% 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_1188__5379282_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:36:23.956

% 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 (63)
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_Oconstant_001t__Polynomial__Opoly_It__Complex__Ocomplex_J_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam466968762omplex : (poly_complex > poly_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_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Polynomial_Ocontent_001t__Nat__Onat, type,
    content_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Complex__Ocomplex, type,
    degree_complex : poly_complex > nat).
thf(sy_c_Polynomial_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_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__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_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_v_a, type,
    a : complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).

% Relevant facts (245)
thf(fact_0_l, axiom,
    ((~ ((p = zero_z1746442943omplex))))). % l
thf(fact_1__092_060open_062_I_092_060forall_062x_O_Apoly_A_IpCons_Aa_Ap_J_Ax_A_061_A0_A_092_060longrightarrow_062_Apoly_Aq_Ax_A_061_A0_J_A_061_A_IpCons_Aa_Ap_Advd_Aq_A_094_Adegree_A_IpCons_Aa_Ap_J_A_092_060or_062_ApCons_Aa_Ap_A_061_A0_A_092_060and_062_Aq_A_061_A0_J_092_060close_062, axiom,
    (((![X : complex]: ((((poly_complex2 @ (pCons_complex @ a @ p) @ X) = zero_zero_complex)) => (((poly_complex2 @ q @ X) = zero_zero_complex)))) = (((dvd_dvd_poly_complex @ (pCons_complex @ a @ p) @ (power_184595776omplex @ q @ (degree_complex @ (pCons_complex @ a @ p))))) | (((((pCons_complex @ a @ p) = zero_z1746442943omplex)) & ((q = zero_z1746442943omplex)))))))). % \<open>(\<forall>x. poly (pCons a p) x = 0 \<longrightarrow> poly q x = 0) = (pCons a p dvd q ^ degree (pCons a p) \<or> pCons a p = 0 \<and> q = 0)\<close>
thf(fact_2_dp, axiom,
    (((degree_complex @ (pCons_complex @ a @ p)) = (fundam1709708056omplex @ p)))). % dp
thf(fact_3_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_nat]: ((?[X : poly_nat]: ((poly_poly_nat2 @ (pCons_poly_nat @ C @ zero_z1059985641ly_nat) @ X) = zero_zero_poly_nat)) = (C = zero_zero_poly_nat))))). % basic_cqe_conv1(5)
thf(fact_4_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_poly_complex]: ((?[X : poly_poly_complex]: ((poly_p282434315omplex @ (pCons_1087637536omplex @ C @ zero_z1200043727omplex) @ X) = zero_z1040703943omplex)) = (C = zero_z1040703943omplex))))). % basic_cqe_conv1(5)
thf(fact_5_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_complex]: ((?[X : poly_complex]: ((poly_poly_complex2 @ (pCons_poly_complex @ C @ zero_z1040703943omplex) @ X) = zero_z1746442943omplex)) = (C = zero_z1746442943omplex))))). % basic_cqe_conv1(5)
thf(fact_6_basic__cqe__conv1_I5_J, axiom,
    ((![C : nat]: ((?[X : nat]: ((poly_nat2 @ (pCons_nat @ C @ zero_zero_poly_nat) @ X) = zero_zero_nat)) = (C = zero_zero_nat))))). % basic_cqe_conv1(5)
thf(fact_7_basic__cqe__conv1_I5_J, axiom,
    ((![C : complex]: ((?[X : complex]: ((poly_complex2 @ (pCons_complex @ C @ zero_z1746442943omplex) @ X) = zero_zero_complex)) = (C = zero_zero_complex))))). % basic_cqe_conv1(5)
thf(fact_8_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X2) = zero_zero_poly_nat)))). % basic_cqe_conv1(4)
thf(fact_9_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X2) = zero_z1040703943omplex)))). % basic_cqe_conv1(4)
thf(fact_10_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % basic_cqe_conv1(4)
thf(fact_11_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % basic_cqe_conv1(4)
thf(fact_12_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % basic_cqe_conv1(4)
thf(fact_13_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_nat]: ((?[X : poly_nat]: (~ (((poly_poly_nat2 @ (pCons_poly_nat @ C @ zero_z1059985641ly_nat) @ X) = zero_zero_poly_nat)))) = (~ ((C = zero_zero_poly_nat))))))). % basic_cqe_conv1(3)
thf(fact_14_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_poly_complex]: ((?[X : poly_poly_complex]: (~ (((poly_p282434315omplex @ (pCons_1087637536omplex @ C @ zero_z1200043727omplex) @ X) = zero_z1040703943omplex)))) = (~ ((C = zero_z1040703943omplex))))))). % basic_cqe_conv1(3)
thf(fact_15_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_complex]: ((?[X : poly_complex]: (~ (((poly_poly_complex2 @ (pCons_poly_complex @ C @ zero_z1040703943omplex) @ X) = zero_z1746442943omplex)))) = (~ ((C = zero_z1746442943omplex))))))). % basic_cqe_conv1(3)
thf(fact_16_basic__cqe__conv1_I3_J, axiom,
    ((![C : nat]: ((?[X : nat]: (~ (((poly_nat2 @ (pCons_nat @ C @ zero_zero_poly_nat) @ X) = zero_zero_nat)))) = (~ ((C = zero_zero_nat))))))). % basic_cqe_conv1(3)
thf(fact_17_basic__cqe__conv1_I3_J, axiom,
    ((![C : complex]: ((?[X : complex]: (~ (((poly_complex2 @ (pCons_complex @ C @ zero_z1746442943omplex) @ X) = zero_zero_complex)))) = (~ ((C = zero_zero_complex))))))). % basic_cqe_conv1(3)
thf(fact_18_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_nat]: (~ (((poly_poly_nat2 @ zero_z1059985641ly_nat @ X3) = zero_zero_poly_nat)))))))). % basic_cqe_conv1(2)
