% 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_844__5376090_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:33:36.843

% Could-be-implicit typings (8)
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__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__Set__Oset_It__Real__Oreal_J, type,
    set_real : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (30)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    one_one_poly_complex : poly_complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    one_one_poly_real : poly_real).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_OpCons_001t__Complex__Ocomplex, type,
    pCons_complex : complex > poly_complex > poly_complex).
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__Real__Oreal, type,
    pCons_real : real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
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__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_c____, type,
    c : complex).
thf(sy_v_cs____, type,
    cs : poly_complex).
thf(sy_v_d____, type,
    d : complex).
thf(sy_v_ds____, type,
    ds : poly_complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (162)
thf(fact_0__092_060open_062_092_060exists_062m_0620_O_A_092_060forall_062z_O_Acmod_Az_A_092_060le_062_A1_A_092_060longrightarrow_062_Acmod_A_Ipoly_Ads_Az_J_A_092_060le_062_Am_092_060close_062, axiom,
    ((?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z) @ one_one_real) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ ds @ Z)) @ M))))))). % \<open>\<exists>m>0. \<forall>z. cmod z \<le> 1 \<longrightarrow> cmod (poly ds z) \<le> m\<close>
thf(fact_1_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_2_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_real]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_3_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_complex]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_4_poly__minimum__modulus, axiom,
    ((![P2 : poly_complex]: (?[Z2 : complex]: (![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P2 @ Z2)) @ (real_V638595069omplex @ (poly_complex2 @ P2 @ W)))))))). % poly_minimum_modulus
thf(fact_5_poly__minimum__modulus__disc, axiom,
    ((![R : real, P2 : poly_complex]: (?[Z2 : complex]: (![W : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ W) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P2 @ Z2)) @ (real_V638595069omplex @ (poly_complex2 @ P2 @ W))))))))). % poly_minimum_modulus_disc
thf(fact_6_norm__le__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X3) @ zero_zero_real) = (X3 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_7_norm__le__zero__iff, axiom,
    ((![X3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X3) @ zero_zero_real) = (X3 = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_8_zero__less__norm__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X3)) = (~ ((X3 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_9_zero__less__norm__iff, axiom,
    ((![X3 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X3)) = (~ ((X3 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_10_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_11_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_12_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_13_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_14_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_15_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_16_poly__1, axiom,
    ((![X3 : real]: ((poly_real2 @ one_one_poly_real @ X3) = one_one_real)))). % poly_1
thf(fact_17_poly__1, axiom,
    ((![X3 : complex]: ((poly_complex2 @ one_one_poly_complex @ X3) = one_one_complex)))). % poly_1
thf(fact_18_poly__0, axiom,
    ((![X3 : real]: ((poly_real2 @ zero_zero_poly_real @ X3) = zero_zero_real)))). % poly_0
thf(fact_19_poly__0, axiom,
    ((![X3 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))). % poly_0
thf(fact_20_poly__0, axiom,
    ((![X3 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))). % poly_0
thf(fact_21_norm__ge__zero, axiom,
