% 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_401__5371450_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:51.976

% Could-be-implicit typings (6)
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__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $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).

% Explicit typings (41)
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    one_one_poly_complex : poly_complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    one_one_poly_nat : poly_nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__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_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    plus_p1547158847omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    plus_plus_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    plus_plus_poly_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    uminus1138659839omplex : poly_complex > poly_complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    uminus1613791741y_real : poly_real > poly_real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_real : 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__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_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex, type,
    semiri356525583omplex : nat > complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal, type,
    semiri2110766477t_real : nat > real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
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__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $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__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
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_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat, type,
    divide_divide_nat : nat > nat > nat).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_r, type,
    r : real).
thf(sy_v_s____, type,
    s : real).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (179)
thf(fact_0__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Acmod_A_If_Ax_J_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_092_060close_062, axiom,
    ((?[F : nat > complex]: (![X : nat]: ((ord_less_eq_real @ (real_V638595069omplex @ (F @ X)) @ r) & (ord_less_real @ (real_V638595069omplex @ (poly_complex2 @ p @ (F @ X))) @ (plus_plus_real @ (uminus_uminus_real @ s) @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ X)))))))))). % \<open>\<exists>f. \<forall>x. cmod (f x) \<le> r \<and> cmod (poly p (f x)) < - s + 1 / real (Suc x)\<close>
thf(fact_1_s, axiom,
    ((![Y : real]: ((?[X2 : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X2)))))) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ s))))). % s
thf(fact_2_True, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % True
thf(fact_3_mth1, axiom,
    ((?[X3 : real, Z2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z2) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ Z2)) = (uminus_uminus_real @ X3)))))). % mth1
thf(fact_4__092_060open_062_092_060exists_062s_O_A_092_060forall_062y_O_A_I_092_060exists_062x_O_A_I_092_060exists_062z_O_Acmod_Az_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_092_060and_062_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_092_060close_062, axiom,
    ((?[S : real]: (![Y : real]: ((?[X2 : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X2)))))) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S)))))). % \<open>\<exists>s. \<forall>y. (\<exists>x. (\<exists>z. cmod z \<le> r \<and> cmod (poly p z) = - x) \<and> y < x) = (y < s)\<close>
thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060forall_062y_O_A_I_092_060exists_062x_O_A_I_092_060exists_062z_O_Acmod_Az_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_092_060and_062_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![S : real]: (~ ((![Y : real]: ((?[X2 : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X2)))))) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S)))))))))). % \<open>\<And>thesis. (\<And>s. \<forall>y. (\<exists>x. (\<exists>z. cmod z \<le> r \<and> cmod (poly p z) = - x) \<and> y < x) = (y < s) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_6_mth2, axiom,
    ((?[Z2 : real]: (![X : real]: ((?[Za : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Za) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ Za)) = (uminus_uminus_real @ X)))) => (ord_less_real @ X @ Z2)))))). % mth2
