% 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_327__5370762_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:15.874

% Could-be-implicit typings (8)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    poly_poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    poly_poly_a : $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__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $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 (44)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Real__Oreal, type,
    fundam1947011094e_real : poly_real > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001tf__a, type,
    fundam247907092size_a : poly_a > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    minus_181436949y_real : poly_poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    minus_240770701y_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_Itf__a_J, type,
    minus_minus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001tf__a, type,
    minus_minus_a : a > a > a).
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__Polynomial__Opoly_Itf__a_J, type,
    plus_plus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Oplus__class_Oplus_001tf__a, type,
    plus_plus_a : a > a > a).
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__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    zero_z1423781445y_real : poly_poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    zero_z2096148049poly_a : poly_poly_a).
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__Polynomial__Opoly_Itf__a_J, type,
    zero_zero_poly_a : poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_less_poly_real : poly_real > poly_real > $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__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_le1180086932y_real : poly_real > poly_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_Odegree_001t__Real__Oreal, type,
    degree_real : poly_real > nat).
thf(sy_c_Polynomial_Odegree_001tf__a, type,
    degree_a : poly_a > nat).
thf(sy_c_Polynomial_Ois__zero_001t__Real__Oreal, type,
    is_zero_real : poly_real > $o).
thf(sy_c_Polynomial_Ois__zero_001tf__a, type,
    is_zero_a : poly_a > $o).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_poly_real2 : poly_poly_real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_poly_a2 : poly_poly_a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opoly_001tf__a, type,
    poly_a2 : poly_a > a > a).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Real__Oreal, type,
    poly_cutoff_real : nat > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly__cutoff_001tf__a, type,
    poly_cutoff_a : nat > poly_a > poly_a).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    reflec1522834046y_real : poly_poly_real > poly_poly_real).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_Itf__a_J, type,
    reflect_poly_poly_a : poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Oreflect__poly_001t__Real__Oreal, type,
    reflect_poly_real : poly_real > poly_real).
thf(sy_c_Polynomial_Oreflect__poly_001tf__a, type,
    reflect_poly_a : poly_a > poly_a).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001tf__a, type,
    real_V1022479215norm_a : a > 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_e, type,
    e : real).
thf(sy_v_p, type,
    p : poly_a).
thf(sy_v_q____, type,
    q : poly_a).
thf(sy_v_z, type,
    z : a).

% Relevant facts (239)
thf(fact_0_ep, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % ep
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_th, axiom,
    ((![W : a]: ((poly_a2 @ q @ (minus_minus_a @ W @ z)) = (poly_a2 @ p @ W))))). % th
thf(fact_3_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_4_zero__less__norm__iff, axiom,
    ((![X3 : a]: ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ X3)) = (~ ((X3 = zero_zero_a))))))). % zero_less_norm_iff
thf(fact_5_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_6_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_7_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_8_norm__eq__zero, axiom,
    ((![X3 : a]: (((real_V1022479215norm_a @ X3) = zero_zero_real) = (X3 = zero_zero_a))))). % norm_eq_zero
thf(fact_9_diff__gt__0__iff__gt, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (minus_240770701y_real @ A @ B)) = (ord_less_poly_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_10_diff__gt__0__iff__gt, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_11_poly__diff, axiom,
    ((![P2 : poly_poly_real, Q : poly_poly_real, X3 : poly_real]: ((poly_poly_real2 @ (minus_181436949y_real @ P2 @ Q) @ X3) = (minus_240770701y_real @ (poly_poly_real2 @ P2 @ X3) @ (poly_poly_real2 @ Q @ X3)))))). % poly_diff
thf(fact_12_poly__diff, axiom,
