% 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_963__5376972_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:34:46.190

% 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 (51)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
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_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    times_1246143675omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    times_times_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    times_1460995011omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    times_2061725899omplex : poly_p1267267526omplex > poly_p1267267526omplex > poly_p1267267526omplex).
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_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Polynomial_Odegree_001t__Complex__Ocomplex, type,
    degree_complex : poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Complex__Ocomplex, type,
    order_complex : complex > poly_complex > nat).
thf(sy_c_Polynomial_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_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    power_184595776omplex : poly_complex > nat > 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_v_a____, type,
    a : complex).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_pa____, type,
    pa : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).
thf(sy_v_qa____, type,
    qa : poly_complex).
thf(sy_v_r____, type,
    r : poly_complex).
thf(sy_v_s____, type,
    s : poly_complex).
thf(sy_v_x____, type,
    x : complex).

% Relevant facts (247)
thf(fact_0_xa, axiom,
    ((~ ((x = a))))). % xa
thf(fact_1__092_060open_062poly_Aq_Ax_A_061_A0_092_060close_062, axiom,
    (((poly_complex2 @ qa @ x) = zero_zero_complex))). % \<open>poly q x = 0\<close>
thf(fact_2_assms_I1_J, axiom,
    ((![X : complex]: (((poly_complex2 @ p @ X) = zero_zero_complex) => ((poly_complex2 @ q @ X) = zero_zero_complex))))). % assms(1)
thf(fact_3_that, axiom,
    (((poly_complex2 @ s @ x) = zero_zero_complex))). % that
thf(fact_4_True, axiom,
    ((?[A : complex]: ((poly_complex2 @ pa @ A) = zero_zero_complex)))). % True
thf(fact_5_r, axiom,
    ((qa = (times_1246143675omplex @ (pCons_complex @ (uminus1204672759omplex @ a) @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ r)))). % r
thf(fact_6_pq0, axiom,
    ((![X : complex]: (((poly_complex2 @ pa @ X) = zero_zero_complex) => ((poly_complex2 @ qa @ X) = zero_zero_complex))))). % pq0
thf(fact_7_a, axiom,
    (((poly_complex2 @ pa @ a) = zero_zero_complex))). % a
thf(fact_8_poly__0, axiom,
    ((![X2 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X2) = zero_zero_poly_nat)))). % poly_0
thf(fact_9_poly__0, axiom,
    ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X2) = zero_z1040703943omplex)))). % poly_0
thf(fact_10_poly__0, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
thf(fact_11_poly__0, axiom,
    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
thf(fact_12_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_13__092_060open_062poly_Ap_Ax_A_061_A0_092_060close_062, axiom,
    (((poly_complex2 @ pa @ x) = zero_zero_complex))). % \<open>poly p x = 0\<close>
thf(fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062a_O_Apoly_Ap_Aa_A_061_A0_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![A : complex]: (~ (((poly_complex2 @ pa @ A) = zero_zero_complex)))))))). % \<open>\<And>thesis. (\<And>a. poly p a = 0 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_15_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X3 : complex]: ((poly_complex2 @ P @ X3) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_16_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X3 : poly_complex]: ((poly_poly_complex2 @ P @ X3) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_17_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X3 : poly_poly_complex]: ((poly_p282434315omplex @ P @ X3) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_18_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_19_fundamental__theorem__of__algebra__alt, axiom,
    ((![P : poly_complex]: ((~ ((?[A : complex, L : poly_complex]: ((~ ((A = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (P = (pCons_complex @ A @ L))))))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra_alt
thf(fact_20_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_21_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_22_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_23_zero__reorient, axiom,
    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) = (X2 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_24_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_25_zero__reorient, axiom,
    ((![X2 : poly_nat]: ((zero_zero_poly_nat = X2) = (X2 = zero_zero_poly_nat))))). % zero_reorient
thf(fact_26_zero__reorient, axiom,
    ((![X2 : poly_poly_complex]: ((zero_z1040703943omplex = X2) = (X2 = zero_z1040703943omplex))))). % zero_reorient
thf(fact_27_assms_I3_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(3)
thf(fact_28_mult__zero__left, axiom,
    ((![A2 : complex]: ((times_times_complex @ zero_zero_complex @ A2) = zero_zero_complex)))). % mult_zero_left
thf(fact_29_mult__zero__left, axiom,
    ((![A2 : poly_nat]: ((times_times_poly_nat @ zero_zero_poly_nat @ A2) = zero_zero_poly_nat)))). % mult_zero_left
thf(fact_30_mult__zero__left, axiom,
    ((![A2 : poly_poly_complex]: ((times_1460995011omplex @ zero_z1040703943omplex @ A2) = zero_z1040703943omplex)))). % mult_zero_left
thf(fact_31_mult__zero__left, axiom,
    ((![A2 : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ A2) = zero_z1746442943omplex)))). % mult_zero_left
thf(fact_32_mult__zero__left, axiom,
    ((![A2 : nat]: ((times_times_nat @ zero_zero_nat @ A2) = zero_zero_nat)))). % mult_zero_left
thf(fact_33_n0, axiom,
