% 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_993__5377230_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:06.227

% 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 (60)
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_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    zero_z1059985641ly_nat : poly_poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    zero_z1200043727omplex : poly_p1267267526omplex).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_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_Odegree_001t__Nat__Onat, type,
    degree_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    degree_poly_complex : poly_poly_complex > nat).
thf(sy_c_Polynomial_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat, type,
    is_zero_nat : poly_nat > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    is_zero_poly_complex : poly_poly_complex > $o).
thf(sy_c_Polynomial_OpCons_001t__Complex__Ocomplex, type,
    pCons_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Nat__Onat, type,
    pCons_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    pCons_poly_complex : poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    pCons_poly_nat : poly_nat > poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    pCons_1087637536omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Nat__Onat, type,
    poly_cutoff_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_c622223248omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_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_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > poly_complex).
thf(sy_c_Polynomial_Osynthetic__div_001t__Nat__Onat, type,
    synthetic_div_nat : poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Osynthetic__div_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    synthe1985144195omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex, type,
    power_power_complex : complex > nat > complex).
thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat, type,
    power_power_nat : nat > nat > nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    power_184595776omplex : poly_complex > nat > poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    power_power_poly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    power_432682568omplex : poly_poly_complex > nat > poly_poly_complex).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex, type,
    dvd_dvd_complex : complex > complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    dvd_dvd_poly_complex : poly_complex > poly_complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    dvd_dvd_poly_nat : poly_nat > poly_nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    dvd_dv598755940omplex : poly_poly_complex > poly_poly_complex > $o).
thf(sy_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_thesis____, type,
    thesis : $o).

% Relevant facts (242)
thf(fact_0_False, axiom,
    ((~ ((?[A : complex]: ((poly_complex2 @ pa @ A) = zero_zero_complex)))))). % False
thf(fact_1__092_060open_062_092_060nexists_062a_Al_O_Aa_A_092_060noteq_062_A0_A_092_060and_062_Al_A_061_A0_A_092_060and_062_Ap_A_061_ApCons_Aa_Al_A_092_060Longrightarrow_062_A_092_060exists_062z_O_Apoly_Ap_Az_A_061_A0_092_060close_062, axiom,
    (((~ ((?[A2 : complex, L : poly_complex]: ((~ ((A2 = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (pa = (pCons_complex @ A2 @ L))))))) => (?[Z : complex]: ((poly_complex2 @ pa @ Z) = zero_zero_complex))))). % \<open>\<nexists>a l. a \<noteq> 0 \<and> l = 0 \<and> p = pCons a l \<Longrightarrow> \<exists>z. poly p z = 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_pq0, axiom,
    ((![X : complex]: (((poly_complex2 @ pa @ X) = zero_zero_complex) => ((poly_complex2 @ qa @ X) = zero_zero_complex))))). % pq0
thf(fact_4_pne, axiom,
    ((~ ((pa = zero_z1746442943omplex))))). % pne
thf(fact_5_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_6_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_7_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_8_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_9_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_10_pCons__eq__0__iff, axiom,
    ((![A3 : poly_nat, P : poly_poly_nat]: (((pCons_poly_nat @ A3 @ P) = zero_z1059985641ly_nat) = (((A3 = zero_zero_poly_nat)) & ((P = zero_z1059985641ly_nat))))))). % pCons_eq_0_iff
thf(fact_11_pCons__eq__0__iff, axiom,
    ((![A3 : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A3 @ P) = zero_z1200043727omplex) = (((A3 = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_12_pCons__eq__0__iff, axiom,
