% 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_421__5371646_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:00.558

% Could-be-implicit typings (9)
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Int__Oint_J, type,
    poly_int : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Int__Oint, type,
    int : $tType).

% Explicit typings (49)
thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint, type,
    abs_abs_int : int > int).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint, type,
    minus_minus_int : int > int > int).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    minus_174331535omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    minus_240770701y_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint, type,
    uminus_uminus_int : int > int).
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__Int__Oint_J, type,
    uminus1869338749ly_int : poly_int > poly_int).
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__Int__Oint, type,
    zero_zero_int : int).
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__Int__Oint_J, type,
    zero_zero_poly_int : poly_int).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex, type,
    semiri356525583omplex : nat > complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint, type,
    semiri2019852685at_int : nat > int).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal, type,
    semiri2110766477t_real : nat > real).
thf(sy_c_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex, type,
    numera632737353omplex : num > complex).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint, type,
    numeral_numeral_int : num > int).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint, type,
    ord_less_int : int > int > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum, type,
    ord_less_num : num > num > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_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__Int__Oint, type,
    poly_int2 : poly_int > int > int).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_v_d____, type,
    d : real).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_s____, type,
    s : real).
thf(sy_v_thesis____, type,
    thesis : $o).
thf(sy_v_z____, type,
    z : complex).

% Relevant facts (241)
thf(fact_0__092_060open_062_092_060exists_062n_O_A2_A_P_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_060_Areal_An_092_060close_062, axiom,
    ((?[N : nat]: (ord_less_real @ (divide_divide_real @ (numeral_numeral_real @ (bit0 @ one)) @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s)))) @ (semiri2110766477t_real @ N))))). % \<open>\<exists>n. 2 / \<bar>cmod (poly p z) - - s\<bar> < real n\<close>
thf(fact_1_e, axiom,
    ((ord_less_real @ zero_zero_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s)))))). % e
thf(fact_2_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_3_e2, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))). % e2
thf(fact_4_norm__divide__numeral, axiom,
    ((![A : complex, W : num]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ (numera632737353omplex @ W))) = (divide_divide_real @ (real_V638595069omplex @ A) @ (numeral_numeral_real @ W)))))). % norm_divide_numeral
thf(fact_5_norm__divide__numeral, axiom,
    ((![A : real, W : num]: ((real_V646646907m_real @ (divide_divide_real @ A @ (numeral_numeral_real @ W))) = (divide_divide_real @ (real_V646646907m_real @ A) @ (numeral_numeral_real @ W)))))). % norm_divide_numeral
thf(fact_6_norm__neg__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (uminus1204672759omplex @ (numera632737353omplex @ W))) = (numeral_numeral_real @ W))))). % norm_neg_numeral
thf(fact_7_norm__neg__numeral, axiom,
    ((![W : num]: ((real_V646646907m_real @ (uminus_uminus_real @ (numeral_numeral_real @ W))) = (numeral_numeral_real @ W))))). % norm_neg_numeral
thf(fact_8_norm__of__nat, axiom,
    ((![N2 : nat]: ((real_V638595069omplex @ (semiri356525583omplex @ N2)) = (semiri2110766477t_real @ N2))))). % norm_of_nat
thf(fact_9_norm__of__nat, axiom,
    ((![N2 : nat]: ((real_V646646907m_real @ (semiri2110766477t_real @ N2)) = (semiri2110766477t_real @ N2))))). % norm_of_nat
thf(fact_10_norm__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (numera632737353omplex @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_11_norm__numeral, axiom,