thf(fact_7__092_060open_062_092_060And_062z_Ax_O_A_092_060lbrakk_062cmod_Az_A_092_060le_062_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_092_060not_062_Ax_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((![Z3 : complex, X4 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ r) => (((real_V638595069omplex @ (poly_complex2 @ p @ Z3)) = (uminus_uminus_real @ X4)) => (ord_less_real @ X4 @ one_one_real)))))). % \<open>\<And>z x. \<lbrakk>cmod z \<le> r; cmod (poly p z) = - x; \<not> x < 1\<rbrakk> \<Longrightarrow> False\<close>
thf(fact_8_s1m, axiom,
    ((![Z3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ r) => (ord_less_eq_real @ (uminus_uminus_real @ s) @ (real_V638595069omplex @ (poly_complex2 @ p @ Z3))))))). % s1m
thf(fact_9__092_060open_062_092_060And_062n_O_A_092_060exists_062z_O_Acmod_Az_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_092_060close_062, axiom,
    ((![N : nat]: (?[Z2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z2) @ r) & (ord_less_real @ (real_V638595069omplex @ (poly_complex2 @ p @ Z2)) @ (plus_plus_real @ (uminus_uminus_real @ s) @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ N)))))))))). % \<open>\<And>n. \<exists>z. cmod z \<le> r \<and> cmod (poly p z) < - s + 1 / real (Suc n)\<close>
thf(fact_10_th, axiom,
    ((![N2 : nat]: (?[Z2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z2) @ r) & (ord_less_real @ (real_V638595069omplex @ (poly_complex2 @ p @ Z2)) @ (plus_plus_real @ (uminus_uminus_real @ s) @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ N2)))))))))). % th
thf(fact_11_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z4 : real]: (![X3 : real]: ((P @ X3) => (ord_less_real @ X3 @ Z4)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_12_of__nat__Suc, axiom,
    ((![M : nat]: ((semiri1382578993at_nat @ (suc @ M)) = (plus_plus_nat @ one_one_nat @ (semiri1382578993at_nat @ M)))))). % of_nat_Suc
thf(fact_13_of__nat__Suc, axiom,
    ((![M : nat]: ((semiri356525583omplex @ (suc @ M)) = (plus_plus_complex @ one_one_complex @ (semiri356525583omplex @ M)))))). % of_nat_Suc
thf(fact_14_of__nat__Suc, axiom,
    ((![M : nat]: ((semiri2110766477t_real @ (suc @ M)) = (plus_plus_real @ one_one_real @ (semiri2110766477t_real @ M)))))). % of_nat_Suc
thf(fact_15__092_060open_062cmod_A0_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_092_060close_062, axiom,
    (((ord_less_eq_real @ (real_V638595069omplex @ zero_zero_complex) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ zero_zero_complex)) = (uminus_uminus_real @ (uminus_uminus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ zero_zero_complex)))))))). % \<open>cmod 0 \<le> r \<and> cmod (poly p 0) = - (- cmod (poly p 0))\<close>
thf(fact_16_norm__of__nat, axiom,
    ((![N : nat]: ((real_V646646907m_real @ (semiri2110766477t_real @ N)) = (semiri2110766477t_real @ N))))). % norm_of_nat
thf(fact_17_norm__of__nat, axiom,
    ((![N : nat]: ((real_V638595069omplex @ (semiri356525583omplex @ N)) = (semiri2110766477t_real @ N))))). % norm_of_nat
thf(fact_18_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_19_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_20_divide__minus1, axiom,
    ((![X4 : real]: ((divide_divide_real @ X4 @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ X4))))). % divide_minus1
thf(fact_21_poly__minus, axiom,
    ((![P2 : poly_complex, X4 : complex]: ((poly_complex2 @ (uminus1138659839omplex @ P2) @ X4) = (uminus1204672759omplex @ (poly_complex2 @ P2 @ X4)))))). % poly_minus
thf(fact_22_poly__minus, axiom,
    ((![P2 : poly_real, X4 : real]: ((poly_real2 @ (uminus1613791741y_real @ P2) @ X4) = (uminus_uminus_real @ (poly_real2 @ P2 @ X4)))))). % poly_minus
thf(fact_23_poly__1, axiom,
    ((![X4 : complex]: ((poly_complex2 @ one_one_poly_complex @ X4) = one_one_complex)))). % poly_1
thf(fact_24_poly__1, axiom,
    ((![X4 : real]: ((poly_real2 @ one_one_poly_real @ X4) = one_one_real)))). % poly_1
thf(fact_25_poly__1, axiom,
    ((![X4 : nat]: ((poly_nat2 @ one_one_poly_nat @ X4) = one_one_nat)))). % poly_1
thf(fact_26_poly__add, axiom,
    ((![P2 : poly_real, Q : poly_real, X4 : real]: ((poly_real2 @ (plus_plus_poly_real @ P2 @ Q) @ X4) = (plus_plus_real @ (poly_real2 @ P2 @ X4) @ (poly_real2 @ Q @ X4)))))). % poly_add
thf(fact_27_poly__add, axiom,
    ((![P2 : poly_nat, Q : poly_nat, X4 : nat]: ((poly_nat2 @ (plus_plus_poly_nat @ P2 @ Q) @ X4) = (plus_plus_nat @ (poly_nat2 @ P2 @ X4) @ (poly_nat2 @ Q @ X4)))))). % poly_add
thf(fact_28_poly__add, axiom,
    ((![P2 : poly_complex, Q : poly_complex, X4 : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P2 @ Q) @ X4) = (plus_plus_complex @ (poly_complex2 @ P2 @ X4) @ (poly_complex2 @ Q @ X4)))))). % poly_add
thf(fact_29_norm__minus__cancel, axiom,
    ((![X4 : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X4)) = (real_V646646907m_real @ X4))))). % norm_minus_cancel
