% 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_688__5374658_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:32:10.735

% 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 (37)
thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex, type,
    invers502456322omplex : complex > complex).
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_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    times_1246143675omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    times_times_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    times_1460995011omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Groups_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_OLeast_001t__Nat__Onat, type,
    ord_Least_nat : (nat > $o) > nat).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
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_Osmult_001t__Complex__Ocomplex, type,
    smult_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Osmult_001t__Nat__Onat, type,
    smult_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Osmult_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    smult_poly_complex : poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Osmult_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    smult_poly_nat : poly_nat > poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Osmult_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    smult_107044098omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_v_c____, type,
    c : complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_pa____, type,
    pa : poly_complex).
thf(sy_v_q____, type,
    q : poly_complex).

% Relevant facts (196)
thf(fact_0_a00, axiom,
    ((~ (((poly_complex2 @ q @ zero_zero_complex) = zero_zero_complex))))). % a00
thf(fact_1_nc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ p)))))). % nc
thf(fact_2__092_060open_062constant_A_Ipoly_Aq_J_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ q)))))). % \<open>constant (poly q) \<Longrightarrow> False\<close>
thf(fact_3_qnc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ q)))))). % qnc
thf(fact_4_smult__0__left, axiom,
    ((![P : poly_poly_nat]: ((smult_poly_nat @ zero_zero_poly_nat @ P) = zero_z1059985641ly_nat)))). % smult_0_left
thf(fact_5_smult__0__left, axiom,
    ((![P : poly_p1267267526omplex]: ((smult_107044098omplex @ zero_z1040703943omplex @ P) = zero_z1200043727omplex)))). % smult_0_left
thf(fact_6_smult__0__left, axiom,
    ((![P : poly_poly_complex]: ((smult_poly_complex @ zero_z1746442943omplex @ P) = zero_z1040703943omplex)))). % smult_0_left
thf(fact_7_smult__0__left, axiom,
    ((![P : poly_nat]: ((smult_nat @ zero_zero_nat @ P) = zero_zero_poly_nat)))). % smult_0_left
thf(fact_8_smult__0__left, axiom,
    ((![P : poly_complex]: ((smult_complex @ zero_zero_complex @ P) = zero_z1746442943omplex)))). % smult_0_left
thf(fact_9_smult__eq__0__iff, axiom,
    ((![A : poly_nat, P : poly_poly_nat]: (((smult_poly_nat @ A @ P) = zero_z1059985641ly_nat) = (((A = zero_zero_poly_nat)) | ((P = zero_z1059985641ly_nat))))))). % smult_eq_0_iff
thf(fact_10_smult__eq__0__iff, axiom,
    ((![A : poly_poly_complex, P : poly_p1267267526omplex]: (((smult_107044098omplex @ A @ P) = zero_z1200043727omplex) = (((A = zero_z1040703943omplex)) | ((P = zero_z1200043727omplex))))))). % smult_eq_0_iff
thf(fact_11_smult__eq__0__iff, axiom,
    ((![A : poly_complex, P : poly_poly_complex]: (((smult_poly_complex @ A @ P) = zero_z1040703943omplex) = (((A = zero_z1746442943omplex)) | ((P = zero_z1040703943omplex))))))). % smult_eq_0_iff
thf(fact_12_smult__eq__0__iff, axiom,
    ((![A : nat, P : poly_nat]: (((smult_nat @ A @ P) = zero_zero_poly_nat) = (((A = zero_zero_nat)) | ((P = zero_zero_poly_nat))))))). % smult_eq_0_iff
thf(fact_13_smult__eq__0__iff, axiom,
    ((![A : complex, P : poly_complex]: (((smult_complex @ A @ P) = zero_z1746442943omplex) = (((A = zero_zero_complex)) | ((P = zero_z1746442943omplex))))))). % smult_eq_0_iff
thf(fact_14_poly__0, axiom,
    ((![X : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X) = zero_zero_poly_nat)))). % poly_0