thf(fact_19_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_poly_complex]: (~ (((poly_p282434315omplex @ zero_z1200043727omplex @ X3) = zero_z1040703943omplex)))))))). % basic_cqe_conv1(2)
thf(fact_20_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_complex]: (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))))))). % basic_cqe_conv1(2)
thf(fact_21_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : nat]: (~ (((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))))))). % basic_cqe_conv1(2)
thf(fact_22_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : complex]: (~ (((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))))))). % basic_cqe_conv1(2)
thf(fact_23_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_poly_nat]: (~ ((?[X3 : poly_nat]: (((poly_poly_nat2 @ P @ X3) = zero_zero_poly_nat) & (~ (((poly_poly_nat2 @ zero_z1059985641ly_nat @ X3) = zero_zero_poly_nat)))))))))). % basic_cqe_conv1(1)
thf(fact_24_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_p1267267526omplex]: (~ ((?[X3 : poly_poly_complex]: (((poly_p282434315omplex @ P @ X3) = zero_z1040703943omplex) & (~ (((poly_p282434315omplex @ zero_z1200043727omplex @ X3) = zero_z1040703943omplex)))))))))). % basic_cqe_conv1(1)
thf(fact_25_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_complex]: (~ ((?[X3 : complex]: (((poly_complex2 @ P @ X3) = zero_zero_complex) & (~ (((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))))))))). % basic_cqe_conv1(1)
thf(fact_26_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_poly_complex]: (~ ((?[X3 : poly_complex]: (((poly_poly_complex2 @ P @ X3) = zero_z1746442943omplex) & (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))))))))). % basic_cqe_conv1(1)
thf(fact_27_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_nat]: (~ ((?[X3 : nat]: (((poly_nat2 @ P @ X3) = zero_zero_nat) & (~ (((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))))))))). % basic_cqe_conv1(1)
thf(fact_28_mpoly__base__conv_I1_J, axiom,
    ((![X4 : poly_poly_complex]: (zero_z1040703943omplex = (poly_p282434315omplex @ zero_z1200043727omplex @ X4))))). % mpoly_base_conv(1)
thf(fact_29_mpoly__base__conv_I1_J, axiom,
    ((![X4 : complex]: (zero_zero_complex = (poly_complex2 @ zero_z1746442943omplex @ X4))))). % mpoly_base_conv(1)
thf(fact_30_mpoly__base__conv_I1_J, axiom,
    ((![X4 : poly_complex]: (zero_z1746442943omplex = (poly_poly_complex2 @ zero_z1040703943omplex @ X4))))). % mpoly_base_conv(1)
thf(fact_31_mpoly__norm__conv_I1_J, axiom,
    ((![X4 : poly_poly_complex]: ((poly_p282434315omplex @ (pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) @ X4) = (poly_p282434315omplex @ zero_z1200043727omplex @ X4))))). % mpoly_norm_conv(1)
thf(fact_32_mpoly__norm__conv_I1_J, axiom,
    ((![X4 : complex]: ((poly_complex2 @ (pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) @ X4) = (poly_complex2 @ zero_z1746442943omplex @ X4))))). % mpoly_norm_conv(1)
thf(fact_33_mpoly__norm__conv_I1_J, axiom,
    ((![X4 : poly_complex]: ((poly_poly_complex2 @ (pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) @ X4) = (poly_poly_complex2 @ zero_z1040703943omplex @ X4))))). % mpoly_norm_conv(1)
thf(fact_34_poly__pad__rule, axiom,
    ((![P : poly_complex, X4 : complex]: (((poly_complex2 @ P @ X4) = zero_zero_complex) => ((poly_complex2 @ (pCons_complex @ zero_zero_complex @ P) @ X4) = zero_zero_complex))))). % poly_pad_rule
thf(fact_35_poly__pad__rule, axiom,
    ((![P : poly_poly_complex, X4 : poly_complex]: (((poly_poly_complex2 @ P @ X4) = zero_z1746442943omplex) => ((poly_poly_complex2 @ (pCons_poly_complex @ zero_z1746442943omplex @ P) @ X4) = zero_z1746442943omplex))))). % poly_pad_rule
thf(fact_36_poly__pad__rule, axiom,
    ((![P : poly_nat, X4 : nat]: (((poly_nat2 @ P @ X4) = zero_zero_nat) => ((poly_nat2 @ (pCons_nat @ zero_zero_nat @ P) @ X4) = zero_zero_nat))))). % poly_pad_rule
thf(fact_37_poly__pad__rule, axiom,
    ((![P : poly_poly_nat, X4 : poly_nat]: (((poly_poly_nat2 @ P @ X4) = zero_zero_poly_nat) => ((poly_poly_nat2 @ (pCons_poly_nat @ zero_zero_poly_nat @ P) @ X4) = zero_zero_poly_nat))))). % poly_pad_rule
thf(fact_38_poly__pad__rule, axiom,
    ((![P : poly_p1267267526omplex, X4 : poly_poly_complex]: (((poly_p282434315omplex @ P @ X4) = zero_z1040703943omplex) => ((poly_p282434315omplex @ (pCons_1087637536omplex @ zero_z1040703943omplex @ P) @ X4) = zero_z1040703943omplex))))). % poly_pad_rule
thf(fact_39_poly__divides__pad__rule, axiom,
    ((![P : poly_complex, Q : poly_complex]: ((dvd_dvd_poly_complex @ P @ Q) => (dvd_dvd_poly_complex @ P @ (pCons_complex @ zero_zero_complex @ Q)))))). % poly_divides_pad_rule
thf(fact_40_poly__divides__pad__rule, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex]: ((dvd_dv598755940omplex @ P @ Q) => (dvd_dv598755940omplex @ P @ (pCons_poly_complex @ zero_z1746442943omplex @ Q)))))). % poly_divides_pad_rule
thf(fact_41_poly__divides__pad__rule, axiom,
