% 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_533__5373156_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:59.039

% Could-be-implicit typings (7)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    poly_p1267267526omplex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__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_Ooffset__poly_001t__Complex__Ocomplex, type,
    fundam1201687030omplex : poly_complex > complex > poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1307691262omplex : poly_poly_complex > poly_complex > poly_poly_complex).
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__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1956464160omplex : poly_poly_complex > nat).
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__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    zero_z1200043727omplex : poly_p1267267526omplex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    is_zero_poly_complex : poly_poly_complex > $o).
thf(sy_c_Polynomial_OpCons_001t__Complex__Ocomplex, type,
    pCons_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    pCons_poly_complex : poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    pCons_1087637536omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_c_Polynomial_OpCons_001t__Real__Oreal, type,
    pCons_real : real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_c622223248omplex : nat > poly_poly_complex > poly_poly_complex).
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__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_s558570093omplex : nat > poly_poly_complex > poly_poly_complex).
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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    reflec1997789704omplex : poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Real__Oreal, type,
    reflect_poly_real : poly_real > poly_real).
thf(sy_c_Polynomial_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > poly_complex).
thf(sy_c_Polynomial_Osynthetic__div_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    synthe1985144195omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_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).

% Relevant facts (172)
thf(fact_0_poly__minimum__modulus__disc, axiom,
    ((![R : real, P : poly_complex]: (?[Z : complex]: (![W : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ W) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W))))))))). % poly_minimum_modulus_disc
thf(fact_1_poly__0, axiom,
    ((![X : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X) = zero_z1040703943omplex)))). % poly_0
thf(fact_2_poly__0, axiom,
    ((![X : real]: ((poly_real2 @ zero_zero_poly_real @ X) = zero_zero_real)))). % poly_0
thf(fact_3_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_4_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_5_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_6_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_7_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_8_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_9_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_10_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_11_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ P @ X2) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_12_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_13_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_14_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_15_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_16_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_17_poly__infinity, axiom,
    ((![P : poly_complex, D : real, A : complex]: ((~ ((P = zero_z1746442943omplex))) => (?[R2 : real]: (![Z2 : complex]: ((ord_less_eq_real @ R2 @ (real_V638595069omplex @ Z2)) => (ord_less_eq_real @ D @ (real_V638595069omplex @ (poly_complex2 @ (pCons_complex @ A @ P) @ Z2)))))))))). % poly_infinity
thf(fact_18_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_19_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex]: (((poly_poly_complex2 @ P) = (poly_poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_20_pCons__eq__0__iff, axiom,