    ((![P2 : poly_real, Q : poly_real, X3 : real]: ((poly_real2 @ (minus_240770701y_real @ P2 @ Q) @ X3) = (minus_minus_real @ (poly_real2 @ P2 @ X3) @ (poly_real2 @ Q @ X3)))))). % poly_diff
thf(fact_13_poly__0, axiom,
    ((![X3 : poly_real]: ((poly_poly_real2 @ zero_z1423781445y_real @ X3) = zero_zero_poly_real)))). % poly_0
thf(fact_14_poly__0, axiom,
    ((![X3 : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X3) = zero_zero_poly_a)))). % poly_0
thf(fact_15_poly__0, axiom,
    ((![X3 : a]: ((poly_a2 @ zero_zero_poly_a @ X3) = zero_zero_a)))). % poly_0
thf(fact_16_poly__0, axiom,
    ((![X3 : real]: ((poly_real2 @ zero_zero_poly_real @ X3) = zero_zero_real)))). % poly_0
thf(fact_17_diff__self, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % diff_self
thf(fact_18_diff__self, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ A) = zero_zero_poly_real)))). % diff_self
thf(fact_19_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_20_diff__self, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % diff_self
thf(fact_21_diff__0__right, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_0_right
thf(fact_22_diff__0__right, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_0_right
thf(fact_23_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_24_diff__0__right, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ zero_zero_poly_real) = A)))). % diff_0_right
thf(fact_25_diff__zero, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_zero
thf(fact_26_diff__zero, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_zero
thf(fact_27_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_28_diff__zero, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ zero_zero_poly_real) = A)))). % diff_zero
thf(fact_29_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_30_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_31_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_32_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ A) = zero_zero_poly_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_33_q_I1_J, axiom,
    (((degree_a @ q) = (degree_a @ p)))). % q(1)
thf(fact_34_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_35_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_36_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_37_zero__reorient, axiom,
    ((![X3 : a]: ((zero_zero_a = X3) = (X3 = zero_zero_a))))). % zero_reorient
thf(fact_38_zero__reorient, axiom,
    ((![X3 : poly_real]: ((zero_zero_poly_real = X3) = (X3 = zero_zero_poly_real))))). % zero_reorient
thf(fact_39_zero__reorient, axiom,
    ((![X3 : poly_a]: ((zero_zero_poly_a = X3) = (X3 = zero_zero_poly_a))))). % zero_reorient
thf(fact_40_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : a, C : a, B : a]: ((minus_minus_a @ (minus_minus_a @ A @ C) @ B) = (minus_minus_a @ (minus_minus_a @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_41_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (minus_minus_real @ A @ C) @ B) = (minus_minus_real @ (minus_minus_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_42_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((minus_240770701y_real @ (minus_240770701y_real @ A @ C) @ B) = (minus_240770701y_real @ (minus_240770701y_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_43_diff__eq__diff__eq, axiom,
    ((![A : a, B : a, C : a, D : a]: (((minus_minus_a @ A @ B) = (minus_minus_a @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_44_diff__eq__diff__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_45_diff__eq__diff__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_46_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_47_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_a]: (^[Z2 : poly_a]: (Y2 = Z2))) = (^[A2 : poly_a]: (^[B2 : poly_a]: ((minus_minus_poly_a @ A2 @ B2) = zero_zero_poly_a)))))). % eq_iff_diff_eq_0
thf(fact_48_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : a]: (^[Z2 : a]: (Y2 = Z2))) = (^[A2 : a]: (^[B2 : a]: ((minus_minus_a @ A2 @ B2) = zero_zero_a)))))). % eq_iff_diff_eq_0
thf(fact_49_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : real]: (^[Z2 : real]: (Y2 = Z2))) = (^[A2 : real]: (^[B2 : real]: ((minus_minus_real @ A2 @ B2) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_50_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_real]: (^[Z2 : poly_real]: (Y2 = Z2))) = (^[A2 : poly_real]: (^[B2 : poly_real]: ((minus_240770701y_real @ A2 @ B2) = zero_zero_poly_real)))))). % eq_iff_diff_eq_0
thf(fact_51_diff__strict__right__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_less_poly_real @ A @ B) => (ord_less_poly_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ C)))))). % diff_strict_right_mono
thf(fact_52_diff__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_strict_right_mono
