% 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_1171__5378886_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:36:16.744

% 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 (79)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Complex__Ocomplex, type,
    fundam1201687030omplex : poly_complex > complex > poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Nat__Onat, type,
    fundam170929432ly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1307691262omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Nat__Onat, type,
    fundam1567013434ze_nat : poly_nat > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1956464160omplex : poly_poly_complex > nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    one_one_poly_complex : poly_complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    one_one_poly_nat : poly_nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    one_on1331105667omplex : poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    zero_z1059985641ly_nat : poly_poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    zero_z1200043727omplex : poly_p1267267526omplex).
thf(sy_c_If_001t__Complex__Ocomplex, type,
    if_complex : $o > complex > complex > complex).
thf(sy_c_If_001t__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
thf(sy_c_If_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    if_poly_complex : $o > poly_complex > poly_complex > poly_complex).
thf(sy_c_If_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    if_poly_nat : $o > poly_nat > poly_nat > poly_nat).
thf(sy_c_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    if_poly_poly_complex : $o > poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Complex__Ocomplex, type,
    divide23485933omplex : complex > poly_complex > poly_complex > poly_complex > nat > nat > poly_complex).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    divide219992821omplex : poly_complex > poly_poly_complex > poly_poly_complex > poly_poly_complex > nat > nat > poly_poly_complex).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    divide713971197omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex > poly_p1267267526omplex > nat > nat > poly_p1267267526omplex).
thf(sy_c_Polynomial_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat, type,
    is_zero_nat : poly_nat > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    is_zero_poly_complex : poly_poly_complex > $o).
thf(sy_c_Polynomial_Omonom_001t__Complex__Ocomplex, type,
    monom_complex : complex > nat > poly_complex).
thf(sy_c_Polynomial_Omonom_001t__Nat__Onat, type,
    monom_nat : nat > nat > poly_nat).
thf(sy_c_Polynomial_Omonom_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    monom_poly_complex : poly_complex > nat > poly_poly_complex).
thf(sy_c_Polynomial_Omonom_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    monom_poly_nat : poly_nat > nat > poly_poly_nat).
thf(sy_c_Polynomial_Omonom_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    monom_1210178217omplex : poly_poly_complex > nat > poly_p1267267526omplex).
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_Opcompose_001t__Complex__Ocomplex, type,
    pcompose_complex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opcompose_001t__Nat__Onat, type,
    pcompose_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opcompose_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    pcompo1411605209omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opcompose_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    pcompose_poly_nat : poly_poly_nat > poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Opcompose_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    pcompo611487201omplex : poly_p1267267526omplex > poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Complex__Ocomplex, type,
    coeff_complex : poly_complex > nat > complex).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Nat__Onat, type,
    coeff_nat : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    coeff_poly_complex : poly_poly_complex > nat > poly_complex).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    coeff_poly_nat : poly_poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    coeff_1429652124omplex : poly_p1267267526omplex > nat > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Nat__Onat, type,
    poly_cutoff_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_c622223248omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__shift_001t__Complex__Ocomplex, type,
    poly_shift_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly__shift_001t__Nat__Onat, type,
    poly_shift_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__shift_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_s558570093omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_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_Orsquarefree_001t__Complex__Ocomplex, type,
    rsquarefree_complex : poly_complex > $o).
thf(sy_c_Polynomial_Orsquarefree_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    rsquar936197586omplex : poly_poly_complex > $o).
thf(sy_c_Polynomial_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > poly_complex).
thf(sy_c_Polynomial_Osynthetic__div_001t__Nat__Onat, type,
    synthetic_div_nat : poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Osynthetic__div_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    synthe1985144195omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_v_a, type,
    a : complex).
thf(sy_v_b, type,
    b : complex).
thf(sy_v_p, type,
    p : poly_complex).