    ((![A : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A @ P) = zero_z1200043727omplex) = (((A = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_21_pCons__eq__0__iff, axiom,
    ((![A : real, P : poly_real]: (((pCons_real @ A @ P) = zero_zero_poly_real) = (((A = zero_zero_real)) & ((P = zero_zero_poly_real))))))). % pCons_eq_0_iff
thf(fact_22_pCons__eq__0__iff, axiom,
    ((![A : complex, P : poly_complex]: (((pCons_complex @ A @ P) = zero_z1746442943omplex) = (((A = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_23_pCons__eq__0__iff, axiom,
    ((![A : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A @ P) = zero_z1040703943omplex) = (((A = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_24_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_25_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_26_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_27_pCons__0__0, axiom,
    (((pCons_real @ zero_zero_real @ zero_zero_poly_real) = zero_zero_poly_real))). % pCons_0_0
thf(fact_28_pderiv_Oinduct, axiom,
    ((![P2 : poly_complex > $o, A0 : poly_complex]: ((![A2 : complex, P3 : poly_complex]: (((~ ((P3 = zero_z1746442943omplex))) => (P2 @ P3)) => (P2 @ (pCons_complex @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_29_pderiv_Oinduct, axiom,
    ((![P2 : poly_poly_complex > $o, A0 : poly_poly_complex]: ((![A2 : poly_complex, P3 : poly_poly_complex]: (((~ ((P3 = zero_z1040703943omplex))) => (P2 @ P3)) => (P2 @ (pCons_poly_complex @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_30_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_complex > $o, P : poly_complex, Q : poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A2 : complex, P3 : poly_complex, B : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A2 @ P3) @ (pCons_complex @ B @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_31_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_poly_complex > $o, P : poly_complex, Q : poly_poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1040703943omplex) => ((![A2 : complex, P3 : poly_complex, B : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A2 @ P3) @ (pCons_poly_complex @ B @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_32_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_complex > $o, P : poly_poly_complex, Q : poly_complex]: ((P2 @ zero_z1040703943omplex @ zero_z1746442943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex, B : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A2 @ P3) @ (pCons_complex @ B @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_33_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_poly_complex > $o, P : poly_poly_complex, Q : poly_poly_complex]: ((P2 @ zero_z1040703943omplex @ zero_z1040703943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex, B : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A2 @ P3) @ (pCons_poly_complex @ B @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_34_pCons__induct, axiom,
    ((![P2 : poly_p1267267526omplex > $o, P : poly_p1267267526omplex]: ((P2 @ zero_z1200043727omplex) => ((![A2 : poly_poly_complex, P3 : poly_p1267267526omplex]: (((~ ((A2 = zero_z1040703943omplex))) | (~ ((P3 = zero_z1200043727omplex)))) => ((P2 @ P3) => (P2 @ (pCons_1087637536omplex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_35_pCons__induct, axiom,
    ((![P2 : poly_real > $o, P : poly_real]: ((P2 @ zero_zero_poly_real) => ((![A2 : real, P3 : poly_real]: (((~ ((A2 = zero_zero_real))) | (~ ((P3 = zero_zero_poly_real)))) => ((P2 @ P3) => (P2 @ (pCons_real @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_36_pCons__induct, axiom,
    ((![P2 : poly_complex > $o, P : poly_complex]: ((P2 @ zero_z1746442943omplex) => ((![A2 : complex, P3 : poly_complex]: (((~ ((A2 = zero_zero_complex))) | (~ ((P3 = zero_z1746442943omplex)))) => ((P2 @ P3) => (P2 @ (pCons_complex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_37_pCons__induct, axiom,
    ((![P2 : poly_poly_complex > $o, P : poly_poly_complex]: ((P2 @ zero_z1040703943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex]: (((~ ((A2 = zero_z1746442943omplex))) | (~ ((P3 = zero_z1040703943omplex)))) => ((P2 @ P3) => (P2 @ (pCons_poly_complex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_38_norm__ge__zero, axiom,