    ((![A3 : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A3 @ P) = zero_z1040703943omplex) = (((A3 = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_13_pCons__eq__0__iff, axiom,
    ((![A3 : nat, P : poly_nat]: (((pCons_nat @ A3 @ P) = zero_zero_poly_nat) = (((A3 = zero_zero_nat)) & ((P = zero_zero_poly_nat))))))). % pCons_eq_0_iff
thf(fact_14_pCons__eq__0__iff, axiom,
    ((![A3 : complex, P : poly_complex]: (((pCons_complex @ A3 @ P) = zero_z1746442943omplex) = (((A3 = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_15_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_16_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_17_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_18_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_19_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_20_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_21_pCons__eq__iff, axiom,
    ((![A3 : nat, P : poly_nat, B : nat, Q : poly_nat]: (((pCons_nat @ A3 @ P) = (pCons_nat @ B @ Q)) = (((A3 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_22_pCons__eq__iff, axiom,
    ((![A3 : poly_complex, P : poly_poly_complex, B : poly_complex, Q : poly_poly_complex]: (((pCons_poly_complex @ A3 @ P) = (pCons_poly_complex @ B @ Q)) = (((A3 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_23_pCons__eq__iff, axiom,
    ((![A3 : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A3 @ P) = (pCons_complex @ B @ Q)) = (((A3 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_24_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_25_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_26_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_27_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_28_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_29_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_30_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_31_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_32_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_33_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_34_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_35_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_36_dpn, axiom,
    (((degree_complex @ pa) = na))). % dpn
thf(fact_37_poly__0, axiom,
    ((![X2 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X2) = zero_zero_poly_nat)))). % poly_0
thf(fact_38_poly__0, axiom,
    ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X2) = zero_z1040703943omplex)))). % poly_0
thf(fact_39_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_40_poly__0, axiom,
    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
thf(fact_41_poly__0, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
thf(fact_42_offset__poly__single, axiom,
    ((![A3 : complex, H : complex]: ((fundam1201687030omplex @ (pCons_complex @ A3 @ zero_z1746442943omplex) @ H) = (pCons_complex @ A3 @ zero_z1746442943omplex))))). % offset_poly_single
thf(fact_43_offset__poly__single, axiom,
    ((![A3 : nat, H : nat]: ((fundam170929432ly_nat @ (pCons_nat @ A3 @ zero_zero_poly_nat) @ H) = (pCons_nat @ A3 @ zero_zero_poly_nat))))). % offset_poly_single
thf(fact_44_offset__poly__single, axiom,
    ((![A3 : poly_complex, H : poly_complex]: ((fundam1307691262omplex @ (pCons_poly_complex @ A3 @ zero_z1040703943omplex) @ H) = (pCons_poly_complex @ A3 @ zero_z1040703943omplex))))). % offset_poly_single
thf(fact_45_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A2 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_46_pCons__cases, axiom,
    ((![P : poly_nat]: (~ ((![A2 : nat, Q2 : poly_nat]: (~ ((P = (pCons_nat @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_47_pCons__cases, axiom,
    ((![P : poly_poly_complex]: (~ ((![A2 : poly_complex, Q2 : poly_poly_complex]: (~ ((P = (pCons_poly_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_48_n0, axiom,
    ((~ ((na = zero_zero_nat))))). % n0
thf(fact_49_assms_I2_J, axiom,
    (((degree_complex @ p) = n))). % assms(2)
thf(fact_50_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_51_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_52_degree__0, axiom,
    (((degree_poly_complex @ zero_z1040703943omplex) = zero_zero_nat))). % degree_0
thf(fact_53_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_54_degree__offset__poly, axiom,
    ((![P : poly_complex, H : complex]: ((degree_complex @ (fundam1201687030omplex @ P @ H)) = (degree_complex @ P))))). % degree_offset_poly
thf(fact_55_degree__eq__zeroE, axiom,
    ((![P : poly_complex]: (((degree_complex @ P) = zero_zero_nat) => (~ ((![A2 : complex]: (~ ((P = (pCons_complex @ A2 @ zero_z1746442943omplex))))))))))). % degree_eq_zeroE
thf(fact_56_degree__eq__zeroE, axiom,