thf(fact_53_diff__strict__left__mono, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: ((ord_less_poly_real @ B @ A) => (ord_less_poly_real @ (minus_240770701y_real @ C @ A) @ (minus_240770701y_real @ C @ B)))))). % diff_strict_left_mono
thf(fact_54_diff__strict__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => (ord_less_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_strict_left_mono
thf(fact_55_diff__eq__diff__less, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((ord_less_poly_real @ A @ B) = (ord_less_poly_real @ C @ D)))))). % diff_eq_diff_less
thf(fact_56_diff__eq__diff__less, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_real @ A @ B) = (ord_less_real @ C @ D)))))). % diff_eq_diff_less
thf(fact_57_diff__strict__mono, axiom,
    ((![A : poly_real, B : poly_real, D : poly_real, C : poly_real]: ((ord_less_poly_real @ A @ B) => ((ord_less_poly_real @ D @ C) => (ord_less_poly_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ D))))))). % diff_strict_mono
thf(fact_58_diff__strict__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ D @ C) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_strict_mono
thf(fact_59_norm__minus__commute, axiom,
    ((![A : a, B : a]: ((real_V1022479215norm_a @ (minus_minus_a @ A @ B)) = (real_V1022479215norm_a @ (minus_minus_a @ B @ A)))))). % norm_minus_commute
thf(fact_60_norm__minus__commute, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (minus_minus_real @ A @ B)) = (real_V646646907m_real @ (minus_minus_real @ B @ A)))))). % norm_minus_commute
thf(fact_61_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_62_poly__all__0__iff__0, axiom,
    ((![P2 : poly_poly_real]: ((![X2 : poly_real]: ((poly_poly_real2 @ P2 @ X2) = zero_zero_poly_real)) = (P2 = zero_z1423781445y_real))))). % poly_all_0_iff_0
thf(fact_63_less__iff__diff__less__0, axiom,
    ((ord_less_poly_real = (^[A2 : poly_real]: (^[B2 : poly_real]: (ord_less_poly_real @ (minus_240770701y_real @ A2 @ B2) @ zero_zero_poly_real)))))). % less_iff_diff_less_0
thf(fact_64_less__iff__diff__less__0, axiom,
    ((ord_less_real = (^[A2 : real]: (^[B2 : real]: (ord_less_real @ (minus_minus_real @ A2 @ B2) @ zero_zero_real)))))). % less_iff_diff_less_0
thf(fact_65_norm__not__less__zero, axiom,
    ((![X3 : a]: (~ ((ord_less_real @ (real_V1022479215norm_a @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_66_norm__not__less__zero, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_67_q_I2_J, axiom,
    ((![X3 : a]: ((poly_a2 @ q @ X3) = (poly_a2 @ p @ (plus_plus_a @ z @ X3)))))). % q(2)
thf(fact_68_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_69_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real))))). % less_numeral_extra(3)
thf(fact_70_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_71_psize__eq__0__iff, axiom,
    ((![P2 : poly_real]: (((fundam1947011094e_real @ P2) = zero_zero_nat) = (P2 = zero_zero_poly_real))))). % psize_eq_0_iff
thf(fact_72_psize__eq__0__iff, axiom,
    ((![P2 : poly_a]: (((fundam247907092size_a @ P2) = zero_zero_nat) = (P2 = zero_zero_poly_a))))). % psize_eq_0_iff
thf(fact_73_is__zero__null, axiom,
    ((is_zero_real = (^[P3 : poly_real]: (P3 = zero_zero_poly_real))))). % is_zero_null
thf(fact_74_is__zero__null, axiom,
    ((is_zero_a = (^[P3 : poly_a]: (P3 = zero_zero_poly_a))))). % is_zero_null
thf(fact_75_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_real @ N @ zero_zero_poly_real) = zero_zero_poly_real)))). % poly_cutoff_0
thf(fact_76_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_cutoff_0
thf(fact_77_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_real]: (((poly_real2 @ (reflect_poly_real @ P2) @ zero_zero_real) = zero_zero_real) = (P2 = zero_zero_poly_real))))). % reflect_poly_at_0_eq_0_iff
thf(fact_78_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_a]: (((poly_a2 @ (reflect_poly_a @ P2) @ zero_zero_a) = zero_zero_a) = (P2 = zero_zero_poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_79_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_poly_real]: (((poly_poly_real2 @ (reflec1522834046y_real @ P2) @ zero_zero_poly_real) = zero_zero_poly_real) = (P2 = zero_z1423781445y_real))))). % reflect_poly_at_0_eq_0_iff
thf(fact_80_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_poly_a]: (((poly_poly_a2 @ (reflect_poly_poly_a @ P2) @ zero_zero_poly_a) = zero_zero_poly_a) = (P2 = zero_z2096148049poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_81__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062q_O_A_092_060lbrakk_062degree_Aq_A_061_Adegree_Ap_059_A_092_060And_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Iz_A_L_Ax_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Q2 : poly_a]: (((degree_a @ Q2) = (degree_a @ p)) => (~ ((![X4 : a]: ((poly_a2 @ Q2 @ X4) = (poly_a2 @ p @ (plus_plus_a @ z @ X4)))))))))))). % \<open>\<And>thesis. (\<And>q. \<lbrakk>degree q = degree p; \<And>x. poly q x = poly p (z + x)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_82_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_83_Collect__mem__eq, axiom,