    ((![X : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X))))). % norm_ge_zero
thf(fact_39_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_40_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_41_zero__reorient, axiom,
    ((![X : poly_poly_complex]: ((zero_z1040703943omplex = X) = (X = zero_z1040703943omplex))))). % zero_reorient
thf(fact_42_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_43_dual__order_Oantisym, axiom,
    ((![B2 : real, A : real]: ((ord_less_eq_real @ B2 @ A) => ((ord_less_eq_real @ A @ B2) => (A = B2)))))). % dual_order.antisym
thf(fact_44_dual__order_Oeq__iff, axiom,
    (((^[Y : real]: (^[Z3 : real]: (Y = Z3))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((ord_less_eq_real @ A3 @ B3)))))))). % dual_order.eq_iff
thf(fact_45_dual__order_Otrans, axiom,
    ((![B2 : real, A : real, C : real]: ((ord_less_eq_real @ B2 @ A) => ((ord_less_eq_real @ C @ B2) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_46_linorder__wlog, axiom,
    ((![P2 : real > real > $o, A : real, B2 : real]: ((![A2 : real, B : real]: ((ord_less_eq_real @ A2 @ B) => (P2 @ A2 @ B))) => ((![A2 : real, B : real]: ((P2 @ B @ A2) => (P2 @ A2 @ B))) => (P2 @ A @ B2)))))). % linorder_wlog
thf(fact_47_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_48_order__trans, axiom,
    ((![X : real, Y2 : real, Z4 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ Z4) => (ord_less_eq_real @ X @ Z4)))))). % order_trans
thf(fact_49_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B2 : real]: ((ord_less_eq_real @ A @ B2) => ((ord_less_eq_real @ B2 @ A) => (A = B2)))))). % order_class.order.antisym
thf(fact_50_ord__le__eq__trans, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_eq_real @ A @ B2) => ((B2 = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_51_ord__eq__le__trans, axiom,
    ((![A : real, B2 : real, C : real]: ((A = B2) => ((ord_less_eq_real @ B2 @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_52_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y : real]: (^[Z3 : real]: (Y = Z3))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ A3 @ B3)) & ((ord_less_eq_real @ B3 @ A3)))))))). % order_class.order.eq_iff
thf(fact_53_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_54_le__cases3, axiom,
    ((![X : real, Y2 : real, Z4 : real]: (((ord_less_eq_real @ X @ Y2) => (~ ((ord_less_eq_real @ Y2 @ Z4)))) => (((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_eq_real @ X @ Z4)))) => (((ord_less_eq_real @ X @ Z4) => (~ ((ord_less_eq_real @ Z4 @ Y2)))) => (((ord_less_eq_real @ Z4 @ Y2) => (~ ((ord_less_eq_real @ Y2 @ X)))) => (((ord_less_eq_real @ Y2 @ Z4) => (~ ((ord_less_eq_real @ Z4 @ X)))) => (~ (((ord_less_eq_real @ Z4 @ X) => (~ ((ord_less_eq_real @ X @ Y2)))))))))))))). % le_cases3
thf(fact_55_order_Otrans, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_eq_real @ A @ B2) => ((ord_less_eq_real @ B2 @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_56_le__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_eq_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % le_cases
thf(fact_57_eq__refl, axiom,
    ((![X : real, Y2 : real]: ((X = Y2) => (ord_less_eq_real @ X @ Y2))))). % eq_refl
thf(fact_58_linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) | (ord_less_eq_real @ Y2 @ X))))). % linear
thf(fact_59_antisym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ X) => (X = Y2)))))). % antisym
thf(fact_60_eq__iff, axiom,
    (((^[Y : real]: (^[Z3 : real]: (Y = Z3))) = (^[X2 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X2 @ Y3)) & ((ord_less_eq_real @ Y3 @ X2)))))))). % eq_iff
thf(fact_61_ord__le__eq__subst, axiom,
    ((![A : real, B2 : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B2) => (((F @ B2) = 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_62_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B2 : real, C : real]: ((A = (F @ B2)) => ((ord_less_eq_real @ B2 @ 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_63_order__subst2, axiom,
    ((![A : real, B2 : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B2) => ((ord_less_eq_real @ (F @ B2) @ 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_64_order__subst1, axiom,