thf(fact_15_poly__0, axiom,
    ((![X : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X) = zero_z1040703943omplex)))). % poly_0
thf(fact_16_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_17_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_18_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_19_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_20_coeff__0, axiom,
    ((![N : nat]: ((coeff_1429652124omplex @ zero_z1200043727omplex @ N) = zero_z1040703943omplex)))). % coeff_0
thf(fact_21_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_complex @ zero_z1040703943omplex @ N) = zero_z1746442943omplex)))). % coeff_0
thf(fact_22_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_23_coeff__0, axiom,
    ((![N : nat]: ((coeff_complex @ zero_z1746442943omplex @ N) = zero_zero_complex)))). % coeff_0
thf(fact_24_less__Suc0, axiom,
    ((![N : nat]: ((ord_less_nat @ N @ (suc @ zero_zero_nat)) = (N = zero_zero_nat))))). % less_Suc0
thf(fact_25_zero__less__Suc, axiom,
    ((![N : nat]: (ord_less_nat @ zero_zero_nat @ (suc @ N))))). % zero_less_Suc
thf(fact_26_qr, axiom,
    ((![Z : complex]: ((poly_complex2 @ q @ Z) = (times_times_complex @ (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ Z) @ (poly_complex2 @ q @ zero_zero_complex)))))). % qr
thf(fact_27_Least__eq__0, axiom,
    ((![P2 : nat > $o]: ((P2 @ zero_zero_nat) => ((ord_Least_nat @ P2) = zero_zero_nat))))). % Least_eq_0
thf(fact_28_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_29_nat_Oinject, axiom,
    ((![X2 : nat, Y2 : nat]: (((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))). % nat.inject
thf(fact_30_inverse__inverse__eq, axiom,
    ((![A : complex]: ((invers502456322omplex @ (invers502456322omplex @ A)) = A)))). % inverse_inverse_eq
thf(fact_31_inverse__eq__iff__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) = (A = B))))). % inverse_eq_iff_eq
thf(fact_32_inverse__nonzero__iff__nonzero, axiom,
    ((![A : complex]: (((invers502456322omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % inverse_nonzero_iff_nonzero
thf(fact_33_inverse__zero, axiom,
    (((invers502456322omplex @ zero_zero_complex) = zero_zero_complex))). % inverse_zero
thf(fact_34_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_35_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_36_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_37_Suc__less__eq, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ (suc @ M) @ (suc @ N)) = (ord_less_nat @ M @ N))))). % Suc_less_eq
thf(fact_38_Suc__mono, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (ord_less_nat @ (suc @ M) @ (suc @ N)))))). % Suc_mono
thf(fact_39_lessI, axiom,
    ((![N : nat]: (ord_less_nat @ N @ (suc @ N))))). % lessI
thf(fact_40_inverse__mult__distrib, axiom,
    ((![A : complex, B : complex]: ((invers502456322omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers502456322omplex @ A) @ (invers502456322omplex @ B)))))). % inverse_mult_distrib
thf(fact_41_poly__mult, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (times_1460995011omplex @ P @ Q) @ X) = (times_1246143675omplex @ (poly_poly_complex2 @ P @ X) @ (poly_poly_complex2 @ Q @ X)))))). % poly_mult
thf(fact_42_poly__mult, axiom,
    ((![P : poly_complex, Q : poly_complex, X : complex]: ((poly_complex2 @ (times_1246143675omplex @ P @ Q) @ X) = (times_times_complex @ (poly_complex2 @ P @ X) @ (poly_complex2 @ Q @ X)))))). % poly_mult
thf(fact_43_poly__mult, axiom,
    ((![P : poly_nat, Q : poly_nat, X : nat]: ((poly_nat2 @ (times_times_poly_nat @ P @ Q) @ X) = (times_times_nat @ (poly_nat2 @ P @ X) @ (poly_nat2 @ Q @ X)))))). % poly_mult
thf(fact_44_smult__smult, axiom,
    ((![A : poly_complex, B : poly_complex, P : poly_poly_complex]: ((smult_poly_complex @ A @ (smult_poly_complex @ B @ P)) = (smult_poly_complex @ (times_1246143675omplex @ A @ B) @ P))))). % smult_smult
thf(fact_45_smult__smult, axiom,
    ((![A : complex, B : complex, P : poly_complex]: ((smult_complex @ A @ (smult_complex @ B @ P)) = (smult_complex @ (times_times_complex @ A @ B) @ P))))). % smult_smult
thf(fact_46_smult__smult, axiom,