    ((~ ((na = zero_zero_nat))))). % n0
thf(fact_34_pne, axiom,
    ((~ ((pa = zero_z1746442943omplex))))). % pne
thf(fact_35_sne, axiom,
    ((~ ((s = zero_z1746442943omplex))))). % sne
thf(fact_36_add_Oinverse__inverse, axiom,
    ((![A2 : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A2)) = A2)))). % add.inverse_inverse
thf(fact_37_neg__equal__iff__equal, axiom,
    ((![A2 : complex, B : complex]: (((uminus1204672759omplex @ A2) = (uminus1204672759omplex @ B)) = (A2 = B))))). % neg_equal_iff_equal
thf(fact_38_pCons__eq__iff, axiom,
    ((![A2 : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A2 @ P) = (pCons_complex @ B @ Q)) = (((A2 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_39_mult__cancel__right, axiom,
    ((![A2 : complex, C : complex, B : complex]: (((times_times_complex @ A2 @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_40_mult__cancel__right, axiom,
    ((![A2 : poly_poly_complex, C : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A2 @ C) = (times_1460995011omplex @ B @ C)) = (((C = zero_z1040703943omplex)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_41_mult__cancel__right, axiom,
    ((![A2 : poly_complex, C : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A2 @ C) = (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_42_mult__cancel__right, axiom,
    ((![A2 : nat, C : nat, B : nat]: (((times_times_nat @ A2 @ C) = (times_times_nat @ B @ C)) = (((C = zero_zero_nat)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_43_mult__cancel__left, axiom,
    ((![C : complex, A2 : complex, B : complex]: (((times_times_complex @ C @ A2) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_44_mult__cancel__left, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ C @ A2) = (times_1460995011omplex @ C @ B)) = (((C = zero_z1040703943omplex)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_45_mult__cancel__left, axiom,
    ((![C : poly_complex, A2 : poly_complex, B : poly_complex]: (((times_1246143675omplex @ C @ A2) = (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_46_mult__cancel__left, axiom,
    ((![C : nat, A2 : nat, B : nat]: (((times_times_nat @ C @ A2) = (times_times_nat @ C @ B)) = (((C = zero_zero_nat)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_47_mult__eq__0__iff, axiom,
    ((![A2 : complex, B : complex]: (((times_times_complex @ A2 @ B) = zero_zero_complex) = (((A2 = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_48_mult__eq__0__iff, axiom,
    ((![A2 : poly_nat, B : poly_nat]: (((times_times_poly_nat @ A2 @ B) = zero_zero_poly_nat) = (((A2 = zero_zero_poly_nat)) | ((B = zero_zero_poly_nat))))))). % mult_eq_0_iff
thf(fact_49_mult__eq__0__iff, axiom,
    ((![A2 : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A2 @ B) = zero_z1040703943omplex) = (((A2 = zero_z1040703943omplex)) | ((B = zero_z1040703943omplex))))))). % mult_eq_0_iff
thf(fact_50_mult__eq__0__iff, axiom,
    ((![A2 : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A2 @ B) = zero_z1746442943omplex) = (((A2 = zero_z1746442943omplex)) | ((B = zero_z1746442943omplex))))))). % mult_eq_0_iff
thf(fact_51_mult__eq__0__iff, axiom,
    ((![A2 : nat, B : nat]: (((times_times_nat @ A2 @ B) = zero_zero_nat) = (((A2 = zero_zero_nat)) | ((B = zero_zero_nat))))))). % mult_eq_0_iff
thf(fact_52_mult__zero__right, axiom,
    ((![A2 : complex]: ((times_times_complex @ A2 @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_53_mult__zero__right, axiom,
    ((![A2 : poly_nat]: ((times_times_poly_nat @ A2 @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % mult_zero_right
thf(fact_54_mult__zero__right, axiom,
    ((![A2 : poly_poly_complex]: ((times_1460995011omplex @ A2 @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % mult_zero_right
thf(fact_55_mult__zero__right, axiom,
    ((![A2 : poly_complex]: ((times_1246143675omplex @ A2 @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % mult_zero_right
thf(fact_56_mult__zero__right, axiom,
    ((![A2 : nat]: ((times_times_nat @ A2 @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_57_neg__equal__0__iff__equal, axiom,
    ((![A2 : poly_complex]: (((uminus1138659839omplex @ A2) = zero_z1746442943omplex) = (A2 = zero_z1746442943omplex))))). % neg_equal_0_iff_equal
thf(fact_58_neg__equal__0__iff__equal, axiom,
    ((![A2 : poly_poly_complex]: (((uminus1762810119omplex @ A2) = zero_z1040703943omplex) = (A2 = zero_z1040703943omplex))))). % neg_equal_0_iff_equal
thf(fact_59_neg__equal__0__iff__equal, axiom,
    ((![A2 : complex]: (((uminus1204672759omplex @ A2) = zero_zero_complex) = (A2 = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_60_neg__0__equal__iff__equal, axiom,
    ((![A2 : poly_complex]: ((zero_z1746442943omplex = (uminus1138659839omplex @ A2)) = (zero_z1746442943omplex = A2))))). % neg_0_equal_iff_equal
thf(fact_61_neg__0__equal__iff__equal, axiom,
    ((![A2 : poly_poly_complex]: ((zero_z1040703943omplex = (uminus1762810119omplex @ A2)) = (zero_z1040703943omplex = A2))))). % neg_0_equal_iff_equal
thf(fact_62_neg__0__equal__iff__equal, axiom,
    ((![A2 : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A2)) = (zero_zero_complex = A2))))). % neg_0_equal_iff_equal
thf(fact_63_add_Oinverse__neutral, axiom,
    (((uminus1138659839omplex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % add.inverse_neutral
thf(fact_64_add_Oinverse__neutral, axiom,
    (((uminus1762810119omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % add.inverse_neutral
thf(fact_65_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_66_mult_Oleft__neutral, axiom,
    ((![A2 : complex]: ((times_times_complex @ one_one_complex @ A2) = A2)))). % mult.left_neutral
thf(fact_67_mult_Oleft__neutral, axiom,
    ((![A2 : poly_complex]: ((times_1246143675omplex @ one_one_poly_complex @ A2) = A2)))). % mult.left_neutral
thf(fact_68_mult_Oleft__neutral, axiom,