    ((![W : num]: ((real_V646646907m_real @ (numeral_numeral_real @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_12_abs__neg__numeral, axiom,
    ((![N2 : num]: ((abs_abs_int @ (uminus_uminus_int @ (numeral_numeral_int @ N2))) = (numeral_numeral_int @ N2))))). % abs_neg_numeral
thf(fact_13_abs__neg__numeral, axiom,
    ((![N2 : num]: ((abs_abs_real @ (uminus_uminus_real @ (numeral_numeral_real @ N2))) = (numeral_numeral_real @ N2))))). % abs_neg_numeral
thf(fact_14_neg__numeral__less__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (uminus_uminus_int @ (numeral_numeral_int @ N2))) = (ord_less_num @ N2 @ M))))). % neg_numeral_less_iff
thf(fact_15_neg__numeral__less__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N2))) = (ord_less_num @ N2 @ M))))). % neg_numeral_less_iff
thf(fact_16_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_17_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_18_poly__minus, axiom,
    ((![P2 : poly_real, X3 : real]: ((poly_real2 @ (uminus1613791741y_real @ P2) @ X3) = (uminus_uminus_real @ (poly_real2 @ P2 @ X3)))))). % poly_minus
thf(fact_19_poly__minus, axiom,
    ((![P2 : poly_complex, X3 : complex]: ((poly_complex2 @ (uminus1138659839omplex @ P2) @ X3) = (uminus1204672759omplex @ (poly_complex2 @ P2 @ X3)))))). % poly_minus
thf(fact_20_poly__minus, axiom,
    ((![P2 : poly_int, X3 : int]: ((poly_int2 @ (uminus1869338749ly_int @ P2) @ X3) = (uminus_uminus_int @ (poly_int2 @ P2 @ X3)))))). % poly_minus
thf(fact_21_poly__diff, axiom,
    ((![P2 : poly_real, Q : poly_real, X3 : real]: ((poly_real2 @ (minus_240770701y_real @ P2 @ Q) @ X3) = (minus_minus_real @ (poly_real2 @ P2 @ X3) @ (poly_real2 @ Q @ X3)))))). % poly_diff
thf(fact_22_poly__diff, axiom,
    ((![P2 : poly_complex, Q : poly_complex, X3 : complex]: ((poly_complex2 @ (minus_174331535omplex @ P2 @ Q) @ X3) = (minus_minus_complex @ (poly_complex2 @ P2 @ X3) @ (poly_complex2 @ Q @ X3)))))). % poly_diff
thf(fact_23_abs__of__nat, axiom,
    ((![N2 : nat]: ((abs_abs_real @ (semiri2110766477t_real @ N2)) = (semiri2110766477t_real @ N2))))). % abs_of_nat
thf(fact_24_abs__of__nat, axiom,
    ((![N2 : nat]: ((abs_abs_int @ (semiri2019852685at_int @ N2)) = (semiri2019852685at_int @ N2))))). % abs_of_nat
thf(fact_25_norm__minus__cancel, axiom,
    ((![X3 : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X3)) = (real_V638595069omplex @ X3))))). % norm_minus_cancel
thf(fact_26_norm__minus__cancel, axiom,
    ((![X3 : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X3)) = (real_V646646907m_real @ X3))))). % norm_minus_cancel
thf(fact_27_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_28_numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N2)) = (M = N2))))). % numeral_eq_iff
thf(fact_29_numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N2)) = (M = N2))))). % numeral_eq_iff
thf(fact_30_numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N2)) = (M = N2))))). % numeral_eq_iff
thf(fact_31_numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N2)) = (M = N2))))). % numeral_eq_iff
thf(fact_32_of__nat__eq__iff, axiom,
    ((![M : nat, N2 : nat]: (((semiri2110766477t_real @ M) = (semiri2110766477t_real @ N2)) = (M = N2))))). % of_nat_eq_iff
thf(fact_33_of__nat__eq__iff, axiom,
    ((![M : nat, N2 : nat]: (((semiri2019852685at_int @ M) = (semiri2019852685at_int @ N2)) = (M = N2))))). % of_nat_eq_iff
thf(fact_34_of__nat__eq__iff, axiom,
    ((![M : nat, N2 : nat]: (((semiri356525583omplex @ M) = (semiri356525583omplex @ N2)) = (M = N2))))). % of_nat_eq_iff
thf(fact_35_of__nat__0, axiom,
    (((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat))). % of_nat_0
thf(fact_36_of__nat__0, axiom,
    (((semiri2110766477t_real @ zero_zero_nat) = zero_zero_real))). % of_nat_0
thf(fact_37_of__nat__0, axiom,
    (((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int))). % of_nat_0
thf(fact_38_of__nat__0, axiom,
    (((semiri356525583omplex @ zero_zero_nat) = zero_zero_complex))). % of_nat_0
thf(fact_39_of__nat__0__eq__iff, axiom,
    ((![N2 : nat]: ((zero_zero_nat = (semiri1382578993at_nat @ N2)) = (zero_zero_nat = N2))))). % of_nat_0_eq_iff
thf(fact_40_of__nat__0__eq__iff, axiom,
    ((![N2 : nat]: ((zero_zero_real = (semiri2110766477t_real @ N2)) = (zero_zero_nat = N2))))). % of_nat_0_eq_iff
thf(fact_41_of__nat__0__eq__iff, axiom,