    ((![A3 : set_real]: ((collect_real @ (^[X2 : real]: (member_real @ X2 @ A3))) = A3)))). % Collect_mem_eq
thf(fact_84_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_a]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ R) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_85_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_86_add__left__cancel, axiom,
    ((![A : a, B : a, C : a]: (((plus_plus_a @ A @ B) = (plus_plus_a @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_87_add__right__cancel, axiom,
    ((![B : a, A : a, C : a]: (((plus_plus_a @ B @ A) = (plus_plus_a @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_88_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_89_add_Oleft__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ zero_zero_a @ A) = A)))). % add.left_neutral
thf(fact_90_add_Oleft__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % add.left_neutral
thf(fact_91_add_Oleft__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ zero_zero_poly_a @ A) = A)))). % add.left_neutral
thf(fact_92_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_93_add_Oright__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ A @ zero_zero_a) = A)))). % add.right_neutral
thf(fact_94_add_Oright__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ A @ zero_zero_poly_real) = A)))). % add.right_neutral
thf(fact_95_add_Oright__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ A @ zero_zero_poly_a) = A)))). % add.right_neutral
thf(fact_96_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_97_double__zero, axiom,
    ((![A : poly_real]: (((plus_plus_poly_real @ A @ A) = zero_zero_poly_real) = (A = zero_zero_poly_real))))). % double_zero
thf(fact_98_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_99_double__zero__sym, axiom,
    ((![A : poly_real]: ((zero_zero_poly_real = (plus_plus_poly_real @ A @ A)) = (A = zero_zero_poly_real))))). % double_zero_sym
thf(fact_100_add__cancel__left__left, axiom,
    ((![B : real, A : real]: (((plus_plus_real @ B @ A) = A) = (B = zero_zero_real))))). % add_cancel_left_left
thf(fact_101_add__cancel__left__left, axiom,
    ((![B : a, A : a]: (((plus_plus_a @ B @ A) = A) = (B = zero_zero_a))))). % add_cancel_left_left
thf(fact_102_add__cancel__left__left, axiom,
    ((![B : poly_real, A : poly_real]: (((plus_plus_poly_real @ B @ A) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_left
thf(fact_103_add__cancel__left__left, axiom,
    ((![B : poly_a, A : poly_a]: (((plus_plus_poly_a @ B @ A) = A) = (B = zero_zero_poly_a))))). % add_cancel_left_left
thf(fact_104_add__cancel__left__right, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real))))). % add_cancel_left_right
thf(fact_105_add__cancel__left__right, axiom,
    ((![A : a, B : a]: (((plus_plus_a @ A @ B) = A) = (B = zero_zero_a))))). % add_cancel_left_right
thf(fact_106_add__cancel__left__right, axiom,
    ((![A : poly_real, B : poly_real]: (((plus_plus_poly_real @ A @ B) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_right
thf(fact_107_add__cancel__left__right, axiom,
    ((![A : poly_a, B : poly_a]: (((plus_plus_poly_a @ A @ B) = A) = (B = zero_zero_poly_a))))). % add_cancel_left_right
thf(fact_108_add__cancel__right__left, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real))))). % add_cancel_right_left
thf(fact_109_add__cancel__right__left, axiom,
    ((![A : a, B : a]: ((A = (plus_plus_a @ B @ A)) = (B = zero_zero_a))))). % add_cancel_right_left
thf(fact_110_add__cancel__right__left, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (plus_plus_poly_real @ B @ A)) = (B = zero_zero_poly_real))))). % add_cancel_right_left
thf(fact_111_add__cancel__right__left, axiom,
    ((![A : poly_a, B : poly_a]: ((A = (plus_plus_poly_a @ B @ A)) = (B = zero_zero_poly_a))))). % add_cancel_right_left
thf(fact_112_add__cancel__right__right, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real))))). % add_cancel_right_right
thf(fact_113_add__cancel__right__right, axiom,
    ((![A : a, B : a]: ((A = (plus_plus_a @ A @ B)) = (B = zero_zero_a))))). % add_cancel_right_right
thf(fact_114_add__cancel__right__right, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (plus_plus_poly_real @ A @ B)) = (B = zero_zero_poly_real))))). % add_cancel_right_right
thf(fact_115_add__cancel__right__right, axiom,
    ((![A : poly_a, B : poly_a]: ((A = (plus_plus_poly_a @ A @ B)) = (B = zero_zero_poly_a))))). % add_cancel_right_right
thf(fact_116_add__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_left