    ((![A : nat, B : nat, P : poly_nat]: ((smult_nat @ A @ (smult_nat @ B @ P)) = (smult_nat @ (times_times_nat @ A @ B) @ P))))). % smult_smult
thf(fact_47_smult__0__right, axiom,
    ((![A : complex]: ((smult_complex @ A @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % smult_0_right
thf(fact_48_smult__0__right, axiom,
    ((![A : nat]: ((smult_nat @ A @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % smult_0_right
thf(fact_49_smult__0__right, axiom,
    ((![A : poly_complex]: ((smult_poly_complex @ A @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % smult_0_right
thf(fact_50_less_Oprems, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ pa)))))). % less.prems
thf(fact_51_coeff__smult, axiom,
    ((![A : poly_complex, P : poly_poly_complex, N : nat]: ((coeff_poly_complex @ (smult_poly_complex @ A @ P) @ N) = (times_1246143675omplex @ A @ (coeff_poly_complex @ P @ N)))))). % coeff_smult
thf(fact_52_coeff__smult, axiom,
    ((![A : complex, P : poly_complex, N : nat]: ((coeff_complex @ (smult_complex @ A @ P) @ N) = (times_times_complex @ A @ (coeff_complex @ P @ N)))))). % coeff_smult
thf(fact_53_coeff__smult, axiom,
    ((![A : nat, P : poly_nat, N : nat]: ((coeff_nat @ (smult_nat @ A @ P) @ N) = (times_times_nat @ A @ (coeff_nat @ P @ N)))))). % coeff_smult
thf(fact_54_poly__smult, axiom,
    ((![A : poly_complex, P : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (smult_poly_complex @ A @ P) @ X) = (times_1246143675omplex @ A @ (poly_poly_complex2 @ P @ X)))))). % poly_smult
thf(fact_55_poly__smult, axiom,
    ((![A : complex, P : poly_complex, X : complex]: ((poly_complex2 @ (smult_complex @ A @ P) @ X) = (times_times_complex @ A @ (poly_complex2 @ P @ X)))))). % poly_smult
thf(fact_56_poly__smult, axiom,
    ((![A : nat, P : poly_nat, X : nat]: ((poly_nat2 @ (smult_nat @ A @ P) @ X) = (times_times_nat @ A @ (poly_nat2 @ P @ X)))))). % poly_smult
thf(fact_57_mult__commute__imp__mult__inverse__commute, axiom,
    ((![Y : complex, X : complex]: (((times_times_complex @ Y @ X) = (times_times_complex @ X @ Y)) => ((times_times_complex @ (invers502456322omplex @ Y) @ X) = (times_times_complex @ X @ (invers502456322omplex @ Y))))))). % mult_commute_imp_mult_inverse_commute
thf(fact_58_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y3 : complex]: ((F @ X3) = (F @ Y3)))))))). % constant_def
thf(fact_59_nonzero__inverse__mult__distrib, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => ((invers502456322omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers502456322omplex @ B) @ (invers502456322omplex @ A)))))))). % nonzero_inverse_mult_distrib
thf(fact_60_smult_Orep__eq, axiom,
    ((![X : poly_complex, Xa : poly_poly_complex]: ((coeff_poly_complex @ (smult_poly_complex @ X @ Xa)) = (^[N2 : nat]: (times_1246143675omplex @ X @ (coeff_poly_complex @ Xa @ N2))))))). % smult.rep_eq
thf(fact_61_smult_Orep__eq, axiom,
    ((![X : complex, Xa : poly_complex]: ((coeff_complex @ (smult_complex @ X @ Xa)) = (^[N2 : nat]: (times_times_complex @ X @ (coeff_complex @ Xa @ N2))))))). % smult.rep_eq
thf(fact_62_smult_Orep__eq, axiom,
    ((![X : nat, Xa : poly_nat]: ((coeff_nat @ (smult_nat @ X @ Xa)) = (^[N2 : nat]: (times_times_nat @ X @ (coeff_nat @ Xa @ N2))))))). % smult.rep_eq
thf(fact_63_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_64_Suc__inject, axiom,
    ((![X : nat, Y : nat]: (((suc @ X) = (suc @ Y)) => (X = Y))))). % Suc_inject
thf(fact_65_linorder__neqE__nat, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % linorder_neqE_nat
thf(fact_66_infinite__descent, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N3 : nat]: ((~ ((P2 @ N3))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N3) & (~ ((P2 @ M2))))))) => (P2 @ N))))). % infinite_descent
thf(fact_67_nat__less__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N3 : nat]: ((![M2 : nat]: ((ord_less_nat @ M2 @ N3) => (P2 @ M2))) => (P2 @ N3))) => (P2 @ N))))). % nat_less_induct
thf(fact_68_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_69_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_70_less__not__refl2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ N @ M) => (~ ((M = N))))))). % less_not_refl2