    ((![N2 : nat]: ((zero_zero_int = (semiri2019852685at_int @ N2)) = (zero_zero_nat = N2))))). % of_nat_0_eq_iff
thf(fact_42_of__nat__0__eq__iff, axiom,
    ((![N2 : nat]: ((zero_zero_complex = (semiri356525583omplex @ N2)) = (zero_zero_nat = N2))))). % of_nat_0_eq_iff
thf(fact_43_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri1382578993at_nat @ M) = zero_zero_nat) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_44_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri2110766477t_real @ M) = zero_zero_real) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_45_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri2019852685at_int @ M) = zero_zero_int) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_46_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri356525583omplex @ M) = zero_zero_complex) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_47_neg__numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N2))) = (M = N2))))). % neg_numeral_eq_iff
thf(fact_48_neg__numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (uminus1204672759omplex @ (numera632737353omplex @ N2))) = (M = N2))))). % neg_numeral_eq_iff
thf(fact_49_neg__numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((uminus_uminus_int @ (numeral_numeral_int @ M)) = (uminus_uminus_int @ (numeral_numeral_int @ N2))) = (M = N2))))). % neg_numeral_eq_iff
thf(fact_50_of__nat__less__iff, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N2)) = (ord_less_nat @ M @ N2))))). % of_nat_less_iff
thf(fact_51_of__nat__less__iff, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N2)) = (ord_less_nat @ M @ N2))))). % of_nat_less_iff
thf(fact_52_of__nat__less__iff, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N2)) = (ord_less_nat @ M @ N2))))). % of_nat_less_iff
thf(fact_53_of__nat__numeral, axiom,
    ((![N2 : num]: ((semiri1382578993at_nat @ (numeral_numeral_nat @ N2)) = (numeral_numeral_nat @ N2))))). % of_nat_numeral
thf(fact_54_of__nat__numeral, axiom,
    ((![N2 : num]: ((semiri2110766477t_real @ (numeral_numeral_nat @ N2)) = (numeral_numeral_real @ N2))))). % of_nat_numeral
thf(fact_55_of__nat__numeral, axiom,
    ((![N2 : num]: ((semiri2019852685at_int @ (numeral_numeral_nat @ N2)) = (numeral_numeral_int @ N2))))). % of_nat_numeral
thf(fact_56_of__nat__numeral, axiom,
    ((![N2 : num]: ((semiri356525583omplex @ (numeral_numeral_nat @ N2)) = (numera632737353omplex @ N2))))). % of_nat_numeral
thf(fact_57_abs__numeral, axiom,
    ((![N2 : num]: ((abs_abs_real @ (numeral_numeral_real @ N2)) = (numeral_numeral_real @ N2))))). % abs_numeral
thf(fact_58_abs__numeral, axiom,
    ((![N2 : num]: ((abs_abs_int @ (numeral_numeral_int @ N2)) = (numeral_numeral_int @ N2))))). % abs_numeral
thf(fact_59_poly__0, axiom,
    ((![X3 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))). % poly_0
thf(fact_60_poly__0, axiom,
    ((![X3 : real]: ((poly_real2 @ zero_zero_poly_real @ X3) = zero_zero_real)))). % poly_0
thf(fact_61_poly__0, axiom,
    ((![X3 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))). % poly_0
thf(fact_62_poly__0, axiom,
    ((![X3 : int]: ((poly_int2 @ zero_zero_poly_int @ X3) = zero_zero_int)))). % poly_0
thf(fact_63_of__nat__0__less__iff, axiom,
    ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1382578993at_nat @ N2)) = (ord_less_nat @ zero_zero_nat @ N2))))). % of_nat_0_less_iff
thf(fact_64_of__nat__0__less__iff, axiom,
    ((![N2 : nat]: ((ord_less_real @ zero_zero_real @ (semiri2110766477t_real @ N2)) = (ord_less_nat @ zero_zero_nat @ N2))))). % of_nat_0_less_iff
thf(fact_65_of__nat__0__less__iff, axiom,
    ((![N2 : nat]: ((ord_less_int @ zero_zero_int @ (semiri2019852685at_int @ N2)) = (ord_less_nat @ zero_zero_nat @ N2))))). % of_nat_0_less_iff
thf(fact_66_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_67_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_68_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_69_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_70_numeral__less__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N2)) = (ord_less_num @ M @ N2))))). % numeral_less_iff
thf(fact_71_numeral__less__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N2)) = (ord_less_num @ M @ N2))))). % numeral_less_iff
thf(fact_72_numeral__less__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N2)) = (ord_less_num @ M @ N2))))). % numeral_less_iff