    ((![P : poly_p1267267526omplex, Q : poly_p1267267526omplex]: ((dvd_dv1870147948omplex @ P @ Q) => (dvd_dv1870147948omplex @ P @ (pCons_1087637536omplex @ zero_z1040703943omplex @ Q)))))). % poly_divides_pad_rule
thf(fact_42_poly__power, axiom,
    ((![P : poly_poly_complex, N : nat, X4 : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P @ N) @ X4) = (power_184595776omplex @ (poly_poly_complex2 @ P @ X4) @ N))))). % poly_power
thf(fact_43_poly__power, axiom,
    ((![P : poly_nat, N : nat, X4 : nat]: ((poly_nat2 @ (power_power_poly_nat @ P @ N) @ X4) = (power_power_nat @ (poly_nat2 @ P @ X4) @ N))))). % poly_power
thf(fact_44_poly__power, axiom,
    ((![P : poly_complex, N : nat, X4 : complex]: ((poly_complex2 @ (power_184595776omplex @ P @ N) @ X4) = (power_power_complex @ (poly_complex2 @ P @ X4) @ N))))). % poly_power
thf(fact_45_basic__cqe__conv2, axiom,
    ((![P : poly_complex, A : complex, B : complex]: ((~ ((P = zero_z1746442943omplex))) => (?[X2 : complex]: ((poly_complex2 @ (pCons_complex @ A @ (pCons_complex @ B @ P)) @ X2) = zero_zero_complex)))))). % basic_cqe_conv2
thf(fact_46_fundamental__theorem__of__algebra__alt, axiom,
    ((![P : poly_complex]: ((~ ((?[A2 : complex, L : poly_complex]: ((~ ((A2 = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (P = (pCons_complex @ A2 @ L))))))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra_alt
thf(fact_47_poly__0, axiom,
    ((![X4 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X4) = zero_zero_poly_nat)))). % poly_0
thf(fact_48_poly__0, axiom,
    ((![X4 : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X4) = zero_z1040703943omplex)))). % poly_0
thf(fact_49_poly__0, axiom,
    ((![X4 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X4) = zero_zero_complex)))). % poly_0
thf(fact_50_poly__0, axiom,
    ((![X4 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X4) = zero_zero_nat)))). % poly_0
thf(fact_51_poly__0, axiom,
    ((![X4 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X4) = zero_z1746442943omplex)))). % poly_0
thf(fact_52_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_53_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_54_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_55_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_56_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_57_pCons__eq__0__iff, axiom,
    ((![A : poly_nat, P : poly_poly_nat]: (((pCons_poly_nat @ A @ P) = zero_z1059985641ly_nat) = (((A = zero_zero_poly_nat)) & ((P = zero_z1059985641ly_nat))))))). % pCons_eq_0_iff
thf(fact_58_pCons__eq__0__iff, axiom,
    ((![A : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A @ P) = zero_z1200043727omplex) = (((A = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_59_pCons__eq__0__iff, axiom,
    ((![A : complex, P : poly_complex]: (((pCons_complex @ A @ P) = zero_z1746442943omplex) = (((A = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_60_pCons__eq__0__iff, axiom,
    ((![A : nat, P : poly_nat]: (((pCons_nat @ A @ P) = zero_zero_poly_nat) = (((A = zero_zero_nat)) & ((P = zero_zero_poly_nat))))))). % pCons_eq_0_iff
thf(fact_61_pCons__eq__0__iff, axiom,
    ((![A : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A @ P) = zero_z1040703943omplex) = (((A = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_62_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_63_dvd__0__right, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_64_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_65_dvd__0__right, axiom,
    ((![A : poly_nat]: (dvd_dvd_poly_nat @ A @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_66_dvd__0__right, axiom,
    ((![A : poly_poly_complex]: (dvd_dv598755940omplex @ A @ zero_z1040703943omplex)))). % dvd_0_right
thf(fact_67_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_68_dvd__0__left__iff, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) = (A = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_69_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_70_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_71_dvd__0__left__iff, axiom,
    ((![A : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A) = (A = zero_z1040703943omplex))))). % dvd_0_left_iff
thf(fact_72_nullstellensatz__univariate, axiom,
    ((![P : poly_complex, Q : poly_complex]: ((![X : complex]: ((((poly_complex2 @ P @ X) = zero_zero_complex)) => (((poly_complex2 @ Q @ X) = zero_zero_complex)))) = (((dvd_dvd_poly_complex @ P @ (power_184595776omplex @ Q @ (degree_complex @ P)))) | ((((P = zero_z1746442943omplex)) & ((Q = zero_z1746442943omplex))))))))). % nullstellensatz_univariate
thf(fact_73_basic__cqe__conv__2b, axiom,
    ((![P : poly_complex]: ((?[X : complex]: (~ (((poly_complex2 @ P @ X) = zero_zero_complex)))) = (~ ((P = zero_z1746442943omplex))))))). % basic_cqe_conv_2b
thf(fact_74_mpoly__base__conv_I2_J, axiom,
    ((![C : complex, X4 : complex]: (C = (poly_complex2 @ (pCons_complex @ C @ zero_z1746442943omplex) @ X4))))). % mpoly_base_conv(2)
thf(fact_75_mpoly__base__conv_I2_J, axiom,
    ((![C : poly_complex, X4 : poly_complex]: (C = (poly_poly_complex2 @ (pCons_poly_complex @ C @ zero_z1040703943omplex) @ X4))))). % mpoly_base_conv(2)