thf(fact_71_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_72_nat__neq__iff, axiom,
    ((![M : nat, N : nat]: ((~ ((M = N))) = (((ord_less_nat @ M @ N)) | ((ord_less_nat @ N @ M))))))). % nat_neq_iff
thf(fact_73_inverse__eq__imp__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) => (A = B))))). % inverse_eq_imp_eq
thf(fact_74_coeff__inject, axiom,
    ((![X : poly_complex, Y : poly_complex]: (((coeff_complex @ X) = (coeff_complex @ Y)) = (X = Y))))). % coeff_inject
thf(fact_75_coeff__inject, axiom,
    ((![X : poly_nat, Y : poly_nat]: (((coeff_nat @ X) = (coeff_nat @ Y)) = (X = Y))))). % coeff_inject
thf(fact_76_coeff__inject, axiom,
    ((![X : poly_poly_complex, Y : poly_poly_complex]: (((coeff_poly_complex @ X) = (coeff_poly_complex @ Y)) = (X = Y))))). % coeff_inject
thf(fact_77_poly__eq__iff, axiom,
    (((^[Y4 : poly_complex]: (^[Z2 : poly_complex]: (Y4 = Z2))) = (^[P3 : poly_complex]: (^[Q2 : poly_complex]: (![N2 : nat]: ((coeff_complex @ P3 @ N2) = (coeff_complex @ Q2 @ N2)))))))). % poly_eq_iff
thf(fact_78_poly__eq__iff, axiom,
    (((^[Y4 : poly_nat]: (^[Z2 : poly_nat]: (Y4 = Z2))) = (^[P3 : poly_nat]: (^[Q2 : poly_nat]: (![N2 : nat]: ((coeff_nat @ P3 @ N2) = (coeff_nat @ Q2 @ N2)))))))). % poly_eq_iff
thf(fact_79_poly__eq__iff, axiom,
    (((^[Y4 : poly_poly_complex]: (^[Z2 : poly_poly_complex]: (Y4 = Z2))) = (^[P3 : poly_poly_complex]: (^[Q2 : poly_poly_complex]: (![N2 : nat]: ((coeff_poly_complex @ P3 @ N2) = (coeff_poly_complex @ Q2 @ N2)))))))). % poly_eq_iff
thf(fact_80_poly__eqI, axiom,
    ((![P : poly_complex, Q : poly_complex]: ((![N3 : nat]: ((coeff_complex @ P @ N3) = (coeff_complex @ Q @ N3))) => (P = Q))))). % poly_eqI
thf(fact_81_poly__eqI, axiom,
    ((![P : poly_nat, Q : poly_nat]: ((![N3 : nat]: ((coeff_nat @ P @ N3) = (coeff_nat @ Q @ N3))) => (P = Q))))). % poly_eqI
thf(fact_82_poly__eqI, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex]: ((![N3 : nat]: ((coeff_poly_complex @ P @ N3) = (coeff_poly_complex @ Q @ N3))) => (P = Q))))). % poly_eqI
thf(fact_83_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_84_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex]: (((poly_poly_complex2 @ P) = (poly_poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_85_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M3 : nat]: (N = (suc @ M3))))))). % not0_implies_Suc
thf(fact_86_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_87_old_Onat_Oexhaust, axiom,
    ((![Y : nat]: ((~ ((Y = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_88_Zero__not__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_not_Suc
thf(fact_89_Zero__neq__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_neq_Suc
thf(fact_90_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_91_zero__induct, axiom,
    ((![P2 : nat > $o, K : nat]: ((P2 @ K) => ((![N3 : nat]: ((P2 @ (suc @ N3)) => (P2 @ N3))) => (P2 @ zero_zero_nat)))))). % zero_induct
thf(fact_92_diff__induct, axiom,
    ((![P2 : nat > nat > $o, M : nat, N : nat]: ((![X4 : nat]: (P2 @ X4 @ zero_zero_nat)) => ((![Y5 : nat]: (P2 @ zero_zero_nat @ (suc @ Y5))) => ((![X4 : nat, Y5 : nat]: ((P2 @ X4 @ Y5) => (P2 @ (suc @ X4) @ (suc @ Y5)))) => (P2 @ M @ N))))))). % diff_induct
thf(fact_93_nat__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N3 : nat]: ((P2 @ N3) => (P2 @ (suc @ N3)))) => (P2 @ N)))))). % nat_induct
thf(fact_94_nat_OdiscI, axiom,
    ((![Nat : nat, X2 : nat]: ((Nat = (suc @ X2)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_95_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_96_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_97_nat_Odistinct_I1_J, axiom,
    ((![X2 : nat]: (~ ((zero_zero_nat = (suc @ X2))))))). % nat.distinct(1)
thf(fact_98_nonzero__imp__inverse__nonzero, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => (~ (((invers502456322omplex @ A) = zero_zero_complex))))))). % nonzero_imp_inverse_nonzero
thf(fact_99_nonzero__inverse__inverse__eq, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((invers502456322omplex @ (invers502456322omplex @ A)) = A))))). % nonzero_inverse_inverse_eq
