% 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_374__5371196_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:37.439

% Could-be-implicit typings (7)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    poly_poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__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 (37)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Real__Oreal, type,
    fundam1947011094e_real : poly_real > nat).
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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    uminus1762810119omplex : poly_poly_complex > poly_poly_complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    uminus262047109y_real : poly_poly_real > poly_poly_real).
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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    zero_z1423781445y_real : poly_poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Orderings_Oord__class_Oless_001t__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_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Real__Oreal, type,
    is_zero_real : poly_real > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_poly_real2 : poly_poly_real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Real__Oreal, type,
    poly_cutoff_real : nat > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly__shift_001t__Complex__Ocomplex, type,
    poly_shift_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly__shift_001t__Real__Oreal, type,
    poly_shift_real : nat > poly_real > poly_real).
thf(sy_c_Polynomial_Oreflect__poly_001t__Complex__Ocomplex, type,
    reflect_poly_complex : poly_complex > poly_complex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    reflec309385472omplex : poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_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__Real__Oreal, type,
    reflect_poly_real : poly_real > poly_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_v_p, type,
    p : poly_complex).
thf(sy_v_r, type,
    r : real).

% Relevant facts (196)
thf(fact_0_True, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % True
thf(fact_1_norm__le__zero__iff, axiom,
    ((![X : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X) @ zero_zero_real) = (X = zero_zero_real))))). % norm_le_zero_iff
thf(fact_2_norm__le__zero__iff, axiom,
    ((![X : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X) @ zero_zero_real) = (X = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_3_neg__0__le__iff__le, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ (uminus1613791741y_real @ A)) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % neg_0_le_iff_le
thf(fact_4_neg__0__le__iff__le, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real))))). % neg_0_le_iff_le
thf(fact_5_neg__le__0__iff__le, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ (uminus1613791741y_real @ A) @ zero_zero_poly_real) = (ord_le1180086932y_real @ zero_zero_poly_real @ A))))). % neg_le_0_iff_le
thf(fact_6_neg__le__0__iff__le, axiom,
    ((![A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_eq_real @ zero_zero_real @ A))))). % neg_le_0_iff_le
thf(fact_7_less__eq__neg__nonpos, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ A @ (uminus1613791741y_real @ A)) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % less_eq_neg_nonpos
thf(fact_8_less__eq__neg__nonpos, axiom,
    ((![A : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real))))). % less_eq_neg_nonpos
thf(fact_9_neg__less__eq__nonneg, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ (uminus1613791741y_real @ A) @ A) = (ord_le1180086932y_real @ zero_zero_poly_real @ A))))). % neg_less_eq_nonneg
thf(fact_10_neg__less__eq__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % neg_less_eq_nonneg
thf(fact_11_poly__minus, axiom,
    ((![P : poly_poly_real, X : poly_real]: ((poly_poly_real2 @ (uminus262047109y_real @ P) @ X) = (uminus1613791741y_real @ (poly_poly_real2 @ P @ X)))))). % poly_minus
thf(fact_12_poly__minus, axiom,
    ((![P : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (uminus1762810119omplex @ P) @ X) = (uminus1138659839omplex @ (poly_poly_complex2 @ P @ X)))))). % poly_minus
thf(fact_13_poly__minus, axiom,
    ((![P : poly_complex, X : complex]: ((poly_complex2 @ (uminus1138659839omplex @ P) @ X) = (uminus1204672759omplex @ (poly_complex2 @ P @ X)))))). % poly_minus
thf(fact_14_poly__minus, axiom,
    ((![P : poly_real, X : real]: ((poly_real2 @ (uminus1613791741y_real @ P) @ X) = (uminus_uminus_real @ (poly_real2 @ P @ X)))))). % poly_minus
thf(fact_15_poly__0, axiom,
    ((![X : poly_real]: ((poly_poly_real2 @ zero_z1423781445y_real @ X) = zero_zero_poly_real)))). % poly_0
thf(fact_16_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_17_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_18_poly__0, axiom,