thf(fact_76_mpoly__norm__conv_I2_J, axiom,
    ((![Y : complex, X4 : complex]: ((poly_complex2 @ (pCons_complex @ (poly_complex2 @ zero_z1746442943omplex @ Y) @ zero_z1746442943omplex) @ X4) = (poly_complex2 @ zero_z1746442943omplex @ X4))))). % mpoly_norm_conv(2)
thf(fact_77_mpoly__norm__conv_I2_J, axiom,
    ((![Y : poly_complex, X4 : poly_complex]: ((poly_poly_complex2 @ (pCons_poly_complex @ (poly_poly_complex2 @ zero_z1040703943omplex @ Y) @ zero_z1040703943omplex) @ X4) = (poly_poly_complex2 @ zero_z1040703943omplex @ X4))))). % mpoly_norm_conv(2)
thf(fact_78_pCons__eq__iff, axiom,
    ((![A : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A @ P) = (pCons_complex @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_79_pCons__eq__iff, axiom,
    ((![A : nat, P : poly_nat, B : nat, Q : poly_nat]: (((pCons_nat @ A @ P) = (pCons_nat @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_80_pCons__eq__iff, axiom,
    ((![A : poly_complex, P : poly_poly_complex, B : poly_complex, Q : poly_poly_complex]: (((pCons_poly_complex @ A @ P) = (pCons_poly_complex @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_81_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_82_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_83_degree__0, axiom,
    (((degree_poly_complex @ zero_z1040703943omplex) = zero_zero_nat))). % degree_0
thf(fact_84_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_85_psize__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((fundam1956464160omplex @ P) = zero_zero_nat) = (P = zero_z1040703943omplex))))). % psize_eq_0_iff
thf(fact_86_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_87_const__poly__dvd__const__poly__iff, axiom,
    ((![A : complex, B : complex]: ((dvd_dvd_poly_complex @ (pCons_complex @ A @ zero_z1746442943omplex) @ (pCons_complex @ B @ zero_z1746442943omplex)) = (dvd_dvd_complex @ A @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_88_const__poly__dvd__const__poly__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ A @ zero_zero_poly_nat) @ (pCons_nat @ B @ zero_zero_poly_nat)) = (dvd_dvd_nat @ A @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_89_const__poly__dvd__const__poly__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: ((dvd_dv598755940omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex) @ (pCons_poly_complex @ B @ zero_z1040703943omplex)) = (dvd_dvd_poly_complex @ A @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_90_degree__eq__zeroE, axiom,
    ((![P : poly_complex]: (((degree_complex @ P) = zero_zero_nat) => (~ ((![A2 : complex]: (~ ((P = (pCons_complex @ A2 @ zero_z1746442943omplex))))))))))). % degree_eq_zeroE
thf(fact_91_degree__eq__zeroE, axiom,
    ((![P : poly_nat]: (((degree_nat @ P) = zero_zero_nat) => (~ ((![A2 : nat]: (~ ((P = (pCons_nat @ A2 @ zero_zero_poly_nat))))))))))). % degree_eq_zeroE
thf(fact_92_degree__eq__zeroE, axiom,
    ((![P : poly_poly_complex]: (((degree_poly_complex @ P) = zero_zero_nat) => (~ ((![A2 : poly_complex]: (~ ((P = (pCons_poly_complex @ A2 @ zero_z1040703943omplex))))))))))). % degree_eq_zeroE
thf(fact_93_degree__pCons__0, axiom,
    ((![A : complex]: ((degree_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_94_degree__pCons__0, axiom,
    ((![A : nat]: ((degree_nat @ (pCons_nat @ A @ zero_zero_poly_nat)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_95_degree__pCons__0, axiom,
    ((![A : poly_complex]: ((degree_poly_complex @ (pCons_poly_complex @ A @ zero_z1040703943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_96_pderiv_Oinduct, axiom,
    ((![P2 : poly_complex > $o, A0 : poly_complex]: ((![A2 : complex, P3 : poly_complex]: (((~ ((P3 = zero_z1746442943omplex))) => (P2 @ P3)) => (P2 @ (pCons_complex @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_97_pderiv_Oinduct, axiom,
    ((![P2 : poly_nat > $o, A0 : poly_nat]: ((![A2 : nat, P3 : poly_nat]: (((~ ((P3 = zero_zero_poly_nat))) => (P2 @ P3)) => (P2 @ (pCons_nat @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_98_pderiv_Oinduct, axiom,
    ((![P2 : poly_poly_complex > $o, A0 : poly_poly_complex]: ((![A2 : poly_complex, P3 : poly_poly_complex]: (((~ ((P3 = zero_z1040703943omplex))) => (P2 @ P3)) => (P2 @ (pCons_poly_complex @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_99_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_complex > $o, P : poly_complex, Q : poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A2 : complex, P3 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A2 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_100_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_nat > $o, P : poly_complex, Q : poly_nat]: ((P2 @ zero_z1746442943omplex @ zero_zero_poly_nat) => ((![A2 : complex, P3 : poly_complex, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_101_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_poly_complex > $o, P : poly_complex, Q : poly_poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1040703943omplex) => ((![A2 : complex, P3 : poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A2 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_102_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_complex > $o, P : poly_nat, Q : poly_complex]: ((P2 @ zero_zero_poly_nat @ zero_z1746442943omplex) => ((![A2 : nat, P3 : poly_nat, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_103_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_nat > $o, P : poly_nat, Q : poly_nat]: ((P2 @ zero_zero_poly_nat @ zero_zero_poly_nat) => ((![A2 : nat, P3 : poly_nat, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_104_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_poly_complex > $o, P : poly_nat, Q : poly_poly_complex]: ((P2 @ zero_zero_poly_nat @ zero_z1040703943omplex) => ((![A2 : nat, P3 : poly_nat, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_105_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_complex > $o, P : poly_poly_complex, Q : poly_complex]: ((P2 @ zero_z1040703943omplex @ zero_z1746442943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A2 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_106_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_nat > $o, P : poly_poly_complex, Q : poly_nat]: ((P2 @ zero_z1040703943omplex @ zero_zero_poly_nat) => ((![A2 : poly_complex, P3 : poly_poly_complex, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_107_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_poly_complex > $o, P : poly_poly_complex, Q : poly_poly_complex]: ((P2 @ zero_z1040703943omplex @ zero_z1040703943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A2 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_108_dvd__trans, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((dvd_dvd_poly_complex @ B @ C) => (dvd_dvd_poly_complex @ A @ C)))))). % dvd_trans
thf(fact_109_dvd__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A @ C)))))). % dvd_trans
thf(fact_110_dvd__refl, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ A)))). % dvd_refl
thf(fact_111_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_112_pderiv_Ocases, axiom,
    ((![X4 : poly_complex]: (~ ((![A2 : complex, P3 : poly_complex]: (~ ((X4 = (pCons_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_113_pderiv_Ocases, axiom,
    ((![X4 : poly_nat]: (~ ((![A2 : nat, P3 : poly_nat]: (~ ((X4 = (pCons_nat @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_114_pderiv_Ocases, axiom,
    ((![X4 : poly_poly_complex]: (~ ((![A2 : poly_complex, P3 : poly_poly_complex]: (~ ((X4 = (pCons_poly_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_115_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A2 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_116_pCons__cases, axiom,
    ((![P : poly_nat]: (~ ((![A2 : nat, Q2 : poly_nat]: (~ ((P = (pCons_nat @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_117_pCons__cases, axiom,
    ((![P : poly_poly_complex]: (~ ((![A2 : poly_complex, Q2 : poly_poly_complex]: (~ ((P = (pCons_poly_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_118_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_119_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_120_nullstellensatz__lemma, axiom,
    ((![P : poly_complex, Q : poly_complex, N : nat]: ((![X2 : complex]: (((poly_complex2 @ P @ X2) = zero_zero_complex) => ((poly_complex2 @ Q @ X2) = zero_zero_complex))) => (((degree_complex @ P) = N) => ((~ ((N = zero_zero_nat))) => (dvd_dvd_poly_complex @ P @ (power_184595776omplex @ Q @ N)))))))). % nullstellensatz_lemma
thf(fact_121_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_122_dvd__0__left, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) => (A = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_123_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_124_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_125_dvd__0__left, axiom,
    ((![A : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A) => (A = zero_z1040703943omplex))))). % dvd_0_left
thf(fact_126_pCons__induct, axiom,
    ((![P2 : poly_poly_nat > $o, P : poly_poly_nat]: ((P2 @ zero_z1059985641ly_nat) => ((![A2 : poly_nat, P3 : poly_poly_nat]: (((~ ((A2 = zero_zero_poly_nat))) | (~ ((P3 = zero_z1059985641ly_nat)))) => ((P2 @ P3) => (P2 @ (pCons_poly_nat @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_127_pCons__induct, axiom,
    ((![P2 : poly_p1267267526omplex > $o, P : poly_p1267267526omplex]: ((P2 @ zero_z1200043727omplex) => ((![A2 : poly_poly_complex, P3 : poly_p1267267526omplex]: (((~ ((A2 = zero_z1040703943omplex))) | (~ ((P3 = zero_z1200043727omplex)))) => ((P2 @ P3) => (P2 @ (pCons_1087637536omplex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_128_pCons__induct, axiom,
    ((![P2 : poly_complex > $o, P : poly_complex]: ((P2 @ zero_z1746442943omplex) => ((![A2 : complex, P3 : poly_complex]: (((~ ((A2 = zero_zero_complex))) | (~ ((P3 = zero_z1746442943omplex)))) => ((P2 @ P3) => (P2 @ (pCons_complex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_129_pCons__induct, axiom,