thf(fact_30_norm__minus__cancel, axiom,
    ((![X4 : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X4)) = (real_V638595069omplex @ X4))))). % norm_minus_cancel
thf(fact_31_of__nat__1, axiom,
    (((semiri1382578993at_nat @ one_one_nat) = one_one_nat))). % of_nat_1
thf(fact_32_of__nat__1, axiom,
    (((semiri2110766477t_real @ one_one_nat) = one_one_real))). % of_nat_1
thf(fact_33_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_nat = (semiri1382578993at_nat @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_34_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_real = (semiri2110766477t_real @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_35_add__Suc__right, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ M @ (suc @ N)) = (suc @ (plus_plus_nat @ M @ N)))))). % add_Suc_right
thf(fact_36_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_37_nat_Oinject, axiom,
    ((![X22 : nat, Y2 : nat]: (((suc @ X22) = (suc @ Y2)) = (X22 = Y2))))). % nat.inject
thf(fact_38_of__nat__eq__iff, axiom,
    ((![M : nat, N : nat]: (((semiri2110766477t_real @ M) = (semiri2110766477t_real @ N)) = (M = N))))). % of_nat_eq_iff
thf(fact_39_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_40_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_41_divide__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_right
thf(fact_42_divide__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((divide_divide_real @ A @ C) = (divide_divide_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_right
thf(fact_43_divide__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((divide1210191872omplex @ C @ A) = (divide1210191872omplex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_left
thf(fact_44_divide__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((divide_divide_real @ C @ A) = (divide_divide_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_left
thf(fact_45_divide__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % divide_eq_0_iff
thf(fact_46_divide__eq__0__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % divide_eq_0_iff
thf(fact_47_of__nat__0, axiom,
    (((semiri356525583omplex @ zero_zero_nat) = zero_zero_complex))). % of_nat_0
thf(fact_48_of__nat__0, axiom,
    (((semiri2110766477t_real @ zero_zero_nat) = zero_zero_real))). % of_nat_0
thf(fact_49_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_complex = (semiri356525583omplex @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_50_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_real = (semiri2110766477t_real @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_51_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri356525583omplex @ M) = zero_zero_complex) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_52_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri2110766477t_real @ M) = zero_zero_real) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_53_of__nat__le__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)) = (ord_less_eq_nat @ M @ N))))). % of_nat_le_iff
thf(fact_54_of__nat__less__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)) = (ord_less_nat @ M @ N))))). % of_nat_less_iff
thf(fact_55_of__nat__add, axiom,
    ((![M : nat, N : nat]: ((semiri1382578993at_nat @ (plus_plus_nat @ M @ N)) = (plus_plus_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)))))). % of_nat_add
thf(fact_56_of__nat__add, axiom,
    ((![M : nat, N : nat]: ((semiri356525583omplex @ (plus_plus_nat @ M @ N)) = (plus_plus_complex @ (semiri356525583omplex @ M) @ (semiri356525583omplex @ N)))))). % of_nat_add
thf(fact_57_of__nat__add, axiom,
    ((![M : nat, N : nat]: ((semiri2110766477t_real @ (plus_plus_nat @ M @ N)) = (plus_plus_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)))))). % of_nat_add
thf(fact_58_poly__0, axiom,
    ((![X4 : real]: ((poly_real2 @ zero_zero_poly_real @ X4) = zero_zero_real)))). % poly_0
thf(fact_59_poly__0, axiom,
    ((![X4 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X4) = zero_zero_complex)))). % poly_0
thf(fact_60_zero__eq__1__divide__iff, axiom,
    ((![A : real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real))))). % zero_eq_1_divide_iff
thf(fact_61_one__divide__eq__0__iff, axiom,
    ((![A : real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % one_divide_eq_0_iff
thf(fact_62_eq__divide__eq__1, axiom,
    ((![B : real, A : real]: ((one_one_real = (divide_divide_real @ B @ A)) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % eq_divide_eq_1
thf(fact_63_divide__eq__eq__1, axiom,
    ((![B : real, A : real]: (((divide_divide_real @ B @ A) = one_one_real) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % divide_eq_eq_1