    ((![P : poly_nat]: (((degree_nat @ P) = zero_zero_nat) => (~ ((![A2 : nat]: (~ ((P = (pCons_nat @ A2 @ zero_zero_poly_nat))))))))))). % degree_eq_zeroE
thf(fact_57_degree__eq__zeroE, axiom,
    ((![P : poly_poly_complex]: (((degree_poly_complex @ P) = zero_zero_nat) => (~ ((![A2 : poly_complex]: (~ ((P = (pCons_poly_complex @ A2 @ zero_z1040703943omplex))))))))))). % degree_eq_zeroE
thf(fact_58_degree__pCons__0, axiom,
    ((![A3 : complex]: ((degree_complex @ (pCons_complex @ A3 @ zero_z1746442943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_59_degree__pCons__0, axiom,
    ((![A3 : nat]: ((degree_nat @ (pCons_nat @ A3 @ zero_zero_poly_nat)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_60_degree__pCons__0, axiom,
    ((![A3 : poly_complex]: ((degree_poly_complex @ (pCons_poly_complex @ A3 @ zero_z1040703943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_61_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_62_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_63_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_64_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_65_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_66_offset__poly__0, axiom,
    ((![H : poly_complex]: ((fundam1307691262omplex @ zero_z1040703943omplex @ H) = zero_z1040703943omplex)))). % offset_poly_0
thf(fact_67_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_68_zero__reorient, axiom,
    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) = (X2 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_69_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_70_zero__reorient, axiom,
    ((![X2 : poly_nat]: ((zero_zero_poly_nat = X2) = (X2 = zero_zero_poly_nat))))). % zero_reorient
thf(fact_71_zero__reorient, axiom,
    ((![X2 : poly_poly_complex]: ((zero_z1040703943omplex = X2) = (X2 = zero_z1040703943omplex))))). % zero_reorient
thf(fact_72_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_73_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_74_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_75_pderiv_Ocases, axiom,
    ((![X2 : poly_complex]: (~ ((![A2 : complex, P3 : poly_complex]: (~ ((X2 = (pCons_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_76_pderiv_Ocases, axiom,
    ((![X2 : poly_nat]: (~ ((![A2 : nat, P3 : poly_nat]: (~ ((X2 = (pCons_nat @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_77_pderiv_Ocases, axiom,
    ((![X2 : poly_poly_complex]: (~ ((![A2 : poly_complex, P3 : poly_poly_complex]: (~ ((X2 = (pCons_poly_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_78_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_79_synthetic__div__pCons, axiom,
    ((![A3 : complex, P : poly_complex, C : complex]: ((synthe151143547omplex @ (pCons_complex @ A3 @ P) @ C) = (pCons_complex @ (poly_complex2 @ P @ C) @ (synthe151143547omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_80_synthetic__div__pCons, axiom,
    ((![A3 : nat, P : poly_nat, C : nat]: ((synthetic_div_nat @ (pCons_nat @ A3 @ P) @ C) = (pCons_nat @ (poly_nat2 @ P @ C) @ (synthetic_div_nat @ P @ C)))))). % synthetic_div_pCons
thf(fact_81_synthetic__div__pCons, axiom,
    ((![A3 : poly_complex, P : poly_poly_complex, C : poly_complex]: ((synthe1985144195omplex @ (pCons_poly_complex @ A3 @ P) @ C) = (pCons_poly_complex @ (poly_poly_complex2 @ P @ C) @ (synthe1985144195omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_82_is__zero__null, axiom,
    ((is_zero_complex = (^[P4 : poly_complex]: (P4 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_83_is__zero__null, axiom,
    ((is_zero_nat = (^[P4 : poly_nat]: (P4 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_84_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P4 : poly_poly_complex]: (P4 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_85_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_86_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_87_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_c622223248omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_88_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_89_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_90_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_91_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_92_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_93_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_complex, C : complex]: (((synthe151143547omplex @ P @ C) = zero_z1746442943omplex) = ((degree_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_94_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_nat, C : nat]: (((synthetic_div_nat @ P @ C) = zero_zero_poly_nat) = ((degree_nat @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_95_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_poly_complex, C : poly_complex]: (((synthe1985144195omplex @ P @ C) = zero_z1040703943omplex) = ((degree_poly_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_96_degree__pCons__eq__if, axiom,