    ((![P2 : poly_nat > $o, P : poly_nat]: ((P2 @ zero_zero_poly_nat) => ((![A2 : nat, P3 : poly_nat]: (((~ ((A2 = zero_zero_nat))) | (~ ((P3 = zero_zero_poly_nat)))) => ((P2 @ P3) => (P2 @ (pCons_nat @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_130_pCons__induct, axiom,
    ((![P2 : poly_poly_complex > $o, P : poly_poly_complex]: ((P2 @ zero_z1040703943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex]: (((~ ((A2 = zero_z1746442943omplex))) | (~ ((P3 = zero_z1040703943omplex)))) => ((P2 @ P3) => (P2 @ (pCons_poly_complex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_131_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X : complex]: ((poly_complex2 @ P @ X) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_132_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X : poly_complex]: ((poly_poly_complex2 @ P @ X) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_133_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X : poly_poly_complex]: ((poly_p282434315omplex @ P @ X) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_134_dvd__power__same, axiom,
    ((![X4 : poly_complex, Y : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X4 @ Y) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X4 @ N) @ (power_184595776omplex @ Y @ N)))))). % dvd_power_same
thf(fact_135_dvd__power__same, axiom,
    ((![X4 : nat, Y : nat, N : nat]: ((dvd_dvd_nat @ X4 @ Y) => (dvd_dvd_nat @ (power_power_nat @ X4 @ N) @ (power_power_nat @ Y @ N)))))). % dvd_power_same
thf(fact_136_dvd__field__iff, axiom,
    ((dvd_dvd_complex = (^[A3 : complex]: (^[B3 : complex]: (((A3 = zero_zero_complex)) => ((B3 = zero_zero_complex)))))))). % dvd_field_iff
thf(fact_137_power__not__zero, axiom,
    ((![A : complex, N : nat]: ((~ ((A = zero_zero_complex))) => (~ (((power_power_complex @ A @ N) = zero_zero_complex))))))). % power_not_zero
thf(fact_138_power__not__zero, axiom,
    ((![A : poly_nat, N : nat]: ((~ ((A = zero_zero_poly_nat))) => (~ (((power_power_poly_nat @ A @ N) = zero_zero_poly_nat))))))). % power_not_zero
thf(fact_139_power__not__zero, axiom,
    ((![A : poly_poly_complex, N : nat]: ((~ ((A = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A @ N) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_140_power__not__zero, axiom,
    ((![A : poly_complex, N : nat]: ((~ ((A = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_141_power__not__zero, axiom,
    ((![A : nat, N : nat]: ((~ ((A = zero_zero_nat))) => (~ (((power_power_nat @ A @ N) = zero_zero_nat))))))). % power_not_zero
thf(fact_142_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_143_constant__degree, axiom,
    ((![P : poly_poly_complex]: ((fundam466968762omplex @ (poly_poly_complex2 @ P)) = ((degree_poly_complex @ P) = zero_zero_nat))))). % constant_degree
thf(fact_144_constant__degree, axiom,
    ((![P : poly_complex]: ((fundam1158420650omplex @ (poly_complex2 @ P)) = ((degree_complex @ P) = zero_zero_nat))))). % constant_degree
thf(fact_145_synthetic__div__pCons, axiom,
    ((![A : complex, P : poly_complex, C : complex]: ((synthe151143547omplex @ (pCons_complex @ A @ P) @ C) = (pCons_complex @ (poly_complex2 @ P @ C) @ (synthe151143547omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_146_synthetic__div__pCons, axiom,
    ((![A : nat, P : poly_nat, C : nat]: ((synthetic_div_nat @ (pCons_nat @ A @ P) @ C) = (pCons_nat @ (poly_nat2 @ P @ C) @ (synthetic_div_nat @ P @ C)))))). % synthetic_div_pCons
thf(fact_147_synthetic__div__pCons, axiom,
    ((![A : poly_complex, P : poly_poly_complex, C : poly_complex]: ((synthe1985144195omplex @ (pCons_poly_complex @ A @ P) @ C) = (pCons_poly_complex @ (poly_poly_complex2 @ P @ C) @ (synthe1985144195omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_148_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_149_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_150_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_151_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_152_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_153_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_154_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_155_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X : complex]: (![Y2 : complex]: ((F @ X) = (F @ Y2)))))))). % constant_def
thf(fact_156_zero__reorient, axiom,
    ((![X4 : complex]: ((zero_zero_complex = X4) = (X4 = zero_zero_complex))))). % zero_reorient
thf(fact_157_zero__reorient, axiom,
    ((![X4 : poly_complex]: ((zero_z1746442943omplex = X4) = (X4 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_158_zero__reorient, axiom,
    ((![X4 : nat]: ((zero_zero_nat = X4) = (X4 = zero_zero_nat))))). % zero_reorient
thf(fact_159_zero__reorient, axiom,
    ((![X4 : poly_nat]: ((zero_zero_poly_nat = X4) = (X4 = zero_zero_poly_nat))))). % zero_reorient
thf(fact_160_zero__reorient, axiom,
    ((![X4 : poly_poly_complex]: ((zero_z1040703943omplex = X4) = (X4 = zero_z1040703943omplex))))). % zero_reorient
thf(fact_161_content__dvd, axiom,
    ((![P : poly_nat]: (dvd_dvd_poly_nat @ (pCons_nat @ (content_nat @ P) @ zero_zero_poly_nat) @ P)))). % content_dvd
