% 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_376__5371214_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:38.907

% Could-be-implicit typings (6)
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).

% Explicit typings (26)
thf(sy_c_Complex_Oarg, type,
    arg : complex > real).
thf(sy_c_Complex_Orcis, type,
    rcis : real > real > complex).
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__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_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_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_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex, type,
    real_V1560324349omplex : real > complex > complex).
thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal, type,
    real_V453051771R_real : real > real > real).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_r, type,
    r : real).

% Relevant facts (186)
thf(fact_0__092_060open_062cmod_A0_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_092_060close_062, axiom,
    (((ord_less_eq_real @ (real_V638595069omplex @ zero_zero_complex) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ zero_zero_complex)) = (uminus_uminus_real @ (uminus_uminus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ zero_zero_complex)))))))). % \<open>cmod 0 \<le> r \<and> cmod (poly p 0) = - (- cmod (poly p 0))\<close>
thf(fact_1_True, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % True
thf(fact_2_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_3_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_4_poly__minus, axiom,
    ((![P : poly_complex, X : complex]: ((poly_complex2 @ (uminus1138659839omplex @ P) @ X) = (uminus1204672759omplex @ (poly_complex2 @ P @ X)))))). % poly_minus
thf(fact_5_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_6_norm__minus__cancel, axiom,
    ((![X : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X)) = (real_V646646907m_real @ X))))). % norm_minus_cancel
thf(fact_7_norm__minus__cancel, axiom,
    ((![X : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X)) = (real_V638595069omplex @ X))))). % norm_minus_cancel
thf(fact_8_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_9_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_10_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_11_verit__minus__simplify_I4_J, axiom,
    ((![B : poly_real]: ((uminus1613791741y_real @ (uminus1613791741y_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_12_verit__minus__simplify_I4_J, axiom,
    ((![B : poly_complex]: ((uminus1138659839omplex @ (uminus1138659839omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_13_verit__minus__simplify_I4_J, axiom,
    ((![B : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_14_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_15_add_Oinverse__inverse, axiom,
    ((![A : poly_real]: ((uminus1613791741y_real @ (uminus1613791741y_real @ A)) = A)))). % add.inverse_inverse
thf(fact_16_add_Oinverse__inverse, axiom,
    ((![A : poly_complex]: ((uminus1138659839omplex @ (uminus1138659839omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_17_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_18_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_19_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_20_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_21_neg__equal__iff__equal, axiom,
    ((![A : poly_complex, B : poly_complex]: (((uminus1138659839omplex @ A) = (uminus1138659839omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_22_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_23_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_24_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_25_neg__equal__zero, axiom,
    ((![A : poly_real]: (((uminus1613791741y_real @ A) = A) = (A = zero_zero_poly_real))))). % neg_equal_zero
thf(fact_26_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_27_equal__neg__zero, axiom,
    ((![A : poly_real]: ((A = (uminus1613791741y_real @ A)) = (A = zero_zero_poly_real))))). % equal_neg_zero
thf(fact_28_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_29_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_30_neg__equal__0__iff__equal, axiom,
    ((![A : poly_complex]: (((uminus1138659839omplex @ A) = zero_z1746442943omplex) = (A = zero_z1746442943omplex))))). % neg_equal_0_iff_equal
thf(fact_31_neg__equal__0__iff__equal, axiom,
    ((![A : complex]: (((uminus1204672759omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_32_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_33_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_34_neg__0__equal__iff__equal, axiom,