    ((![P : poly_complex, A3 : complex]: (((P = zero_z1746442943omplex) => ((degree_complex @ (pCons_complex @ A3 @ P)) = zero_zero_nat)) & ((~ ((P = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A3 @ P)) = (suc @ (degree_complex @ P)))))))). % degree_pCons_eq_if
thf(fact_97_degree__pCons__eq__if, axiom,
    ((![P : poly_nat, A3 : nat]: (((P = zero_zero_poly_nat) => ((degree_nat @ (pCons_nat @ A3 @ P)) = zero_zero_nat)) & ((~ ((P = zero_zero_poly_nat))) => ((degree_nat @ (pCons_nat @ A3 @ P)) = (suc @ (degree_nat @ P)))))))). % degree_pCons_eq_if
thf(fact_98_degree__pCons__eq__if, axiom,
    ((![P : poly_poly_complex, A3 : poly_complex]: (((P = zero_z1040703943omplex) => ((degree_poly_complex @ (pCons_poly_complex @ A3 @ P)) = zero_zero_nat)) & ((~ ((P = zero_z1040703943omplex))) => ((degree_poly_complex @ (pCons_poly_complex @ A3 @ P)) = (suc @ (degree_poly_complex @ P)))))))). % degree_pCons_eq_if
thf(fact_99_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_100_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_101_poly__shift__0, axiom,
    ((![N : nat]: ((poly_s558570093omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_shift_0
thf(fact_102_IH, axiom,
    ((![M : nat]: ((ord_less_nat @ M @ na) => (![P5 : poly_complex, Q3 : poly_complex]: ((![X4 : complex]: (((poly_complex2 @ P5 @ X4) = zero_zero_complex) => ((poly_complex2 @ Q3 @ X4) = zero_zero_complex))) => (((degree_complex @ P5) = M) => ((~ ((M = zero_zero_nat))) => (dvd_dvd_poly_complex @ P5 @ (power_184595776omplex @ Q3 @ M)))))))))). % IH
thf(fact_103_assms_I3_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(3)
thf(fact_104_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_105_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_106_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_107_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_108_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_109_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_110_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_111_poly__power, axiom,
    ((![P : poly_poly_complex, N : nat, X2 : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P @ N) @ X2) = (power_184595776omplex @ (poly_poly_complex2 @ P @ X2) @ N))))). % poly_power
thf(fact_112_poly__power, axiom,
    ((![P : poly_nat, N : nat, X2 : nat]: ((poly_nat2 @ (power_power_poly_nat @ P @ N) @ X2) = (power_power_nat @ (poly_nat2 @ P @ X2) @ N))))). % poly_power
thf(fact_113_poly__power, axiom,
    ((![P : poly_complex, N : nat, X2 : complex]: ((poly_complex2 @ (power_184595776omplex @ P @ N) @ X2) = (power_power_complex @ (poly_complex2 @ P @ X2) @ N))))). % poly_power
thf(fact_114_reflect__poly__const, axiom,
    ((![A3 : complex]: ((reflect_poly_complex @ (pCons_complex @ A3 @ zero_z1746442943omplex)) = (pCons_complex @ A3 @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_115_reflect__poly__const, axiom,
    ((![A3 : nat]: ((reflect_poly_nat @ (pCons_nat @ A3 @ zero_zero_poly_nat)) = (pCons_nat @ A3 @ zero_zero_poly_nat))))). % reflect_poly_const
thf(fact_116_reflect__poly__const, axiom,
    ((![A3 : poly_complex]: ((reflec309385472omplex @ (pCons_poly_complex @ A3 @ zero_z1040703943omplex)) = (pCons_poly_complex @ A3 @ zero_z1040703943omplex))))). % reflect_poly_const
thf(fact_117_const__poly__dvd__const__poly__iff, axiom,
    ((![A3 : complex, B : complex]: ((dvd_dvd_poly_complex @ (pCons_complex @ A3 @ zero_z1746442943omplex) @ (pCons_complex @ B @ zero_z1746442943omplex)) = (dvd_dvd_complex @ A3 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_118_const__poly__dvd__const__poly__iff, axiom,
    ((![A3 : nat, B : nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ A3 @ zero_zero_poly_nat) @ (pCons_nat @ B @ zero_zero_poly_nat)) = (dvd_dvd_nat @ A3 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_119_const__poly__dvd__const__poly__iff, axiom,
    ((![A3 : poly_complex, B : poly_complex]: ((dvd_dv598755940omplex @ (pCons_poly_complex @ A3 @ zero_z1040703943omplex) @ (pCons_poly_complex @ B @ zero_z1040703943omplex)) = (dvd_dvd_poly_complex @ A3 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_120_reflect__poly__power, axiom,
    ((![P : poly_complex, N : nat]: ((reflect_poly_complex @ (power_184595776omplex @ P @ N)) = (power_184595776omplex @ (reflect_poly_complex @ P) @ N))))). % reflect_poly_power
thf(fact_121_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y : complex]: ((F @ X3) = (F @ Y)))))))). % constant_def