thf(fact_73_zero__less__norm__iff, axiom,
    ((![X3 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X3)) = (~ ((X3 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_74_zero__less__norm__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X3)) = (~ ((X3 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_75__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_A_092_060lbrakk_0620_A_060_Ad_059_A_092_060forall_062w_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_092_060and_062_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_092_060longrightarrow_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_P_A2_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![D : real]: ((ord_less_real @ zero_zero_real @ D) => (~ ((![W2 : complex]: (((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z))) & (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z)) @ D)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ W2) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))))))))))). % \<open>\<And>thesis. (\<And>d. \<lbrakk>0 < d; \<forall>w. 0 < cmod (w - z) \<and> cmod (w - z) < d \<longrightarrow> cmod (poly p w - poly p z) < \<bar>cmod (poly p z) - - s\<bar> / 2\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_76__092_060open_062_092_060exists_062d_0620_O_A_092_060forall_062w_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_092_060and_062_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_092_060longrightarrow_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_P_A2_092_060close_062, axiom,
    ((?[D : real]: ((ord_less_real @ zero_zero_real @ D) & (![W2 : complex]: (((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z))) & (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z)) @ D)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ W2) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))))))). % \<open>\<exists>d>0. \<forall>w. 0 < cmod (w - z) \<and> cmod (w - z) < d \<longrightarrow> cmod (poly p w - poly p z) < \<bar>cmod (poly p z) - - s\<bar> / 2\<close>
thf(fact_77_d_I2_J, axiom,
    ((![W2 : complex]: (((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z))) & (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z)) @ d)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ W2) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))))). % d(2)
thf(fact_78_poly__IVT__neg, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ A)) => ((ord_less_real @ (poly_real2 @ P2 @ B) @ zero_zero_real) => (?[X : real]: ((ord_less_real @ A @ X) & ((ord_less_real @ X @ B) & ((poly_real2 @ P2 @ X) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_79_poly__IVT__pos, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P2 @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ B)) => (?[X : real]: ((ord_less_real @ A @ X) & ((ord_less_real @ X @ B) & ((poly_real2 @ P2 @ X) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_80_poly__all__0__iff__0, axiom,
    ((![P2 : poly_complex]: ((![X2 : complex]: ((poly_complex2 @ P2 @ X2) = zero_zero_complex)) = (P2 = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_81_poly__all__0__iff__0, axiom,
    ((![P2 : poly_real]: ((![X2 : real]: ((poly_real2 @ P2 @ X2) = zero_zero_real)) = (P2 = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_82_poly__all__0__iff__0, axiom,
    ((![P2 : poly_int]: ((![X2 : int]: ((poly_int2 @ P2 @ X2) = zero_zero_int)) = (P2 = zero_zero_poly_int))))). % poly_all_0_iff_0
thf(fact_83_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_84_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_85_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_numeral_extra(3)
thf(fact_86_zero__neq__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_real = (numeral_numeral_real @ N2))))))). % zero_neq_numeral
thf(fact_87_zero__neq__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N2))))))). % zero_neq_numeral
thf(fact_88_zero__neq__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N2))))))). % zero_neq_numeral
thf(fact_89_zero__neq__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N2))))))). % zero_neq_numeral
thf(fact_90_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_91_not__numeral__less__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N2) @ zero_zero_real)))))). % not_numeral_less_zero