    ((![A : real, F : real > real, B2 : real, C : real]: ((ord_less_eq_real @ A @ (F @ B2)) => ((ord_less_eq_real @ B2 @ 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_65_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_66_psize__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((fundam1956464160omplex @ P) = zero_zero_nat) = (P = zero_z1040703943omplex))))). % psize_eq_0_iff
thf(fact_67_synthetic__div__pCons, axiom,
    ((![A : complex, P : poly_complex, C : complex]: ((synthe151143547omplex @ (pCons_complex @ A @ P) @ C) = (pCons_complex @ (poly_complex2 @ P @ C) @ (synthe151143547omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_68_synthetic__div__pCons, axiom,
    ((![A : poly_complex, P : poly_poly_complex, C : poly_complex]: ((synthe1985144195omplex @ (pCons_poly_complex @ A @ P) @ C) = (pCons_poly_complex @ (poly_poly_complex2 @ P @ C) @ (synthe1985144195omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_69_is__zero__null, axiom,
    ((is_zero_complex = (^[P4 : poly_complex]: (P4 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_70_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P4 : poly_poly_complex]: (P4 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_71_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_72_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_c622223248omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_73_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_74_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_75_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((poly_p282434315omplex @ (reflec1997789704omplex @ P) @ zero_z1040703943omplex) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_76_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_77_poly__bound__exists, axiom,
    ((![R : real, P : poly_complex]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z2) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z2)) @ M)))))))). % poly_bound_exists
thf(fact_78_offset__poly__single, axiom,
    ((![A : complex, H : complex]: ((fundam1201687030omplex @ (pCons_complex @ A @ zero_z1746442943omplex) @ H) = (pCons_complex @ A @ zero_z1746442943omplex))))). % offset_poly_single
thf(fact_79_offset__poly__single, axiom,
    ((![A : poly_complex, H : poly_complex]: ((fundam1307691262omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex) @ H) = (pCons_poly_complex @ A @ zero_z1040703943omplex))))). % offset_poly_single
thf(fact_80_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_81_poly__shift__0, axiom,
    ((![N : nat]: ((poly_s558570093omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_shift_0
thf(fact_82_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_83_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_84_scaleR__mono_H, axiom,
    ((![A : real, B2 : real, C : real, D : real]: ((ord_less_eq_real @ A @ B2) => ((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 @ B2 @ D))))))))). % scaleR_mono'
thf(fact_85_scale__zero__right, axiom,
    ((![A : real]: ((real_V1560324349omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % scale_zero_right
thf(fact_86_scale__zero__right, axiom,
    ((![A : real]: ((real_V453051771R_real @ A @ zero_zero_real) = zero_zero_real)))). % scale_zero_right
thf(fact_87_scale__cancel__right, axiom,
    ((![A : real, X : complex, B2 : real]: (((real_V1560324349omplex @ A @ X) = (real_V1560324349omplex @ B2 @ X)) = (((A = B2)) | ((X = zero_zero_complex))))))). % scale_cancel_right
thf(fact_88_scale__cancel__right, axiom,
    ((![A : real, X : real, B2 : real]: (((real_V453051771R_real @ A @ X) = (real_V453051771R_real @ B2 @ X)) = (((A = B2)) | ((X = zero_zero_real))))))). % scale_cancel_right
thf(fact_89_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_90_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_91_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_92_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_93_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_94_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_95_scale__zero__left, axiom,
    ((![X : complex]: ((real_V1560324349omplex @ zero_zero_real @ X) = zero_zero_complex)))). % scale_zero_left
thf(fact_96_scale__zero__left, axiom,