thf(fact_64_divide__self__if, axiom,
    ((![A : complex]: (((A = zero_zero_complex) => ((divide1210191872omplex @ A @ A) = zero_zero_complex)) & ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex)))))). % divide_self_if
thf(fact_65_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_66_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_67_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_68_one__eq__divide__iff, axiom,
    ((![A : complex, B : complex]: ((one_one_complex = (divide1210191872omplex @ A @ B)) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_69_one__eq__divide__iff, axiom,
    ((![A : real, B : real]: ((one_one_real = (divide_divide_real @ A @ B)) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_70_divide__eq__1__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = one_one_complex) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_71_divide__eq__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = one_one_real) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_72_of__nat__le__0__iff, axiom,
    ((![M : nat]: ((ord_less_eq_real @ (semiri2110766477t_real @ M) @ zero_zero_real) = (M = zero_zero_nat))))). % of_nat_le_0_iff
thf(fact_73_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_real @ zero_zero_real @ (semiri2110766477t_real @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_74_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_75_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_76_norm__eq__zero, axiom,
    ((![X4 : real]: (((real_V646646907m_real @ X4) = zero_zero_real) = (X4 = zero_zero_real))))). % norm_eq_zero
thf(fact_77_norm__eq__zero, axiom,
    ((![X4 : complex]: (((real_V638595069omplex @ X4) = zero_zero_real) = (X4 = zero_zero_complex))))). % norm_eq_zero
thf(fact_78_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri1382578993at_nat @ N) = one_one_nat) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_79_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri2110766477t_real @ N) = one_one_real) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_80_zero__le__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_divide_1_iff
thf(fact_81_divide__le__0__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % divide_le_0_1_iff
thf(fact_82_zero__less__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_divide_1_iff
thf(fact_83_less__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)))))). % less_divide_eq_1_pos
thf(fact_84_less__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)))))). % less_divide_eq_1_neg
thf(fact_85_divide__less__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)))))). % divide_less_eq_1_pos
thf(fact_86_divide__less__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B)))))). % divide_less_eq_1_neg
thf(fact_87_divide__less__0__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % divide_less_0_1_iff
thf(fact_88_zero__less__norm__iff, axiom,
    ((![X4 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X4)) = (~ ((X4 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_89_zero__less__norm__iff, axiom,
    ((![X4 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X4)) = (~ ((X4 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_90_norm__le__zero__iff, axiom,
    ((![X4 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X4) @ zero_zero_real) = (X4 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_91_norm__le__zero__iff, axiom,
    ((![X4 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X4) @ zero_zero_real) = (X4 = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_92_le__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B)))))). % le_divide_eq_1_pos
thf(fact_93_le__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ B @ A)))))). % le_divide_eq_1_neg
thf(fact_94_divide__le__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A)))))). % divide_le_eq_1_pos
thf(fact_95_divide__le__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B)))))). % divide_le_eq_1_neg
thf(fact_96_Suc__eq__plus1, axiom,
    ((suc = (^[N3 : nat]: (plus_plus_nat @ N3 @ one_one_nat))))). % Suc_eq_plus1
thf(fact_97_plus__1__eq__Suc, axiom,
    (((plus_plus_nat @ one_one_nat) = suc))). % plus_1_eq_Suc
thf(fact_98_Suc__eq__plus1__left, axiom,
    ((suc = (plus_plus_nat @ one_one_nat)))). % Suc_eq_plus1_left
thf(fact_99_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) => (?[X3 : real]: ((ord_less_real @ A @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P2 @ X3) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_100_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)) => (?[X3 : real]: ((ord_less_real @ A @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P2 @ X3) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_101_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_102_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_103_add__Suc, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ (suc @ M) @ N) = (suc @ (plus_plus_nat @ M @ N)))))). % add_Suc