thf(fact_92_not__numeral__less__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N2) @ zero_zero_nat)))))). % not_numeral_less_zero
thf(fact_93_not__numeral__less__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N2) @ zero_zero_int)))))). % not_numeral_less_zero
thf(fact_94_zero__less__numeral, axiom,
    ((![N2 : num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ N2))))). % zero_less_numeral
thf(fact_95_zero__less__numeral, axiom,
    ((![N2 : num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ N2))))). % zero_less_numeral
thf(fact_96_zero__less__numeral, axiom,
    ((![N2 : num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ N2))))). % zero_less_numeral
thf(fact_97_zero__neq__neg__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_real = (uminus_uminus_real @ (numeral_numeral_real @ N2)))))))). % zero_neq_neg_numeral
thf(fact_98_zero__neq__neg__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_complex = (uminus1204672759omplex @ (numera632737353omplex @ N2)))))))). % zero_neq_neg_numeral
thf(fact_99_zero__neq__neg__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_int = (uminus_uminus_int @ (numeral_numeral_int @ N2)))))))). % zero_neq_neg_numeral
thf(fact_100_of__nat__less__0__iff, axiom,
    ((![M : nat]: (~ ((ord_less_nat @ (semiri1382578993at_nat @ M) @ zero_zero_nat)))))). % of_nat_less_0_iff
thf(fact_101_of__nat__less__0__iff, axiom,
    ((![M : nat]: (~ ((ord_less_real @ (semiri2110766477t_real @ M) @ zero_zero_real)))))). % of_nat_less_0_iff
thf(fact_102_of__nat__less__0__iff, axiom,
    ((![M : nat]: (~ ((ord_less_int @ (semiri2019852685at_int @ M) @ zero_zero_int)))))). % of_nat_less_0_iff
thf(fact_103_norm__not__less__zero, axiom,
    ((![X3 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_104_norm__not__less__zero, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_105_not__zero__less__neg__numeral, axiom,
    ((![N2 : num]: (~ ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ N2)))))))). % not_zero_less_neg_numeral
thf(fact_106_not__zero__less__neg__numeral, axiom,
    ((![N2 : num]: (~ ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ N2)))))))). % not_zero_less_neg_numeral
thf(fact_107_neg__numeral__less__zero, axiom,
    ((![N2 : num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ N2)) @ zero_zero_real)))). % neg_numeral_less_zero
thf(fact_108_neg__numeral__less__zero, axiom,
    ((![N2 : num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ N2)) @ zero_zero_int)))). % neg_numeral_less_zero
thf(fact_109_nonzero__norm__divide, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B))))))). % nonzero_norm_divide
thf(fact_110_nonzero__norm__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B))))))). % nonzero_norm_divide
thf(fact_111_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_complex, Q : poly_complex]: (((poly_complex2 @ P2) = (poly_complex2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_112_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_real, Q : poly_real]: (((poly_real2 @ P2) = (poly_real2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_113_half__gt__zero__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) = (ord_less_real @ zero_zero_real @ A))))). % half_gt_zero_iff
thf(fact_114_half__gt__zero, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))))))). % half_gt_zero
thf(fact_115_poly__cont, axiom,
    ((![E : real, Z2 : complex, P2 : poly_complex]: ((ord_less_real @ zero_zero_real @ E) => (?[D : real]: ((ord_less_real @ zero_zero_real @ D) & (![W2 : complex]: (((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ Z2))) & (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ Z2)) @ D)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ P2 @ W2) @ (poly_complex2 @ P2 @ Z2))) @ E))))))))). % poly_cont
thf(fact_116_poly__cont, axiom,
    ((![E : real, Z2 : real, P2 : poly_real]: ((ord_less_real @ zero_zero_real @ E) => (?[D : real]: ((ord_less_real @ zero_zero_real @ D) & (![W2 : real]: (((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ (minus_minus_real @ W2 @ Z2))) & (ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ W2 @ Z2)) @ D)) => (ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ (poly_real2 @ P2 @ W2) @ (poly_real2 @ P2 @ Z2))) @ E))))))))). % poly_cont
thf(fact_117_numeral__neq__neg__numeral, axiom,
    ((![M : num, N2 : num]: (~ (((numeral_numeral_real @ M) = (uminus_uminus_real @ (numeral_numeral_real @ N2)))))))). % numeral_neq_neg_numeral