% Relevant facts (245)
thf(fact_0_l, axiom,
    ((~ ((p = zero_z1746442943omplex))))). % l
thf(fact_1__092_060open_062_092_060And_062t_Ah_O_A_092_060lbrakk_062h_A_092_060noteq_062_A0_059_At_A_061_A0_059_ApCons_Aa_A_IpCons_Ab_Ap_J_A_061_ApCons_Ah_At_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((![H : complex, T : poly_complex]: ((~ ((H = zero_zero_complex))) => ((T = zero_z1746442943omplex) => (~ (((pCons_complex @ a @ (pCons_complex @ b @ p)) = (pCons_complex @ H @ T))))))))). % \<open>\<And>t h. \<lbrakk>h \<noteq> 0; t = 0; pCons a (pCons b p) = pCons h t\<rbrakk> \<Longrightarrow> False\<close>
thf(fact_2_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_3_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_4_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_5_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_6_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_7_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_8_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_9_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_10_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_11_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_12_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_13_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_14_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_15_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_16_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_17_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_18_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_19_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_20_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_21_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_22_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_23_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_24_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_25_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_26_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_27_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_28_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_29_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_30_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_31_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_32_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_33_offset__poly__single, axiom,
    ((![A : complex, H : complex]: ((fundam1201687030omplex @ (pCons_complex @ A @ zero_z1746442943omplex) @ H) = (pCons_complex @ A @ zero_z1746442943omplex))))). % offset_poly_single
thf(fact_34_offset__poly__single, axiom,
    ((![A : nat, H : nat]: ((fundam170929432ly_nat @ (pCons_nat @ A @ zero_zero_poly_nat) @ H) = (pCons_nat @ A @ zero_zero_poly_nat))))). % offset_poly_single
thf(fact_35_offset__poly__single, axiom,
    ((![A : poly_complex, H : poly_complex]: ((fundam1307691262omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex) @ H) = (pCons_poly_complex @ A @ zero_z1040703943omplex))))). % offset_poly_single
thf(fact_36_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A2 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_37_pCons__cases, axiom,
    ((![P : poly_nat]: (~ ((![A2 : nat, Q2 : poly_nat]: (~ ((P = (pCons_nat @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_38_pCons__cases, axiom,
    ((![P : poly_poly_complex]: (~ ((![A2 : poly_complex, Q2 : poly_poly_complex]: (~ ((P = (pCons_poly_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_39_pderiv_Ocases, axiom,
    ((![X : poly_complex]: (~ ((![A2 : complex, P3 : poly_complex]: (~ ((X = (pCons_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_40_pderiv_Ocases, axiom,
    ((![X : poly_nat]: (~ ((![A2 : nat, P3 : poly_nat]: (~ ((X = (pCons_nat @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_41_pderiv_Ocases, axiom,
    ((![X : poly_poly_complex]: (~ ((![A2 : poly_complex, P3 : poly_poly_complex]: (~ ((X = (pCons_poly_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_42_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_43_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_44_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_45_zero__reorient, axiom,
    ((![X : poly_nat]: ((zero_zero_poly_nat = X) = (X = zero_zero_poly_nat))))). % zero_reorient
thf(fact_46_zero__reorient, axiom,
    ((![X : poly_poly_complex]: ((zero_z1040703943omplex = X) = (X = zero_z1040703943omplex))))). % zero_reorient
thf(fact_47_poly__0, axiom,
    ((![X : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X) = zero_zero_poly_nat)))). % poly_0
thf(fact_48_poly__0, axiom,
    ((![X : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X) = zero_z1040703943omplex)))). % poly_0
thf(fact_49_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_50_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_51_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_52_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_53_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X2 : complex]: ((poly_complex2 @ P @ X2) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_54_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X2 : poly_complex]: ((poly_poly_complex2 @ P @ X2) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_55_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ P @ X2) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_56_mpoly__base__conv_I1_J, axiom,