thf(fact_104_nat__arith_Osuc1, axiom,
    ((![A2 : nat, K : nat, A : nat]: ((A2 = (plus_plus_nat @ K @ A)) => ((suc @ A2) = (plus_plus_nat @ K @ (suc @ A))))))). % nat_arith.suc1
thf(fact_105_add__Suc__shift, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ (suc @ M) @ N) = (plus_plus_nat @ M @ (suc @ N)))))). % add_Suc_shift
thf(fact_106_divide__right__mono__neg, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C))))))). % divide_right_mono_neg
thf(fact_107_divide__nonpos__nonpos, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ zero_zero_real) => ((ord_less_eq_real @ Y3 @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X4 @ Y3))))))). % divide_nonpos_nonpos
thf(fact_108_divide__nonpos__nonneg, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ Y3) => (ord_less_eq_real @ (divide_divide_real @ X4 @ Y3) @ zero_zero_real)))))). % divide_nonpos_nonneg
thf(fact_109_divide__nonneg__nonpos, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X4) => ((ord_less_eq_real @ Y3 @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ X4 @ Y3) @ zero_zero_real)))))). % divide_nonneg_nonpos
thf(fact_110_divide__nonneg__nonneg, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X4) => ((ord_less_eq_real @ zero_zero_real @ Y3) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X4 @ Y3))))))). % divide_nonneg_nonneg
thf(fact_111_zero__le__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ zero_zero_real))))))))). % zero_le_divide_iff
thf(fact_112_divide__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_right_mono
thf(fact_113_divide__le__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ zero_zero_real)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B))))))))). % divide_le_0_iff
thf(fact_114_divide__strict__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono_neg
thf(fact_115_divide__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono
thf(fact_116_zero__less__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ zero_zero_real @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real))))))))). % zero_less_divide_iff
thf(fact_117_divide__less__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A)))) & ((~ ((C = zero_zero_real))))))))))). % divide_less_cancel
thf(fact_118_divide__less__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ zero_zero_real)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B))))))))). % divide_less_0_iff
thf(fact_119_divide__pos__pos, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_real @ zero_zero_real @ X4) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X4 @ Y3))))))). % divide_pos_pos
thf(fact_120_divide__pos__neg, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_real @ zero_zero_real @ X4) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X4 @ Y3) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_121_divide__neg__pos, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_real @ X4 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_real @ (divide_divide_real @ X4 @ Y3) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_122_divide__neg__neg, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_real @ X4 @ zero_zero_real) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X4 @ Y3))))))). % divide_neg_neg
thf(fact_123_right__inverse__eq, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => (((divide1210191872omplex @ A @ B) = one_one_complex) = (A = B)))))). % right_inverse_eq
thf(fact_124_right__inverse__eq, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => (((divide_divide_real @ A @ B) = one_one_real) = (A = B)))))). % right_inverse_eq
thf(fact_125_of__nat__0__le__iff, axiom,
    ((![N : nat]: (ord_less_eq_real @ zero_zero_real @ (semiri2110766477t_real @ N))))). % of_nat_0_le_iff
thf(fact_126_of__nat__less__0__iff, axiom,
    ((![M : nat]: (~ ((ord_less_real @ (semiri2110766477t_real @ M) @ zero_zero_real)))))). % of_nat_less_0_iff
thf(fact_127_nonzero__minus__divide__divide, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ (uminus1204672759omplex @ A) @ (uminus1204672759omplex @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_minus_divide_divide
thf(fact_128_nonzero__minus__divide__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((divide_divide_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (divide_divide_real @ A @ B)))))). % nonzero_minus_divide_divide