thf(fact_122_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_123_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_124_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_125_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_126_degree__pCons__eq, axiom,
    ((![P : poly_complex, A3 : complex]: ((~ ((P = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A3 @ P)) = (suc @ (degree_complex @ P))))))). % degree_pCons_eq
thf(fact_127_degree__pCons__eq, axiom,
    ((![P : poly_nat, A3 : nat]: ((~ ((P = zero_zero_poly_nat))) => ((degree_nat @ (pCons_nat @ A3 @ P)) = (suc @ (degree_nat @ P))))))). % degree_pCons_eq
thf(fact_128_degree__pCons__eq, axiom,
    ((![P : poly_poly_complex, A3 : poly_complex]: ((~ ((P = zero_z1040703943omplex))) => ((degree_poly_complex @ (pCons_poly_complex @ A3 @ P)) = (suc @ (degree_poly_complex @ P))))))). % degree_pCons_eq
thf(fact_129_pow__divides__pow__iff, axiom,
    ((![N : nat, A3 : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((dvd_dvd_nat @ (power_power_nat @ A3 @ N) @ (power_power_nat @ B @ N)) = (dvd_dvd_nat @ A3 @ B)))))). % pow_divides_pow_iff
thf(fact_130_power__eq__0__iff, axiom,
    ((![A3 : complex, N : nat]: (((power_power_complex @ A3 @ N) = zero_zero_complex) = (((A3 = zero_zero_complex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_131_power__eq__0__iff, axiom,
    ((![A3 : poly_nat, N : nat]: (((power_power_poly_nat @ A3 @ N) = zero_zero_poly_nat) = (((A3 = zero_zero_poly_nat)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_132_power__eq__0__iff, axiom,
    ((![A3 : poly_poly_complex, N : nat]: (((power_432682568omplex @ A3 @ N) = zero_z1040703943omplex) = (((A3 = zero_z1040703943omplex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_133_power__eq__0__iff, axiom,
    ((![A3 : poly_complex, N : nat]: (((power_184595776omplex @ A3 @ N) = zero_z1746442943omplex) = (((A3 = zero_z1746442943omplex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_134_power__eq__0__iff, axiom,
    ((![A3 : nat, N : nat]: (((power_power_nat @ A3 @ N) = zero_zero_nat) = (((A3 = zero_zero_nat)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_135_less__Suc0, axiom,
    ((![N : nat]: ((ord_less_nat @ N @ (suc @ zero_zero_nat)) = (N = zero_zero_nat))))). % less_Suc0
thf(fact_136_zero__less__Suc, axiom,
    ((![N : nat]: (ord_less_nat @ zero_zero_nat @ (suc @ N))))). % zero_less_Suc
thf(fact_137_power__Suc0__right, axiom,
    ((![A3 : poly_complex]: ((power_184595776omplex @ A3 @ (suc @ zero_zero_nat)) = A3)))). % power_Suc0_right
thf(fact_138_power__Suc0__right, axiom,
    ((![A3 : nat]: ((power_power_nat @ A3 @ (suc @ zero_zero_nat)) = A3)))). % power_Suc0_right
thf(fact_139_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_complex @ zero_zero_complex @ (suc @ N)) = zero_zero_complex)))). % power_0_Suc
thf(fact_140_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_poly_nat @ zero_zero_poly_nat @ (suc @ N)) = zero_zero_poly_nat)))). % power_0_Suc
thf(fact_141_power__0__Suc, axiom,
    ((![N : nat]: ((power_432682568omplex @ zero_z1040703943omplex @ (suc @ N)) = zero_z1040703943omplex)))). % power_0_Suc
thf(fact_142_power__0__Suc, axiom,
    ((![N : nat]: ((power_184595776omplex @ zero_z1746442943omplex @ (suc @ N)) = zero_z1746442943omplex)))). % power_0_Suc
thf(fact_143_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_nat @ zero_zero_nat @ (suc @ N)) = zero_zero_nat)))). % power_0_Suc
thf(fact_144_Suc__less__eq, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (suc @ M2) @ (suc @ N)) = (ord_less_nat @ M2 @ N))))). % Suc_less_eq
thf(fact_145_nat_Oinject, axiom,
    ((![X22 : nat, Y2 : nat]: (((suc @ X22) = (suc @ Y2)) = (X22 = Y2))))). % nat.inject
thf(fact_146_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_147_nat__power__eq__Suc__0__iff, axiom,
    ((![X2 : nat, M2 : nat]: (((power_power_nat @ X2 @ M2) = (suc @ zero_zero_nat)) = (((M2 = zero_zero_nat)) | ((X2 = (suc @ zero_zero_nat)))))))). % nat_power_eq_Suc_0_iff
thf(fact_148_power__Suc__0, axiom,
    ((![N : nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ N) = (suc @ zero_zero_nat))))). % power_Suc_0
thf(fact_149_dvd__1__iff__1, axiom,
    ((![M2 : nat]: ((dvd_dvd_nat @ M2 @ (suc @ zero_zero_nat)) = (M2 = (suc @ zero_zero_nat)))))). % dvd_1_iff_1
thf(fact_150_dvd__1__left, axiom,
    ((![K : nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ K)))). % dvd_1_left
thf(fact_151_nat__zero__less__power__iff, axiom,
    ((![X2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ X2 @ N)) = (((ord_less_nat @ zero_zero_nat @ X2)) | ((N = zero_zero_nat))))))). % nat_zero_less_power_iff
