% 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_995__5377246_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:07.564

% Could-be-implicit typings (5)
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__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 (44)
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_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
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_If_001t__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
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_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_Oorder_001t__Complex__Ocomplex, type,
    order_complex : complex > poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    order_poly_complex : poly_complex > poly_poly_complex > nat).
thf(sy_c_Polynomial_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_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__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > 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_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > 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_c____, type,
    c : complex).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_pa____, type,
    pa : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).
thf(sy_v_qa____, type,
    qa : poly_complex).
thf(sy_v_x____, type,
    x : complex).

% Relevant facts (169)
thf(fact_0_ccs_I1_J, axiom,
    ((~ ((c = zero_zero_complex))))). % ccs(1)
thf(fact_1_False, axiom,
    ((~ ((?[A : complex]: ((poly_complex2 @ pa @ A) = zero_zero_complex)))))). % False
thf(fact_2_ccs_I2_J, axiom,
    ((pa = (pCons_complex @ c @ zero_z1746442943omplex)))). % ccs(2)
thf(fact_3_assms_I1_J, axiom,
    ((![X : complex]: (((poly_complex2 @ p @ X) = zero_zero_complex) => ((poly_complex2 @ q @ X) = zero_zero_complex))))). % assms(1)
thf(fact_4_pq0, axiom,
    ((![X : complex]: (((poly_complex2 @ pa @ X) = zero_zero_complex) => ((poly_complex2 @ qa @ X) = zero_zero_complex))))). % pq0
thf(fact_5_pne, axiom,
    ((~ ((pa = zero_z1746442943omplex))))). % pne
thf(fact_6__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_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_O_A_092_060lbrakk_062c_A_092_060noteq_062_A0_059_Ap_A_061_A_091_058c_058_093_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![C : complex]: ((~ ((C = zero_zero_complex))) => (~ ((pa = (pCons_complex @ C @ zero_z1746442943omplex)))))))))). % \<open>\<And>thesis. (\<And>c. \<lbrakk>c \<noteq> 0; p = [:c:]\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_8_dpn, axiom,
    (((degree_complex @ pa) = na))). % dpn
thf(fact_9_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_10_assms_I3_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(3)
thf(fact_11_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_12_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_13_poly__0, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
thf(fact_14_poly__0, axiom,
    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
thf(fact_15_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_16_n0, axiom,
    ((~ ((na = zero_zero_nat))))). % n0
thf(fact_17_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_18_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_19_synthetic__div__pCons, axiom,
    ((![A3 : complex, P : poly_complex, C2 : complex]: ((synthe151143547omplex @ (pCons_complex @ A3 @ P) @ C2) = (pCons_complex @ (poly_complex2 @ P @ C2) @ (synthe151143547omplex @ P @ C2)))))). % synthetic_div_pCons
thf(fact_20_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y : complex]: ((F @ X3) = (F @ Y)))))))). % constant_def
thf(fact_21_assms_I2_J, axiom,
    (((degree_complex @ p) = n))). % assms(2)
thf(fact_22_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_23_synthetic__div__0, axiom,
    ((![C2 : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C2) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_24_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_25_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_26_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_27_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_28_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_29_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_30_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_31_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A2 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_32_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_33_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_34_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_35_pderiv_Ocases, axiom,
    ((![X2 : poly_complex]: (~ ((![A2 : complex, P3 : poly_complex]: (~ ((X2 = (pCons_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_36_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_37_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_38_degree__pCons__0, axiom,
    ((![A3 : complex]: ((degree_complex @ (pCons_complex @ A3 @ zero_z1746442943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_39_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_40_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_complex, C2 : complex]: (((synthe151143547omplex @ P @ C2) = zero_z1746442943omplex) = ((degree_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_41_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_42_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_43_is__zero__null, axiom,
    ((is_zero_complex = (^[P4 : poly_complex]: (P4 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_44_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_45_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_46_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_47_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_48_order__root, axiom,