    ((![X : real]: ((poly_real2 @ zero_zero_poly_real @ X) = zero_zero_real)))). % poly_0
thf(fact_19_norm__minus__cancel, axiom,
    ((![X : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X)) = (real_V646646907m_real @ X))))). % norm_minus_cancel
thf(fact_20_norm__minus__cancel, axiom,
    ((![X : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X)) = (real_V638595069omplex @ X))))). % norm_minus_cancel
thf(fact_21_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_22_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_23_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_24_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_25_neg__le__iff__le, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ (uminus1613791741y_real @ B) @ (uminus1613791741y_real @ A)) = (ord_le1180086932y_real @ A @ B))))). % neg_le_iff_le
thf(fact_26_neg__le__iff__le, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ B))))). % neg_le_iff_le
thf(fact_27_neg__equal__iff__equal, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_28_neg__equal__iff__equal, axiom,
    ((![A : poly_real, B : poly_real]: (((uminus1613791741y_real @ A) = (uminus1613791741y_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_29_neg__equal__iff__equal, axiom,
    ((![A : poly_complex, B : poly_complex]: (((uminus1138659839omplex @ A) = (uminus1138659839omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_30_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_31_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_32_add_Oinverse__inverse, axiom,
    ((![A : poly_real]: ((uminus1613791741y_real @ (uminus1613791741y_real @ A)) = A)))). % add.inverse_inverse
thf(fact_33_add_Oinverse__inverse, axiom,
    ((![A : poly_complex]: ((uminus1138659839omplex @ (uminus1138659839omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_34_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_35_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_36_neg__equal__zero, axiom,
    ((![A : poly_real]: (((uminus1613791741y_real @ A) = A) = (A = zero_zero_poly_real))))). % neg_equal_zero
thf(fact_37_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_38_equal__neg__zero, axiom,
    ((![A : poly_real]: ((A = (uminus1613791741y_real @ A)) = (A = zero_zero_poly_real))))). % equal_neg_zero
thf(fact_39_neg__equal__0__iff__equal, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % neg_equal_0_iff_equal
thf(fact_40_neg__equal__0__iff__equal, axiom,
    ((![A : poly_real]: (((uminus1613791741y_real @ A) = zero_zero_poly_real) = (A = zero_zero_poly_real))))). % neg_equal_0_iff_equal
thf(fact_41_neg__equal__0__iff__equal, axiom,
    ((![A : poly_complex]: (((uminus1138659839omplex @ A) = zero_z1746442943omplex) = (A = zero_z1746442943omplex))))). % neg_equal_0_iff_equal
thf(fact_42_neg__equal__0__iff__equal, axiom,
    ((![A : complex]: (((uminus1204672759omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_43_neg__0__equal__iff__equal, axiom,
    ((![A : real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A))))). % neg_0_equal_iff_equal
thf(fact_44_neg__0__equal__iff__equal, axiom,
    ((![A : poly_real]: ((zero_zero_poly_real = (uminus1613791741y_real @ A)) = (zero_zero_poly_real = A))))). % neg_0_equal_iff_equal
thf(fact_45_neg__0__equal__iff__equal, axiom,
    ((![A : poly_complex]: ((zero_z1746442943omplex = (uminus1138659839omplex @ A)) = (zero_z1746442943omplex = A))))). % neg_0_equal_iff_equal
thf(fact_46_neg__0__equal__iff__equal, axiom,
    ((![A : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A)) = (zero_zero_complex = A))))). % neg_0_equal_iff_equal
thf(fact_47_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_48_add_Oinverse__neutral, axiom,
    (((uminus1613791741y_real @ zero_zero_poly_real) = zero_zero_poly_real))). % add.inverse_neutral
thf(fact_49_add_Oinverse__neutral, axiom,
    (((uminus1138659839omplex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % add.inverse_neutral
thf(fact_50_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_51_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_52_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_53_zero__reorient, axiom,
    ((![X : poly_real]: ((zero_zero_poly_real = X) = (X = zero_zero_poly_real))))). % zero_reorient
thf(fact_54_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_55_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_56_minus__equation__iff, axiom,
    ((![A : poly_real, B : poly_real]: (((uminus1613791741y_real @ A) = B) = ((uminus1613791741y_real @ B) = A))))). % minus_equation_iff
thf(fact_57_minus__equation__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: (((uminus1138659839omplex @ A) = B) = ((uminus1138659839omplex @ B) = A))))). % minus_equation_iff
thf(fact_58_minus__equation__iff, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((uminus1204672759omplex @ B) = A))))). % minus_equation_iff