    ((![X3 : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X3))))). % norm_ge_zero
thf(fact_22_norm__ge__zero, axiom,
    ((![X3 : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X3))))). % norm_ge_zero
thf(fact_23_norm__not__less__zero, axiom,
    ((![X3 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_24_norm__not__less__zero, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_25_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_26_pCons_Ohyps_I2_J, axiom,
    (((![W2 : complex]: ((~ ((W2 = zero_zero_complex))) => ((poly_complex2 @ ds @ W2) = zero_zero_complex))) => (ds = zero_z1746442943omplex)))). % pCons.hyps(2)
thf(fact_27_pCons_Ohyps_I1_J, axiom,
    (((~ ((d = zero_zero_complex))) | (~ ((ds = zero_z1746442943omplex)))))). % pCons.hyps(1)
thf(fact_28__092_060open_062_092_060forall_062w_O_Aw_A_092_060noteq_062_A0_A_092_060longrightarrow_062_Apoly_Acs_Aw_A_061_A0_092_060close_062, axiom,
    ((![W : complex]: ((~ ((W = zero_zero_complex))) => ((poly_complex2 @ cs @ W) = zero_zero_complex))))). % \<open>\<forall>w. w \<noteq> 0 \<longrightarrow> poly cs w = 0\<close>
thf(fact_29_poly__IVT__pos, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P2 @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ B)) => (?[X : real]: ((ord_less_real @ A @ X) & ((ord_less_real @ X @ B) & ((poly_real2 @ P2 @ X) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_30_poly__IVT__neg, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ A)) => ((ord_less_real @ (poly_real2 @ P2 @ B) @ zero_zero_real) => (?[X : real]: ((ord_less_real @ A @ X) & ((ord_less_real @ X @ B) & ((poly_real2 @ P2 @ X) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_31_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_32_zero__reorient, axiom,
    ((![X3 : complex]: ((zero_zero_complex = X3) = (X3 = zero_zero_complex))))). % zero_reorient
thf(fact_33_zero__reorient, axiom,
    ((![X3 : poly_complex]: ((zero_z1746442943omplex = X3) = (X3 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_34_one__reorient, axiom,
    ((![X3 : real]: ((one_one_real = X3) = (X3 = one_one_real))))). % one_reorient
thf(fact_35_one__reorient, axiom,
    ((![X3 : complex]: ((one_one_complex = X3) = (X3 = one_one_complex))))). % one_reorient
thf(fact_36_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_complex, Q : poly_complex]: (((poly_complex2 @ P2) = (poly_complex2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_37_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_real, Q : poly_real]: (((poly_real2 @ P2) = (poly_real2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_38_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_39_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_40_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_41_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_42_poly__all__0__iff__0, axiom,
    ((![P2 : poly_real]: ((![X2 : real]: ((poly_real2 @ P2 @ X2) = zero_zero_real)) = (P2 = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_43_poly__all__0__iff__0, axiom,
    ((![P2 : poly_complex]: ((![X2 : complex]: ((poly_complex2 @ P2 @ X2) = zero_zero_complex)) = (P2 = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_44_poly__all__0__iff__0, axiom,
    ((![P2 : poly_poly_complex]: ((![X2 : poly_complex]: ((poly_poly_complex2 @ P2 @ X2) = zero_z1746442943omplex)) = (P2 = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_45_pCons_Oprems, axiom,
    ((![W : complex]: ((~ ((W = zero_zero_complex))) => ((poly_complex2 @ (pCons_complex @ d @ ds) @ W) = zero_zero_complex))))). % pCons.prems
thf(fact_46_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_47_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_48_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_49_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_50_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_complex @ N @ one_one_poly_complex) = zero_z1746442943omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_complex @ N @ one_one_poly_complex) = one_one_poly_complex)))))). % poly_cutoff_1