thf(fact_118_numeral__neq__neg__numeral, axiom,
    ((![M : num, N2 : num]: (~ (((numera632737353omplex @ M) = (uminus1204672759omplex @ (numera632737353omplex @ N2)))))))). % numeral_neq_neg_numeral
thf(fact_119_numeral__neq__neg__numeral, axiom,
    ((![M : num, N2 : num]: (~ (((numeral_numeral_int @ M) = (uminus_uminus_int @ (numeral_numeral_int @ N2)))))))). % numeral_neq_neg_numeral
thf(fact_120_neg__numeral__neq__numeral, axiom,
    ((![M : num, N2 : num]: (~ (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (numeral_numeral_real @ N2))))))). % neg_numeral_neq_numeral
thf(fact_121_neg__numeral__neq__numeral, axiom,
    ((![M : num, N2 : num]: (~ (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (numera632737353omplex @ N2))))))). % neg_numeral_neq_numeral
thf(fact_122_neg__numeral__neq__numeral, axiom,
    ((![M : num, N2 : num]: (~ (((uminus_uminus_int @ (numeral_numeral_int @ M)) = (numeral_numeral_int @ N2))))))). % neg_numeral_neq_numeral
thf(fact_123_of__nat__less__imp__less, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N2)) => (ord_less_nat @ M @ N2))))). % of_nat_less_imp_less
thf(fact_124_of__nat__less__imp__less, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N2)) => (ord_less_nat @ M @ N2))))). % of_nat_less_imp_less
thf(fact_125_of__nat__less__imp__less, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N2)) => (ord_less_nat @ M @ N2))))). % of_nat_less_imp_less
thf(fact_126_less__imp__of__nat__less, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ M @ N2) => (ord_less_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N2)))))). % less_imp_of_nat_less
thf(fact_127_less__imp__of__nat__less, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ M @ N2) => (ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N2)))))). % less_imp_of_nat_less
thf(fact_128_less__imp__of__nat__less, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ M @ N2) => (ord_less_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N2)))))). % less_imp_of_nat_less
thf(fact_129_norm__minus__commute, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (minus_minus_complex @ A @ B)) = (real_V638595069omplex @ (minus_minus_complex @ B @ A)))))). % norm_minus_commute
thf(fact_130_norm__minus__commute, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (minus_minus_real @ A @ B)) = (real_V646646907m_real @ (minus_minus_real @ B @ A)))))). % norm_minus_commute
thf(fact_131_not__numeral__less__neg__numeral, axiom,
    ((![M : num, N2 : num]: (~ ((ord_less_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N2)))))))). % not_numeral_less_neg_numeral
thf(fact_132_not__numeral__less__neg__numeral, axiom,
    ((![M : num, N2 : num]: (~ ((ord_less_int @ (numeral_numeral_int @ M) @ (uminus_uminus_int @ (numeral_numeral_int @ N2)))))))). % not_numeral_less_neg_numeral
thf(fact_133_neg__numeral__less__numeral, axiom,
    ((![M : num, N2 : num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N2))))). % neg_numeral_less_numeral
thf(fact_134_neg__numeral__less__numeral, axiom,
    ((![M : num, N2 : num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (numeral_numeral_int @ N2))))). % neg_numeral_less_numeral
thf(fact_135_divide__numeral__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A)))). % divide_numeral_1
thf(fact_136_divide__numeral__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ (numera632737353omplex @ one)) = A)))). % divide_numeral_1
thf(fact_137_norm__divide, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_divide
thf(fact_138_norm__divide, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_divide
thf(fact_139_th1, axiom,
    ((![W : complex]: ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W @ z)) @ d) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ W) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))))). % th1
thf(fact_140_semiring__norm_I76_J, axiom,
    ((![N2 : num]: (ord_less_num @ one @ (bit0 @ N2))))). % semiring_norm(76)
thf(fact_141_real__of__nat__less__numeral__iff, axiom,
    ((![N2 : nat, W : num]: ((ord_less_real @ (semiri2110766477t_real @ N2) @ (numeral_numeral_real @ W)) = (ord_less_nat @ N2 @ (numeral_numeral_nat @ W)))))). % real_of_nat_less_numeral_iff
thf(fact_142_numeral__less__real__of__nat__iff, axiom,