    ((![X : real]: ((real_V453051771R_real @ zero_zero_real @ X) = zero_zero_real)))). % scale_zero_left
thf(fact_97_reflect__poly__const, axiom,
    ((![A : complex]: ((reflect_poly_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = (pCons_complex @ A @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_98_reflect__poly__const, axiom,
    ((![A : poly_complex]: ((reflec309385472omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex)) = (pCons_poly_complex @ A @ zero_z1040703943omplex))))). % reflect_poly_const
thf(fact_99_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B2 : real, C : real]: ((A = (F @ B2)) => ((ord_less_real @ B2 @ 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_100_ord__less__eq__subst, axiom,
    ((![A : real, B2 : real, F : real > real, C : real]: ((ord_less_real @ A @ B2) => (((F @ B2) = 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_101_order__less__subst1, axiom,
    ((![A : real, F : real > real, B2 : real, C : real]: ((ord_less_real @ A @ (F @ B2)) => ((ord_less_real @ B2 @ 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_102_order__less__subst2, axiom,
    ((![A : real, B2 : real, F : real > real, C : real]: ((ord_less_real @ A @ B2) => ((ord_less_real @ (F @ B2) @ 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_103_lt__ex, axiom,
    ((![X : real]: (?[Y4 : real]: (ord_less_real @ Y4 @ X))))). % lt_ex
thf(fact_104_gt__ex, axiom,
    ((![X : real]: (?[X_1 : real]: (ord_less_real @ X @ X_1))))). % gt_ex
thf(fact_105_neqE, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) => ((~ ((ord_less_real @ X @ Y2))) => (ord_less_real @ Y2 @ X)))))). % neqE
thf(fact_106_neq__iff, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) = (((ord_less_real @ X @ Y2)) | ((ord_less_real @ Y2 @ X))))))). % neq_iff
thf(fact_107_order_Oasym, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (~ ((ord_less_real @ B2 @ A))))))). % order.asym
thf(fact_108_dense, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (?[Z : real]: ((ord_less_real @ X @ Z) & (ord_less_real @ Z @ Y2))))))). % dense
thf(fact_109_less__imp__neq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_neq
thf(fact_110_less__asym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_asym
thf(fact_111_less__asym_H, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (~ ((ord_less_real @ B2 @ A))))))). % less_asym'
thf(fact_112_less__trans, axiom,
    ((![X : real, Y2 : real, Z4 : real]: ((ord_less_real @ X @ Y2) => ((ord_less_real @ Y2 @ Z4) => (ord_less_real @ X @ Z4)))))). % less_trans
thf(fact_113_less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) | ((X = Y2) | (ord_less_real @ Y2 @ X)))))). % less_linear
thf(fact_114_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_115_ord__eq__less__trans, axiom,
    ((![A : real, B2 : real, C : real]: ((A = B2) => ((ord_less_real @ B2 @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_116_ord__less__eq__trans, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_real @ A @ B2) => ((B2 = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_117_dual__order_Oasym, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ B2 @ A) => (~ ((ord_less_real @ A @ B2))))))). % dual_order.asym
thf(fact_118_less__imp__not__eq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_not_eq
thf(fact_119_less__not__sym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_not_sym
thf(fact_120_antisym__conv3, axiom,
    ((![Y2 : real, X : real]: ((~ ((ord_less_real @ Y2 @ X))) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv3
thf(fact_121_less__imp__not__eq2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((Y2 = X))))))). % less_imp_not_eq2
thf(fact_122_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_123_linorder__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((~ ((X = Y2))) => (ord_less_real @ Y2 @ X)))))). % linorder_cases
thf(fact_124_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_125_order_Ostrict__trans, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_real @ A @ B2) => ((ord_less_real @ B2 @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_126_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_127_linorder__less__wlog, axiom,