    ((![A2 : nat]: ((times_times_nat @ one_one_nat @ A2) = A2)))). % mult.left_neutral
thf(fact_69_mult_Oright__neutral, axiom,
    ((![A2 : complex]: ((times_times_complex @ A2 @ one_one_complex) = A2)))). % mult.right_neutral
thf(fact_70_mult_Oright__neutral, axiom,
    ((![A2 : poly_complex]: ((times_1246143675omplex @ A2 @ one_one_poly_complex) = A2)))). % mult.right_neutral
thf(fact_71_mult_Oright__neutral, axiom,
    ((![A2 : nat]: ((times_times_nat @ A2 @ one_one_nat) = A2)))). % mult.right_neutral
thf(fact_72_mult__minus__left, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((times_1246143675omplex @ (uminus1138659839omplex @ A2) @ B) = (uminus1138659839omplex @ (times_1246143675omplex @ A2 @ B)))))). % mult_minus_left
thf(fact_73_mult__minus__left, axiom,
    ((![A2 : complex, B : complex]: ((times_times_complex @ (uminus1204672759omplex @ A2) @ B) = (uminus1204672759omplex @ (times_times_complex @ A2 @ B)))))). % mult_minus_left
thf(fact_74_minus__mult__minus, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((times_1246143675omplex @ (uminus1138659839omplex @ A2) @ (uminus1138659839omplex @ B)) = (times_1246143675omplex @ A2 @ B))))). % minus_mult_minus
thf(fact_75_minus__mult__minus, axiom,
    ((![A2 : complex, B : complex]: ((times_times_complex @ (uminus1204672759omplex @ A2) @ (uminus1204672759omplex @ B)) = (times_times_complex @ A2 @ B))))). % minus_mult_minus
thf(fact_76_mult__minus__right, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((times_1246143675omplex @ A2 @ (uminus1138659839omplex @ B)) = (uminus1138659839omplex @ (times_1246143675omplex @ A2 @ B)))))). % mult_minus_right
thf(fact_77_mult__minus__right, axiom,
    ((![A2 : complex, B : complex]: ((times_times_complex @ A2 @ (uminus1204672759omplex @ B)) = (uminus1204672759omplex @ (times_times_complex @ A2 @ B)))))). % mult_minus_right
thf(fact_78_minus__pCons, axiom,
    ((![A2 : complex, P : poly_complex]: ((uminus1138659839omplex @ (pCons_complex @ A2 @ P)) = (pCons_complex @ (uminus1204672759omplex @ A2) @ (uminus1138659839omplex @ P)))))). % minus_pCons
thf(fact_79_poly__1, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ one_on1331105667omplex @ X2) = one_one_poly_complex)))). % poly_1
thf(fact_80_poly__1, axiom,
    ((![X2 : complex]: ((poly_complex2 @ one_one_poly_complex @ X2) = one_one_complex)))). % poly_1
thf(fact_81_poly__1, axiom,
    ((![X2 : nat]: ((poly_nat2 @ one_one_poly_nat @ X2) = one_one_nat)))). % poly_1
thf(fact_82_poly__minus, axiom,
    ((![P : poly_poly_complex, X2 : poly_complex]: ((poly_poly_complex2 @ (uminus1762810119omplex @ P) @ X2) = (uminus1138659839omplex @ (poly_poly_complex2 @ P @ X2)))))). % poly_minus
thf(fact_83_poly__minus, axiom,
    ((![P : poly_complex, X2 : complex]: ((poly_complex2 @ (uminus1138659839omplex @ P) @ X2) = (uminus1204672759omplex @ (poly_complex2 @ P @ X2)))))). % poly_minus
thf(fact_84__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062r_O_Aq_A_061_A_091_058_N_Aa_M_A1_058_093_A_K_Ar_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![R : poly_complex]: (~ ((qa = (times_1246143675omplex @ (pCons_complex @ (uminus1204672759omplex @ a) @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ R))))))))). % \<open>\<And>thesis. (\<And>r. q = [:- a, 1:] * r \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_85_mult__cancel__right2, axiom,
    ((![A2 : complex, C : complex]: (((times_times_complex @ A2 @ C) = C) = (((C = zero_zero_complex)) | ((A2 = one_one_complex))))))). % mult_cancel_right2
thf(fact_86_mult__cancel__right2, axiom,
    ((![A2 : poly_poly_complex, C : poly_poly_complex]: (((times_1460995011omplex @ A2 @ C) = C) = (((C = zero_z1040703943omplex)) | ((A2 = one_on1331105667omplex))))))). % mult_cancel_right2
thf(fact_87_mult__cancel__right2, axiom,
    ((![A2 : poly_complex, C : poly_complex]: (((times_1246143675omplex @ A2 @ C) = C) = (((C = zero_z1746442943omplex)) | ((A2 = one_one_poly_complex))))))). % mult_cancel_right2
thf(fact_88_mult__cancel__right1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_right1
thf(fact_89_mult__cancel__right1, axiom,
    ((![C : poly_poly_complex, B : poly_poly_complex]: ((C = (times_1460995011omplex @ B @ C)) = (((C = zero_z1040703943omplex)) | ((B = one_on1331105667omplex))))))). % mult_cancel_right1
thf(fact_90_mult__cancel__right1, axiom,
    ((![C : poly_complex, B : poly_complex]: ((C = (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((B = one_one_poly_complex))))))). % mult_cancel_right1
thf(fact_91_mult__cancel__left2, axiom,
    ((![C : complex, A2 : complex]: (((times_times_complex @ C @ A2) = C) = (((C = zero_zero_complex)) | ((A2 = one_one_complex))))))). % mult_cancel_left2
thf(fact_92_mult__cancel__left2, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex]: (((times_1460995011omplex @ C @ A2) = C) = (((C = zero_z1040703943omplex)) | ((A2 = one_on1331105667omplex))))))). % mult_cancel_left2
thf(fact_93_mult__cancel__left2, axiom,
    ((![C : poly_complex, A2 : poly_complex]: (((times_1246143675omplex @ C @ A2) = C) = (((C = zero_z1746442943omplex)) | ((A2 = one_one_poly_complex))))))). % mult_cancel_left2
thf(fact_94_mult__cancel__left1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_left1
thf(fact_95_mult__cancel__left1, axiom,
    ((![C : poly_poly_complex, B : poly_poly_complex]: ((C = (times_1460995011omplex @ C @ B)) = (((C = zero_z1040703943omplex)) | ((B = one_on1331105667omplex))))))). % mult_cancel_left1
thf(fact_96_mult__cancel__left1, axiom,
    ((![C : poly_complex, B : poly_complex]: ((C = (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((B = one_one_poly_complex))))))). % mult_cancel_left1
thf(fact_97_pCons__eq__0__iff, axiom,
    ((![A2 : poly_nat, P : poly_poly_nat]: (((pCons_poly_nat @ A2 @ P) = zero_z1059985641ly_nat) = (((A2 = zero_zero_poly_nat)) & ((P = zero_z1059985641ly_nat))))))). % pCons_eq_0_iff