    ((![A : poly_complex]: ((zero_z1746442943omplex = (uminus1138659839omplex @ A)) = (zero_z1746442943omplex = A))))). % neg_0_equal_iff_equal
thf(fact_35_neg__0__equal__iff__equal, axiom,
    ((![A : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A)) = (zero_zero_complex = A))))). % neg_0_equal_iff_equal
thf(fact_36_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_37_add_Oinverse__neutral, axiom,
    (((uminus1613791741y_real @ zero_zero_poly_real) = zero_zero_poly_real))). % add.inverse_neutral
thf(fact_38_add_Oinverse__neutral, axiom,
    (((uminus1138659839omplex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % add.inverse_neutral
thf(fact_39_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_40_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_41_poly__0, axiom,
    ((![X : real]: ((poly_real2 @ zero_zero_poly_real @ X) = zero_zero_real)))). % poly_0
thf(fact_42_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_43_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_44_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_45_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_46_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_47_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_48_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_49_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_50_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_51_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_52_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_53_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_54_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_55_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_56_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_57_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_58_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_59_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_60_norm__ge__zero, axiom,
    ((![X : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X))))). % norm_ge_zero
thf(fact_61_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_62_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_63_dual__order_Oeq__iff, axiom,
    (((^[Y : real]: (^[Z : real]: (Y = Z))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A2)) & ((ord_less_eq_real @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_64_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_65_linorder__wlog, axiom,
    ((![P2 : real > real > $o, A : real, B : real]: ((![A3 : real, B3 : real]: ((ord_less_eq_real @ A3 @ B3) => (P2 @ A3 @ B3))) => ((![A3 : real, B3 : real]: ((P2 @ B3 @ A3) => (P2 @ A3 @ B3))) => (P2 @ A @ B)))))). % linorder_wlog
thf(fact_66_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_67_order__trans, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ Z2) => (ord_less_eq_real @ X @ Z2)))))). % order_trans
thf(fact_68_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_69_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_70_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_71_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y : real]: (^[Z : real]: (Y = Z))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ A2 @ B2)) & ((ord_less_eq_real @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_72_antisym__conv, axiom,
    ((![Y2 : real, X : real]: ((ord_less_eq_real @ Y2 @ X) => ((ord_less_eq_real @ X @ Y2) = (X = Y2)))))). % antisym_conv
thf(fact_73_le__cases3, axiom,
    ((![X : real, Y2 : real, Z2 : real]: (((ord_less_eq_real @ X @ Y2) => (~ ((ord_less_eq_real @ Y2 @ Z2)))) => (((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_eq_real @ X @ Z2)))) => (((ord_less_eq_real @ X @ Z2) => (~ ((ord_less_eq_real @ Z2 @ Y2)))) => (((ord_less_eq_real @ Z2 @ Y2) => (~ ((ord_less_eq_real @ Y2 @ X)))) => (((ord_less_eq_real @ Y2 @ Z2) => (~ ((ord_less_eq_real @ Z2 @ X)))) => (~ (((ord_less_eq_real @ Z2 @ X) => (~ ((ord_less_eq_real @ X @ Y2)))))))))))))). % le_cases3
thf(fact_74_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_75_le__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_eq_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % le_cases
thf(fact_76_eq__refl, axiom,
    ((![X : real, Y2 : real]: ((X = Y2) => (ord_less_eq_real @ X @ Y2))))). % eq_refl
thf(fact_77_linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) | (ord_less_eq_real @ Y2 @ X))))). % linear
thf(fact_78_antisym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ X) => (X = Y2)))))). % antisym
thf(fact_79_eq__iff, axiom,
    (((^[Y : real]: (^[Z : real]: (Y = Z))) = (^[X2 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X2 @ Y3)) & ((ord_less_eq_real @ Y3 @ X2)))))))). % eq_iff