    ((![X : complex]: (zero_zero_complex = (poly_complex2 @ zero_z1746442943omplex @ X))))). % mpoly_base_conv(1)
thf(fact_57_mpoly__base__conv_I1_J, axiom,
    ((![X : poly_complex]: (zero_z1746442943omplex = (poly_poly_complex2 @ zero_z1040703943omplex @ X))))). % mpoly_base_conv(1)
thf(fact_58_mpoly__base__conv_I1_J, axiom,
    ((![X : poly_poly_complex]: (zero_z1040703943omplex = (poly_p282434315omplex @ zero_z1200043727omplex @ X))))). % mpoly_base_conv(1)
thf(fact_59_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_60_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_61_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_62_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_63_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_64_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_65_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_poly_complex]: (~ (((poly_p282434315omplex @ zero_z1200043727omplex @ X3) = zero_z1040703943omplex)))))))). % basic_cqe_conv1(2)
thf(fact_66_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : complex]: (~ (((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))))))). % basic_cqe_conv1(2)
thf(fact_67_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : nat]: (~ (((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))))))). % basic_cqe_conv1(2)
thf(fact_68_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_complex]: (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))))))). % basic_cqe_conv1(2)
thf(fact_69_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X4) = zero_zero_poly_nat)))). % basic_cqe_conv1(4)
thf(fact_70_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X4) = zero_z1040703943omplex)))). % basic_cqe_conv1(4)
thf(fact_71_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X4) = zero_zero_complex)))). % basic_cqe_conv1(4)
thf(fact_72_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X4) = zero_zero_nat)))). % basic_cqe_conv1(4)
thf(fact_73_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X4) = zero_z1746442943omplex)))). % basic_cqe_conv1(4)
thf(fact_74_poly__pad__rule, axiom,
    ((![P : poly_complex, X : complex]: (((poly_complex2 @ P @ X) = zero_zero_complex) => ((poly_complex2 @ (pCons_complex @ zero_zero_complex @ P) @ X) = zero_zero_complex))))). % poly_pad_rule
thf(fact_75_poly__pad__rule, axiom,
    ((![P : poly_poly_complex, X : poly_complex]: (((poly_poly_complex2 @ P @ X) = zero_z1746442943omplex) => ((poly_poly_complex2 @ (pCons_poly_complex @ zero_z1746442943omplex @ P) @ X) = zero_z1746442943omplex))))). % poly_pad_rule
thf(fact_76_poly__pad__rule, axiom,
    ((![P : poly_nat, X : nat]: (((poly_nat2 @ P @ X) = zero_zero_nat) => ((poly_nat2 @ (pCons_nat @ zero_zero_nat @ P) @ X) = zero_zero_nat))))). % poly_pad_rule
thf(fact_77_poly__pad__rule, axiom,
    ((![P : poly_poly_nat, X : poly_nat]: (((poly_poly_nat2 @ P @ X) = zero_zero_poly_nat) => ((poly_poly_nat2 @ (pCons_poly_nat @ zero_zero_poly_nat @ P) @ X) = zero_zero_poly_nat))))). % poly_pad_rule
thf(fact_78_poly__pad__rule, axiom,
    ((![P : poly_p1267267526omplex, X : poly_poly_complex]: (((poly_p282434315omplex @ P @ X) = zero_z1040703943omplex) => ((poly_p282434315omplex @ (pCons_1087637536omplex @ zero_z1040703943omplex @ P) @ X) = zero_z1040703943omplex))))). % poly_pad_rule
thf(fact_79_mpoly__norm__conv_I2_J, axiom,
    ((![Y : complex, X : complex]: ((poly_complex2 @ (pCons_complex @ (poly_complex2 @ zero_z1746442943omplex @ Y) @ zero_z1746442943omplex) @ X) = (poly_complex2 @ zero_z1746442943omplex @ X))))). % mpoly_norm_conv(2)
thf(fact_80_mpoly__norm__conv_I2_J, axiom,
    ((![Y : poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (pCons_poly_complex @ (poly_poly_complex2 @ zero_z1040703943omplex @ Y) @ zero_z1040703943omplex) @ X) = (poly_poly_complex2 @ zero_z1040703943omplex @ X))))). % mpoly_norm_conv(2)
thf(fact_81_mpoly__base__conv_I2_J, axiom,
    ((![C : complex, X : complex]: (C = (poly_complex2 @ (pCons_complex @ C @ zero_z1746442943omplex) @ X))))). % mpoly_base_conv(2)
thf(fact_82_mpoly__base__conv_I2_J, axiom,
    ((![C : poly_complex, X : poly_complex]: (C = (poly_poly_complex2 @ (pCons_poly_complex @ C @ zero_z1040703943omplex) @ X))))). % mpoly_base_conv(2)
thf(fact_83_offset__poly__eq__0__iff, axiom,
    ((![P : poly_complex, H : complex]: (((fundam1201687030omplex @ P @ H) = zero_z1746442943omplex) = (P = zero_z1746442943omplex))))). % offset_poly_eq_0_iff
thf(fact_84_offset__poly__eq__0__iff, axiom,
    ((![P : poly_nat, H : nat]: (((fundam170929432ly_nat @ P @ H) = zero_zero_poly_nat) = (P = zero_zero_poly_nat))))). % offset_poly_eq_0_iff
thf(fact_85_offset__poly__eq__0__iff, axiom,
    ((![P : poly_poly_complex, H : poly_complex]: (((fundam1307691262omplex @ P @ H) = zero_z1040703943omplex) = (P = zero_z1040703943omplex))))). % offset_poly_eq_0_iff
thf(fact_86_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_87_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_88_offset__poly__0, axiom,
    ((![H : poly_complex]: ((fundam1307691262omplex @ zero_z1040703943omplex @ H) = zero_z1040703943omplex)))). % offset_poly_0
thf(fact_89_mpoly__norm__conv_I1_J, axiom,