thf(fact_100_nonzero__inverse__eq__imp__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) => ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (A = B))))))). % nonzero_inverse_eq_imp_eq
thf(fact_101_inverse__zero__imp__zero, axiom,
    ((![A : complex]: (((invers502456322omplex @ A) = zero_zero_complex) => (A = zero_zero_complex))))). % inverse_zero_imp_zero
thf(fact_102_field__class_Ofield__inverse__zero, axiom,
    (((invers502456322omplex @ zero_zero_complex) = zero_zero_complex))). % field_class.field_inverse_zero
thf(fact_103_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_104_infinite__descent0, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N3 : nat]: ((ord_less_nat @ zero_zero_nat @ N3) => ((~ ((P2 @ N3))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N3) & (~ ((P2 @ M2)))))))) => (P2 @ N)))))). % infinite_descent0
thf(fact_105_gr__implies__not0, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_106_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_107_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_108_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_109_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_110_not__less__less__Suc__eq, axiom,
    ((![N : nat, M : nat]: ((~ ((ord_less_nat @ N @ M))) => ((ord_less_nat @ N @ (suc @ M)) = (N = M)))))). % not_less_less_Suc_eq
thf(fact_111_strict__inc__induct, axiom,
    ((![I : nat, J : nat, P2 : nat > $o]: ((ord_less_nat @ I @ J) => ((![I2 : nat]: ((J = (suc @ I2)) => (P2 @ I2))) => ((![I2 : nat]: ((ord_less_nat @ I2 @ J) => ((P2 @ (suc @ I2)) => (P2 @ I2)))) => (P2 @ I))))))). % strict_inc_induct
thf(fact_112_less__Suc__induct, axiom,
    ((![I : nat, J : nat, P2 : nat > nat > $o]: ((ord_less_nat @ I @ J) => ((![I2 : nat]: (P2 @ I2 @ (suc @ I2))) => ((![I2 : nat, J2 : nat, K2 : nat]: ((ord_less_nat @ I2 @ J2) => ((ord_less_nat @ J2 @ K2) => ((P2 @ I2 @ J2) => ((P2 @ J2 @ K2) => (P2 @ I2 @ K2)))))) => (P2 @ I @ J))))))). % less_Suc_induct
thf(fact_113_less__trans__Suc, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_nat @ I @ J) => ((ord_less_nat @ J @ K) => (ord_less_nat @ (suc @ I) @ K)))))). % less_trans_Suc
thf(fact_114_Suc__less__SucD, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ (suc @ M) @ (suc @ N)) => (ord_less_nat @ M @ N))))). % Suc_less_SucD
thf(fact_115_less__antisym, axiom,
    ((![N : nat, M : nat]: ((~ ((ord_less_nat @ N @ M))) => ((ord_less_nat @ N @ (suc @ M)) => (M = N)))))). % less_antisym
thf(fact_116_Suc__less__eq2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ (suc @ N) @ M) = (?[M4 : nat]: (((M = (suc @ M4))) & ((ord_less_nat @ N @ M4)))))))). % Suc_less_eq2
thf(fact_117_All__less__Suc, axiom,
    ((![N : nat, P2 : nat > $o]: ((![I3 : nat]: (((ord_less_nat @ I3 @ (suc @ N))) => ((P2 @ I3)))) = (((P2 @ N)) & ((![I3 : nat]: (((ord_less_nat @ I3 @ N)) => ((P2 @ I3)))))))))). % All_less_Suc
thf(fact_118_not__less__eq, axiom,
    ((![M : nat, N : nat]: ((~ ((ord_less_nat @ M @ N))) = (ord_less_nat @ N @ (suc @ M)))))). % not_less_eq
thf(fact_119_less__Suc__eq, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ (suc @ N)) = (((ord_less_nat @ M @ N)) | ((M = N))))))). % less_Suc_eq
thf(fact_120_Ex__less__Suc, axiom,
    ((![N : nat, P2 : nat > $o]: ((?[I3 : nat]: (((ord_less_nat @ I3 @ (suc @ N))) & ((P2 @ I3)))) = (((P2 @ N)) | ((?[I3 : nat]: (((ord_less_nat @ I3 @ N)) & ((P2 @ I3)))))))))). % Ex_less_Suc
thf(fact_121_less__SucI, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (ord_less_nat @ M @ (suc @ N)))))). % less_SucI
thf(fact_122_less__SucE, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ (suc @ N)) => ((~ ((ord_less_nat @ M @ N))) => (M = N)))))). % less_SucE
thf(fact_123_Suc__lessI, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => ((~ (((suc @ M) = N))) => (ord_less_nat @ (suc @ M) @ N)))))). % Suc_lessI
thf(fact_124_Suc__lessE, axiom,
    ((![I : nat, K : nat]: ((ord_less_nat @ (suc @ I) @ K) => (~ ((![J2 : nat]: ((ord_less_nat @ I @ J2) => (~ ((K = (suc @ J2)))))))))))). % Suc_lessE
thf(fact_125_Suc__lessD, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ (suc @ M) @ N) => (ord_less_nat @ M @ N))))). % Suc_lessD