thf(fact_98_pCons__eq__0__iff, axiom,
    ((![A2 : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A2 @ P) = zero_z1200043727omplex) = (((A2 = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_99_pCons__eq__0__iff, axiom,
    ((![A2 : complex, P : poly_complex]: (((pCons_complex @ A2 @ P) = zero_z1746442943omplex) = (((A2 = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_100_pCons__eq__0__iff, axiom,
    ((![A2 : nat, P : poly_nat]: (((pCons_nat @ A2 @ P) = zero_zero_poly_nat) = (((A2 = zero_zero_nat)) & ((P = zero_zero_poly_nat))))))). % pCons_eq_0_iff
thf(fact_101_pCons__eq__0__iff, axiom,
    ((![A2 : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A2 @ P) = zero_z1040703943omplex) = (((A2 = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_102_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_103_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_104_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_105_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_106_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_107_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_108_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_109_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_110_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_111_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_112_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_113_oa, axiom,
    ((~ (((order_complex @ a @ pa) = zero_zero_nat))))). % oa
thf(fact_114_poly__mult, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, X2 : poly_complex]: ((poly_poly_complex2 @ (times_1460995011omplex @ P @ Q) @ X2) = (times_1246143675omplex @ (poly_poly_complex2 @ P @ X2) @ (poly_poly_complex2 @ Q @ X2)))))). % poly_mult
thf(fact_115_poly__mult, axiom,
    ((![P : poly_nat, Q : poly_nat, X2 : nat]: ((poly_nat2 @ (times_times_poly_nat @ P @ Q) @ X2) = (times_times_nat @ (poly_nat2 @ P @ X2) @ (poly_nat2 @ Q @ X2)))))). % poly_mult
thf(fact_116_poly__mult, axiom,
    ((![P : poly_complex, Q : poly_complex, X2 : complex]: ((poly_complex2 @ (times_1246143675omplex @ P @ Q) @ X2) = (times_times_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q @ X2)))))). % poly_mult
thf(fact_117_False, axiom,
    ((~ (((degree_complex @ s) = zero_zero_nat))))). % False
thf(fact_118_assms_I2_J, axiom,
    (((degree_complex @ p) = n))). % assms(2)
thf(fact_119_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A2 : poly_complex, B : poly_complex, C : poly_complex]: ((times_1246143675omplex @ (times_1246143675omplex @ A2 @ B) @ C) = (times_1246143675omplex @ A2 @ (times_1246143675omplex @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_120_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((times_times_nat @ (times_times_nat @ A2 @ B) @ C) = (times_times_nat @ A2 @ (times_times_nat @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_121_one__reorient, axiom,
    ((![X2 : complex]: ((one_one_complex = X2) = (X2 = one_one_complex))))). % one_reorient
thf(fact_122_one__reorient, axiom,
    ((![X2 : nat]: ((one_one_nat = X2) = (X2 = one_one_nat))))). % one_reorient
thf(fact_123_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_124_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_125_pCons__one, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % pCons_one
thf(fact_126_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A @ Q2)))))))))). % pCons_cases
thf(fact_127_pderiv_Ocases, axiom,
    ((![X2 : poly_complex]: (~ ((![A : complex, P2 : poly_complex]: (~ ((X2 = (pCons_complex @ A @ P2)))))))))). % pderiv.cases
thf(fact_128_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_complex > $o, P : poly_complex, Q : poly_complex]: ((P3 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A : complex, P2 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_129_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_nat > $o, P : poly_complex, Q : poly_nat]: ((P3 @ zero_z1746442943omplex @ zero_zero_poly_nat) => ((![A : complex, P2 : poly_complex, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_130_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_poly_complex > $o, P : poly_complex, Q : poly_poly_complex]: ((P3 @ zero_z1746442943omplex @ zero_z1040703943omplex) => ((![A : complex, P2 : poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_131_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_complex > $o, P : poly_nat, Q : poly_complex]: ((P3 @ zero_zero_poly_nat @ zero_z1746442943omplex) => ((![A : nat, P2 : poly_nat, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_132_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_nat > $o, P : poly_nat, Q : poly_nat]: ((P3 @ zero_zero_poly_nat @ zero_zero_poly_nat) => ((![A : nat, P2 : poly_nat, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_133_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_poly_complex > $o, P : poly_nat, Q : poly_poly_complex]: ((P3 @ zero_zero_poly_nat @ zero_z1040703943omplex) => ((![A : nat, P2 : poly_nat, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_134_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_complex > $o, P : poly_poly_complex, Q : poly_complex]: ((P3 @ zero_z1040703943omplex @ zero_z1746442943omplex) => ((![A : poly_complex, P2 : poly_poly_complex, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_135_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_nat > $o, P : poly_poly_complex, Q : poly_nat]: ((P3 @ zero_z1040703943omplex @ zero_zero_poly_nat) => ((![A : poly_complex, P2 : poly_poly_complex, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_136_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_poly_complex > $o, P : poly_poly_complex, Q : poly_poly_complex]: ((P3 @ zero_z1040703943omplex @ zero_z1040703943omplex) => ((![A : poly_complex, P2 : poly_poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_137_pderiv_Oinduct, axiom,