thf(fact_80_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y4 : real]: ((ord_less_eq_real @ X3 @ Y4) => (ord_less_eq_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_81_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y4 : real]: ((ord_less_eq_real @ X3 @ Y4) => (ord_less_eq_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_82_verit__la__disequality, axiom,
    ((![A : real, B : real]: ((A = B) | ((~ ((ord_less_eq_real @ A @ B))) | (~ ((ord_less_eq_real @ B @ A)))))))). % verit_la_disequality
thf(fact_83_order__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X3 : real, Y4 : real]: ((ord_less_eq_real @ X3 @ Y4) => (ord_less_eq_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_84_order__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y4 : real]: ((ord_less_eq_real @ X3 @ Y4) => (ord_less_eq_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_85_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_86_minus__equation__iff, axiom,
    ((![A : poly_real, B : poly_real]: (((uminus1613791741y_real @ A) = B) = ((uminus1613791741y_real @ B) = A))))). % minus_equation_iff
thf(fact_87_minus__equation__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: (((uminus1138659839omplex @ A) = B) = ((uminus1138659839omplex @ B) = A))))). % minus_equation_iff
thf(fact_88_minus__equation__iff, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((uminus1204672759omplex @ B) = A))))). % minus_equation_iff
thf(fact_89_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_90_equation__minus__iff, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (uminus1613791741y_real @ B)) = (B = (uminus1613791741y_real @ A)))))). % equation_minus_iff
thf(fact_91_equation__minus__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: ((A = (uminus1138659839omplex @ B)) = (B = (uminus1138659839omplex @ A)))))). % equation_minus_iff
thf(fact_92_equation__minus__iff, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = (B = (uminus1204672759omplex @ A)))))). % equation_minus_iff
thf(fact_93_verit__negate__coefficient_I3_J, axiom,
    ((![A : real, B : real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B)))))). % verit_negate_coefficient(3)
thf(fact_94_verit__negate__coefficient_I3_J, axiom,
    ((![A : poly_real, B : poly_real]: ((A = B) => ((uminus1613791741y_real @ A) = (uminus1613791741y_real @ B)))))). % verit_negate_coefficient(3)
thf(fact_95_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_96_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_97_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_98_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_99_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_100_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_101_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_102_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_103_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_104_poly__bound__exists, axiom,
    ((![R : real, P : poly_complex]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z3)) @ M)))))))). % poly_bound_exists
thf(fact_105_poly__bound__exists, axiom,
    ((![R : real, P : poly_real]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z3) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P @ Z3)) @ M)))))))). % poly_bound_exists
thf(fact_106_rcis__zero__mod, axiom,
    ((![A : real]: ((rcis @ zero_zero_real @ A) = zero_zero_complex)))). % rcis_zero_mod
thf(fact_107_rcis__eq__zero__iff, axiom,
    ((![R : real, A : real]: (((rcis @ R @ A) = zero_zero_complex) = (R = zero_zero_real))))). % rcis_eq_zero_iff
thf(fact_108_arg__zero, axiom,
    (((arg @ zero_zero_complex) = zero_zero_real))). % arg_zero
thf(fact_109_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_110_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_111_scaleR__mono_H, 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 @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V453051771R_real @ A @ C) @ (real_V453051771R_real @ B @ D))))))))). % scaleR_mono'
thf(fact_112_scaleR__mono, axiom,
    ((![A : real, B : real, X : real, Y2 : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ X @ Y2) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ X) => (ord_less_eq_real @ (real_V453051771R_real @ A @ X) @ (real_V453051771R_real @ B @ Y2))))))))). % scaleR_mono
thf(fact_113_scaleR__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 @ zero_zero_real @ (real_V453051771R_real @ A @ B))))))). % scaleR_nonpos_nonpos
thf(fact_114_scaleR__nonpos__nonneg, axiom,
    ((![A : real, X : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ X) => (ord_less_eq_real @ (real_V453051771R_real @ A @ X) @ zero_zero_real)))))). % scaleR_nonpos_nonneg