    ((![P : poly_complex, A3 : complex]: (((poly_complex2 @ P @ A3) = zero_zero_complex) = (((P = zero_z1746442943omplex)) | ((~ (((order_complex @ A3 @ P) = zero_zero_nat))))))))). % order_root
thf(fact_49_order__root, axiom,
    ((![P : poly_poly_complex, A3 : poly_complex]: (((poly_poly_complex2 @ P @ A3) = zero_z1746442943omplex) = (((P = zero_z1040703943omplex)) | ((~ (((order_poly_complex @ A3 @ P) = zero_zero_nat))))))))). % order_root
thf(fact_50_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_51_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_52_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_53_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_54_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_55_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_56_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_57_reflect__poly__const, axiom,
    ((![A3 : complex]: ((reflect_poly_complex @ (pCons_complex @ A3 @ zero_z1746442943omplex)) = (pCons_complex @ A3 @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_58_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_59_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_60_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_61_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_62_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_63_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_64_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_65_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_66_psize__def, axiom,
    ((fundam1709708056omplex = (^[P4 : poly_complex]: (if_nat @ (P4 = zero_z1746442943omplex) @ zero_zero_nat @ (suc @ (degree_complex @ P4))))))). % psize_def
thf(fact_67_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_68_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_69_degree__offset__poly, axiom,
    ((![P : poly_complex, H : complex]: ((degree_complex @ (fundam1201687030omplex @ P @ H)) = (degree_complex @ P))))). % degree_offset_poly
thf(fact_70_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_71_zero__reorient, axiom,
    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) = (X2 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_72_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_73_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_74_order__0I, axiom,
    ((![P : poly_complex, A3 : complex]: ((~ (((poly_complex2 @ P @ A3) = zero_zero_complex))) => ((order_complex @ A3 @ P) = zero_zero_nat))))). % order_0I
thf(fact_75_order__0I, axiom,
    ((![P : poly_poly_complex, A3 : poly_complex]: ((~ (((poly_poly_complex2 @ P @ A3) = zero_z1746442943omplex))) => ((order_poly_complex @ A3 @ P) = zero_zero_nat))))). % order_0I
thf(fact_76_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_77_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_78_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_79_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_80_less__Suc0, axiom,
    ((![N : nat]: ((ord_less_nat @ N @ (suc @ zero_zero_nat)) = (N = zero_zero_nat))))). % less_Suc0
thf(fact_81_zero__less__Suc, axiom,
    ((![N : nat]: (ord_less_nat @ zero_zero_nat @ (suc @ N))))). % zero_less_Suc
thf(fact_82_power__Suc0__right, axiom,
    ((![A3 : poly_complex]: ((power_184595776omplex @ A3 @ (suc @ zero_zero_nat)) = A3)))). % power_Suc0_right
thf(fact_83_power__Suc0__right, axiom,
    ((![A3 : nat]: ((power_power_nat @ A3 @ (suc @ zero_zero_nat)) = A3)))). % power_Suc0_right
thf(fact_84_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_complex @ zero_zero_complex @ (suc @ N)) = zero_zero_complex)))). % power_0_Suc
thf(fact_85_power__0__Suc, axiom,
    ((![N : nat]: ((power_184595776omplex @ zero_z1746442943omplex @ (suc @ N)) = zero_z1746442943omplex)))). % power_0_Suc
thf(fact_86_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_nat @ zero_zero_nat @ (suc @ N)) = zero_zero_nat)))). % power_0_Suc
thf(fact_87_nat_Oinject, axiom,
    ((![X22 : nat, Y2 : nat]: (((suc @ X22) = (suc @ Y2)) = (X22 = Y2))))). % nat.inject
thf(fact_88_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_89_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_90_power__Suc__0, axiom,
    ((![N : nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ N) = (suc @ zero_zero_nat))))). % power_Suc_0
thf(fact_91_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_92_dvd__1__left, axiom,
    ((![K : nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ K)))). % dvd_1_left
thf(fact_93_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_94_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_95_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_96_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_97_lessI, axiom,
    ((![N : nat]: (ord_less_nat @ N @ (suc @ N))))). % lessI
thf(fact_98_Suc__mono, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_nat @ (suc @ M2) @ (suc @ N)))))). % Suc_mono
thf(fact_99_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_100_gcd__nat_Oextremum, axiom,
    ((![A3 : nat]: (dvd_dvd_nat @ A3 @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_101_gcd__nat_Oextremum__strict, axiom,
    ((![A3 : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A3) & (~ ((zero_zero_nat = A3))))))))). % gcd_nat.extremum_strict