thf(fact_59_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_60_equation__minus__iff, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (uminus1613791741y_real @ B)) = (B = (uminus1613791741y_real @ A)))))). % equation_minus_iff
thf(fact_61_equation__minus__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: ((A = (uminus1138659839omplex @ B)) = (B = (uminus1138659839omplex @ A)))))). % equation_minus_iff
thf(fact_62_equation__minus__iff, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = (B = (uminus1204672759omplex @ A)))))). % equation_minus_iff
thf(fact_63_norm__ge__zero, axiom,
    ((![X : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X))))). % norm_ge_zero
thf(fact_64_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_65_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_66_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_real, Q : poly_real]: (((poly_real2 @ P) = (poly_real2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_67_le__imp__neg__le, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (uminus1613791741y_real @ B) @ (uminus1613791741y_real @ A)))))). % le_imp_neg_le
thf(fact_68_le__imp__neg__le, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % le_imp_neg_le
thf(fact_69_minus__le__iff, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (uminus1613791741y_real @ A) @ B) = (ord_le1180086932y_real @ (uminus1613791741y_real @ B) @ A))))). % minus_le_iff
thf(fact_70_minus__le__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ A))))). % minus_le_iff
thf(fact_71_le__minus__iff, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (uminus1613791741y_real @ B)) = (ord_le1180086932y_real @ B @ (uminus1613791741y_real @ A)))))). % le_minus_iff
thf(fact_72_le__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A)))))). % le_minus_iff
thf(fact_73_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X2 : complex]: ((poly_complex2 @ P @ X2) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_74_poly__all__0__iff__0, axiom,
    ((![P : poly_real]: ((![X2 : real]: ((poly_real2 @ P @ X2) = zero_zero_real)) = (P = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_75_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_real]: ((![X2 : poly_real]: ((poly_poly_real2 @ P @ X2) = zero_zero_poly_real)) = (P = zero_z1423781445y_real))))). % poly_all_0_iff_0
thf(fact_76_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X2 : poly_complex]: ((poly_poly_complex2 @ P @ X2) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_77_complex__mod__minus__le__complex__mod, axiom,
    ((![X : complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V638595069omplex @ X)) @ (real_V638595069omplex @ X))))). % complex_mod_minus_le_complex_mod
thf(fact_78_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_79_verit__minus__simplify_I4_J, axiom,
    ((![B : poly_real]: ((uminus1613791741y_real @ (uminus1613791741y_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_80_verit__minus__simplify_I4_J, axiom,
    ((![B : poly_complex]: ((uminus1138659839omplex @ (uminus1138659839omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_81_verit__minus__simplify_I4_J, axiom,
    ((![B : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_82_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_83_le__numeral__extra_I3_J, axiom,
    ((ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real))). % le_numeral_extra(3)
thf(fact_84_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_85_psize__eq__0__iff, axiom,
    ((![P : poly_real]: (((fundam1947011094e_real @ P) = zero_zero_nat) = (P = zero_zero_poly_real))))). % psize_eq_0_iff
thf(fact_86_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_87_is__zero__null, axiom,
    ((is_zero_real = (^[P2 : poly_real]: (P2 = zero_zero_poly_real))))). % is_zero_null
thf(fact_88_is__zero__null, axiom,
    ((is_zero_complex = (^[P2 : poly_complex]: (P2 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_89_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_real @ N @ zero_zero_poly_real) = zero_zero_poly_real)))). % poly_cutoff_0
thf(fact_90_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_91_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_complex]: (((poly_complex2 @ (reflect_poly_complex @ P) @ zero_zero_complex) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_92_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_real]: (((poly_real2 @ (reflect_poly_real @ P) @ zero_zero_real) = zero_zero_real) = (P = zero_zero_poly_real))))). % reflect_poly_at_0_eq_0_iff
thf(fact_93_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_real]: (((poly_poly_real2 @ (reflec1522834046y_real @ P) @ zero_zero_poly_real) = zero_zero_poly_real) = (P = zero_z1423781445y_real))))). % reflect_poly_at_0_eq_0_iff