    ((![P2 : real > real > $o, A : real, B2 : real]: ((![A2 : real, B : real]: ((ord_less_real @ A2 @ B) => (P2 @ A2 @ B))) => ((![A2 : real]: (P2 @ A2 @ A2)) => ((![A2 : real, B : real]: ((P2 @ B @ A2) => (P2 @ A2 @ B))) => (P2 @ A @ B2))))))). % linorder_less_wlog
thf(fact_128_dual__order_Ostrict__trans, axiom,
    ((![B2 : real, A : real, C : real]: ((ord_less_real @ B2 @ A) => ((ord_less_real @ C @ B2) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_129_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_130_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (~ ((A = B2))))))). % order.strict_implies_not_eq
thf(fact_131_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ B2 @ A) => (~ ((A = B2))))))). % dual_order.strict_implies_not_eq
thf(fact_132_real__sup__exists, axiom,
    ((![P2 : real > $o]: ((?[X_12 : real]: (P2 @ X_12)) => ((?[Z2 : real]: (![X3 : real]: ((P2 @ X3) => (ord_less_real @ X3 @ Z2)))) => (?[S : real]: (![Y5 : real]: ((?[X2 : real]: (((P2 @ X2)) & ((ord_less_real @ Y5 @ X2)))) = (ord_less_real @ Y5 @ S))))))))). % real_sup_exists
thf(fact_133_scaleR__le__cancel__left__pos, axiom,
    ((![C : real, A : real, B2 : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_eq_real @ (real_V453051771R_real @ C @ A) @ (real_V453051771R_real @ C @ B2)) = (ord_less_eq_real @ A @ B2)))))). % scaleR_le_cancel_left_pos
thf(fact_134_scaleR__le__cancel__left__neg, axiom,
    ((![C : real, A : real, B2 : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_eq_real @ (real_V453051771R_real @ C @ A) @ (real_V453051771R_real @ C @ B2)) = (ord_less_eq_real @ B2 @ A)))))). % scaleR_le_cancel_left_neg
thf(fact_135_scaleR__le__cancel__left, axiom,
    ((![C : real, A : real, B2 : real]: ((ord_less_eq_real @ (real_V453051771R_real @ C @ A) @ (real_V453051771R_real @ C @ B2)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B2)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B2 @ A))))))))). % scaleR_le_cancel_left
thf(fact_136_scale__right__imp__eq, axiom,
    ((![X : complex, A : real, B2 : real]: ((~ ((X = zero_zero_complex))) => (((real_V1560324349omplex @ A @ X) = (real_V1560324349omplex @ B2 @ X)) => (A = B2)))))). % scale_right_imp_eq
thf(fact_137_scale__right__imp__eq, axiom,
    ((![X : real, A : real, B2 : real]: ((~ ((X = zero_zero_real))) => (((real_V453051771R_real @ A @ X) = (real_V453051771R_real @ B2 @ X)) => (A = B2)))))). % scale_right_imp_eq
thf(fact_138_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_139_leD, axiom,
    ((![Y2 : real, X : real]: ((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_real @ X @ Y2))))))). % leD
thf(fact_140_leI, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % leI
thf(fact_141_le__less, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y3 : real]: (((ord_less_real @ X2 @ Y3)) | ((X2 = Y3)))))))). % le_less
thf(fact_142_less__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X2 @ Y3)) & ((~ ((X2 = Y3)))))))))). % less_le
thf(fact_143_order__le__less__subst1, axiom,
    ((![A : real, F : real > real, B2 : real, C : real]: ((ord_less_eq_real @ A @ (F @ B2)) => ((ord_less_real @ B2 @ C) => ((![X3 : real, Y4 : real]: ((ord_less_real @ X3 @ Y4) => (ord_less_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_le_less_subst1
thf(fact_144_order__le__less__subst2, axiom,
    ((![A : real, B2 : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B2) => ((ord_less_real @ (F @ B2) @ C) => ((![X3 : real, Y4 : real]: ((ord_less_eq_real @ X3 @ Y4) => (ord_less_eq_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % order_le_less_subst2
thf(fact_145_order__less__le__subst1, axiom,
    ((![A : real, F : real > real, B2 : real, C : real]: ((ord_less_real @ A @ (F @ B2)) => ((ord_less_eq_real @ B2 @ C) => ((![X3 : real, Y4 : real]: ((ord_less_eq_real @ X3 @ Y4) => (ord_less_eq_real @ (F @ X3) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_le_subst1
thf(fact_146_order__less__le__subst2, axiom,
    ((![A : real, B2 : real, F : real > real, C : real]: ((ord_less_real @ A @ B2) => ((ord_less_eq_real @ (F @ B2) @ 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_le_subst2
thf(fact_147_not__le, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_eq_real @ X @ Y2))) = (ord_less_real @ Y2 @ X))))). % not_le