thf(fact_117_add__le__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_right
thf(fact_118_add__less__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_real @ A @ B))))). % add_less_cancel_left
thf(fact_119_add__less__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_real @ A @ B))))). % add_less_cancel_right
thf(fact_120_add__diff__cancel, axiom,
    ((![A : a, B : a]: ((minus_minus_a @ (plus_plus_a @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_121_add__diff__cancel, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_122_add__diff__cancel, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_123_diff__add__cancel, axiom,
    ((![A : a, B : a]: ((plus_plus_a @ (minus_minus_a @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_124_diff__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_125_diff__add__cancel, axiom,
    ((![A : poly_real, B : poly_real]: ((plus_plus_poly_real @ (minus_240770701y_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_126_add__diff__cancel__left, axiom,
    ((![C : a, A : a, B : a]: ((minus_minus_a @ (plus_plus_a @ C @ A) @ (plus_plus_a @ C @ B)) = (minus_minus_a @ A @ B))))). % add_diff_cancel_left
thf(fact_127_add__diff__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_left
thf(fact_128_add__diff__cancel__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)) = (minus_240770701y_real @ A @ B))))). % add_diff_cancel_left
thf(fact_129_add__diff__cancel__left_H, axiom,
    ((![A : a, B : a]: ((minus_minus_a @ (plus_plus_a @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_130_add__diff__cancel__left_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_131_add__diff__cancel__left_H, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_132_add__diff__cancel__right, axiom,
    ((![A : a, C : a, B : a]: ((minus_minus_a @ (plus_plus_a @ A @ C) @ (plus_plus_a @ B @ C)) = (minus_minus_a @ A @ B))))). % add_diff_cancel_right
thf(fact_133_add__diff__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_right
thf(fact_134_add__diff__cancel__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)) = (minus_240770701y_real @ A @ B))))). % add_diff_cancel_right
thf(fact_135_add__diff__cancel__right_H, axiom,
    ((![A : a, B : a]: ((minus_minus_a @ (plus_plus_a @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_136_add__diff__cancel__right_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_137_add__diff__cancel__right_H, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_138_poly__add, axiom,
    ((![P2 : poly_real, Q : poly_real, X3 : real]: ((poly_real2 @ (plus_plus_poly_real @ P2 @ Q) @ X3) = (plus_plus_real @ (poly_real2 @ P2 @ X3) @ (poly_real2 @ Q @ X3)))))). % poly_add
thf(fact_139_poly__add, axiom,
    ((![P2 : poly_a, Q : poly_a, X3 : a]: ((poly_a2 @ (plus_plus_poly_a @ P2 @ Q) @ X3) = (plus_plus_a @ (poly_a2 @ P2 @ X3) @ (poly_a2 @ Q @ X3)))))). % poly_add
thf(fact_140_reflect__poly__0, axiom,
    (((reflect_poly_real @ zero_zero_poly_real) = zero_zero_poly_real))). % reflect_poly_0
thf(fact_141_reflect__poly__0, axiom,
    (((reflect_poly_a @ zero_zero_poly_a) = zero_zero_poly_a))). % reflect_poly_0
thf(fact_142_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ A)) = (ord_le1180086932y_real @ zero_zero_poly_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_143_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_144_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ A) @ zero_zero_poly_real) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_145_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_146_le__add__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (plus_plus_poly_real @ B @ A)) = (ord_le1180086932y_real @ zero_zero_poly_real @ B))))). % le_add_same_cancel2
thf(fact_147_le__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel2
thf(fact_148_le__add__same__cancel1, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (plus_plus_poly_real @ A @ B)) = (ord_le1180086932y_real @ zero_zero_poly_real @ B))))). % le_add_same_cancel1
thf(fact_149_le__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel1
thf(fact_150_add__le__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ B) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % add_le_same_cancel2
thf(fact_151_add__le__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel2
thf(fact_152_add__le__same__cancel1, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ B @ A) @ B) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % add_le_same_cancel1
thf(fact_153_add__le__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel1
thf(fact_154_add__less__same__cancel1, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ B @ A) @ B) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % add_less_same_cancel1