thf(fact_51_order__refl, axiom,
    ((![X3 : real]: (ord_less_eq_real @ X3 @ X3)))). % order_refl
thf(fact_52_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y2 : real]: (((ord_less_real @ X2 @ Y2)) | ((X2 = Y2)))))))). % less_eq_real_def
thf(fact_53_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_54_Collect__mem__eq, axiom,
    ((![A2 : set_real]: ((collect_real @ (^[X2 : real]: (member_real @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_55_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_56_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_57_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_58_False, axiom,
    ((~ ((d = zero_zero_complex))))). % False
thf(fact_59_assms, axiom,
    ((~ ((?[A3 : complex, L : poly_complex]: ((~ ((A3 = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (p = (pCons_complex @ A3 @ L))))))))). % assms
thf(fact_60_pCons__eq__iff, axiom,
    ((![A : complex, P2 : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A @ P2) = (pCons_complex @ B @ Q)) = (((A = B)) & ((P2 = Q))))))). % pCons_eq_iff
thf(fact_61_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_62_pCons__0__0, axiom,
    (((pCons_real @ zero_zero_real @ zero_zero_poly_real) = zero_zero_poly_real))). % pCons_0_0
thf(fact_63_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_64_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_65_pCons__eq__0__iff, axiom,
    ((![A : real, P2 : poly_real]: (((pCons_real @ A @ P2) = zero_zero_poly_real) = (((A = zero_zero_real)) & ((P2 = zero_zero_poly_real))))))). % pCons_eq_0_iff
thf(fact_66_pCons__eq__0__iff, axiom,
    ((![A : poly_complex, P2 : poly_poly_complex]: (((pCons_poly_complex @ A @ P2) = zero_z1040703943omplex) = (((A = zero_z1746442943omplex)) & ((P2 = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_67_pCons__eq__0__iff, axiom,
    ((![A : complex, P2 : poly_complex]: (((pCons_complex @ A @ P2) = zero_z1746442943omplex) = (((A = zero_zero_complex)) & ((P2 = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_68_nc, axiom,
    ((fundam1158420650omplex @ (poly_complex2 @ (pCons_complex @ c @ cs))))). % nc
thf(fact_69_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_real = (pCons_real @ one_one_real @ zero_zero_poly_real)))). % one_poly_eq_simps(1)
thf(fact_70_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_complex = (pCons_complex @ one_one_complex @ zero_z1746442943omplex)))). % one_poly_eq_simps(1)
thf(fact_71_one__poly__eq__simps_I2_J, axiom,
    (((pCons_real @ one_one_real @ zero_zero_poly_real) = one_one_poly_real))). % one_poly_eq_simps(2)
thf(fact_72_one__poly__eq__simps_I2_J, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % one_poly_eq_simps(2)
thf(fact_73__092_060open_062_092_060And_062y_O_Apoly_A_IpCons_Ac_Acs_J_A0_A_061_Apoly_A_IpCons_Ac_Acs_J_Ay_092_060close_062, axiom,
    ((![Y3 : complex]: ((poly_complex2 @ (pCons_complex @ c @ cs) @ zero_zero_complex) = (poly_complex2 @ (pCons_complex @ c @ cs) @ Y3))))). % \<open>\<And>y. poly (pCons c cs) 0 = poly (pCons c cs) y\<close>
thf(fact_74_pCons__cases, axiom,
    ((![P2 : poly_complex]: (~ ((![A4 : complex, Q2 : poly_complex]: (~ ((P2 = (pCons_complex @ A4 @ Q2)))))))))). % pCons_cases
thf(fact_75_pderiv_Ocases, axiom,
    ((![X3 : poly_complex]: (~ ((![A4 : complex, P3 : poly_complex]: (~ ((X3 = (pCons_complex @ A4 @ P3)))))))))). % pderiv.cases
thf(fact_76_pderiv_Oinduct, axiom,
    ((![P : poly_complex > $o, A0 : poly_complex]: ((![A4 : complex, P3 : poly_complex]: (((~ ((P3 = zero_z1746442943omplex))) => (P @ P3)) => (P @ (pCons_complex @ A4 @ P3)))) => (P @ A0))))). % pderiv.induct
thf(fact_77_poly__induct2, axiom,
    ((![P : poly_complex > poly_complex > $o, P2 : poly_complex, Q : poly_complex]: ((P @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A4 : complex, P3 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P @ P3 @ Q2) => (P @ (pCons_complex @ A4 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P @ P2 @ Q)))))). % poly_induct2
thf(fact_78_pCons__induct, axiom,