thf(fact_152_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A3 : nat]: ((~ ((A3 = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A3))))). % bot_nat_0.not_eq_extremum
thf(fact_153_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_154_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_155_lessI, axiom,
    ((![N : nat]: (ord_less_nat @ N @ (suc @ N))))). % lessI
thf(fact_156_Suc__mono, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_nat @ (suc @ M2) @ (suc @ N)))))). % Suc_mono
thf(fact_157_gcd__nat_Oextremum, axiom,
    ((![A3 : nat]: (dvd_dvd_nat @ A3 @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_158_gcd__nat_Oextremum__strict, axiom,
    ((![A3 : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A3) & (~ ((zero_zero_nat = A3))))))))). % gcd_nat.extremum_strict
thf(fact_159_gcd__nat_Oextremum__unique, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) = (A3 = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_160_gcd__nat_Onot__eq__extremum, axiom,
    ((![A3 : nat]: ((~ ((A3 = zero_zero_nat))) = (((dvd_dvd_nat @ A3 @ zero_zero_nat)) & ((~ ((A3 = zero_zero_nat))))))))). % gcd_nat.not_eq_extremum
thf(fact_161_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) => (A3 = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_162_nat__power__less__imp__less, axiom,
    ((![I : nat, M2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ I) => ((ord_less_nat @ (power_power_nat @ I @ M2) @ (power_power_nat @ I @ N)) => (ord_less_nat @ M2 @ N)))))). % nat_power_less_imp_less
thf(fact_163_nat__dvd__not__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ M2) => ((ord_less_nat @ M2 @ N) => (~ ((dvd_dvd_nat @ N @ M2)))))))). % nat_dvd_not_less
thf(fact_164_dvd__pos__nat, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((dvd_dvd_nat @ M2 @ N) => (ord_less_nat @ zero_zero_nat @ M2)))))). % dvd_pos_nat
thf(fact_165_power__gt__expt, axiom,
    ((![N : nat, K : nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ N) => (ord_less_nat @ K @ (power_power_nat @ N @ K)))))). % power_gt_expt
thf(fact_166_Suc__inject, axiom,
    ((![X2 : nat, Y3 : nat]: (((suc @ X2) = (suc @ Y3)) => (X2 = Y3))))). % Suc_inject
thf(fact_167_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_168_nat__neq__iff, axiom,
    ((![M2 : nat, N : nat]: ((~ ((M2 = N))) = (((ord_less_nat @ M2 @ N)) | ((ord_less_nat @ N @ M2))))))). % nat_neq_iff
thf(fact_169_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_170_less__not__refl2, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ N @ M2) => (~ ((M2 = N))))))). % less_not_refl2
thf(fact_171_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_172_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_173_nat__less__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N2 : nat]: ((![M : nat]: ((ord_less_nat @ M @ N2) => (P2 @ M))) => (P2 @ N2))) => (P2 @ N))))). % nat_less_induct
thf(fact_174_infinite__descent, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N2 : nat]: ((~ ((P2 @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P2 @ M))))))) => (P2 @ N))))). % infinite_descent
thf(fact_175_linorder__neqE__nat, axiom,
    ((![X2 : nat, Y3 : nat]: ((~ ((X2 = Y3))) => ((~ ((ord_less_nat @ X2 @ Y3))) => (ord_less_nat @ Y3 @ X2)))))). % linorder_neqE_nat
thf(fact_176_power__not__zero, axiom,
    ((![A3 : complex, N : nat]: ((~ ((A3 = zero_zero_complex))) => (~ (((power_power_complex @ A3 @ N) = zero_zero_complex))))))). % power_not_zero
thf(fact_177_power__not__zero, axiom,
    ((![A3 : poly_nat, N : nat]: ((~ ((A3 = zero_zero_poly_nat))) => (~ (((power_power_poly_nat @ A3 @ N) = zero_zero_poly_nat))))))). % power_not_zero
thf(fact_178_power__not__zero, axiom,
    ((![A3 : poly_poly_complex, N : nat]: ((~ ((A3 = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A3 @ N) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_179_power__not__zero, axiom,
    ((![A3 : poly_complex, N : nat]: ((~ ((A3 = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A3 @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_180_power__not__zero, axiom,
    ((![A3 : nat, N : nat]: ((~ ((A3 = zero_zero_nat))) => (~ (((power_power_nat @ A3 @ N) = zero_zero_nat))))))). % power_not_zero
thf(fact_181_dvd__power__same, axiom,
    ((![X2 : poly_complex, Y3 : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X2 @ Y3) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X2 @ N) @ (power_184595776omplex @ Y3 @ N)))))). % dvd_power_same
thf(fact_182_dvd__power__same, axiom,
    ((![X2 : nat, Y3 : nat, N : nat]: ((dvd_dvd_nat @ X2 @ Y3) => (dvd_dvd_nat @ (power_power_nat @ X2 @ N) @ (power_power_nat @ Y3 @ N)))))). % dvd_power_same
thf(fact_183_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M3 : nat]: (N = (suc @ M3))))))). % not0_implies_Suc