thf(fact_115_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_116_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_117_scale__cancel__right, axiom,
    ((![A : real, X : complex, B : real]: (((real_V1560324349omplex @ A @ X) = (real_V1560324349omplex @ B @ X)) = (((A = B)) | ((X = zero_zero_complex))))))). % scale_cancel_right
thf(fact_118_scale__cancel__right, axiom,
    ((![A : real, X : real, B : real]: (((real_V453051771R_real @ A @ X) = (real_V453051771R_real @ B @ X)) = (((A = B)) | ((X = zero_zero_real))))))). % scale_cancel_right
thf(fact_119_scale__zero__right, axiom,
    ((![A : real]: ((real_V1560324349omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % scale_zero_right
thf(fact_120_scale__zero__right, axiom,
    ((![A : real]: ((real_V453051771R_real @ A @ zero_zero_real) = zero_zero_real)))). % scale_zero_right
thf(fact_121_scale__minus__right, axiom,
    ((![A : real, X : real]: ((real_V453051771R_real @ A @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (real_V453051771R_real @ A @ X)))))). % scale_minus_right
thf(fact_122_scale__minus__right, axiom,
    ((![A : real, X : complex]: ((real_V1560324349omplex @ A @ (uminus1204672759omplex @ X)) = (uminus1204672759omplex @ (real_V1560324349omplex @ A @ X)))))). % scale_minus_right
thf(fact_123_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_124_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_125_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_126_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_127_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_128_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_129_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_130_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_131_scale__zero__left, axiom,
    ((![X : complex]: ((real_V1560324349omplex @ zero_zero_real @ X) = zero_zero_complex)))). % scale_zero_left
thf(fact_132_scale__zero__left, axiom,
    ((![X : real]: ((real_V453051771R_real @ zero_zero_real @ X) = zero_zero_real)))). % scale_zero_left
thf(fact_133_scale__eq__0__iff, axiom,
    ((![A : real, X : complex]: (((real_V1560324349omplex @ A @ X) = zero_zero_complex) = (((A = zero_zero_real)) | ((X = zero_zero_complex))))))). % scale_eq_0_iff
thf(fact_134_scale__eq__0__iff, axiom,
    ((![A : real, X : real]: (((real_V453051771R_real @ A @ X) = zero_zero_real) = (((A = zero_zero_real)) | ((X = zero_zero_real))))))). % scale_eq_0_iff
thf(fact_135_scaleR__left_Ominus, axiom,
    ((![X : real, Xa : real]: ((real_V453051771R_real @ (uminus_uminus_real @ X) @ Xa) = (uminus_uminus_real @ (real_V453051771R_real @ X @ Xa)))))). % scaleR_left.minus
thf(fact_136_scaleR__left_Ominus, axiom,
    ((![X : real, Xa : complex]: ((real_V1560324349omplex @ (uminus_uminus_real @ X) @ Xa) = (uminus1204672759omplex @ (real_V1560324349omplex @ X @ Xa)))))). % scaleR_left.minus
thf(fact_137_scale__minus__left, axiom,
    ((![A : real, X : real]: ((real_V453051771R_real @ (uminus_uminus_real @ A) @ X) = (uminus_uminus_real @ (real_V453051771R_real @ A @ X)))))). % scale_minus_left
thf(fact_138_scale__minus__left, axiom,
    ((![A : real, X : complex]: ((real_V1560324349omplex @ (uminus_uminus_real @ A) @ X) = (uminus1204672759omplex @ (real_V1560324349omplex @ A @ X)))))). % scale_minus_left
thf(fact_139_verit__comp__simplify1_I1_J, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_140_rcis__Ex, axiom,
    ((![Z2 : complex]: (?[R2 : real, A3 : real]: (Z2 = (rcis @ R2 @ A3)))))). % rcis_Ex
thf(fact_141_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y4 : real]: ((ord_less_real @ X3 @ Y4) => (ord_less_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_142_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y4 : real]: ((ord_less_real @ X3 @ Y4) => (ord_less_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_143_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, Y4 : real]: ((ord_less_real @ X3 @ Y4) => (ord_less_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_144_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, Y4 : real]: ((ord_less_real @ X3 @ Y4) => (ord_less_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_145_lt__ex, axiom,
    ((![X : real]: (?[Y4 : real]: (ord_less_real @ Y4 @ X))))). % lt_ex
thf(fact_146_gt__ex, axiom,
    ((![X : real]: (?[X_1 : real]: (ord_less_real @ X @ X_1))))). % gt_ex
thf(fact_147_neqE, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) => ((~ ((ord_less_real @ X @ Y2))) => (ord_less_real @ Y2 @ X)))))). % neqE
thf(fact_148_neq__iff, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) = (((ord_less_real @ X @ Y2)) | ((ord_less_real @ Y2 @ X))))))). % neq_iff