    ((![P : poly_real > $o, P2 : poly_real]: ((P @ zero_zero_poly_real) => ((![A4 : real, P3 : poly_real]: (((~ ((A4 = zero_zero_real))) | (~ ((P3 = zero_zero_poly_real)))) => ((P @ P3) => (P @ (pCons_real @ A4 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_79_pCons__induct, axiom,
    ((![P : poly_poly_complex > $o, P2 : poly_poly_complex]: ((P @ zero_z1040703943omplex) => ((![A4 : poly_complex, P3 : poly_poly_complex]: (((~ ((A4 = zero_z1746442943omplex))) | (~ ((P3 = zero_z1040703943omplex)))) => ((P @ P3) => (P @ (pCons_poly_complex @ A4 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_80_pCons__induct, axiom,
    ((![P : poly_complex > $o, P2 : poly_complex]: ((P @ zero_z1746442943omplex) => ((![A4 : complex, P3 : poly_complex]: (((~ ((A4 = zero_zero_complex))) | (~ ((P3 = zero_z1746442943omplex)))) => ((P @ P3) => (P @ (pCons_complex @ A4 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_81_pCons__one, axiom,
    (((pCons_real @ one_one_real @ zero_zero_poly_real) = one_one_poly_real))). % pCons_one
thf(fact_82_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_83_order__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_84_order__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_85_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_86_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_87_eq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[X2 : real]: (^[Y2 : real]: (((ord_less_eq_real @ X2 @ Y2)) & ((ord_less_eq_real @ Y2 @ X2)))))))). % eq_iff
thf(fact_88_antisym, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ Y3) => ((ord_less_eq_real @ Y3 @ X3) => (X3 = Y3)))))). % antisym
thf(fact_89_linear, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ Y3) | (ord_less_eq_real @ Y3 @ X3))))). % linear
thf(fact_90_eq__refl, axiom,
    ((![X3 : real, Y3 : real]: ((X3 = Y3) => (ord_less_eq_real @ X3 @ Y3))))). % eq_refl
thf(fact_91_le__cases, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((ord_less_eq_real @ X3 @ Y3))) => (ord_less_eq_real @ Y3 @ X3))))). % le_cases
thf(fact_92_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_93_le__cases3, axiom,
    ((![X3 : real, Y3 : real, Z4 : real]: (((ord_less_eq_real @ X3 @ Y3) => (~ ((ord_less_eq_real @ Y3 @ Z4)))) => (((ord_less_eq_real @ Y3 @ X3) => (~ ((ord_less_eq_real @ X3 @ Z4)))) => (((ord_less_eq_real @ X3 @ Z4) => (~ ((ord_less_eq_real @ Z4 @ Y3)))) => (((ord_less_eq_real @ Z4 @ Y3) => (~ ((ord_less_eq_real @ Y3 @ X3)))) => (((ord_less_eq_real @ Y3 @ Z4) => (~ ((ord_less_eq_real @ Z4 @ X3)))) => (~ (((ord_less_eq_real @ Z4 @ X3) => (~ ((ord_less_eq_real @ X3 @ Y3)))))))))))))). % le_cases3
thf(fact_94_antisym__conv, axiom,
    ((![Y3 : real, X3 : real]: ((ord_less_eq_real @ Y3 @ X3) => ((ord_less_eq_real @ X3 @ Y3) = (X3 = Y3)))))). % antisym_conv
thf(fact_95_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[A5 : real]: (^[B3 : real]: (((ord_less_eq_real @ A5 @ B3)) & ((ord_less_eq_real @ B3 @ A5)))))))). % order_class.order.eq_iff
thf(fact_96_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_97_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_98_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_99_order__trans, axiom,
    ((![X3 : real, Y3 : real, Z4 : real]: ((ord_less_eq_real @ X3 @ Y3) => ((ord_less_eq_real @ Y3 @ Z4) => (ord_less_eq_real @ X3 @ Z4)))))). % order_trans
thf(fact_100_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_101_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B2 : real]: ((ord_less_eq_real @ A4 @ B2) => (P @ A4 @ B2))) => ((![A4 : real, B2 : real]: ((P @ B2 @ A4) => (P @ A4 @ B2))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_102_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_103_dual__order_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[A5 : real]: (^[B3 : real]: (((ord_less_eq_real @ B3 @ A5)) & ((ord_less_eq_real @ A5 @ B3)))))))). % dual_order.eq_iff
thf(fact_104_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_105_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_106_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_107_order__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_108_order__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_109_lt__ex, axiom,