    ((![X : complex]: ((poly_complex2 @ (pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) @ X) = (poly_complex2 @ zero_z1746442943omplex @ X))))). % mpoly_norm_conv(1)
thf(fact_90_mpoly__norm__conv_I1_J, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ (pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) @ X) = (poly_poly_complex2 @ zero_z1040703943omplex @ X))))). % mpoly_norm_conv(1)
thf(fact_91_mpoly__norm__conv_I1_J, axiom,
    ((![X : poly_poly_complex]: ((poly_p282434315omplex @ (pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) @ X) = (poly_p282434315omplex @ zero_z1200043727omplex @ X))))). % mpoly_norm_conv(1)
thf(fact_92_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_nat]: ((?[X2 : poly_nat]: (~ (((poly_poly_nat2 @ (pCons_poly_nat @ C @ zero_z1059985641ly_nat) @ X2) = zero_zero_poly_nat)))) = (~ ((C = zero_zero_poly_nat))))))). % basic_cqe_conv1(3)
thf(fact_93_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_poly_complex]: ((?[X2 : poly_poly_complex]: (~ (((poly_p282434315omplex @ (pCons_1087637536omplex @ C @ zero_z1200043727omplex) @ X2) = zero_z1040703943omplex)))) = (~ ((C = zero_z1040703943omplex))))))). % basic_cqe_conv1(3)
thf(fact_94_basic__cqe__conv1_I3_J, axiom,
    ((![C : complex]: ((?[X2 : complex]: (~ (((poly_complex2 @ (pCons_complex @ C @ zero_z1746442943omplex) @ X2) = zero_zero_complex)))) = (~ ((C = zero_zero_complex))))))). % basic_cqe_conv1(3)
thf(fact_95_basic__cqe__conv1_I3_J, axiom,
    ((![C : nat]: ((?[X2 : nat]: (~ (((poly_nat2 @ (pCons_nat @ C @ zero_zero_poly_nat) @ X2) = zero_zero_nat)))) = (~ ((C = zero_zero_nat))))))). % basic_cqe_conv1(3)
thf(fact_96_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_complex]: ((?[X2 : poly_complex]: (~ (((poly_poly_complex2 @ (pCons_poly_complex @ C @ zero_z1040703943omplex) @ X2) = zero_z1746442943omplex)))) = (~ ((C = zero_z1746442943omplex))))))). % basic_cqe_conv1(3)
thf(fact_97_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_nat]: ((?[X2 : poly_nat]: ((poly_poly_nat2 @ (pCons_poly_nat @ C @ zero_z1059985641ly_nat) @ X2) = zero_zero_poly_nat)) = (C = zero_zero_poly_nat))))). % basic_cqe_conv1(5)
thf(fact_98_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_poly_complex]: ((?[X2 : poly_poly_complex]: ((poly_p282434315omplex @ (pCons_1087637536omplex @ C @ zero_z1200043727omplex) @ X2) = zero_z1040703943omplex)) = (C = zero_z1040703943omplex))))). % basic_cqe_conv1(5)
thf(fact_99_basic__cqe__conv1_I5_J, axiom,
    ((![C : complex]: ((?[X2 : complex]: ((poly_complex2 @ (pCons_complex @ C @ zero_z1746442943omplex) @ X2) = zero_zero_complex)) = (C = zero_zero_complex))))). % basic_cqe_conv1(5)
thf(fact_100_basic__cqe__conv1_I5_J, axiom,
    ((![C : nat]: ((?[X2 : nat]: ((poly_nat2 @ (pCons_nat @ C @ zero_zero_poly_nat) @ X2) = zero_zero_nat)) = (C = zero_zero_nat))))). % basic_cqe_conv1(5)
thf(fact_101_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_complex]: ((?[X2 : poly_complex]: ((poly_poly_complex2 @ (pCons_poly_complex @ C @ zero_z1040703943omplex) @ X2) = zero_z1746442943omplex)) = (C = zero_z1746442943omplex))))). % basic_cqe_conv1(5)
thf(fact_102_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_103_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_104_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_105_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_106_is__zero__null, axiom,
    ((is_zero_complex = (^[P4 : poly_complex]: (P4 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_107_is__zero__null, axiom,
    ((is_zero_nat = (^[P4 : poly_nat]: (P4 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_108_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P4 : poly_poly_complex]: (P4 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_109_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_110_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_111_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_c622223248omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_112_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_113_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_114_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_115_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_116_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_117_mpoly__base__conv_I3_J, axiom,
    ((![X : complex]: (X = (poly_complex2 @ (pCons_complex @ zero_zero_complex @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ X))))). % mpoly_base_conv(3)
thf(fact_118_mpoly__base__conv_I3_J, axiom,
    ((![X : poly_complex]: (X = (poly_poly_complex2 @ (pCons_poly_complex @ zero_z1746442943omplex @ (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex)) @ X))))). % mpoly_base_conv(3)
thf(fact_119_mpoly__base__conv_I3_J, axiom,
    ((![X : poly_poly_complex]: (X = (poly_p282434315omplex @ (pCons_1087637536omplex @ zero_z1040703943omplex @ (pCons_1087637536omplex @ one_on1331105667omplex @ zero_z1200043727omplex)) @ X))))). % mpoly_base_conv(3)
thf(fact_120_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_121_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_122_poly__shift__0, axiom,
    ((![N : nat]: ((poly_s558570093omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_shift_0