thf(fact_149_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_150_dense, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (?[Z4 : real]: ((ord_less_real @ X @ Z4) & (ord_less_real @ Z4 @ Y2))))))). % dense
thf(fact_151_less__imp__neq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_neq
thf(fact_152_less__asym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_asym
thf(fact_153_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_154_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_155_less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) | ((X = Y2) | (ord_less_real @ Y2 @ X)))))). % less_linear
thf(fact_156_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_157_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_158_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_159_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_160_less__imp__not__eq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_not_eq
thf(fact_161_less__not__sym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_not_sym
thf(fact_162_antisym__conv3, axiom,
    ((![Y2 : real, X : real]: ((~ ((ord_less_real @ Y2 @ X))) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv3
thf(fact_163_less__imp__not__eq2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((Y2 = X))))))). % less_imp_not_eq2
thf(fact_164_less__imp__triv, axiom,
    ((![X : real, Y2 : real, P2 : $o]: ((ord_less_real @ X @ Y2) => ((ord_less_real @ Y2 @ X) => P2))))). % less_imp_triv
thf(fact_165_linorder__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((~ ((X = Y2))) => (ord_less_real @ Y2 @ X)))))). % linorder_cases
thf(fact_166_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_167_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_168_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_169_linorder__less__wlog, axiom,
    ((![P2 : real > real > $o, A : real, B : real]: ((![A3 : real, B3 : real]: ((ord_less_real @ A3 @ B3) => (P2 @ A3 @ B3))) => ((![A3 : real]: (P2 @ A3 @ A3)) => ((![A3 : real, B3 : real]: ((P2 @ B3 @ A3) => (P2 @ A3 @ B3))) => (P2 @ A @ B))))))). % linorder_less_wlog
thf(fact_170_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_171_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_172_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_173_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_174_real__sup__exists, axiom,
    ((![P2 : real > $o]: ((?[X_12 : real]: (P2 @ X_12)) => ((?[Z3 : real]: (![X3 : real]: ((P2 @ X3) => (ord_less_real @ X3 @ Z3)))) => (?[S : real]: (![Y5 : real]: ((?[X2 : real]: (((P2 @ X2)) & ((ord_less_real @ Y5 @ X2)))) = (ord_less_real @ Y5 @ S))))))))). % real_sup_exists
thf(fact_175_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_176_rcis__cmod__arg, axiom,
    ((![Z2 : complex]: ((rcis @ (real_V638595069omplex @ Z2) @ (arg @ Z2)) = Z2)))). % rcis_cmod_arg
thf(fact_177_scaleR__le__cancel__left__pos, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_eq_real @ (real_V453051771R_real @ C @ A) @ (real_V453051771R_real @ C @ B)) = (ord_less_eq_real @ A @ B)))))). % scaleR_le_cancel_left_pos
thf(fact_178_scaleR__le__cancel__left__neg, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_eq_real @ (real_V453051771R_real @ C @ A) @ (real_V453051771R_real @ C @ B)) = (ord_less_eq_real @ B @ A)))))). % scaleR_le_cancel_left_neg
thf(fact_179_scaleR__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (real_V453051771R_real @ C @ A) @ (real_V453051771R_real @ C @ B)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ A))))))))). % scaleR_le_cancel_left
thf(fact_180_scale__right__imp__eq, axiom,
    ((![X : complex, A : real, B : real]: ((~ ((X = zero_zero_complex))) => (((real_V1560324349omplex @ A @ X) = (real_V1560324349omplex @ B @ X)) => (A = B)))))). % scale_right_imp_eq
thf(fact_181_scale__right__imp__eq, axiom,
    ((![X : real, A : real, B : real]: ((~ ((X = zero_zero_real))) => (((real_V453051771R_real @ A @ X) = (real_V453051771R_real @ B @ X)) => (A = B)))))). % scale_right_imp_eq
thf(fact_182_verit__comp__simplify1_I3_J, axiom,
    ((![B4 : real, A4 : real]: ((~ ((ord_less_eq_real @ B4 @ A4))) = (ord_less_real @ A4 @ B4))))). % verit_comp_simplify1(3)
thf(fact_183_leD, axiom,
    ((![Y2 : real, X : real]: ((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_real @ X @ Y2))))))). % leD
thf(fact_184_leI, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % leI
thf(fact_185_le__less, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y3 : real]: (((ord_less_real @ X2 @ Y3)) | ((X2 = Y3)))))))). % le_less

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[X4 : real, Z3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ Z3)) = (uminus_uminus_real @ X4)))))).