thf(fact_162_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_163_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_164_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_165_degree__pCons__eq__if, axiom,
    ((![P : poly_complex, A : complex]: (((P = zero_z1746442943omplex) => ((degree_complex @ (pCons_complex @ A @ P)) = zero_zero_nat)) & ((~ ((P = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A @ P)) = (suc @ (degree_complex @ P)))))))). % degree_pCons_eq_if
thf(fact_166_degree__pCons__eq__if, axiom,
    ((![P : poly_nat, A : nat]: (((P = zero_zero_poly_nat) => ((degree_nat @ (pCons_nat @ A @ P)) = zero_zero_nat)) & ((~ ((P = zero_zero_poly_nat))) => ((degree_nat @ (pCons_nat @ A @ P)) = (suc @ (degree_nat @ P)))))))). % degree_pCons_eq_if
thf(fact_167_degree__pCons__eq__if, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: (((P = zero_z1040703943omplex) => ((degree_poly_complex @ (pCons_poly_complex @ A @ P)) = zero_zero_nat)) & ((~ ((P = zero_z1040703943omplex))) => ((degree_poly_complex @ (pCons_poly_complex @ A @ P)) = (suc @ (degree_poly_complex @ P)))))))). % degree_pCons_eq_if
thf(fact_168_is__zero__null, axiom,
    ((is_zero_complex = (^[P4 : poly_complex]: (P4 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_169_is__zero__null, axiom,
    ((is_zero_nat = (^[P4 : poly_nat]: (P4 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_170_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P4 : poly_poly_complex]: (P4 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_171_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_172_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_173_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_c622223248omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_174_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_175_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_176_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_177_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_178_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_179_order__root, axiom,
    ((![P : poly_complex, A : complex]: (((poly_complex2 @ P @ A) = zero_zero_complex) = (((P = zero_z1746442943omplex)) | ((~ (((order_complex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_180_order__root, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: (((poly_poly_complex2 @ P @ A) = zero_z1746442943omplex) = (((P = zero_z1040703943omplex)) | ((~ (((order_poly_complex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_181_order__root, axiom,
    ((![P : poly_p1267267526omplex, A : poly_poly_complex]: (((poly_p282434315omplex @ P @ A) = zero_z1040703943omplex) = (((P = zero_z1200043727omplex)) | ((~ (((order_1735763309omplex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_182_degree__linear__power, axiom,
    ((![A : nat, N : nat]: ((degree_nat @ (power_power_poly_nat @ (pCons_nat @ A @ (pCons_nat @ one_one_nat @ zero_zero_poly_nat)) @ N)) = N)))). % degree_linear_power
thf(fact_183_degree__linear__power, axiom,
    ((![A : poly_complex, N : nat]: ((degree_poly_complex @ (power_432682568omplex @ (pCons_poly_complex @ A @ (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex)) @ N)) = N)))). % degree_linear_power
thf(fact_184_degree__linear__power, axiom,
    ((![A : complex, N : nat]: ((degree_complex @ (power_184595776omplex @ (pCons_complex @ A @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ N)) = N)))). % degree_linear_power
thf(fact_185_power__one__right, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_186_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_187_power__one, axiom,
    ((![N : nat]: ((power_184595776omplex @ one_one_poly_complex @ N) = one_one_poly_complex)))). % power_one
thf(fact_188_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_189_nat__power__eq__Suc__0__iff, axiom,
    ((![X4 : nat, M : nat]: (((power_power_nat @ X4 @ M) = (suc @ zero_zero_nat)) = (((M = zero_zero_nat)) | ((X4 = (suc @ zero_zero_nat)))))))). % nat_power_eq_Suc_0_iff
thf(fact_190_power__Suc__0, axiom,
    ((![N : nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ N) = (suc @ zero_zero_nat))))). % power_Suc_0
thf(fact_191_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_192_poly__1, axiom,
    ((![X4 : complex]: ((poly_complex2 @ one_one_poly_complex @ X4) = one_one_complex)))). % poly_1
thf(fact_193_poly__1, axiom,
    ((![X4 : poly_complex]: ((poly_poly_complex2 @ one_on1331105667omplex @ X4) = one_one_poly_complex)))). % poly_1
thf(fact_194_poly__1, axiom,
    ((![X4 : nat]: ((poly_nat2 @ one_one_poly_nat @ X4) = one_one_nat)))). % poly_1
thf(fact_195_content__1, axiom,
    (((content_nat @ one_one_poly_nat) = one_one_nat))). % content_1
thf(fact_196_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_197_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_198_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_199_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_complex @ zero_zero_complex @ (suc @ N)) = zero_zero_complex)))). % power_0_Suc