thf(fact_126_Nat_OlessE, axiom,
    ((![I : nat, K : nat]: ((ord_less_nat @ I @ K) => ((~ ((K = (suc @ I)))) => (~ ((![J2 : nat]: ((ord_less_nat @ I @ J2) => (~ ((K = (suc @ J2))))))))))))). % Nat.lessE
thf(fact_127_lift__Suc__mono__less__iff, axiom,
    ((![F2 : nat > nat, N : nat, M : nat]: ((![N3 : nat]: (ord_less_nat @ (F2 @ N3) @ (F2 @ (suc @ N3)))) => ((ord_less_nat @ (F2 @ N) @ (F2 @ M)) = (ord_less_nat @ N @ M)))))). % lift_Suc_mono_less_iff
thf(fact_128_lift__Suc__mono__less, axiom,
    ((![F2 : nat > nat, N : nat, N4 : nat]: ((![N3 : nat]: (ord_less_nat @ (F2 @ N3) @ (F2 @ (suc @ N3)))) => ((ord_less_nat @ N @ N4) => (ord_less_nat @ (F2 @ N) @ (F2 @ N4))))))). % lift_Suc_mono_less
thf(fact_129_less__Suc__eq__0__disj, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ (suc @ N)) = (((M = zero_zero_nat)) | ((?[J3 : nat]: (((M = (suc @ J3))) & ((ord_less_nat @ J3 @ N)))))))))). % less_Suc_eq_0_disj
thf(fact_130_gr0__implies__Suc, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => (?[M3 : nat]: (N = (suc @ M3))))))). % gr0_implies_Suc
thf(fact_131_All__less__Suc2, axiom,
    ((![N : nat, P2 : nat > $o]: ((![I3 : nat]: (((ord_less_nat @ I3 @ (suc @ N))) => ((P2 @ I3)))) = (((P2 @ zero_zero_nat)) & ((![I3 : nat]: (((ord_less_nat @ I3 @ N)) => ((P2 @ (suc @ I3))))))))))). % All_less_Suc2
thf(fact_132_gr0__conv__Suc, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (?[M5 : nat]: (N = (suc @ M5))))))). % gr0_conv_Suc
thf(fact_133_Ex__less__Suc2, axiom,
    ((![N : nat, P2 : nat > $o]: ((?[I3 : nat]: (((ord_less_nat @ I3 @ (suc @ N))) & ((P2 @ I3)))) = (((P2 @ zero_zero_nat)) | ((?[I3 : nat]: (((ord_less_nat @ I3 @ N)) & ((P2 @ (suc @ I3))))))))))). % Ex_less_Suc2
thf(fact_134_zero__poly_Orep__eq, axiom,
    (((coeff_poly_nat @ zero_z1059985641ly_nat) = (^[Uu : nat]: zero_zero_poly_nat)))). % zero_poly.rep_eq
thf(fact_135_zero__poly_Orep__eq, axiom,
    (((coeff_1429652124omplex @ zero_z1200043727omplex) = (^[Uu : nat]: zero_z1040703943omplex)))). % zero_poly.rep_eq
thf(fact_136_zero__poly_Orep__eq, axiom,
    (((coeff_complex @ zero_z1746442943omplex) = (^[Uu : nat]: zero_zero_complex)))). % zero_poly.rep_eq
thf(fact_137_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_138_zero__poly_Orep__eq, axiom,
    (((coeff_poly_complex @ zero_z1040703943omplex) = (^[Uu : nat]: zero_z1746442943omplex)))). % zero_poly.rep_eq
thf(fact_139_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_140_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_141_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_142_Least__Suc2, axiom,
    ((![P2 : nat > $o, N : nat, Q3 : nat > $o, M : nat]: ((P2 @ N) => ((Q3 @ M) => ((~ ((P2 @ zero_zero_nat))) => ((![K2 : nat]: ((P2 @ (suc @ K2)) = (Q3 @ K2))) => ((ord_Least_nat @ P2) = (suc @ (ord_Least_nat @ Q3)))))))))). % Least_Suc2
thf(fact_143_Least__Suc, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ N) => ((~ ((P2 @ zero_zero_nat))) => ((ord_Least_nat @ P2) = (suc @ (ord_Least_nat @ (^[M5 : nat]: (P2 @ (suc @ M5))))))))))). % Least_Suc
thf(fact_144_poly__0__coeff__0, axiom,
    ((![P : poly_poly_complex]: ((poly_poly_complex2 @ P @ zero_z1746442943omplex) = (coeff_poly_complex @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_145_poly__0__coeff__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ P @ zero_zero_nat) = (coeff_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_146_poly__0__coeff__0, axiom,
    ((![P : poly_complex]: ((poly_complex2 @ P @ zero_zero_complex) = (coeff_complex @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_147_poly__0__coeff__0, axiom,
    ((![P : poly_poly_nat]: ((poly_poly_nat2 @ P @ zero_zero_poly_nat) = (coeff_poly_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_148_poly__0__coeff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((poly_p282434315omplex @ P @ zero_z1040703943omplex) = (coeff_1429652124omplex @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_149_mult__cancel__right, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A @ C) = (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((A = B))))))). % mult_cancel_right