thf(fact_148_not__less, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) = (ord_less_eq_real @ Y2 @ X))))). % not_less
thf(fact_149_le__neq__trans, axiom,
    ((![A : real, B2 : real]: ((ord_less_eq_real @ A @ B2) => ((~ ((A = B2))) => (ord_less_real @ A @ B2)))))). % le_neq_trans
thf(fact_150_antisym__conv1, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((ord_less_eq_real @ X @ Y2) = (X = Y2)))))). % antisym_conv1
thf(fact_151_antisym__conv2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv2
thf(fact_152_less__imp__le, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (ord_less_eq_real @ X @ Y2))))). % less_imp_le
thf(fact_153_le__less__trans, axiom,
    ((![X : real, Y2 : real, Z4 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_real @ Y2 @ Z4) => (ord_less_real @ X @ Z4)))))). % le_less_trans
thf(fact_154_less__le__trans, axiom,
    ((![X : real, Y2 : real, Z4 : real]: ((ord_less_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ Z4) => (ord_less_real @ X @ Z4)))))). % less_le_trans
thf(fact_155_dense__ge, axiom,
    ((![Z4 : real, Y2 : real]: ((![X3 : real]: ((ord_less_real @ Z4 @ X3) => (ord_less_eq_real @ Y2 @ X3))) => (ord_less_eq_real @ Y2 @ Z4))))). % dense_ge
thf(fact_156_dense__le, axiom,
    ((![Y2 : real, Z4 : real]: ((![X3 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_eq_real @ X3 @ Z4))) => (ord_less_eq_real @ Y2 @ Z4))))). % dense_le
thf(fact_157_le__less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) | (ord_less_real @ Y2 @ X))))). % le_less_linear
thf(fact_158_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_159_less__le__not__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X2 @ Y3)) & ((~ ((ord_less_eq_real @ Y3 @ X2)))))))))). % less_le_not_le
thf(fact_160_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_161_order_Ostrict__trans1, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_eq_real @ A @ B2) => ((ord_less_real @ B2 @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans1
thf(fact_162_order_Ostrict__trans2, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_real @ A @ B2) => ((ord_less_eq_real @ B2 @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans2
thf(fact_163_order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[A3 : real]: (^[B3 : real]: (((ord_less_real @ A3 @ B3)) | ((A3 = B3)))))))). % order.order_iff_strict
thf(fact_164_order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ A3 @ B3)) & ((~ ((A3 = B3)))))))))). % order.strict_iff_order
thf(fact_165_dual__order_Ostrict__trans1, axiom,
    ((![B2 : real, A : real, C : real]: ((ord_less_eq_real @ B2 @ A) => ((ord_less_real @ C @ B2) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans1
thf(fact_166_dual__order_Ostrict__trans2, axiom,
    ((![B2 : real, A : real, C : real]: ((ord_less_real @ B2 @ A) => ((ord_less_eq_real @ C @ B2) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans2
thf(fact_167_dense__ge__bounded, axiom,
    ((![Z4 : real, X : real, Y2 : real]: ((ord_less_real @ Z4 @ X) => ((![W2 : real]: ((ord_less_real @ Z4 @ W2) => ((ord_less_real @ W2 @ X) => (ord_less_eq_real @ Y2 @ W2)))) => (ord_less_eq_real @ Y2 @ Z4)))))). % dense_ge_bounded
thf(fact_168_dense__le__bounded, axiom,
    ((![X : real, Y2 : real, Z4 : real]: ((ord_less_real @ X @ Y2) => ((![W2 : real]: ((ord_less_real @ X @ W2) => ((ord_less_real @ W2 @ Y2) => (ord_less_eq_real @ W2 @ Z4)))) => (ord_less_eq_real @ Y2 @ Z4)))))). % dense_le_bounded
thf(fact_169_order_Ostrict__implies__order, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (ord_less_eq_real @ A @ B2))))). % order.strict_implies_order
thf(fact_170_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[B3 : real]: (^[A3 : real]: (((ord_less_real @ B3 @ A3)) | ((A3 = B3)))))))). % dual_order.order_iff_strict
thf(fact_171_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[B3 : real]: (^[A3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((~ ((A3 = B3)))))))))). % dual_order.strict_iff_order

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[Z2 : complex]: (![W2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ zero_z1746442943omplex @ Z2)) @ (real_V638595069omplex @ (poly_complex2 @ zero_z1746442943omplex @ W2))))))).