thf(fact_200_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_poly_nat @ zero_zero_poly_nat @ (suc @ N)) = zero_zero_poly_nat)))). % power_0_Suc
thf(fact_201_power__0__Suc, axiom,
    ((![N : nat]: ((power_432682568omplex @ zero_z1040703943omplex @ (suc @ N)) = zero_z1040703943omplex)))). % power_0_Suc
thf(fact_202_power__0__Suc, axiom,
    ((![N : nat]: ((power_184595776omplex @ zero_z1746442943omplex @ (suc @ N)) = zero_z1746442943omplex)))). % power_0_Suc
thf(fact_203_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_nat @ zero_zero_nat @ (suc @ N)) = zero_zero_nat)))). % power_0_Suc
thf(fact_204_power__Suc0__right, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_205_power__Suc0__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_206_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_207_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_208_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_209_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_210_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_211_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_212_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_213_reflect__poly__const, axiom,
    ((![A : complex]: ((reflect_poly_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = (pCons_complex @ A @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_214_reflect__poly__const, axiom,
    ((![A : nat]: ((reflect_poly_nat @ (pCons_nat @ A @ zero_zero_poly_nat)) = (pCons_nat @ A @ zero_zero_poly_nat))))). % reflect_poly_const
thf(fact_215_reflect__poly__const, axiom,
    ((![A : poly_complex]: ((reflec309385472omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex)) = (pCons_poly_complex @ A @ zero_z1040703943omplex))))). % reflect_poly_const
thf(fact_216_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_217_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_218_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_219_one__reorient, axiom,
    ((![X4 : nat]: ((one_one_nat = X4) = (X4 = one_one_nat))))). % one_reorient
thf(fact_220_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_221_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_222_pCons__one, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % pCons_one
thf(fact_223_dvd__1__left, axiom,
    ((![K : nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ K)))). % dvd_1_left
thf(fact_224_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_225_nat_Oinject, axiom,
    ((![X22 : nat, Y22 : nat]: (((suc @ X22) = (suc @ Y22)) = (X22 = Y22))))). % nat.inject
thf(fact_226_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_227_nat__dvd__1__iff__1, axiom,
    ((![M : nat]: ((dvd_dvd_nat @ M @ one_one_nat) = (M = one_one_nat))))). % nat_dvd_1_iff_1
thf(fact_228_dvd__antisym, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_nat @ M @ N) => ((dvd_dvd_nat @ N @ M) => (M = N)))))). % dvd_antisym
thf(fact_229_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_230_Suc__inject, axiom,
    ((![X4 : nat, Y : nat]: (((suc @ X4) = (suc @ Y)) => (X4 = Y))))). % Suc_inject
thf(fact_231_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M2 : nat]: (N = (suc @ M2))))))). % not0_implies_Suc
thf(fact_232_old_Onat_Oinducts, axiom,
    ((![P2 : nat > $o, Nat : nat]: ((P2 @ zero_zero_nat) => ((![Nat3 : nat]: ((P2 @ Nat3) => (P2 @ (suc @ Nat3)))) => (P2 @ Nat)))))). % old.nat.inducts
thf(fact_233_old_Onat_Oexhaust, axiom,
    ((![Y : nat]: ((~ ((Y = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_234_Zero__not__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_not_Suc
thf(fact_235_Zero__neq__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_neq_Suc
thf(fact_236_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_237_zero__induct, axiom,
    ((![P2 : nat > $o, K : nat]: ((P2 @ K) => ((![N2 : nat]: ((P2 @ (suc @ N2)) => (P2 @ N2))) => (P2 @ zero_zero_nat)))))). % zero_induct
thf(fact_238_diff__induct, axiom,
    ((![P2 : nat > nat > $o, M : nat, N : nat]: ((![X2 : nat]: (P2 @ X2 @ zero_zero_nat)) => ((![Y3 : nat]: (P2 @ zero_zero_nat @ (suc @ Y3))) => ((![X2 : nat, Y3 : nat]: ((P2 @ X2 @ Y3) => (P2 @ (suc @ X2) @ (suc @ Y3)))) => (P2 @ M @ N))))))). % diff_induct
thf(fact_239_One__nat__def, axiom,
    ((one_one_nat = (suc @ zero_zero_nat)))). % One_nat_def
thf(fact_240_nat__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N2 : nat]: ((P2 @ N2) => (P2 @ (suc @ N2)))) => (P2 @ N)))))). % nat_induct
thf(fact_241_nat_OdiscI, axiom,
    ((![Nat : nat, X22 : nat]: ((Nat = (suc @ X22)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_242_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_243_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_244_nat_Odistinct_I1_J, axiom,
    ((![X22 : nat]: (~ ((zero_zero_nat = (suc @ X22))))))). % nat.distinct(1)

% Conjectures (1)
thf(conj_0, conjecture,
    (((?[X : complex]: ((((poly_complex2 @ (pCons_complex @ a @ p) @ X) = zero_zero_complex)) & ((~ (((poly_complex2 @ q @ X) = zero_zero_complex)))))) = (~ ((dvd_dvd_poly_complex @ (pCons_complex @ a @ p) @ (power_184595776omplex @ q @ (fundam1709708056omplex @ p)))))))).