    ((![X3 : real]: (?[Y4 : real]: (ord_less_real @ Y4 @ X3))))). % lt_ex
thf(fact_110_gt__ex, axiom,
    ((![X3 : real]: (?[X_12 : real]: (ord_less_real @ X3 @ X_12))))). % gt_ex
thf(fact_111_neqE, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((X3 = Y3))) => ((~ ((ord_less_real @ X3 @ Y3))) => (ord_less_real @ Y3 @ X3)))))). % neqE
thf(fact_112_neq__iff, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((X3 = Y3))) = (((ord_less_real @ X3 @ Y3)) | ((ord_less_real @ Y3 @ X3))))))). % neq_iff
thf(fact_113_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_114_dense, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (?[Z2 : real]: ((ord_less_real @ X3 @ Z2) & (ord_less_real @ Z2 @ Y3))))))). % dense
thf(fact_115_less__imp__neq, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (~ ((X3 = Y3))))))). % less_imp_neq
thf(fact_116_less__asym, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (~ ((ord_less_real @ Y3 @ X3))))))). % less_asym
thf(fact_117_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_118_less__trans, axiom,
    ((![X3 : real, Y3 : real, Z4 : real]: ((ord_less_real @ X3 @ Y3) => ((ord_less_real @ Y3 @ Z4) => (ord_less_real @ X3 @ Z4)))))). % less_trans
thf(fact_119_less__linear, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) | ((X3 = Y3) | (ord_less_real @ Y3 @ X3)))))). % less_linear
thf(fact_120_less__irrefl, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ X3 @ X3)))))). % less_irrefl
thf(fact_121_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_122_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_123_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_124_less__imp__not__eq, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (~ ((X3 = Y3))))))). % less_imp_not_eq
thf(fact_125_less__not__sym, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (~ ((ord_less_real @ Y3 @ X3))))))). % less_not_sym
thf(fact_126_antisym__conv3, axiom,
    ((![Y3 : real, X3 : real]: ((~ ((ord_less_real @ Y3 @ X3))) => ((~ ((ord_less_real @ X3 @ Y3))) = (X3 = Y3)))))). % antisym_conv3
thf(fact_127_less__imp__not__eq2, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (~ ((Y3 = X3))))))). % less_imp_not_eq2
thf(fact_128_less__imp__triv, axiom,
    ((![X3 : real, Y3 : real, P : $o]: ((ord_less_real @ X3 @ Y3) => ((ord_less_real @ Y3 @ X3) => P))))). % less_imp_triv
thf(fact_129_linorder__cases, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((ord_less_real @ X3 @ Y3))) => ((~ ((X3 = Y3))) => (ord_less_real @ Y3 @ X3)))))). % linorder_cases
thf(fact_130_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_131_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_132_less__imp__not__less, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (~ ((ord_less_real @ Y3 @ X3))))))). % less_imp_not_less
thf(fact_133_linorder__less__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B2 : real]: ((ord_less_real @ A4 @ B2) => (P @ A4 @ B2))) => ((![A4 : real]: (P @ A4 @ A4)) => ((![A4 : real, B2 : real]: ((P @ B2 @ A4) => (P @ A4 @ B2))) => (P @ A @ B))))))). % linorder_less_wlog
thf(fact_134_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_135_not__less__iff__gr__or__eq, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((ord_less_real @ X3 @ Y3))) = (((ord_less_real @ Y3 @ X3)) | ((X3 = Y3))))))). % not_less_iff_gr_or_eq
thf(fact_136_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_137_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_138_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((X3 = Y3))) => ((~ ((ord_less_real @ X3 @ Y3))) => (ord_less_real @ Y3 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_139_complete__real, axiom,
    ((![S2 : set_real]: ((?[X4 : real]: (member_real @ X4 @ S2)) => ((?[Z : real]: (![X : real]: ((member_real @ X @ S2) => (ord_less_eq_real @ X @ Z)))) => (?[Y4 : real]: ((![X4 : real]: ((member_real @ X4 @ S2) => (ord_less_eq_real @ X4 @ Y4))) & (![Z : real]: ((![X : real]: ((member_real @ X @ S2) => (ord_less_eq_real @ X @ Z))) => (ord_less_eq_real @ Y4 @ Z)))))))))). % complete_real