thf(fact_150_mult__cancel__right, axiom,
    ((![A : poly_poly_complex, C : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A @ C) = (times_1460995011omplex @ B @ C)) = (((C = zero_z1040703943omplex)) | ((A = B))))))). % mult_cancel_right
thf(fact_151_mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_right
thf(fact_152_mult__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_right
thf(fact_153_mult__cancel__left, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: (((times_1246143675omplex @ C @ A) = (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((A = B))))))). % mult_cancel_left
thf(fact_154_mult__cancel__left, axiom,
    ((![C : poly_poly_complex, A : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ C @ A) = (times_1460995011omplex @ C @ B)) = (((C = zero_z1040703943omplex)) | ((A = B))))))). % mult_cancel_left
thf(fact_155_mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_left
thf(fact_156_mult__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_left
thf(fact_157_mult__eq__0__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex) = (((A = zero_z1746442943omplex)) | ((B = zero_z1746442943omplex))))))). % mult_eq_0_iff
thf(fact_158_mult__eq__0__iff, axiom,
    ((![A : poly_nat, B : poly_nat]: (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat) = (((A = zero_zero_poly_nat)) | ((B = zero_zero_poly_nat))))))). % mult_eq_0_iff
thf(fact_159_mult__eq__0__iff, axiom,
    ((![A : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A @ B) = zero_z1040703943omplex) = (((A = zero_z1040703943omplex)) | ((B = zero_z1040703943omplex))))))). % mult_eq_0_iff
thf(fact_160_mult__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_161_mult__eq__0__iff, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = (((A = zero_zero_nat)) | ((B = zero_zero_nat))))))). % mult_eq_0_iff
thf(fact_162_mult__zero__right, axiom,
    ((![A : poly_complex]: ((times_1246143675omplex @ A @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % mult_zero_right
thf(fact_163_mult__zero__right, axiom,
    ((![A : poly_nat]: ((times_times_poly_nat @ A @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % mult_zero_right
thf(fact_164_mult__zero__right, axiom,
    ((![A : poly_poly_complex]: ((times_1460995011omplex @ A @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % mult_zero_right
thf(fact_165_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_166_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_167_mult__zero__left, axiom,
    ((![A : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ A) = zero_z1746442943omplex)))). % mult_zero_left
thf(fact_168_mult__zero__left, axiom,
    ((![A : poly_nat]: ((times_times_poly_nat @ zero_zero_poly_nat @ A) = zero_zero_poly_nat)))). % mult_zero_left
thf(fact_169_mult__zero__left, axiom,
    ((![A : poly_poly_complex]: ((times_1460995011omplex @ zero_z1040703943omplex @ A) = zero_z1040703943omplex)))). % mult_zero_left
thf(fact_170_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_171_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_172_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_173_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_174_mult__strict__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))))). % mult_strict_right_mono
thf(fact_175_mult__is__0, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = zero_zero_nat) = (((M = zero_zero_nat)) | ((N = zero_zero_nat))))))). % mult_is_0
thf(fact_176_mult__0__right, axiom,
    ((![M : nat]: ((times_times_nat @ M @ zero_zero_nat) = zero_zero_nat)))). % mult_0_right
thf(fact_177_mult__cancel1, axiom,
    ((![K : nat, M : nat, N : nat]: (((times_times_nat @ K @ M) = (times_times_nat @ K @ N)) = (((M = N)) | ((K = zero_zero_nat))))))). % mult_cancel1
thf(fact_178_mult__cancel2, axiom,
    ((![M : nat, K : nat, N : nat]: (((times_times_nat @ M @ K) = (times_times_nat @ N @ K)) = (((M = N)) | ((K = zero_zero_nat))))))). % mult_cancel2
thf(fact_179_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_180_q_I1_J, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ pa)))). % q(1)