thf(fact_102_gcd__nat_Oextremum__unique, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) = (A3 = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_103_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_104_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A3 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A3) => (A3 = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_105_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_106_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_107_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_108_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_109_Suc__inject, axiom,
    ((![X2 : nat, Y3 : nat]: (((suc @ X2) = (suc @ Y3)) => (X2 = Y3))))). % Suc_inject
thf(fact_110_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_111_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_112_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_113_less__not__refl2, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ N @ M2) => (~ ((M2 = N))))))). % less_not_refl2
thf(fact_114_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_115_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_116_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_117_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_118_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_119_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_120_power__not__zero, axiom,
    ((![A3 : poly_complex, N : nat]: ((~ ((A3 = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A3 @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_121_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_122_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_123_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_124_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M3 : nat]: (N = (suc @ M3))))))). % not0_implies_Suc
thf(fact_125_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_126_old_Onat_Oexhaust, axiom,
    ((![Y3 : nat]: ((~ ((Y3 = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y3 = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_127_Zero__not__Suc, axiom,
    ((![M2 : nat]: (~ ((zero_zero_nat = (suc @ M2))))))). % Zero_not_Suc
thf(fact_128_Zero__neq__Suc, axiom,
    ((![M2 : nat]: (~ ((zero_zero_nat = (suc @ M2))))))). % Zero_neq_Suc
thf(fact_129_Suc__neq__Zero, axiom,
    ((![M2 : nat]: (~ (((suc @ M2) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_130_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_131_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_132_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_133_nat_OdiscI, axiom,
    ((![Nat : nat, X22 : nat]: ((Nat = (suc @ X22)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_134_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_135_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_136_nat_Odistinct_I1_J, axiom,
    ((![X22 : nat]: (~ ((zero_zero_nat = (suc @ X22))))))). % nat.distinct(1)
thf(fact_137_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_138_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_139_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_140_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_141_gr__implies__not0, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_142_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_143_bot__nat__0_Oextremum__strict, axiom,
    ((![A3 : nat]: (~ ((ord_less_nat @ A3 @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_144_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_145_Suc__lessD, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (suc @ M2) @ N) => (ord_less_nat @ M2 @ N))))). % Suc_lessD
thf(fact_146_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_147_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_148_less__SucE, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ (suc @ N)) => ((~ ((ord_less_nat @ M2 @ N))) => (M2 = N)))))). % less_SucE
thf(fact_149_less__SucI, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_nat @ M2 @ (suc @ N)))))). % less_SucI
thf(fact_150_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_151_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_152_not__less__eq, axiom,
    ((![M2 : nat, N : nat]: ((~ ((ord_less_nat @ M2 @ N))) = (ord_less_nat @ N @ (suc @ M2)))))). % not_less_eq
thf(fact_153_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_154_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_155_less__antisym, axiom,
    ((![N : nat, M2 : nat]: ((~ ((ord_less_nat @ N @ M2))) => ((ord_less_nat @ N @ (suc @ M2)) => (M2 = N)))))). % less_antisym
thf(fact_156_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_157_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_158_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_159_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_160_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_161_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_162_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_163_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_164_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_165_gr0__implies__Suc, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => (?[M3 : nat]: (N = (suc @ M3))))))). % gr0_implies_Suc
thf(fact_166_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_167_gr0__conv__Suc, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (?[M5 : nat]: (N = (suc @ M5))))))). % gr0_conv_Suc
thf(fact_168_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

% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T, axiom,
    ((![P2 : $o]: ((P2 = $true) | (P2 = $false))))).
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X2 : nat, Y3 : nat]: ((if_nat @ $false @ X2 @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X2 : nat, Y3 : nat]: ((if_nat @ $true @ X2 @ Y3) = X2)))).

% Conjectures (1)
thf(conj_0, conjecture,
    (((poly_complex2 @ pa @ x) = c))).