thf(fact_129_nonzero__minus__divide__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((uminus1204672759omplex @ (divide1210191872omplex @ A @ B)) = (divide1210191872omplex @ A @ (uminus1204672759omplex @ B))))))). % nonzero_minus_divide_right
thf(fact_130_nonzero__minus__divide__right, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ A @ (uminus_uminus_real @ B))))))). % nonzero_minus_divide_right
thf(fact_131_of__nat__neq__0, axiom,
    ((![N : nat]: (~ (((semiri356525583omplex @ (suc @ N)) = zero_zero_complex)))))). % of_nat_neq_0
thf(fact_132_of__nat__neq__0, axiom,
    ((![N : nat]: (~ (((semiri2110766477t_real @ (suc @ N)) = zero_zero_real)))))). % of_nat_neq_0
thf(fact_133_norm__not__less__zero, axiom,
    ((![X4 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X4) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_134_norm__ge__zero, axiom,
    ((![X4 : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X4))))). % norm_ge_zero
thf(fact_135_field__le__epsilon, axiom,
    ((![X4 : real, Y3 : real]: ((![E : real]: ((ord_less_real @ zero_zero_real @ E) => (ord_less_eq_real @ X4 @ (plus_plus_real @ Y3 @ E)))) => (ord_less_eq_real @ X4 @ Y3))))). % field_le_epsilon
thf(fact_136_divide__nonpos__pos, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_eq_real @ (divide_divide_real @ X4 @ Y3) @ zero_zero_real)))))). % divide_nonpos_pos
thf(fact_137_divide__nonpos__neg, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ zero_zero_real) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X4 @ Y3))))))). % divide_nonpos_neg
thf(fact_138_divide__nonneg__pos, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X4) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X4 @ Y3))))))). % divide_nonneg_pos
thf(fact_139_divide__nonneg__neg, axiom,
    ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X4) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ X4 @ Y3) @ zero_zero_real)))))). % divide_nonneg_neg
thf(fact_140_divide__le__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ A))))))))). % divide_le_cancel
thf(fact_141_frac__less2, axiom,
    ((![X4 : real, Y3 : real, W : real, Z3 : real]: ((ord_less_real @ zero_zero_real @ X4) => ((ord_less_eq_real @ X4 @ Y3) => ((ord_less_real @ zero_zero_real @ W) => ((ord_less_real @ W @ Z3) => (ord_less_real @ (divide_divide_real @ X4 @ Z3) @ (divide_divide_real @ Y3 @ W))))))))). % frac_less2
thf(fact_142_frac__less, axiom,
    ((![X4 : real, Y3 : real, W : real, Z3 : real]: ((ord_less_eq_real @ zero_zero_real @ X4) => ((ord_less_real @ X4 @ Y3) => ((ord_less_real @ zero_zero_real @ W) => ((ord_less_eq_real @ W @ Z3) => (ord_less_real @ (divide_divide_real @ X4 @ Z3) @ (divide_divide_real @ Y3 @ W))))))))). % frac_less
thf(fact_143_frac__le, axiom,
    ((![Y3 : real, X4 : real, W : real, Z3 : real]: ((ord_less_eq_real @ zero_zero_real @ Y3) => ((ord_less_eq_real @ X4 @ Y3) => ((ord_less_real @ zero_zero_real @ W) => ((ord_less_eq_real @ W @ Z3) => (ord_less_eq_real @ (divide_divide_real @ X4 @ Z3) @ (divide_divide_real @ Y3 @ W))))))))). % frac_le
thf(fact_144_less__divide__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ A @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ A))))))))). % less_divide_eq_1
thf(fact_145_divide__less__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ A)))) | ((((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ A @ B)))) | ((A = zero_zero_real))))))))). % divide_less_eq_1
thf(fact_146_div__add__self2, axiom,
    ((![B : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ A @ B) @ B) = (plus_plus_nat @ (divide_divide_nat @ A @ B) @ one_one_nat)))))). % div_add_self2
thf(fact_147_div__add__self1, axiom,
    ((![B : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ B @ A) @ B) = (plus_plus_nat @ (divide_divide_nat @ A @ B) @ one_one_nat)))))). % div_add_self1
thf(fact_148_divide__eq__minus__1__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = (uminus1204672759omplex @ one_one_complex)) = (((~ ((B = zero_zero_complex)))) & ((A = (uminus1204672759omplex @ B)))))))). % divide_eq_minus_1_iff
thf(fact_149_divide__eq__minus__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ one_one_real)) = (((~ ((B = zero_zero_real)))) & ((A = (uminus_uminus_real @ B)))))))). % divide_eq_minus_1_iff
thf(fact_150_nonzero__norm__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B))))))). % nonzero_norm_divide
thf(fact_151_nonzero__norm__divide, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B))))))). % nonzero_norm_divide
thf(fact_152_le__divide__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ A @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ A))))))))). % le_divide_eq_1