thf(fact_140_poly__infinity, axiom,
    ((![P2 : poly_complex, D : real, A : complex]: ((~ ((P2 = zero_z1746442943omplex))) => (?[R2 : real]: (![Z : complex]: ((ord_less_eq_real @ R2 @ (real_V638595069omplex @ Z)) => (ord_less_eq_real @ D @ (real_V638595069omplex @ (poly_complex2 @ (pCons_complex @ A @ P2) @ Z)))))))))). % poly_infinity
thf(fact_141_poly__infinity, axiom,
    ((![P2 : poly_real, D : real, A : real]: ((~ ((P2 = zero_zero_poly_real))) => (?[R2 : real]: (![Z : real]: ((ord_less_eq_real @ R2 @ (real_V646646907m_real @ Z)) => (ord_less_eq_real @ D @ (real_V646646907m_real @ (poly_real2 @ (pCons_real @ A @ P2) @ Z)))))))))). % poly_infinity
thf(fact_142_field__lbound__gt__zero, axiom,
    ((![D1 : real, D2 : real]: ((ord_less_real @ zero_zero_real @ D1) => ((ord_less_real @ zero_zero_real @ D2) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ D1) & (ord_less_real @ E @ D2))))))))). % field_lbound_gt_zero
thf(fact_143_leD, axiom,
    ((![Y3 : real, X3 : real]: ((ord_less_eq_real @ Y3 @ X3) => (~ ((ord_less_real @ X3 @ Y3))))))). % leD
thf(fact_144_leI, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((ord_less_real @ X3 @ Y3))) => (ord_less_eq_real @ Y3 @ X3))))). % leI
thf(fact_145_le__less, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y2 : real]: (((ord_less_real @ X2 @ Y2)) | ((X2 = Y2)))))))). % le_less
thf(fact_146_less__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y2 : real]: (((ord_less_eq_real @ X2 @ Y2)) & ((~ ((X2 = Y2)))))))))). % less_le
thf(fact_147_order__le__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_le_less_subst1
thf(fact_148_order__le__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % order_le_less_subst2
thf(fact_149_order__less__le__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_le_subst1
thf(fact_150_order__less__le__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_le_subst2
thf(fact_151_not__le, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((ord_less_eq_real @ X3 @ Y3))) = (ord_less_real @ Y3 @ X3))))). % not_le
thf(fact_152_not__less, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((ord_less_real @ X3 @ Y3))) = (ord_less_eq_real @ Y3 @ X3))))). % not_less
thf(fact_153_le__neq__trans, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((~ ((A = B))) => (ord_less_real @ A @ B)))))). % le_neq_trans
thf(fact_154_antisym__conv1, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((ord_less_real @ X3 @ Y3))) => ((ord_less_eq_real @ X3 @ Y3) = (X3 = Y3)))))). % antisym_conv1
thf(fact_155_antisym__conv2, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ Y3) => ((~ ((ord_less_real @ X3 @ Y3))) = (X3 = Y3)))))). % antisym_conv2
thf(fact_156_less__imp__le, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (ord_less_eq_real @ X3 @ Y3))))). % less_imp_le
thf(fact_157_le__less__trans, axiom,
    ((![X3 : real, Y3 : real, Z4 : real]: ((ord_less_eq_real @ X3 @ Y3) => ((ord_less_real @ Y3 @ Z4) => (ord_less_real @ X3 @ Z4)))))). % le_less_trans
thf(fact_158_less__le__trans, axiom,
    ((![X3 : real, Y3 : real, Z4 : real]: ((ord_less_real @ X3 @ Y3) => ((ord_less_eq_real @ Y3 @ Z4) => (ord_less_real @ X3 @ Z4)))))). % less_le_trans
thf(fact_159_dense__ge, axiom,
    ((![Z4 : real, Y3 : real]: ((![X : real]: ((ord_less_real @ Z4 @ X) => (ord_less_eq_real @ Y3 @ X))) => (ord_less_eq_real @ Y3 @ Z4))))). % dense_ge
thf(fact_160_dense__le, axiom,
    ((![Y3 : real, Z4 : real]: ((![X : real]: ((ord_less_real @ X @ Y3) => (ord_less_eq_real @ X @ Z4))) => (ord_less_eq_real @ Y3 @ Z4))))). % dense_le
thf(fact_161_le__less__linear, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ Y3) | (ord_less_real @ Y3 @ X3))))). % le_less_linear

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![M2 : real]: ((ord_less_real @ zero_zero_real @ M2) => ((![Z2 : a, Za : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Za) @ one_one_real) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ ds @ Za)) @ M2))) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