thf(fact_123_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_124_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_125_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_126_reflect__poly__const, axiom,
    ((![A : complex]: ((reflect_poly_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = (pCons_complex @ A @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_127_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_128_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_129_divide__poly__main__0, axiom,
    ((![R : poly_complex, D : poly_complex, Dr : nat, N : nat]: ((divide23485933omplex @ zero_zero_complex @ zero_z1746442943omplex @ R @ D @ Dr @ N) = zero_z1746442943omplex)))). % divide_poly_main_0
thf(fact_130_divide__poly__main__0, axiom,
    ((![R : poly_poly_complex, D : poly_poly_complex, Dr : nat, N : nat]: ((divide219992821omplex @ zero_z1746442943omplex @ zero_z1040703943omplex @ R @ D @ Dr @ N) = zero_z1040703943omplex)))). % divide_poly_main_0
thf(fact_131_divide__poly__main__0, axiom,
    ((![R : poly_p1267267526omplex, D : poly_p1267267526omplex, Dr : nat, N : nat]: ((divide713971197omplex @ zero_z1040703943omplex @ zero_z1200043727omplex @ R @ D @ Dr @ N) = zero_z1200043727omplex)))). % divide_poly_main_0
thf(fact_132_poly__1, axiom,
    ((![X : complex]: ((poly_complex2 @ one_one_poly_complex @ X) = one_one_complex)))). % poly_1
thf(fact_133_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_134_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_135_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_136_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_137_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_138_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_139_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_140_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_141_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_142_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_143_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_144_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_145_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_146_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_147_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_148_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_149_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_150_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X2 : complex]: (![Y2 : complex]: ((F @ X2) = (F @ Y2)))))))). % constant_def
thf(fact_151_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_complex @ N @ one_one_poly_complex) = one_one_poly_complex)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_complex @ N @ one_one_poly_complex) = zero_z1746442943omplex)))))). % poly_shift_1
thf(fact_152_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_nat @ N @ one_one_poly_nat) = one_one_poly_nat)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_nat @ N @ one_one_poly_nat) = zero_zero_poly_nat)))))). % poly_shift_1
thf(fact_153_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_s558570093omplex @ N @ one_on1331105667omplex) = one_on1331105667omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_s558570093omplex @ N @ one_on1331105667omplex) = zero_z1040703943omplex)))))). % poly_shift_1
thf(fact_154_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_155_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_156_pCons__one, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % pCons_one
thf(fact_157_order__0I, axiom,
    ((![P : poly_complex, A : complex]: ((~ (((poly_complex2 @ P @ A) = zero_zero_complex))) => ((order_complex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_158_order__0I, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: ((~ (((poly_poly_complex2 @ P @ A) = zero_z1746442943omplex))) => ((order_poly_complex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_159_order__0I, axiom,
    ((![P : poly_p1267267526omplex, A : poly_poly_complex]: ((~ (((poly_p282434315omplex @ P @ A) = zero_z1040703943omplex))) => ((order_1735763309omplex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_160_rsquarefree__def, axiom,
    ((rsquarefree_complex = (^[P4 : poly_complex]: (((~ ((P4 = zero_z1746442943omplex)))) & ((![A3 : complex]: ((((order_complex @ A3 @ P4) = zero_zero_nat)) | (((order_complex @ A3 @ P4) = one_one_nat)))))))))). % rsquarefree_def
thf(fact_161_rsquarefree__def, axiom,
    ((rsquar936197586omplex = (^[P4 : poly_poly_complex]: (((~ ((P4 = zero_z1040703943omplex)))) & ((![A3 : poly_complex]: ((((order_poly_complex @ A3 @ P4) = zero_zero_nat)) | (((order_poly_complex @ A3 @ P4) = one_one_nat)))))))))). % rsquarefree_def
thf(fact_162_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_163_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_164_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_165_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_166_zero__neq__one, axiom,
    ((~ ((zero_z1040703943omplex = one_on1331105667omplex))))). % zero_neq_one
thf(fact_167_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_168_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_169_psize__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((fundam1956464160omplex @ P) = zero_zero_nat) = (P = zero_z1040703943omplex))))). % psize_eq_0_iff