thf(fact_153_divide__le__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ A)))) | ((((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ A @ B)))) | ((A = zero_zero_real))))))))). % divide_le_eq_1
thf(fact_154_linordered__field__no__ub, axiom,
    ((![X : real]: (?[X_12 : real]: (ord_less_real @ X @ X_12))))). % linordered_field_no_ub
thf(fact_155_linordered__field__no__lb, axiom,
    ((![X : real]: (?[Y4 : real]: (ord_less_real @ Y4 @ X))))). % linordered_field_no_lb
thf(fact_156_complex__mod__triangle__sub, axiom,
    ((![W : complex, Z3 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W @ Z3)) @ (real_V638595069omplex @ Z3)))))). % complex_mod_triangle_sub
thf(fact_157_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_158_Suc__inject, axiom,
    ((![X4 : nat, Y3 : nat]: (((suc @ X4) = (suc @ Y3)) => (X4 = Y3))))). % Suc_inject
thf(fact_159_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_160_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_161_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_real]: (?[M2 : real]: ((ord_less_real @ zero_zero_real @ M2) & (![Z4 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z4) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P2 @ Z4)) @ M2)))))))). % poly_bound_exists
thf(fact_162_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_complex]: (?[M2 : real]: ((ord_less_real @ zero_zero_real @ M2) & (![Z4 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z4) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P2 @ Z4)) @ M2)))))))). % poly_bound_exists
thf(fact_163_lift__Suc__antimono__le, axiom,
    ((![F2 : nat > real, N : nat, N4 : nat]: ((![N5 : nat]: (ord_less_eq_real @ (F2 @ (suc @ N5)) @ (F2 @ N5))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_real @ (F2 @ N4) @ (F2 @ N))))))). % lift_Suc_antimono_le
thf(fact_164_lift__Suc__mono__le, axiom,
    ((![F2 : nat > real, N : nat, N4 : nat]: ((![N5 : nat]: (ord_less_eq_real @ (F2 @ N5) @ (F2 @ (suc @ N5)))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_real @ (F2 @ N) @ (F2 @ N4))))))). % lift_Suc_mono_le
thf(fact_165_lift__Suc__mono__less__iff, axiom,
    ((![F2 : nat > real, N : nat, M : nat]: ((![N5 : nat]: (ord_less_real @ (F2 @ N5) @ (F2 @ (suc @ N5)))) => ((ord_less_real @ (F2 @ N) @ (F2 @ M)) = (ord_less_nat @ N @ M)))))). % lift_Suc_mono_less_iff
thf(fact_166_lift__Suc__mono__less, axiom,
    ((![F2 : nat > real, N : nat, N4 : nat]: ((![N5 : nat]: (ord_less_real @ (F2 @ N5) @ (F2 @ (suc @ N5)))) => ((ord_less_nat @ N @ N4) => (ord_less_real @ (F2 @ N) @ (F2 @ N4))))))). % lift_Suc_mono_less
thf(fact_167_add__divide__distrib, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (divide1210191872omplex @ A @ C) @ (divide1210191872omplex @ B @ C)))))). % add_divide_distrib
thf(fact_168_add__divide__distrib, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)))))). % add_divide_distrib
thf(fact_169_of__nat__mono, axiom,
    ((![I : nat, J : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_real @ (semiri2110766477t_real @ I) @ (semiri2110766477t_real @ J)))))). % of_nat_mono
thf(fact_170_of__nat__less__imp__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)) => (ord_less_nat @ M @ N))))). % of_nat_less_imp_less
thf(fact_171_less__imp__of__nat__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)))))). % less_imp_of_nat_less
thf(fact_172_minus__divide__left, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (uminus_uminus_real @ A) @ B))))). % minus_divide_left
thf(fact_173_minus__divide__divide, axiom,
    ((![A : real, B : real]: ((divide_divide_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (divide_divide_real @ A @ B))))). % minus_divide_divide
thf(fact_174_minus__divide__right, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ A @ (uminus_uminus_real @ B)))))). % minus_divide_right
thf(fact_175_norm__divide, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_divide
thf(fact_176_norm__divide, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_divide
thf(fact_177_less__half__sum, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ A @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ one_one_real @ one_one_real))))))). % less_half_sum
thf(fact_178_gt__half__sum, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ one_one_real @ one_one_real)) @ B))))). % gt_half_sum

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![G : nat > complex]: ((![N5 : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (G @ N5)) @ r)) => ((![N5 : nat]: (ord_less_real @ (real_V638595069omplex @ (poly_complex2 @ p @ (G @ N5))) @ (plus_plus_real @ (uminus_uminus_real @ s) @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ N5)))))) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