    ((![W : num, N2 : nat]: ((ord_less_real @ (numeral_numeral_real @ W) @ (semiri2110766477t_real @ N2)) = (ord_less_nat @ (numeral_numeral_nat @ W) @ N2))))). % numeral_less_real_of_nat_iff
thf(fact_143_zero__less__abs__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ A)) = (~ ((A = zero_zero_real))))))). % zero_less_abs_iff
thf(fact_144_zero__less__abs__iff, axiom,
    ((![A : int]: ((ord_less_int @ zero_zero_int @ (abs_abs_int @ A)) = (~ ((A = zero_zero_int))))))). % zero_less_abs_iff
thf(fact_145_diff__0, axiom,
    ((![A : real]: ((minus_minus_real @ zero_zero_real @ A) = (uminus_uminus_real @ A))))). % diff_0
thf(fact_146_diff__0, axiom,
    ((![A : complex]: ((minus_minus_complex @ zero_zero_complex @ A) = (uminus1204672759omplex @ A))))). % diff_0
thf(fact_147_diff__0, axiom,
    ((![A : int]: ((minus_minus_int @ zero_zero_int @ A) = (uminus_uminus_int @ A))))). % diff_0
thf(fact_148_verit__minus__simplify_I3_J, axiom,
    ((![B : real]: ((minus_minus_real @ zero_zero_real @ B) = (uminus_uminus_real @ B))))). % verit_minus_simplify(3)
thf(fact_149_verit__minus__simplify_I3_J, axiom,
    ((![B : complex]: ((minus_minus_complex @ zero_zero_complex @ B) = (uminus1204672759omplex @ B))))). % verit_minus_simplify(3)
thf(fact_150_verit__minus__simplify_I3_J, axiom,
    ((![B : int]: ((minus_minus_int @ zero_zero_int @ B) = (uminus_uminus_int @ B))))). % verit_minus_simplify(3)
thf(fact_151_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_152_neg__less__0__iff__less, axiom,
    ((![A : int]: ((ord_less_int @ (uminus_uminus_int @ A) @ zero_zero_int) = (ord_less_int @ zero_zero_int @ A))))). % neg_less_0_iff_less
thf(fact_153_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_154_neg__0__less__iff__less, axiom,
    ((![A : int]: ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int))))). % neg_0_less_iff_less
thf(fact_155_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_156_neg__less__pos, axiom,
    ((![A : int]: ((ord_less_int @ (uminus_uminus_int @ A) @ A) = (ord_less_int @ zero_zero_int @ A))))). % neg_less_pos
thf(fact_157_verit__eq__simplify_I8_J, axiom,
    ((![X22 : num, Y2 : num]: (((bit0 @ X22) = (bit0 @ Y2)) = (X22 = Y2))))). % verit_eq_simplify(8)
thf(fact_158_semiring__norm_I87_J, axiom,
    ((![M : num, N2 : num]: (((bit0 @ M) = (bit0 @ N2)) = (M = N2))))). % semiring_norm(87)
thf(fact_159_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_160_verit__minus__simplify_I4_J, axiom,
    ((![B : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_161_verit__minus__simplify_I4_J, axiom,
    ((![B : int]: ((uminus_uminus_int @ (uminus_uminus_int @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_162_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_163_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_164_add_Oinverse__inverse, axiom,
    ((![A : int]: ((uminus_uminus_int @ (uminus_uminus_int @ A)) = A)))). % add.inverse_inverse
thf(fact_165_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_166_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_167_neg__equal__iff__equal, axiom,
    ((![A : int, B : int]: (((uminus_uminus_int @ A) = (uminus_uminus_int @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_168_diff__0__eq__0, axiom,
    ((![N2 : nat]: ((minus_minus_nat @ zero_zero_nat @ N2) = zero_zero_nat)))). % diff_0_eq_0
thf(fact_169_diff__self__eq__0, axiom,
    ((![M : nat]: ((minus_minus_nat @ M @ M) = zero_zero_nat)))). % diff_self_eq_0
thf(fact_170_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_171_abs__idempotent, axiom,
    ((![A : int]: ((abs_abs_int @ (abs_abs_int @ A)) = (abs_abs_int @ A))))). % abs_idempotent
thf(fact_172_not__gr__zero, axiom,
    ((![N2 : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N2))) = (N2 = zero_zero_nat))))). % not_gr_zero
thf(fact_173_diff__self, axiom,
    ((![A : int]: ((minus_minus_int @ A @ A) = zero_zero_int)))). % diff_self
thf(fact_174_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_175_diff__self, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % diff_self
thf(fact_176_diff__0__right, axiom,
    ((![A : int]: ((minus_minus_int @ A @ zero_zero_int) = A)))). % diff_0_right
thf(fact_177_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_178_diff__0__right, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_0_right
thf(fact_179_zero__diff, axiom,
    ((![A : nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % zero_diff
