iff__equal, axiom,
    ((![A3 : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A3)) = (zero_zero_complex = A3))))). % neg_0_equal_iff_equal
thf(fact_243_neg__0__equal__iff__equal, axiom,
    ((![A3 : poly_poly_complex]: ((zero_z1040703943omplex = (uminus1762810119omplex @ A3)) = (zero_z1040703943omplex = A3))))). % neg_0_equal_iff_equal
thf(fact_244_neg__equal__0__iff__equal, axiom,
    ((![A3 : poly_complex]: (((uminus1138659839omplex @ A3) = zero_z1746442943omplex) = (A3 = zero_z1746442943omplex))))). % neg_equal_0_iff_equal
thf(fact_245_neg__equal__0__iff__equal, axiom,
    ((![A3 : complex]: (((uminus1204672759omplex @ A3) = zero_zero_complex) = (A3 = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_246_neg__equal__0__iff__equal, axiom,
    ((![A3 : poly_poly_complex]: (((uminus1762810119omplex @ A3) = zero_z1040703943omplex) = (A3 = zero_z1040703943omplex))))). % neg_equal_0_iff_equal

% Conjectures (1)
thf(conj_0, conjecture,
    ((zero_z1746442943omplex = zero_z1746442943omplex))).