thf(fact_184_old_Onat_Oinducts, axiom,
    ((![P2 : nat > $o, Nat : nat]: ((P2 @ zero_zero_nat) => ((![Nat3 : nat]: ((P2 @ Nat3) => (P2 @ (suc @ Nat3)))) => (P2 @ Nat)))))). % old.nat.inducts
thf(fact_185_old_Onat_Oexhaust, axiom,
    ((![Y3 : nat]: ((~ ((Y3 = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y3 = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_186_Zero__not__Suc, axiom,
    ((![M2 : nat]: (~ ((zero_zero_nat = (suc @ M2))))))). % Zero_not_Suc
thf(fact_187_Zero__neq__Suc, axiom,
    ((![M2 : nat]: (~ ((zero_zero_nat = (suc @ M2))))))). % Zero_neq_Suc
thf(fact_188_Suc__neq__Zero, axiom,
    ((![M2 : nat]: (~ (((suc @ M2) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_189_zero__induct, axiom,
    ((![P2 : nat > $o, K : nat]: ((P2 @ K) => ((![N2 : nat]: ((P2 @ (suc @ N2)) => (P2 @ N2))) => (P2 @ zero_zero_nat)))))). % zero_induct
thf(fact_190_diff__induct, axiom,
    ((![P2 : nat > nat > $o, M2 : nat, N : nat]: ((![X4 : nat]: (P2 @ X4 @ zero_zero_nat)) => ((![Y4 : nat]: (P2 @ zero_zero_nat @ (suc @ Y4))) => ((![X4 : nat, Y4 : nat]: ((P2 @ X4 @ Y4) => (P2 @ (suc @ X4) @ (suc @ Y4)))) => (P2 @ M2 @ N))))))). % diff_induct
thf(fact_191_nat__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N2 : nat]: ((P2 @ N2) => (P2 @ (suc @ N2)))) => (P2 @ N)))))). % nat_induct
thf(fact_192_nat_OdiscI, axiom,
    ((![Nat : nat, X22 : nat]: ((Nat = (suc @ X22)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_193_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_194_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_195_nat_Odistinct_I1_J, axiom,
    ((![X22 : nat]: (~ ((zero_zero_nat = (suc @ X22))))))). % nat.distinct(1)
thf(fact_196_bot__nat__0_Oextremum__strict, axiom,
    ((![A3 : nat]: (~ ((ord_less_nat @ A3 @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_197_infinite__descent0, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((~ ((P2 @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P2 @ M)))))))) => (P2 @ N)))))). % infinite_descent0
thf(fact_198_gr__implies__not0, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_199_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_200_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_201_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_202_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_203_Nat_OlessE, axiom,
    ((![I : nat, K : nat]: ((ord_less_nat @ I @ K) => ((~ ((K = (suc @ I)))) => (~ ((![J : nat]: ((ord_less_nat @ I @ J) => (~ ((K = (suc @ J))))))))))))). % Nat.lessE
thf(fact_204_Suc__lessD, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (suc @ M2) @ N) => (ord_less_nat @ M2 @ N))))). % Suc_lessD
thf(fact_205_Suc__lessE, axiom,
    ((![I : nat, K : nat]: ((ord_less_nat @ (suc @ I) @ K) => (~ ((![J : nat]: ((ord_less_nat @ I @ J) => (~ ((K = (suc @ J)))))))))))). % Suc_lessE
thf(fact_206_Suc__lessI, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => ((~ (((suc @ M2) = N))) => (ord_less_nat @ (suc @ M2) @ N)))))). % Suc_lessI
thf(fact_207_less__SucE, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ (suc @ N)) => ((~ ((ord_less_nat @ M2 @ N))) => (M2 = N)))))). % less_SucE
thf(fact_208_less__SucI, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_nat @ M2 @ (suc @ N)))))). % less_SucI
thf(fact_209_Ex__less__Suc, axiom,
    ((![N : nat, P2 : nat > $o]: ((?[I2 : nat]: (((ord_less_nat @ I2 @ (suc @ N))) & ((P2 @ I2)))) = (((P2 @ N)) | ((?[I2 : nat]: (((ord_less_nat @ I2 @ N)) & ((P2 @ I2)))))))))). % Ex_less_Suc
thf(fact_210_less__Suc__eq, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ (suc @ N)) = (((ord_less_nat @ M2 @ N)) | ((M2 = N))))))). % less_Suc_eq
thf(fact_211_not__less__eq, axiom,
    ((![M2 : nat, N : nat]: ((~ ((ord_less_nat @ M2 @ N))) = (ord_less_nat @ N @ (suc @ M2)))))). % not_less_eq
thf(fact_212_All__less__Suc, axiom,
    ((![N : nat, P2 : nat > $o]: ((![I2 : nat]: (((ord_less_nat @ I2 @ (suc @ N))) => ((P2 @ I2)))) = (((P2 @ N)) & ((![I2 : nat]: (((ord_less_nat @ I2 @ N)) => ((P2 @ I2)))))))))). % All_less_Suc
thf(fact_213_Suc__less__eq2, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ (suc @ N) @ M2) = (?[M4 : nat]: (((M2 = (suc @ M4))) & ((ord_less_nat @ N @ M4)))))))). % Suc_less_eq2
thf(fact_214_less__antisym, axiom,
    ((![N : nat, M2 : nat]: ((~ ((ord_less_nat @ N @ M2))) => ((ord_less_nat @ N @ (suc @ M2)) => (M2 = N)))))). % less_antisym
thf(fact_215_Suc__less__SucD, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (suc @ M2) @ (suc @ N)) => (ord_less_nat @ M2 @ N))))). % Suc_less_SucD
thf(fact_216_less__trans__Suc, axiom,
    ((![I : nat, J2 : nat, K : nat]: ((ord_less_nat @ I @ J2) => ((ord_less_nat @ J2 @ K) => (ord_less_nat @ (suc @ I) @ K)))))). % less_trans_Suc