thf(fact_181_mult__eq__1__iff, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = (suc @ zero_zero_nat)) = (((M = (suc @ zero_zero_nat))) & ((N = (suc @ zero_zero_nat)))))))). % mult_eq_1_iff
thf(fact_182_one__eq__mult__iff, axiom,
    ((![M : nat, N : nat]: (((suc @ zero_zero_nat) = (times_times_nat @ M @ N)) = (((M = (suc @ zero_zero_nat))) & ((N = (suc @ zero_zero_nat)))))))). % one_eq_mult_iff
thf(fact_183_mult__less__cancel2, axiom,
    ((![M : nat, K : nat, N : nat]: ((ord_less_nat @ (times_times_nat @ M @ K) @ (times_times_nat @ N @ K)) = (((ord_less_nat @ zero_zero_nat @ K)) & ((ord_less_nat @ M @ N))))))). % mult_less_cancel2
thf(fact_184_nat__0__less__mult__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ M @ N)) = (((ord_less_nat @ zero_zero_nat @ M)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % nat_0_less_mult_iff
thf(fact_185_mult__smult__left, axiom,
    ((![A : complex, P : poly_complex, Q : poly_complex]: ((times_1246143675omplex @ (smult_complex @ A @ P) @ Q) = (smult_complex @ A @ (times_1246143675omplex @ P @ Q)))))). % mult_smult_left
thf(fact_186_mult__smult__left, axiom,
    ((![A : nat, P : poly_nat, Q : poly_nat]: ((times_times_poly_nat @ (smult_nat @ A @ P) @ Q) = (smult_nat @ A @ (times_times_poly_nat @ P @ Q)))))). % mult_smult_left
thf(fact_187_mult__smult__left, axiom,
    ((![A : poly_complex, P : poly_poly_complex, Q : poly_poly_complex]: ((times_1460995011omplex @ (smult_poly_complex @ A @ P) @ Q) = (smult_poly_complex @ A @ (times_1460995011omplex @ P @ Q)))))). % mult_smult_left
thf(fact_188_mult__smult__right, axiom,
    ((![P : poly_complex, A : complex, Q : poly_complex]: ((times_1246143675omplex @ P @ (smult_complex @ A @ Q)) = (smult_complex @ A @ (times_1246143675omplex @ P @ Q)))))). % mult_smult_right
thf(fact_189_mult__smult__right, axiom,
    ((![P : poly_nat, A : nat, Q : poly_nat]: ((times_times_poly_nat @ P @ (smult_nat @ A @ Q)) = (smult_nat @ A @ (times_times_poly_nat @ P @ Q)))))). % mult_smult_right
thf(fact_190_mult__smult__right, axiom,
    ((![P : poly_poly_complex, A : poly_complex, Q : poly_poly_complex]: ((times_1460995011omplex @ P @ (smult_poly_complex @ A @ Q)) = (smult_poly_complex @ A @ (times_1460995011omplex @ P @ Q)))))). % mult_smult_right
thf(fact_191_mult__0, axiom,
    ((![N : nat]: ((times_times_nat @ zero_zero_nat @ N) = zero_zero_nat)))). % mult_0
thf(fact_192_Suc__mult__cancel1, axiom,
    ((![K : nat, M : nat, N : nat]: (((times_times_nat @ (suc @ K) @ M) = (times_times_nat @ (suc @ K) @ N)) = (M = N))))). % Suc_mult_cancel1
thf(fact_193_mult__poly__0__left, axiom,
    ((![Q : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ Q) = zero_z1746442943omplex)))). % mult_poly_0_left
thf(fact_194_mult__poly__0__left, axiom,
    ((![Q : poly_nat]: ((times_times_poly_nat @ zero_zero_poly_nat @ Q) = zero_zero_poly_nat)))). % mult_poly_0_left
thf(fact_195_mult__poly__0__left, axiom,
    ((![Q : poly_poly_complex]: ((times_1460995011omplex @ zero_z1040703943omplex @ Q) = zero_z1040703943omplex)))). % mult_poly_0_left

% Conjectures (1)
thf(conj_0, conjecture,
    (((((smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) = zero_z1746442943omplex) => ((~ ((q = zero_z1746442943omplex))) => ((suc @ (ord_Least_nat @ (^[N2 : nat]: (![I3 : nat]: (((ord_less_nat @ N2 @ I3)) => (((coeff_complex @ q @ I3) = zero_zero_complex))))))) = zero_zero_nat))) & ((~ (((smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) = zero_z1746442943omplex))) => (((q = zero_z1746442943omplex) => (zero_zero_nat = (suc @ (ord_Least_nat @ (^[N2 : nat]: (![I3 : nat]: (((ord_less_nat @ N2 @ I3)) => (((coeff_complex @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ I3) = zero_zero_complex))))))))) & ((~ ((q = zero_z1746442943omplex))) => ((suc @ (ord_Least_nat @ (^[N2 : nat]: (![I3 : nat]: (((ord_less_nat @ N2 @ I3)) => (((coeff_complex @ q @ I3) = zero_zero_complex))))))) = (suc @ (ord_Least_nat @ (^[N2 : nat]: (![I3 : nat]: (((ord_less_nat @ N2 @ I3)) => (((coeff_complex @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ I3) = zero_zero_complex)))))))))))))).