thf(fact_155_add__less__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel1
thf(fact_156_add__less__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ B) @ B) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % add_less_same_cancel2
thf(fact_157_add__less__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel2
thf(fact_158_less__add__same__cancel1, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (plus_plus_poly_real @ A @ B)) = (ord_less_poly_real @ zero_zero_poly_real @ B))))). % less_add_same_cancel1
thf(fact_159_less__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel1
thf(fact_160_less__add__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (plus_plus_poly_real @ B @ A)) = (ord_less_poly_real @ zero_zero_poly_real @ B))))). % less_add_same_cancel2
thf(fact_161_less__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel2
thf(fact_162_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ A) @ zero_zero_poly_real) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_163_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_164_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ A)) = (ord_less_poly_real @ zero_zero_poly_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_165_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_166_diff__ge__0__iff__ge, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ (minus_240770701y_real @ A @ B)) = (ord_le1180086932y_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_167_diff__ge__0__iff__ge, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_168_degree__0, axiom,
    (((degree_real @ zero_zero_poly_real) = zero_zero_nat))). % degree_0
thf(fact_169_degree__0, axiom,
    (((degree_a @ zero_zero_poly_a) = zero_zero_nat))). % degree_0
thf(fact_170_norm__le__zero__iff, axiom,
    ((![X3 : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ X3) @ zero_zero_real) = (X3 = zero_zero_a))))). % norm_le_zero_iff
thf(fact_171_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_172_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : a, B : a, C : a]: ((plus_plus_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_173_add__mono__thms__linordered__field_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(4)
thf(fact_174_add__mono__thms__linordered__field_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(3)
thf(fact_175_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (K = L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_176_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_177_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_178_group__cancel_Oadd1, axiom,
    ((![A3 : a, K : a, A : a, B : a]: ((A3 = (plus_plus_a @ K @ A)) => ((plus_plus_a @ A3 @ B) = (plus_plus_a @ K @ (plus_plus_a @ A @ B))))))). % group_cancel.add1
thf(fact_179_group__cancel_Oadd2, axiom,
    ((![B3 : a, K : a, B : a, A : a]: ((B3 = (plus_plus_a @ K @ B)) => ((plus_plus_a @ A @ B3) = (plus_plus_a @ K @ (plus_plus_a @ A @ B))))))). % group_cancel.add2
thf(fact_180_add_Oassoc, axiom,
    ((![A : a, B : a, C : a]: ((plus_plus_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % add.assoc
thf(fact_181_add_Oleft__cancel, axiom,
    ((![A : a, B : a, C : a]: (((plus_plus_a @ A @ B) = (plus_plus_a @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_182_add_Oright__cancel, axiom,
    ((![B : a, A : a, C : a]: (((plus_plus_a @ B @ A) = (plus_plus_a @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_183_add_Ocommute, axiom,
    ((plus_plus_a = (^[A2 : a]: (^[B2 : a]: (plus_plus_a @ B2 @ A2)))))). % add.commute
thf(fact_184_diff__le__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ (minus_240770701y_real @ A @ B) @ C) = (ord_le1180086932y_real @ A @ (plus_plus_poly_real @ C @ B)))))). % diff_le_eq
thf(fact_185_diff__le__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B)))))). % diff_le_eq
thf(fact_186_le__diff__eq, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (minus_240770701y_real @ C @ B)) = (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ C))))). % le_diff_eq
thf(fact_187_le__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) = (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))))). % le_diff_eq
thf(fact_188_add_Oleft__commute, axiom,
    ((![B : a, A : a, C : a]: ((plus_plus_a @ B @ (plus_plus_a @ A @ C)) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % add.left_commute
thf(fact_189_add__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_mono
thf(fact_190_add__left__imp__eq, axiom,
    ((![A : a, B : a, C : a]: (((plus_plus_a @ A @ B) = (plus_plus_a @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_191_add__right__imp__eq, axiom,
    ((![B : a, A : a, C : a]: (((plus_plus_a @ B @ A) = (plus_plus_a @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_192_add__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_left_mono