    ((![P3 : poly_complex > $o, A0 : poly_complex]: ((![A : complex, P2 : poly_complex]: (((~ ((P2 = zero_z1746442943omplex))) => (P3 @ P2)) => (P3 @ (pCons_complex @ A @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_138_pderiv_Oinduct, axiom,
    ((![P3 : poly_nat > $o, A0 : poly_nat]: ((![A : nat, P2 : poly_nat]: (((~ ((P2 = zero_zero_poly_nat))) => (P3 @ P2)) => (P3 @ (pCons_nat @ A @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_139_pderiv_Oinduct, axiom,
    ((![P3 : poly_poly_complex > $o, A0 : poly_poly_complex]: ((![A : poly_complex, P2 : poly_poly_complex]: (((~ ((P2 = zero_z1040703943omplex))) => (P3 @ P2)) => (P3 @ (pCons_poly_complex @ A @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_140_mult__poly__0__left, axiom,
    ((![Q : poly_nat]: ((times_times_poly_nat @ zero_zero_poly_nat @ Q) = zero_zero_poly_nat)))). % mult_poly_0_left
thf(fact_141_mult__poly__0__left, axiom,
    ((![Q : poly_poly_complex]: ((times_1460995011omplex @ zero_z1040703943omplex @ Q) = zero_z1040703943omplex)))). % mult_poly_0_left
thf(fact_142_mult__poly__0__left, axiom,
    ((![Q : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ Q) = zero_z1746442943omplex)))). % mult_poly_0_left
thf(fact_143_mult__poly__0__right, axiom,
    ((![P : poly_nat]: ((times_times_poly_nat @ P @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % mult_poly_0_right
thf(fact_144_mult__poly__0__right, axiom,
    ((![P : poly_poly_complex]: ((times_1460995011omplex @ P @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % mult_poly_0_right
thf(fact_145_mult__poly__0__right, axiom,
    ((![P : poly_complex]: ((times_1246143675omplex @ P @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % mult_poly_0_right
thf(fact_146_square__eq__iff, axiom,
    ((![A2 : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A2 @ A2) = (times_1246143675omplex @ B @ B)) = (((A2 = B)) | ((A2 = (uminus1138659839omplex @ B)))))))). % square_eq_iff
thf(fact_147_square__eq__iff, axiom,
    ((![A2 : complex, B : complex]: (((times_times_complex @ A2 @ A2) = (times_times_complex @ B @ B)) = (((A2 = B)) | ((A2 = (uminus1204672759omplex @ B)))))))). % square_eq_iff
thf(fact_148_minus__mult__commute, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((times_1246143675omplex @ (uminus1138659839omplex @ A2) @ B) = (times_1246143675omplex @ A2 @ (uminus1138659839omplex @ B)))))). % minus_mult_commute
thf(fact_149_minus__mult__commute, axiom,
    ((![A2 : complex, B : complex]: ((times_times_complex @ (uminus1204672759omplex @ A2) @ B) = (times_times_complex @ A2 @ (uminus1204672759omplex @ B)))))). % minus_mult_commute
thf(fact_150_comm__monoid__mult__class_Omult__1, axiom,
    ((![A2 : complex]: ((times_times_complex @ one_one_complex @ A2) = A2)))). % comm_monoid_mult_class.mult_1
thf(fact_151_comm__monoid__mult__class_Omult__1, axiom,
    ((![A2 : poly_complex]: ((times_1246143675omplex @ one_one_poly_complex @ A2) = A2)))). % comm_monoid_mult_class.mult_1
thf(fact_152_comm__monoid__mult__class_Omult__1, axiom,
    ((![A2 : nat]: ((times_times_nat @ one_one_nat @ A2) = A2)))). % comm_monoid_mult_class.mult_1
thf(fact_153_mult_Oassoc, axiom,
    ((![A2 : poly_complex, B : poly_complex, C : poly_complex]: ((times_1246143675omplex @ (times_1246143675omplex @ A2 @ B) @ C) = (times_1246143675omplex @ A2 @ (times_1246143675omplex @ B @ C)))))). % mult.assoc
thf(fact_154_mult_Oassoc, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((times_times_nat @ (times_times_nat @ A2 @ B) @ C) = (times_times_nat @ A2 @ (times_times_nat @ B @ C)))))). % mult.assoc
thf(fact_155_equation__minus__iff, axiom,
    ((![A2 : complex, B : complex]: ((A2 = (uminus1204672759omplex @ B)) = (B = (uminus1204672759omplex @ A2)))))). % equation_minus_iff
thf(fact_156_minus__equation__iff, axiom,
    ((![A2 : complex, B : complex]: (((uminus1204672759omplex @ A2) = B) = ((uminus1204672759omplex @ B) = A2))))). % minus_equation_iff
thf(fact_157_mult_Ocommute, axiom,
    ((times_1246143675omplex = (^[A3 : poly_complex]: (^[B3 : poly_complex]: (times_1246143675omplex @ B3 @ A3)))))). % mult.commute
thf(fact_158_mult_Ocommute, axiom,
    ((times_times_nat = (^[A3 : nat]: (^[B3 : nat]: (times_times_nat @ B3 @ A3)))))). % mult.commute
thf(fact_159_mult_Ocomm__neutral, axiom,
    ((![A2 : complex]: ((times_times_complex @ A2 @ one_one_complex) = A2)))). % mult.comm_neutral
thf(fact_160_mult_Ocomm__neutral, axiom,
    ((![A2 : poly_complex]: ((times_1246143675omplex @ A2 @ one_one_poly_complex) = A2)))). % mult.comm_neutral
thf(fact_161_mult_Ocomm__neutral, axiom,
    ((![A2 : nat]: ((times_times_nat @ A2 @ one_one_nat) = A2)))). % mult.comm_neutral
thf(fact_162_mult_Oleft__commute, axiom,
    ((![B : poly_complex, A2 : poly_complex, C : poly_complex]: ((times_1246143675omplex @ B @ (times_1246143675omplex @ A2 @ C)) = (times_1246143675omplex @ A2 @ (times_1246143675omplex @ B @ C)))))). % mult.left_commute
thf(fact_163_mult_Oleft__commute, axiom,
    ((![B : nat, A2 : nat, C : nat]: ((times_times_nat @ B @ (times_times_nat @ A2 @ C)) = (times_times_nat @ A2 @ (times_times_nat @ B @ C)))))). % mult.left_commute
thf(fact_164_square__eq__1__iff, axiom,
    ((![X2 : poly_complex]: (((times_1246143675omplex @ X2 @ X2) = one_one_poly_complex) = (((X2 = one_one_poly_complex)) | ((X2 = (uminus1138659839omplex @ one_one_poly_complex)))))))). % square_eq_1_iff
thf(fact_165_square__eq__1__iff, axiom,
    ((![X2 : complex]: (((times_times_complex @ X2 @ X2) = one_one_complex) = (((X2 = one_one_complex)) | ((X2 = (uminus1204672759omplex @ one_one_complex)))))))). % square_eq_1_iff
thf(fact_166_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y : complex]: ((F @ X3) = (F @ Y)))))))). % constant_def
thf(fact_167_poly__root__induct, axiom,