thf(fact_217_less__Suc__induct, axiom,
    ((![I : nat, J2 : nat, P2 : nat > nat > $o]: ((ord_less_nat @ I @ J2) => ((![I3 : nat]: (P2 @ I3 @ (suc @ I3))) => ((![I3 : nat, J : nat, K2 : nat]: ((ord_less_nat @ I3 @ J) => ((ord_less_nat @ J @ K2) => ((P2 @ I3 @ J) => ((P2 @ J @ K2) => (P2 @ I3 @ K2)))))) => (P2 @ I @ J2))))))). % less_Suc_induct
thf(fact_218_strict__inc__induct, axiom,
    ((![I : nat, J2 : nat, P2 : nat > $o]: ((ord_less_nat @ I @ J2) => ((![I3 : nat]: ((J2 = (suc @ I3)) => (P2 @ I3))) => ((![I3 : nat]: ((ord_less_nat @ I3 @ J2) => ((P2 @ (suc @ I3)) => (P2 @ I3)))) => (P2 @ I))))))). % strict_inc_induct
thf(fact_219_not__less__less__Suc__eq, axiom,
    ((![N : nat, M2 : nat]: ((~ ((ord_less_nat @ N @ M2))) => ((ord_less_nat @ N @ (suc @ M2)) = (N = M2)))))). % not_less_less_Suc_eq
thf(fact_220_zero__less__power, axiom,
    ((![A3 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ A3) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A3 @ N)))))). % zero_less_power
thf(fact_221_lift__Suc__mono__less, axiom,
    ((![F2 : nat > nat, N : nat, N3 : nat]: ((![N2 : nat]: (ord_less_nat @ (F2 @ N2) @ (F2 @ (suc @ N2)))) => ((ord_less_nat @ N @ N3) => (ord_less_nat @ (F2 @ N) @ (F2 @ N3))))))). % lift_Suc_mono_less
thf(fact_222_lift__Suc__mono__less__iff, axiom,
    ((![F2 : nat > nat, N : nat, M2 : nat]: ((![N2 : nat]: (ord_less_nat @ (F2 @ N2) @ (F2 @ (suc @ N2)))) => ((ord_less_nat @ (F2 @ N) @ (F2 @ M2)) = (ord_less_nat @ N @ M2)))))). % lift_Suc_mono_less_iff
thf(fact_223_less__Suc__eq__0__disj, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ (suc @ N)) = (((M2 = zero_zero_nat)) | ((?[J3 : nat]: (((M2 = (suc @ J3))) & ((ord_less_nat @ J3 @ N)))))))))). % less_Suc_eq_0_disj
thf(fact_224_gr0__implies__Suc, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => (?[M3 : nat]: (N = (suc @ M3))))))). % gr0_implies_Suc
thf(fact_225_All__less__Suc2, axiom,
    ((![N : nat, P2 : nat > $o]: ((![I2 : nat]: (((ord_less_nat @ I2 @ (suc @ N))) => ((P2 @ I2)))) = (((P2 @ zero_zero_nat)) & ((![I2 : nat]: (((ord_less_nat @ I2 @ N)) => ((P2 @ (suc @ I2))))))))))). % All_less_Suc2
thf(fact_226_gr0__conv__Suc, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (?[M5 : nat]: (N = (suc @ M5))))))). % gr0_conv_Suc
thf(fact_227_Ex__less__Suc2, axiom,
    ((![N : nat, P2 : nat > $o]: ((?[I2 : nat]: (((ord_less_nat @ I2 @ (suc @ N))) & ((P2 @ I2)))) = (((P2 @ zero_zero_nat)) | ((?[I2 : nat]: (((ord_less_nat @ I2 @ N)) & ((P2 @ (suc @ I2))))))))))). % Ex_less_Suc2
thf(fact_228_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex))))). % zero_power
thf(fact_229_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_poly_nat @ zero_zero_poly_nat @ N) = zero_zero_poly_nat))))). % zero_power
thf(fact_230_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_432682568omplex @ zero_z1040703943omplex @ N) = zero_z1040703943omplex))))). % zero_power
thf(fact_231_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_184595776omplex @ zero_z1746442943omplex @ N) = zero_z1746442943omplex))))). % zero_power
thf(fact_232_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat))))). % zero_power
thf(fact_233_dvd__0__left__iff, axiom,
    ((![A3 : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A3) = (A3 = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_234_dvd__0__left__iff, axiom,
    ((![A3 : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A3) = (A3 = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_235_dvd__0__left__iff, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) = (A3 = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_236_dvd__0__left__iff, axiom,
    ((![A3 : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A3) = (A3 = zero_zero_poly_nat))))). % dvd_0_left_iff
thf(fact_237_dvd__0__left__iff, axiom,
    ((![A3 : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A3) = (A3 = zero_z1040703943omplex))))). % dvd_0_left_iff
thf(fact_238_dvd__0__right, axiom,
    ((![A3 : poly_complex]: (dvd_dvd_poly_complex @ A3 @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_239_dvd__0__right, axiom,
    ((![A3 : nat]: (dvd_dvd_nat @ A3 @ zero_zero_nat)))). % dvd_0_right
thf(fact_240_dvd__0__right, axiom,
    ((![A3 : poly_nat]: (dvd_dvd_poly_nat @ A3 @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_241_dvd__0__right, axiom,
    ((![A3 : poly_poly_complex]: (dvd_dv598755940omplex @ A3 @ zero_z1040703943omplex)))). % dvd_0_right

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![C2 : complex]: ((~ ((C2 = zero_zero_complex))) => ((pa = (pCons_complex @ C2 @ zero_z1746442943omplex)) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