thf(fact_193_add__decreasing, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ zero_zero_poly_real) => ((ord_le1180086932y_real @ C @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_194_add__decreasing, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_195_add__increasing, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_le1180086932y_real @ B @ C) => (ord_le1180086932y_real @ B @ (plus_plus_poly_real @ A @ C))))))). % add_increasing
thf(fact_196_add__increasing, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing
thf(fact_197_add__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_right_mono
thf(fact_198_add__decreasing2, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ C @ zero_zero_poly_real) => ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_199_add__decreasing2, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ C @ zero_zero_real) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_200_add__increasing2, axiom,
    ((![C : poly_real, B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ C) => ((ord_le1180086932y_real @ B @ A) => (ord_le1180086932y_real @ B @ (plus_plus_poly_real @ A @ C))))))). % add_increasing2
thf(fact_201_add__increasing2, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing2
thf(fact_202_add__nonneg__nonneg, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_le1180086932y_real @ zero_zero_poly_real @ B) => (ord_le1180086932y_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_203_add__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_204_add__nonpos__nonpos, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ zero_zero_poly_real) => ((ord_le1180086932y_real @ B @ zero_zero_poly_real) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ zero_zero_poly_real)))))). % add_nonpos_nonpos
thf(fact_205_add__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_nonpos
thf(fact_206_add__nonneg__eq__0__iff, axiom,
    ((![X3 : poly_real, Y3 : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ X3) => ((ord_le1180086932y_real @ zero_zero_poly_real @ Y3) => (((plus_plus_poly_real @ X3 @ Y3) = zero_zero_poly_real) = (((X3 = zero_zero_poly_real)) & ((Y3 = zero_zero_poly_real))))))))). % add_nonneg_eq_0_iff
thf(fact_207_add__nonneg__eq__0__iff, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y3) => (((plus_plus_real @ X3 @ Y3) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y3 = zero_zero_real))))))))). % add_nonneg_eq_0_iff
thf(fact_208_add__nonpos__eq__0__iff, axiom,
    ((![X3 : poly_real, Y3 : poly_real]: ((ord_le1180086932y_real @ X3 @ zero_zero_poly_real) => ((ord_le1180086932y_real @ Y3 @ zero_zero_poly_real) => (((plus_plus_poly_real @ X3 @ Y3) = zero_zero_poly_real) = (((X3 = zero_zero_poly_real)) & ((Y3 = zero_zero_poly_real))))))))). % add_nonpos_eq_0_iff
thf(fact_209_add__nonpos__eq__0__iff, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ Y3 @ zero_zero_real) => (((plus_plus_real @ X3 @ Y3) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y3 = zero_zero_real))))))))). % add_nonpos_eq_0_iff
thf(fact_210_norm__add__leD, axiom,
    ((![A : a, B : a, C : real]: ((ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ A @ B)) @ C) => (ord_less_eq_real @ (real_V1022479215norm_a @ B) @ (plus_plus_real @ (real_V1022479215norm_a @ A) @ C)))))). % norm_add_leD
thf(fact_211_norm__add__leD, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ C) => (ord_less_eq_real @ (real_V646646907m_real @ B) @ (plus_plus_real @ (real_V646646907m_real @ A) @ C)))))). % norm_add_leD
thf(fact_212_norm__diff__ineq, axiom,
    ((![A : a, B : a]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022479215norm_a @ A) @ (real_V1022479215norm_a @ B)) @ (real_V1022479215norm_a @ (plus_plus_a @ A @ B)))))). % norm_diff_ineq
thf(fact_213_norm__diff__ineq, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)) @ (real_V646646907m_real @ (plus_plus_real @ A @ B)))))). % norm_diff_ineq
thf(fact_214_norm__triangle__le, axiom,
    ((![X3 : a, Y3 : a, E2 : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1022479215norm_a @ X3) @ (real_V1022479215norm_a @ Y3)) @ E2) => (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ X3 @ Y3)) @ E2))))). % norm_triangle_le
thf(fact_215_norm__triangle__le, axiom,
    ((![X3 : real, Y3 : real, E2 : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y3)) @ E2) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y3)) @ E2))))). % norm_triangle_le
thf(fact_216_add__le__less__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_le_less_mono
thf(fact_217_add__less__le__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_less_le_mono
thf(fact_218_norm__triangle__ineq, axiom,