thf(fact_170_pcompose__idR, axiom,
    ((![P : poly_complex]: ((pcompose_complex @ P @ (pCons_complex @ zero_zero_complex @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex))) = P)))). % pcompose_idR
thf(fact_171_pcompose__idR, axiom,
    ((![P : poly_poly_complex]: ((pcompo1411605209omplex @ P @ (pCons_poly_complex @ zero_z1746442943omplex @ (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex))) = P)))). % pcompose_idR
thf(fact_172_pcompose__idR, axiom,
    ((![P : poly_nat]: ((pcompose_nat @ P @ (pCons_nat @ zero_zero_nat @ (pCons_nat @ one_one_nat @ zero_zero_poly_nat))) = P)))). % pcompose_idR
thf(fact_173_pcompose__idR, axiom,
    ((![P : poly_poly_nat]: ((pcompose_poly_nat @ P @ (pCons_poly_nat @ zero_zero_poly_nat @ (pCons_poly_nat @ one_one_poly_nat @ zero_z1059985641ly_nat))) = P)))). % pcompose_idR
thf(fact_174_pcompose__idR, axiom,
    ((![P : poly_p1267267526omplex]: ((pcompo611487201omplex @ P @ (pCons_1087637536omplex @ zero_z1040703943omplex @ (pCons_1087637536omplex @ one_on1331105667omplex @ zero_z1200043727omplex))) = P)))). % pcompose_idR
thf(fact_175_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_complex]: (((coeff_complex @ (reflect_poly_complex @ P) @ zero_zero_nat) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_176_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_complex]: (((coeff_poly_complex @ (reflec309385472omplex @ P) @ zero_zero_nat) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_177_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_nat]: (((coeff_nat @ (reflect_poly_nat @ P) @ zero_zero_nat) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_178_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_nat]: (((coeff_poly_nat @ (reflec781175074ly_nat @ P) @ zero_zero_nat) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_179_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((coeff_1429652124omplex @ (reflec1997789704omplex @ P) @ zero_zero_nat) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_180_monom__eq__const__iff, axiom,
    ((![C : poly_nat, N : nat, D : poly_nat]: (((monom_poly_nat @ C @ N) = (pCons_poly_nat @ D @ zero_z1059985641ly_nat)) = (((C = D)) & ((((C = zero_zero_poly_nat)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_181_monom__eq__const__iff, axiom,
    ((![C : poly_poly_complex, N : nat, D : poly_poly_complex]: (((monom_1210178217omplex @ C @ N) = (pCons_1087637536omplex @ D @ zero_z1200043727omplex)) = (((C = D)) & ((((C = zero_z1040703943omplex)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_182_monom__eq__const__iff, axiom,
    ((![C : complex, N : nat, D : complex]: (((monom_complex @ C @ N) = (pCons_complex @ D @ zero_z1746442943omplex)) = (((C = D)) & ((((C = zero_zero_complex)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_183_monom__eq__const__iff, axiom,
    ((![C : nat, N : nat, D : nat]: (((monom_nat @ C @ N) = (pCons_nat @ D @ zero_zero_poly_nat)) = (((C = D)) & ((((C = zero_zero_nat)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_184_monom__eq__const__iff, axiom,
    ((![C : poly_complex, N : nat, D : poly_complex]: (((monom_poly_complex @ C @ N) = (pCons_poly_complex @ D @ zero_z1040703943omplex)) = (((C = D)) & ((((C = zero_z1746442943omplex)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_185_pcompose__0, axiom,
    ((![Q : poly_complex]: ((pcompose_complex @ zero_z1746442943omplex @ Q) = zero_z1746442943omplex)))). % pcompose_0
thf(fact_186_pcompose__0, axiom,
    ((![Q : poly_nat]: ((pcompose_nat @ zero_zero_poly_nat @ Q) = zero_zero_poly_nat)))). % pcompose_0
thf(fact_187_pcompose__0, axiom,
    ((![Q : poly_poly_complex]: ((pcompo1411605209omplex @ zero_z1040703943omplex @ Q) = zero_z1040703943omplex)))). % pcompose_0
thf(fact_188_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_189_coeff__0, axiom,
    ((![N : nat]: ((coeff_1429652124omplex @ zero_z1200043727omplex @ N) = zero_z1040703943omplex)))). % coeff_0
thf(fact_190_coeff__0, axiom,
    ((![N : nat]: ((coeff_complex @ zero_z1746442943omplex @ N) = zero_zero_complex)))). % coeff_0
thf(fact_191_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_192_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_complex @ zero_z1040703943omplex @ N) = zero_z1746442943omplex)))). % coeff_0
thf(fact_193_coeff__pCons__0, axiom,
    ((![A : complex, P : poly_complex]: ((coeff_complex @ (pCons_complex @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_194_coeff__pCons__0, axiom,
    ((![A : nat, P : poly_nat]: ((coeff_nat @ (pCons_nat @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_195_coeff__pCons__0, axiom,
    ((![A : poly_complex, P : poly_poly_complex]: ((coeff_poly_complex @ (pCons_poly_complex @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_196_monom__eq__0__iff, axiom,
    ((![A : poly_nat, N : nat]: (((monom_poly_nat @ A @ N) = zero_z1059985641ly_nat) = (A = zero_zero_poly_nat))))). % monom_eq_0_iff
thf(fact_197_monom__eq__0__iff, axiom,
    ((![A : poly_poly_complex, N : nat]: (((monom_1210178217omplex @ A @ N) = zero_z1200043727omplex) = (A = zero_z1040703943omplex))))). % monom_eq_0_iff
thf(fact_198_monom__eq__0__iff, axiom,
    ((![A : complex, N : nat]: (((monom_complex @ A @ N) = zero_z1746442943omplex) = (A = zero_zero_complex))))). % monom_eq_0_iff