thf(fact_94_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((poly_poly_complex2 @ (reflec309385472omplex @ P) @ zero_z1746442943omplex) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_95_poly__bound__exists, axiom,
    ((![R : real, P : poly_complex]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_96_poly__bound__exists, axiom,
    ((![R : real, P : 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 @ P @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_97_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_real @ N @ zero_zero_poly_real) = zero_zero_poly_real)))). % poly_shift_0
thf(fact_98_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_99_neg__less__iff__less, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ B))))). % neg_less_iff_less
thf(fact_100_neg__less__iff__less, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_less_poly_real @ (uminus1613791741y_real @ B) @ (uminus1613791741y_real @ A)) = (ord_less_poly_real @ A @ B))))). % neg_less_iff_less
thf(fact_101_reflect__poly__0, axiom,
    (((reflect_poly_real @ zero_zero_poly_real) = zero_zero_poly_real))). % reflect_poly_0
thf(fact_102_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_103_less__neg__neg, axiom,
    ((![A : real]: ((ord_less_real @ A @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real))))). % less_neg_neg
thf(fact_104_less__neg__neg, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ A @ (uminus1613791741y_real @ A)) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % less_neg_neg
thf(fact_105_neg__less__pos, axiom,
    ((![A : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ A) = (ord_less_real @ zero_zero_real @ A))))). % neg_less_pos
thf(fact_106_neg__less__pos, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ (uminus1613791741y_real @ A) @ A) = (ord_less_poly_real @ zero_zero_poly_real @ A))))). % neg_less_pos
thf(fact_107_neg__0__less__iff__less, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real))))). % neg_0_less_iff_less
thf(fact_108_neg__0__less__iff__less, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (uminus1613791741y_real @ A)) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % neg_0_less_iff_less
thf(fact_109_neg__less__0__iff__less, axiom,
    ((![A : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_real @ zero_zero_real @ A))))). % neg_less_0_iff_less
thf(fact_110_neg__less__0__iff__less, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ (uminus1613791741y_real @ A) @ zero_zero_poly_real) = (ord_less_poly_real @ zero_zero_poly_real @ A))))). % neg_less_0_iff_less
thf(fact_111_zero__less__norm__iff, axiom,
    ((![X : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X)) = (~ ((X = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_112_zero__less__norm__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X)) = (~ ((X = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_113_real__sup__exists, axiom,
    ((![P3 : real > $o]: ((?[X_1 : real]: (P3 @ X_1)) => ((?[Z : real]: (![X3 : real]: ((P3 @ X3) => (ord_less_real @ X3 @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P3 @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_114_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_115_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_116_not__less__iff__gr__or__eq, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) = (((ord_less_real @ Y2 @ X)) | ((X = Y2))))))). % not_less_iff_gr_or_eq
thf(fact_117_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_118_linorder__less__wlog, axiom,
    ((![P3 : real > real > $o, A : real, B : real]: ((![A2 : real, B2 : real]: ((ord_less_real @ A2 @ B2) => (P3 @ A2 @ B2))) => ((![A2 : real]: (P3 @ A2 @ A2)) => ((![A2 : real, B2 : real]: ((P3 @ B2 @ A2) => (P3 @ A2 @ B2))) => (P3 @ A @ B))))))). % linorder_less_wlog
thf(fact_119_less__imp__not__less, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_imp_not_less
thf(fact_120_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_121_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_122_linorder__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((~ ((X = Y2))) => (ord_less_real @ Y2 @ X)))))). % linorder_cases
thf(fact_123_less__imp__triv, axiom,
    ((![X : real, Y2 : real, P3 : $o]: ((ord_less_real @ X @ Y2) => ((ord_less_real @ Y2 @ X) => P3))))). % less_imp_triv
thf(fact_124_less__imp__not__eq2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((Y2 = X))))))). % less_imp_not_eq2
thf(fact_125_antisym__conv3, axiom,
    ((![Y2 : real, X : real]: ((~ ((ord_less_real @ Y2 @ X))) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv3
thf(fact_126_less__not__sym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_not_sym
thf(fact_127_less__imp__not__eq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_not_eq