    ((![X3 : a, Y3 : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ X3 @ Y3)) @ (plus_plus_real @ (real_V1022479215norm_a @ X3) @ (real_V1022479215norm_a @ Y3)))))). % norm_triangle_ineq
thf(fact_219_norm__triangle__ineq, axiom,
    ((![X3 : real, Y3 : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y3)) @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y3)))))). % norm_triangle_ineq
thf(fact_220_norm__triangle__mono, axiom,
    ((![A : a, R : real, B : a, S2 : real]: ((ord_less_eq_real @ (real_V1022479215norm_a @ A) @ R) => ((ord_less_eq_real @ (real_V1022479215norm_a @ B) @ S2) => (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ A @ B)) @ (plus_plus_real @ R @ S2))))))). % norm_triangle_mono
thf(fact_221_norm__triangle__mono, axiom,
    ((![A : real, R : real, B : real, S2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ A) @ R) => ((ord_less_eq_real @ (real_V646646907m_real @ B) @ S2) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ R @ S2))))))). % norm_triangle_mono
thf(fact_222_add__le__imp__le__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_left
thf(fact_223_add__le__imp__le__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_right
thf(fact_224_complete__real, axiom,
    ((![S3 : set_real]: ((?[X4 : real]: (member_real @ X4 @ S3)) => ((?[Z : real]: (![X : real]: ((member_real @ X @ S3) => (ord_less_eq_real @ X @ Z)))) => (?[Y4 : real]: ((![X4 : real]: ((member_real @ X4 @ S3) => (ord_less_eq_real @ X4 @ Y4))) & (![Z : real]: ((![X : real]: ((member_real @ X @ S3) => (ord_less_eq_real @ X @ Z))) => (ord_less_eq_real @ Y4 @ Z)))))))))). % complete_real
thf(fact_225_is__num__normalize_I1_J, axiom,
    ((![A : a, B : a, C : a]: ((plus_plus_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % is_num_normalize(1)
thf(fact_226_le__numeral__extra_I3_J, axiom,
    ((ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real))). % le_numeral_extra(3)
thf(fact_227_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_228_add__diff__add, axiom,
    ((![A : a, C : a, B : a, D : a]: ((minus_minus_a @ (plus_plus_a @ A @ C) @ (plus_plus_a @ B @ D)) = (plus_plus_a @ (minus_minus_a @ A @ B) @ (minus_minus_a @ C @ D)))))). % add_diff_add
thf(fact_229_add__diff__add, axiom,
    ((![A : real, C : real, B : real, D : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) = (plus_plus_real @ (minus_minus_real @ A @ B) @ (minus_minus_real @ C @ D)))))). % add_diff_add
thf(fact_230_add__diff__add, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real, D : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ D)) = (plus_plus_poly_real @ (minus_240770701y_real @ A @ B) @ (minus_240770701y_real @ C @ D)))))). % add_diff_add
thf(fact_231_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y5 : real]: (((ord_less_real @ X2 @ Y5)) | ((X2 = Y5)))))))). % less_eq_real_def
thf(fact_232_norm__diff__triangle__ineq, axiom,
    ((![A : a, B : a, C : a, D : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (minus_minus_a @ (plus_plus_a @ A @ B) @ (plus_plus_a @ C @ D))) @ (plus_plus_real @ (real_V1022479215norm_a @ (minus_minus_a @ A @ C)) @ (real_V1022479215norm_a @ (minus_minus_a @ B @ D))))))). % norm_diff_triangle_ineq
thf(fact_233_norm__diff__triangle__ineq, axiom,
    ((![A : real, B : real, C : real, D : real]: (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (real_V646646907m_real @ (minus_minus_real @ A @ C)) @ (real_V646646907m_real @ (minus_minus_real @ B @ D))))))). % norm_diff_triangle_ineq
thf(fact_234_poly__offset, axiom,
    ((![P2 : poly_real, A : real]: (?[Q2 : poly_real]: (((fundam1947011094e_real @ Q2) = (fundam1947011094e_real @ P2)) & (![X4 : real]: ((poly_real2 @ Q2 @ X4) = (poly_real2 @ P2 @ (plus_plus_real @ A @ X4))))))))). % poly_offset
thf(fact_235_add__neg__nonpos, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ zero_zero_poly_real) => ((ord_le1180086932y_real @ B @ zero_zero_poly_real) => (ord_less_poly_real @ (plus_plus_poly_real @ A @ B) @ zero_zero_poly_real)))))). % add_neg_nonpos
thf(fact_236_add__neg__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_neg_nonpos
thf(fact_237_add__nonneg__pos, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_less_poly_real @ zero_zero_poly_real @ B) => (ord_less_poly_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ B))))))). % add_nonneg_pos
thf(fact_238_add__nonneg__pos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_pos

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[D3 : real]: ((ord_less_real @ zero_zero_real @ D3) & (![W2 : a]: (((~ ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ (minus_minus_a @ W2 @ z))))) | (~ ((ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ W2 @ z)) @ D3)))) | (ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ (poly_a2 @ q @ (minus_minus_a @ W2 @ z)) @ (poly_a2 @ q @ (minus_minus_a @ z @ z)))) @ e))))))).