thf(fact_199_monom__eq__0__iff, axiom,
    ((![A : nat, N : nat]: (((monom_nat @ A @ N) = zero_zero_poly_nat) = (A = zero_zero_nat))))). % monom_eq_0_iff
thf(fact_200_monom__eq__0__iff, axiom,
    ((![A : poly_complex, N : nat]: (((monom_poly_complex @ A @ N) = zero_z1040703943omplex) = (A = zero_z1746442943omplex))))). % monom_eq_0_iff
thf(fact_201_monom__eq__0, axiom,
    ((![N : nat]: ((monom_complex @ zero_zero_complex @ N) = zero_z1746442943omplex)))). % monom_eq_0
thf(fact_202_monom__eq__0, axiom,
    ((![N : nat]: ((monom_poly_complex @ zero_z1746442943omplex @ N) = zero_z1040703943omplex)))). % monom_eq_0
thf(fact_203_monom__eq__0, axiom,
    ((![N : nat]: ((monom_nat @ zero_zero_nat @ N) = zero_zero_poly_nat)))). % monom_eq_0
thf(fact_204_monom__eq__0, axiom,
    ((![N : nat]: ((monom_poly_nat @ zero_zero_poly_nat @ N) = zero_z1059985641ly_nat)))). % monom_eq_0
thf(fact_205_monom__eq__0, axiom,
    ((![N : nat]: ((monom_1210178217omplex @ zero_z1040703943omplex @ N) = zero_z1200043727omplex)))). % monom_eq_0
thf(fact_206_coeff__monom, axiom,
    ((![M : nat, N : nat, A : complex]: (((M = N) => ((coeff_complex @ (monom_complex @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_complex @ (monom_complex @ A @ M) @ N) = zero_zero_complex)))))). % coeff_monom
thf(fact_207_coeff__monom, axiom,
    ((![M : nat, N : nat, A : poly_complex]: (((M = N) => ((coeff_poly_complex @ (monom_poly_complex @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_poly_complex @ (monom_poly_complex @ A @ M) @ N) = zero_z1746442943omplex)))))). % coeff_monom
thf(fact_208_coeff__monom, axiom,
    ((![M : nat, N : nat, A : nat]: (((M = N) => ((coeff_nat @ (monom_nat @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_nat @ (monom_nat @ A @ M) @ N) = zero_zero_nat)))))). % coeff_monom
thf(fact_209_coeff__monom, axiom,
    ((![M : nat, N : nat, A : poly_nat]: (((M = N) => ((coeff_poly_nat @ (monom_poly_nat @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_poly_nat @ (monom_poly_nat @ A @ M) @ N) = zero_zero_poly_nat)))))). % coeff_monom
thf(fact_210_coeff__monom, axiom,
    ((![M : nat, N : nat, A : poly_poly_complex]: (((M = N) => ((coeff_1429652124omplex @ (monom_1210178217omplex @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_1429652124omplex @ (monom_1210178217omplex @ A @ M) @ N) = zero_z1040703943omplex)))))). % coeff_monom
thf(fact_211_order__0__monom, axiom,
    ((![C : complex, N : nat]: ((~ ((C = zero_zero_complex))) => ((order_complex @ zero_zero_complex @ (monom_complex @ C @ N)) = N))))). % order_0_monom
thf(fact_212_order__0__monom, axiom,
    ((![C : poly_complex, N : nat]: ((~ ((C = zero_z1746442943omplex))) => ((order_poly_complex @ zero_z1746442943omplex @ (monom_poly_complex @ C @ N)) = N))))). % order_0_monom
thf(fact_213_order__0__monom, axiom,
    ((![C : poly_poly_complex, N : nat]: ((~ ((C = zero_z1040703943omplex))) => ((order_1735763309omplex @ zero_z1040703943omplex @ (monom_1210178217omplex @ C @ N)) = N))))). % order_0_monom
thf(fact_214_pcompose__const, axiom,
    ((![A : complex, Q : poly_complex]: ((pcompose_complex @ (pCons_complex @ A @ zero_z1746442943omplex) @ Q) = (pCons_complex @ A @ zero_z1746442943omplex))))). % pcompose_const
thf(fact_215_pcompose__const, axiom,
    ((![A : nat, Q : poly_nat]: ((pcompose_nat @ (pCons_nat @ A @ zero_zero_poly_nat) @ Q) = (pCons_nat @ A @ zero_zero_poly_nat))))). % pcompose_const
thf(fact_216_pcompose__const, axiom,
    ((![A : poly_complex, Q : poly_poly_complex]: ((pcompo1411605209omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex) @ Q) = (pCons_poly_complex @ A @ zero_z1040703943omplex))))). % pcompose_const
thf(fact_217_reflect__poly__reflect__poly, axiom,
    ((![P : poly_complex]: ((~ (((coeff_complex @ P @ zero_zero_nat) = zero_zero_complex))) => ((reflect_poly_complex @ (reflect_poly_complex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_218_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_complex]: ((~ (((coeff_poly_complex @ P @ zero_zero_nat) = zero_z1746442943omplex))) => ((reflec309385472omplex @ (reflec309385472omplex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_219_reflect__poly__reflect__poly, axiom,
    ((![P : poly_nat]: ((~ (((coeff_nat @ P @ zero_zero_nat) = zero_zero_nat))) => ((reflect_poly_nat @ (reflect_poly_nat @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_220_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_nat]: ((~ (((coeff_poly_nat @ P @ zero_zero_nat) = zero_zero_poly_nat))) => ((reflec781175074ly_nat @ (reflec781175074ly_nat @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_221_reflect__poly__reflect__poly, axiom,
    ((![P : poly_p1267267526omplex]: ((~ (((coeff_1429652124omplex @ P @ zero_zero_nat) = zero_z1040703943omplex))) => ((reflec1997789704omplex @ (reflec1997789704omplex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_222_monom__eq__1, axiom,
    (((monom_nat @ one_one_nat @ zero_zero_nat) = one_one_poly_nat))). % monom_eq_1
thf(fact_223_monom_Orep__eq, axiom,
    ((![X : complex, Xa : nat]: ((coeff_complex @ (monom_complex @ X @ Xa)) = (^[N2 : nat]: (if_complex @ (Xa = N2) @ X @ zero_zero_complex)))))). % monom.rep_eq
thf(fact_224_monom_Orep__eq, axiom,