thf(fact_128_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_129_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_130_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_131_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_132_less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) | ((X = Y2) | (ord_less_real @ Y2 @ X)))))). % less_linear
thf(fact_133_less__trans, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_real @ X @ Y2) => ((ord_less_real @ Y2 @ Z2) => (ord_less_real @ X @ Z2)))))). % less_trans
thf(fact_134_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_135_less__asym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_asym
thf(fact_136_less__imp__neq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_neq
thf(fact_137_dense, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (?[Z3 : real]: ((ord_less_real @ X @ Z3) & (ord_less_real @ Z3 @ Y2))))))). % dense
thf(fact_138_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_139_neq__iff, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) = (((ord_less_real @ X @ Y2)) | ((ord_less_real @ Y2 @ X))))))). % neq_iff
thf(fact_140_neqE, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) => ((~ ((ord_less_real @ X @ Y2))) => (ord_less_real @ Y2 @ X)))))). % neqE
thf(fact_141_gt__ex, axiom,
    ((![X : real]: (?[X_12 : real]: (ord_less_real @ X @ X_12))))). % gt_ex
thf(fact_142_lt__ex, axiom,
    ((![X : real]: (?[Y3 : real]: (ord_less_real @ Y3 @ X))))). % lt_ex
thf(fact_143_order__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (ord_less_real @ (F @ X3) @ (F @ Y3)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_144_order__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (ord_less_real @ (F @ X3) @ (F @ Y3)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_145_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (ord_less_real @ (F @ X3) @ (F @ Y3)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_146_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (ord_less_real @ (F @ X3) @ (F @ Y3)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_147_verit__comp__simplify1_I1_J, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_148_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real))))). % less_numeral_extra(3)
thf(fact_149_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_150_verit__comp__simplify1_I3_J, axiom,
    ((![B3 : real, A3 : real]: ((~ ((ord_less_eq_real @ B3 @ A3))) = (ord_less_real @ A3 @ B3))))). % verit_comp_simplify1(3)
thf(fact_151_leD, axiom,
    ((![Y2 : real, X : real]: ((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_real @ X @ Y2))))))). % leD
thf(fact_152_leI, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % leI
thf(fact_153_le__less, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y4 : real]: (((ord_less_real @ X2 @ Y4)) | ((X2 = Y4)))))))). % le_less
thf(fact_154_less__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X2 @ Y4)) & ((~ ((X2 = Y4)))))))))). % less_le
thf(fact_155_order__le__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (ord_less_real @ (F @ X3) @ (F @ Y3)))) => (ord_less_real @ A @ (F @ C)))))))). % order_le_less_subst1
thf(fact_156_order__le__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ Y3) => (ord_less_eq_real @ (F @ X3) @ (F @ Y3)))) => (ord_less_real @ (F @ A) @ C))))))). % order_le_less_subst2
thf(fact_157_order__less__le__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ Y3) => (ord_less_eq_real @ (F @ X3) @ (F @ Y3)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_le_subst1
thf(fact_158_order__less__le__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ Y3) => (ord_less_real @ (F @ X3) @ (F @ Y3)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_le_subst2
thf(fact_159_not__le, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_eq_real @ X @ Y2))) = (ord_less_real @ Y2 @ X))))). % not_le
thf(fact_160_not__less, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) = (ord_less_eq_real @ Y2 @ X))))). % not_less
thf(fact_161_le__neq__trans, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((~ ((A = B))) => (ord_less_real @ A @ B)))))). % le_neq_trans
thf(fact_162_antisym__conv1, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((ord_less_eq_real @ X @ Y2) = (X = Y2)))))). % antisym_conv1
thf(fact_163_antisym__conv2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv2
thf(fact_164_less__imp__le, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (ord_less_eq_real @ X @ Y2))))). % less_imp_le
thf(fact_165_le__less__trans, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_real @ Y2 @ Z2) => (ord_less_real @ X @ Z2)))))). % le_less_trans
thf(fact_166_less__le__trans, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ Z2) => (ord_less_real @ X @ Z2)))))). % less_le_trans
thf(fact_167_dense__ge, axiom,
    ((![Z2 : real, Y2 : real]: ((![X3 : real]: ((ord_less_real @ Z2 @ X3) => (ord_less_eq_real @ Y2 @ X3))) => (ord_less_eq_real @ Y2 @ Z2))))). % dense_ge