    ((![Q3 : poly_p1267267526omplex > $o, P3 : poly_poly_complex > $o, P : poly_p1267267526omplex]: ((Q3 @ zero_z1200043727omplex) => ((![P2 : poly_p1267267526omplex]: ((![A4 : poly_poly_complex]: ((P3 @ A4) => (~ (((poly_p282434315omplex @ P2 @ A4) = zero_z1040703943omplex))))) => (Q3 @ P2))) => ((![A : poly_poly_complex, P2 : poly_p1267267526omplex]: ((P3 @ A) => ((Q3 @ P2) => (Q3 @ (times_2061725899omplex @ (pCons_1087637536omplex @ A @ (pCons_1087637536omplex @ (uminus1762810119omplex @ one_on1331105667omplex) @ zero_z1200043727omplex)) @ P2))))) => (Q3 @ P))))))). % poly_root_induct
thf(fact_168_poly__root__induct, axiom,
    ((![Q3 : poly_poly_complex > $o, P3 : poly_complex > $o, P : poly_poly_complex]: ((Q3 @ zero_z1040703943omplex) => ((![P2 : poly_poly_complex]: ((![A4 : poly_complex]: ((P3 @ A4) => (~ (((poly_poly_complex2 @ P2 @ A4) = zero_z1746442943omplex))))) => (Q3 @ P2))) => ((![A : poly_complex, P2 : poly_poly_complex]: ((P3 @ A) => ((Q3 @ P2) => (Q3 @ (times_1460995011omplex @ (pCons_poly_complex @ A @ (pCons_poly_complex @ (uminus1138659839omplex @ one_one_poly_complex) @ zero_z1040703943omplex)) @ P2))))) => (Q3 @ P))))))). % poly_root_induct
thf(fact_169_poly__root__induct, axiom,
    ((![Q3 : poly_complex > $o, P3 : complex > $o, P : poly_complex]: ((Q3 @ zero_z1746442943omplex) => ((![P2 : poly_complex]: ((![A4 : complex]: ((P3 @ A4) => (~ (((poly_complex2 @ P2 @ A4) = zero_zero_complex))))) => (Q3 @ P2))) => ((![A : complex, P2 : poly_complex]: ((P3 @ A) => ((Q3 @ P2) => (Q3 @ (times_1246143675omplex @ (pCons_complex @ A @ (pCons_complex @ (uminus1204672759omplex @ one_one_complex) @ zero_z1746442943omplex)) @ P2))))) => (Q3 @ P))))))). % poly_root_induct
thf(fact_170_pCons__induct, axiom,
    ((![P3 : poly_poly_nat > $o, P : poly_poly_nat]: ((P3 @ zero_z1059985641ly_nat) => ((![A : poly_nat, P2 : poly_poly_nat]: (((~ ((A = zero_zero_poly_nat))) | (~ ((P2 = zero_z1059985641ly_nat)))) => ((P3 @ P2) => (P3 @ (pCons_poly_nat @ A @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_171_pCons__induct, axiom,
    ((![P3 : poly_p1267267526omplex > $o, P : poly_p1267267526omplex]: ((P3 @ zero_z1200043727omplex) => ((![A : poly_poly_complex, P2 : poly_p1267267526omplex]: (((~ ((A = zero_z1040703943omplex))) | (~ ((P2 = zero_z1200043727omplex)))) => ((P3 @ P2) => (P3 @ (pCons_1087637536omplex @ A @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_172_pCons__induct, axiom,
    ((![P3 : poly_complex > $o, P : poly_complex]: ((P3 @ zero_z1746442943omplex) => ((![A : complex, P2 : poly_complex]: (((~ ((A = zero_zero_complex))) | (~ ((P2 = zero_z1746442943omplex)))) => ((P3 @ P2) => (P3 @ (pCons_complex @ A @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_173_pCons__induct, axiom,
    ((![P3 : poly_nat > $o, P : poly_nat]: ((P3 @ zero_zero_poly_nat) => ((![A : nat, P2 : poly_nat]: (((~ ((A = zero_zero_nat))) | (~ ((P2 = zero_zero_poly_nat)))) => ((P3 @ P2) => (P3 @ (pCons_nat @ A @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_174_pCons__induct, axiom,
    ((![P3 : poly_poly_complex > $o, P : poly_poly_complex]: ((P3 @ zero_z1040703943omplex) => ((![A : poly_complex, P2 : poly_poly_complex]: (((~ ((A = zero_z1746442943omplex))) | (~ ((P2 = zero_z1040703943omplex)))) => ((P3 @ P2) => (P3 @ (pCons_poly_complex @ A @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_175_mult__right__cancel, axiom,
    ((![C : complex, A2 : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A2 @ C) = (times_times_complex @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_176_mult__right__cancel, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex, B : poly_poly_complex]: ((~ ((C = zero_z1040703943omplex))) => (((times_1460995011omplex @ A2 @ C) = (times_1460995011omplex @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_177_mult__right__cancel, axiom,
    ((![C : poly_complex, A2 : poly_complex, B : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => (((times_1246143675omplex @ A2 @ C) = (times_1246143675omplex @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_178_mult__right__cancel, axiom,
    ((![C : nat, A2 : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ A2 @ C) = (times_times_nat @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_179_mult__left__cancel, axiom,
    ((![C : complex, A2 : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ C @ A2) = (times_times_complex @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_180_mult__left__cancel, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex, B : poly_poly_complex]: ((~ ((C = zero_z1040703943omplex))) => (((times_1460995011omplex @ C @ A2) = (times_1460995011omplex @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_181_mult__left__cancel, axiom,
    ((![C : poly_complex, A2 : poly_complex, B : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => (((times_1246143675omplex @ C @ A2) = (times_1246143675omplex @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_182_mult__left__cancel, axiom,
    ((![C : nat, A2 : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ C @ A2) = (times_times_nat @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_183_no__zero__divisors, axiom,
    ((![A2 : complex, B : complex]: ((~ ((A2 = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (~ (((times_times_complex @ A2 @ B) = zero_zero_complex)))))))). % no_zero_divisors
thf(fact_184_no__zero__divisors, axiom,
    ((![A2 : poly_nat, B : poly_nat]: ((~ ((A2 = zero_zero_poly_nat))) => ((~ ((B = zero_zero_poly_nat))) => (~ (((times_times_poly_nat @ A2 @ B) = zero_zero_poly_nat)))))))). % no_zero_divisors
thf(fact_185_no__zero__divisors, axiom,
    ((![A2 : poly_poly_complex, B : poly_poly_complex]: ((~ ((A2 = zero_z1040703943omplex))) => ((~ ((B = zero_z1040703943omplex))) => (~ (((times_1460995011omplex @ A2 @ B) = zero_z1040703943omplex)))))))). % no_zero_divisors