    ((![X : poly_complex, Xa : nat]: ((coeff_poly_complex @ (monom_poly_complex @ X @ Xa)) = (^[N2 : nat]: (if_poly_complex @ (Xa = N2) @ X @ zero_z1746442943omplex)))))). % monom.rep_eq
thf(fact_225_monom_Orep__eq, axiom,
    ((![X : nat, Xa : nat]: ((coeff_nat @ (monom_nat @ X @ Xa)) = (^[N2 : nat]: (if_nat @ (Xa = N2) @ X @ zero_zero_nat)))))). % monom.rep_eq
thf(fact_226_monom_Orep__eq, axiom,
    ((![X : poly_nat, Xa : nat]: ((coeff_poly_nat @ (monom_poly_nat @ X @ Xa)) = (^[N2 : nat]: (if_poly_nat @ (Xa = N2) @ X @ zero_zero_poly_nat)))))). % monom.rep_eq
thf(fact_227_monom_Orep__eq, axiom,
    ((![X : poly_poly_complex, Xa : nat]: ((coeff_1429652124omplex @ (monom_1210178217omplex @ X @ Xa)) = (^[N2 : nat]: (if_poly_poly_complex @ (Xa = N2) @ X @ zero_z1040703943omplex)))))). % monom.rep_eq
thf(fact_228_monom__eq__iff_H, axiom,
    ((![C : complex, N : nat, D : complex, M : nat]: (((monom_complex @ C @ N) = (monom_complex @ D @ M)) = (((C = D)) & ((((C = zero_zero_complex)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_229_monom__eq__iff_H, axiom,
    ((![C : poly_complex, N : nat, D : poly_complex, M : nat]: (((monom_poly_complex @ C @ N) = (monom_poly_complex @ D @ M)) = (((C = D)) & ((((C = zero_z1746442943omplex)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_230_monom__eq__iff_H, axiom,
    ((![C : nat, N : nat, D : nat, M : nat]: (((monom_nat @ C @ N) = (monom_nat @ D @ M)) = (((C = D)) & ((((C = zero_zero_nat)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_231_monom__eq__iff_H, axiom,
    ((![C : poly_nat, N : nat, D : poly_nat, M : nat]: (((monom_poly_nat @ C @ N) = (monom_poly_nat @ D @ M)) = (((C = D)) & ((((C = zero_zero_poly_nat)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_232_monom__eq__iff_H, axiom,
    ((![C : poly_poly_complex, N : nat, D : poly_poly_complex, M : nat]: (((monom_1210178217omplex @ C @ N) = (monom_1210178217omplex @ D @ M)) = (((C = D)) & ((((C = zero_z1040703943omplex)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_233_poly__pcompose, axiom,
    ((![P : poly_complex, Q : poly_complex, X : complex]: ((poly_complex2 @ (pcompose_complex @ P @ Q) @ X) = (poly_complex2 @ P @ (poly_complex2 @ Q @ X)))))). % poly_pcompose
thf(fact_234_pcompose__0_H, axiom,
    ((![P : poly_complex]: ((pcompose_complex @ P @ zero_z1746442943omplex) = (pCons_complex @ (coeff_complex @ P @ zero_zero_nat) @ zero_z1746442943omplex))))). % pcompose_0'
thf(fact_235_pcompose__0_H, axiom,
    ((![P : poly_nat]: ((pcompose_nat @ P @ zero_zero_poly_nat) = (pCons_nat @ (coeff_nat @ P @ zero_zero_nat) @ zero_zero_poly_nat))))). % pcompose_0'
thf(fact_236_pcompose__0_H, axiom,
    ((![P : poly_poly_complex]: ((pcompo1411605209omplex @ P @ zero_z1040703943omplex) = (pCons_poly_complex @ (coeff_poly_complex @ P @ zero_zero_nat) @ zero_z1040703943omplex))))). % pcompose_0'
thf(fact_237_One__nat__def, axiom,
    ((one_one_nat = (suc @ zero_zero_nat)))). % One_nat_def
thf(fact_238_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_239_nat_Oinject, axiom,
    ((![X22 : nat, Y22 : nat]: (((suc @ X22) = (suc @ Y22)) = (X22 = Y22))))). % nat.inject
thf(fact_240_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_241_dvd__1__left, axiom,
    ((![K : nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ K)))). % dvd_1_left
thf(fact_242_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_243_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_244_Suc__inject, axiom,
    ((![X : nat, Y : nat]: (((suc @ X) = (suc @ Y)) => (X = Y))))). % Suc_inject

% Helper facts (11)
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X : nat, Y : nat]: ((if_nat @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X : nat, Y : nat]: ((if_nat @ $true @ X @ Y) = X)))).
thf(help_If_2_1_If_001t__Complex__Ocomplex_T, axiom,
    ((![X : complex, Y : complex]: ((if_complex @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Complex__Ocomplex_T, axiom,
    ((![X : complex, Y : complex]: ((if_complex @ $true @ X @ Y) = X)))).
thf(help_If_2_1_If_001t__Polynomial__Opoly_It__Nat__Onat_J_T, axiom,
    ((![X : poly_nat, Y : poly_nat]: ((if_poly_nat @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Polynomial__Opoly_It__Nat__Onat_J_T, axiom,
    ((![X : poly_nat, Y : poly_nat]: ((if_poly_nat @ $true @ X @ Y) = X)))).
thf(help_If_2_1_If_001t__Polynomial__Opoly_It__Complex__Ocomplex_J_T, axiom,
    ((![X : poly_complex, Y : poly_complex]: ((if_poly_complex @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Polynomial__Opoly_It__Complex__Ocomplex_J_T, axiom,
    ((![X : poly_complex, Y : poly_complex]: ((if_poly_complex @ $true @ X @ Y) = X)))).
thf(help_If_3_1_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_T, axiom,
    ((![P2 : $o]: ((P2 = $true) | (P2 = $false))))).
thf(help_If_2_1_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_T, axiom,
    ((![X : poly_poly_complex, Y : poly_poly_complex]: ((if_poly_poly_complex @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_T, axiom,
    ((![X : poly_poly_complex, Y : poly_poly_complex]: ((if_poly_poly_complex @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((![H2 : complex, T2 : poly_complex]: ((H2 = zero_zero_complex) | ((~ ((T2 = zero_z1746442943omplex))) | (~ (((pCons_complex @ a @ (pCons_complex @ b @ p)) = (pCons_complex @ H2 @ T2))))))))).