thf(fact_168_dense__le, axiom,
    ((![Y2 : real, Z2 : real]: ((![X3 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_eq_real @ X3 @ Z2))) => (ord_less_eq_real @ Y2 @ Z2))))). % dense_le
thf(fact_169_le__less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) | (ord_less_real @ Y2 @ X))))). % le_less_linear
thf(fact_170_le__imp__less__or__eq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_real @ X @ Y2) | (X = Y2)))))). % le_imp_less_or_eq
thf(fact_171_less__le__not__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X2 @ Y4)) & ((~ ((ord_less_eq_real @ Y4 @ X2)))))))))). % less_le_not_le
thf(fact_172_not__le__imp__less, axiom,
    ((![Y2 : real, X : real]: ((~ ((ord_less_eq_real @ Y2 @ X))) => (ord_less_real @ X @ Y2))))). % not_le_imp_less
thf(fact_173_order_Ostrict__trans1, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans1
thf(fact_174_order_Ostrict__trans2, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans2
thf(fact_175_order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[A4 : real]: (^[B4 : real]: (((ord_less_real @ A4 @ B4)) | ((A4 = B4)))))))). % order.order_iff_strict
thf(fact_176_order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[A4 : real]: (^[B4 : real]: (((ord_less_eq_real @ A4 @ B4)) & ((~ ((A4 = B4)))))))))). % order.strict_iff_order
thf(fact_177_dual__order_Ostrict__trans1, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans1
thf(fact_178_dual__order_Ostrict__trans2, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans2
thf(fact_179_dense__ge__bounded, axiom,
    ((![Z2 : real, X : real, Y2 : real]: ((ord_less_real @ Z2 @ X) => ((![W : real]: ((ord_less_real @ Z2 @ W) => ((ord_less_real @ W @ X) => (ord_less_eq_real @ Y2 @ W)))) => (ord_less_eq_real @ Y2 @ Z2)))))). % dense_ge_bounded
thf(fact_180_dense__le__bounded, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_real @ X @ Y2) => ((![W : real]: ((ord_less_real @ X @ W) => ((ord_less_real @ W @ Y2) => (ord_less_eq_real @ W @ Z2)))) => (ord_less_eq_real @ Y2 @ Z2)))))). % dense_le_bounded
thf(fact_181_order_Ostrict__implies__order, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B))))). % order.strict_implies_order
thf(fact_182_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[B4 : real]: (^[A4 : real]: (((ord_less_real @ B4 @ A4)) | ((A4 = B4)))))))). % dual_order.order_iff_strict
thf(fact_183_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[B4 : real]: (^[A4 : real]: (((ord_less_eq_real @ B4 @ A4)) & ((~ ((A4 = B4)))))))))). % dual_order.strict_iff_order
thf(fact_184_dual__order_Ostrict__implies__order, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (ord_less_eq_real @ B @ A))))). % dual_order.strict_implies_order
thf(fact_185_order_Onot__eq__order__implies__strict, axiom,
    ((![A : real, B : real]: ((~ ((A = B))) => ((ord_less_eq_real @ A @ B) => (ord_less_real @ A @ B)))))). % order.not_eq_order_implies_strict
thf(fact_186_verit__negate__coefficient_I2_J, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % verit_negate_coefficient(2)
thf(fact_187_verit__negate__coefficient_I2_J, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ B) => (ord_less_poly_real @ (uminus1613791741y_real @ B) @ (uminus1613791741y_real @ A)))))). % verit_negate_coefficient(2)
thf(fact_188_less__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ (uminus_uminus_real @ A)))))). % less_minus_iff
thf(fact_189_less__minus__iff, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (uminus1613791741y_real @ B)) = (ord_less_poly_real @ B @ (uminus1613791741y_real @ A)))))). % less_minus_iff
thf(fact_190_minus__less__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ B) = (ord_less_real @ (uminus_uminus_real @ B) @ A))))). % minus_less_iff
thf(fact_191_minus__less__iff, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ (uminus1613791741y_real @ A) @ B) = (ord_less_poly_real @ (uminus1613791741y_real @ B) @ A))))). % minus_less_iff
thf(fact_192_poly__IVT__pos, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ B)) => (?[X3 : real]: ((ord_less_real @ A @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P @ X3) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_193_poly__IVT__neg, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ A)) => ((ord_less_real @ (poly_real2 @ P @ B) @ zero_zero_real) => (?[X3 : real]: ((ord_less_real @ A @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P @ X3) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_194_norm__not__less__zero, axiom,
    ((![X : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_195_norm__not__less__zero, axiom,
    ((![X : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X) @ zero_zero_real)))))). % norm_not_less_zero

% Conjectures (1)
thf(conj_0, conjecture,
    (((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)))))))).