thf(fact_186_no__zero__divisors, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((~ ((A2 = zero_z1746442943omplex))) => ((~ ((B = zero_z1746442943omplex))) => (~ (((times_1246143675omplex @ A2 @ B) = zero_z1746442943omplex)))))))). % no_zero_divisors
thf(fact_187_no__zero__divisors, axiom,
    ((![A2 : nat, B : nat]: ((~ ((A2 = zero_zero_nat))) => ((~ ((B = zero_zero_nat))) => (~ (((times_times_nat @ A2 @ B) = zero_zero_nat)))))))). % no_zero_divisors
thf(fact_188_divisors__zero, axiom,
    ((![A2 : complex, B : complex]: (((times_times_complex @ A2 @ B) = zero_zero_complex) => ((A2 = zero_zero_complex) | (B = zero_zero_complex)))))). % divisors_zero
thf(fact_189_divisors__zero, axiom,
    ((![A2 : poly_nat, B : poly_nat]: (((times_times_poly_nat @ A2 @ B) = zero_zero_poly_nat) => ((A2 = zero_zero_poly_nat) | (B = zero_zero_poly_nat)))))). % divisors_zero
thf(fact_190_divisors__zero, axiom,
    ((![A2 : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A2 @ B) = zero_z1040703943omplex) => ((A2 = zero_z1040703943omplex) | (B = zero_z1040703943omplex)))))). % divisors_zero
thf(fact_191_divisors__zero, axiom,
    ((![A2 : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A2 @ B) = zero_z1746442943omplex) => ((A2 = zero_z1746442943omplex) | (B = zero_z1746442943omplex)))))). % divisors_zero
thf(fact_192_divisors__zero, axiom,
    ((![A2 : nat, B : nat]: (((times_times_nat @ A2 @ B) = zero_zero_nat) => ((A2 = zero_zero_nat) | (B = zero_zero_nat)))))). % divisors_zero
thf(fact_193_mult__not__zero, axiom,
    ((![A2 : complex, B : complex]: ((~ (((times_times_complex @ A2 @ B) = zero_zero_complex))) => ((~ ((A2 = zero_zero_complex))) & (~ ((B = zero_zero_complex)))))))). % mult_not_zero
thf(fact_194_mult__not__zero, axiom,
    ((![A2 : poly_nat, B : poly_nat]: ((~ (((times_times_poly_nat @ A2 @ B) = zero_zero_poly_nat))) => ((~ ((A2 = zero_zero_poly_nat))) & (~ ((B = zero_zero_poly_nat)))))))). % mult_not_zero
thf(fact_195_mult__not__zero, axiom,
    ((![A2 : poly_poly_complex, B : poly_poly_complex]: ((~ (((times_1460995011omplex @ A2 @ B) = zero_z1040703943omplex))) => ((~ ((A2 = zero_z1040703943omplex))) & (~ ((B = zero_z1040703943omplex)))))))). % mult_not_zero
thf(fact_196_mult__not__zero, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((~ (((times_1246143675omplex @ A2 @ B) = zero_z1746442943omplex))) => ((~ ((A2 = zero_z1746442943omplex))) & (~ ((B = zero_z1746442943omplex)))))))). % mult_not_zero
thf(fact_197_mult__not__zero, axiom,
    ((![A2 : nat, B : nat]: ((~ (((times_times_nat @ A2 @ B) = zero_zero_nat))) => ((~ ((A2 = zero_zero_nat))) & (~ ((B = zero_zero_nat)))))))). % mult_not_zero
thf(fact_198_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_199_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_200_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_201_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_202_zero__neq__one, axiom,
    ((~ ((zero_z1040703943omplex = one_on1331105667omplex))))). % zero_neq_one
thf(fact_203_mult__minus1, axiom,
    ((![Z2 : poly_complex]: ((times_1246143675omplex @ (uminus1138659839omplex @ one_one_poly_complex) @ Z2) = (uminus1138659839omplex @ Z2))))). % mult_minus1
thf(fact_204_mult__minus1, axiom,
    ((![Z2 : complex]: ((times_times_complex @ (uminus1204672759omplex @ one_one_complex) @ Z2) = (uminus1204672759omplex @ Z2))))). % mult_minus1
thf(fact_205_mult__minus1__right, axiom,
    ((![Z2 : poly_complex]: ((times_1246143675omplex @ Z2 @ (uminus1138659839omplex @ one_one_poly_complex)) = (uminus1138659839omplex @ Z2))))). % mult_minus1_right
thf(fact_206_mult__minus1__right, axiom,
    ((![Z2 : complex]: ((times_times_complex @ Z2 @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ Z2))))). % mult_minus1_right
thf(fact_207__092_060open_062_091_058_N_Aa_M_A1_058_093_Advd_Aq_092_060close_062, axiom,
    ((dvd_dvd_poly_complex @ (pCons_complex @ (uminus1204672759omplex @ a) @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ qa))). % \<open>[:- a, 1:] dvd q\<close>
thf(fact_208_s, axiom,
    ((pa = (times_1246143675omplex @ (power_184595776omplex @ (pCons_complex @ (uminus1204672759omplex @ a) @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ (order_complex @ a @ pa)) @ s)))). % s
thf(fact_209_zero__neq__neg__one, axiom,
    ((~ ((zero_z1746442943omplex = (uminus1138659839omplex @ one_one_poly_complex)))))). % zero_neq_neg_one
thf(fact_210_zero__neq__neg__one, axiom,
    ((~ ((zero_z1040703943omplex = (uminus1762810119omplex @ one_on1331105667omplex)))))). % zero_neq_neg_one
thf(fact_211_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_complex = (uminus1204672759omplex @ one_one_complex)))))). % zero_neq_neg_one
thf(fact_212_mult__is__0, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = zero_zero_nat) = (((M = zero_zero_nat)) | ((N = zero_zero_nat))))))). % mult_is_0
thf(fact_213_mult__0__right, axiom,
    ((![M : nat]: ((times_times_nat @ M @ zero_zero_nat) = zero_zero_nat)))). % mult_0_right
thf(fact_214_mult__cancel1, axiom,
    ((![K : nat, M : nat, N : nat]: (((times_times_nat @ K @ M) = (times_times_nat @ K @ N)) = (((M = N)) | ((K = zero_zero_nat))))))). % mult_cancel1
thf(fact_215_mult__cancel2, axiom,
    ((![M : nat, K : nat, N : nat]: (((times_times_nat @ M @ K) = (times_times_nat @ N @ K)) = (((M = N)) | ((K = zero_zero_nat))))))). % mult_cancel2
thf(fact_216_dpn, axiom,
    (((degree_complex @ pa) = na))). % dpn
thf(fact_217_nat__1__eq__mult__iff, axiom,
    ((![M : nat, N : nat]: ((one_one_nat = (times_times_nat @ M @ N)) = (((M = one_one_nat)) & ((N = one_one_nat))))))). % nat_1_eq_mult_iff
thf(fact_218_nat__mult__eq__1__iff, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = one_one_nat) = (((M = one_one_nat)) & ((N = one_one_nat))))))). % nat_mult_eq_1_iff
thf(fact_219_dvd__0__right, axiom,
    ((![A2 : complex]: (dvd_dvd_complex @ A2 @ zero_zero_complex)))). % dvd_0_right
thf(fact_220_dvd__0__right, axiom,
    ((![A2 : poly_complex]: (dvd_dvd_poly_complex @ A2 @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_221_dvd__0__right, axiom,
    ((![A2 : nat]: (dvd_dvd_nat @ A2 @ zero_zero_nat)))). % dvd_0_right
thf(fact_222_dvd__0__right, axiom,
    ((![A2 : poly_nat]: (dvd_dvd_poly_nat @ A2 @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_223_dvd__0__right, axiom,
    ((![A2 : poly_poly_complex]: (dvd_dv598755940omplex @ A2 @ zero_z1040703943omplex)))). % dvd_0_right
thf(fact_224_dvd__0__left__iff, axiom,
    ((![A2 : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A2) = (A2 = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_225_dvd__0__left__iff, axiom,
    ((![A2 : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A2) = (A2 = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_226_dvd__0__left__iff, axiom,
    ((![A2 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A2) = (A2 = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_227_dvd__0__left__iff, axiom,
    ((![A2 : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A2) = (A2 = zero_zero_poly_nat))))). % dvd_0_left_iff
thf(fact_228_dvd__0__left__iff, axiom,
    ((![A2 : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A2) = (A2 = zero_z1040703943omplex))))). % dvd_0_left_iff
thf(fact_229_minus__dvd__iff, axiom,
    ((![X2 : poly_complex, Y2 : poly_complex]: ((dvd_dvd_poly_complex @ (uminus1138659839omplex @ X2) @ Y2) = (dvd_dvd_poly_complex @ X2 @ Y2))))). % minus_dvd_iff
thf(fact_230_minus__dvd__iff, axiom,
    ((![X2 : complex, Y2 : complex]: ((dvd_dvd_complex @ (uminus1204672759omplex @ X2) @ Y2) = (dvd_dvd_complex @ X2 @ Y2))))). % minus_dvd_iff
thf(fact_231_dvd__minus__iff, axiom,
    ((![X2 : poly_complex, Y2 : poly_complex]: ((dvd_dvd_poly_complex @ X2 @ (uminus1138659839omplex @ Y2)) = (dvd_dvd_poly_complex @ X2 @ Y2))))). % dvd_minus_iff
thf(fact_232_dvd__minus__iff, axiom,
    ((![X2 : complex, Y2 : complex]: ((dvd_dvd_complex @ X2 @ (uminus1204672759omplex @ Y2)) = (dvd_dvd_complex @ X2 @ Y2))))). % dvd_minus_iff
thf(fact_233_degree__minus, axiom,
    ((![P : poly_complex]: ((degree_complex @ (uminus1138659839omplex @ P)) = (degree_complex @ P))))). % degree_minus
thf(fact_234_order__uminus, axiom,
    ((![X2 : complex, P : poly_complex]: ((order_complex @ X2 @ (uminus1138659839omplex @ P)) = (order_complex @ X2 @ P))))). % order_uminus
thf(fact_235_dvd__mult__cancel__left, axiom,
    ((![C : complex, A2 : complex, B : complex]: ((dvd_dvd_complex @ (times_times_complex @ C @ A2) @ (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((dvd_dvd_complex @ A2 @ B))))))). % dvd_mult_cancel_left
thf(fact_236_dvd__mult__cancel__left, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex, B : poly_poly_complex]: ((dvd_dv598755940omplex @ (times_1460995011omplex @ C @ A2) @ (times_1460995011omplex @ C @ B)) = (((C = zero_z1040703943omplex)) | ((dvd_dv598755940omplex @ A2 @ B))))))). % dvd_mult_cancel_left
thf(fact_237_dvd__mult__cancel__left, axiom,
    ((![C : poly_complex, A2 : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ C @ A2) @ (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((dvd_dvd_poly_complex @ A2 @ B))))))). % dvd_mult_cancel_left
thf(fact_238_dvd__mult__cancel__right, axiom,
    ((![A2 : complex, C : complex, B : complex]: ((dvd_dvd_complex @ (times_times_complex @ A2 @ C) @ (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((dvd_dvd_complex @ A2 @ B))))))). % dvd_mult_cancel_right
thf(fact_239_dvd__mult__cancel__right, axiom,
    ((![A2 : poly_poly_complex, C : poly_poly_complex, B : poly_poly_complex]: ((dvd_dv598755940omplex @ (times_1460995011omplex @ A2 @ C) @ (times_1460995011omplex @ B @ C)) = (((C = zero_z1040703943omplex)) | ((dvd_dv598755940omplex @ A2 @ B))))))). % dvd_mult_cancel_right
thf(fact_240_dvd__mult__cancel__right, axiom,
    ((![A2 : poly_complex, C : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ (times_1246143675omplex @ A2 @ C) @ (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((dvd_dvd_poly_complex @ A2 @ B))))))). % dvd_mult_cancel_right
thf(fact_241_ap_I1_J, axiom,
    ((dvd_dvd_poly_complex @ (power_184595776omplex @ (pCons_complex @ (uminus1204672759omplex @ a) @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ (order_complex @ a @ pa)) @ pa))). % ap(1)
thf(fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_Ap_A_061_A_091_058_N_Aa_M_A1_058_093_A_094_Aorder_Aa_Ap_A_K_As_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![S : poly_complex]: (~ ((pa = (times_1246143675omplex @ (power_184595776omplex @ (pCons_complex @ (uminus1204672759omplex @ a) @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ (order_complex @ a @ pa)) @ S))))))))). % \<open>\<And>thesis. (\<And>s. p = [:- a, 1:] ^ order a p * s \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_243_IH, axiom,
    ((![M2 : nat]: ((ord_less_nat @ M2 @ na) => (![P4 : poly_complex, Q4 : poly_complex]: ((![X4 : complex]: (((poly_complex2 @ P4 @ X4) = zero_zero_complex) => ((poly_complex2 @ Q4 @ X4) = zero_zero_complex))) => (((degree_complex @ P4) = M2) => ((~ ((M2 = zero_zero_nat))) => (dvd_dvd_poly_complex @ P4 @ (power_184595776omplex @ Q4 @ M2)))))))))). % IH
thf(fact_244_nat__mult__1, axiom,
    ((![N : nat]: ((times_times_nat @ one_one_nat @ N) = N)))). % nat_mult_1
thf(fact_245_nat__mult__1__right, axiom,
    ((![N : nat]: ((times_times_nat @ N @ one_one_nat) = N)))). % nat_mult_1_right
thf(fact_246_mult__eq__self__implies__10, axiom,
    ((![M : nat, N : nat]: ((M = (times_times_nat @ M @ N)) => ((N = one_one_nat) | (M = zero_zero_nat)))))). % mult_eq_self_implies_10

% Conjectures (1)
thf(conj_0, conjecture,
    (((poly_complex2 @ r @ x) = zero_zero_complex))).