thf(fact_180_diff__zero, axiom,
    ((![A : int]: ((minus_minus_int @ A @ zero_zero_int) = A)))). % diff_zero
thf(fact_181_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_182_diff__zero, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_zero
thf(fact_183_diff__zero, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A)))). % diff_zero
thf(fact_184_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : int]: ((minus_minus_int @ A @ A) = zero_zero_int)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_185_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_186_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_187_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_188_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_189_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_190_add_Oinverse__neutral, axiom,
    (((uminus_uminus_int @ zero_zero_int) = zero_zero_int))). % add.inverse_neutral
thf(fact_191_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_192_neg__0__equal__iff__equal, axiom,
    ((![A : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A)) = (zero_zero_complex = A))))). % neg_0_equal_iff_equal
thf(fact_193_neg__0__equal__iff__equal, axiom,
    ((![A : int]: ((zero_zero_int = (uminus_uminus_int @ A)) = (zero_zero_int = A))))). % neg_0_equal_iff_equal
thf(fact_194_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_195_neg__equal__0__iff__equal, axiom,
    ((![A : complex]: (((uminus1204672759omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_196_neg__equal__0__iff__equal, axiom,
    ((![A : int]: (((uminus_uminus_int @ A) = zero_zero_int) = (A = zero_zero_int))))). % neg_equal_0_iff_equal
thf(fact_197_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_198_equal__neg__zero, axiom,
    ((![A : int]: ((A = (uminus_uminus_int @ A)) = (A = zero_zero_int))))). % equal_neg_zero
thf(fact_199_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_200_neg__equal__zero, axiom,
    ((![A : int]: (((uminus_uminus_int @ A) = A) = (A = zero_zero_int))))). % neg_equal_zero
thf(fact_201_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_202_neg__less__iff__less, axiom,
    ((![B : int, A : int]: ((ord_less_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ B))))). % neg_less_iff_less
thf(fact_203_minus__diff__eq, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ B @ A))))). % minus_diff_eq
thf(fact_204_minus__diff__eq, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ B @ A))))). % minus_diff_eq
thf(fact_205_minus__diff__eq, axiom,
    ((![A : int, B : int]: ((uminus_uminus_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ B @ A))))). % minus_diff_eq
thf(fact_206_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_207_semiring__norm_I83_J, axiom,
    ((![N2 : num]: (~ ((one = (bit0 @ N2))))))). % semiring_norm(83)
thf(fact_208_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_209_abs__0__eq, axiom,
    ((![A : int]: ((zero_zero_int = (abs_abs_int @ A)) = (A = zero_zero_int))))). % abs_0_eq
thf(fact_210_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_211_abs__eq__0, axiom,
    ((![A : int]: (((abs_abs_int @ A) = zero_zero_int) = (A = zero_zero_int))))). % abs_eq_0
thf(fact_212_neq0__conv, axiom,
    ((![N2 : nat]: ((~ ((N2 = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N2))))). % neq0_conv
thf(fact_213_zero__less__diff, axiom,
    ((![N2 : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ N2 @ M)) = (ord_less_nat @ M @ N2))))). % zero_less_diff
thf(fact_214_less__nat__zero__code, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_215_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_216_semiring__norm_I78_J, axiom,
    ((![M : num, N2 : num]: ((ord_less_num @ (bit0 @ M) @ (bit0 @ N2)) = (ord_less_num @ M @ N2))))). % semiring_norm(78)
thf(fact_217_semiring__norm_I75_J, axiom,
    ((![M : num]: (~ ((ord_less_num @ M @ one)))))). % semiring_norm(75)
thf(fact_218_int__ops_I3_J, axiom,
    ((![N2 : num]: ((semiri2019852685at_int @ (numeral_numeral_nat @ N2)) = (numeral_numeral_int @ N2))))). % int_ops(3)
thf(fact_219_int__ops_I1_J, axiom,
    (((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int))). % int_ops(1)
thf(fact_220_nat__int__comparison_I2_J, axiom,
    ((ord_less_nat = (^[A2 : nat]: (^[B2 : nat]: (ord_less_int @ (semiri2019852685at_int @ A2) @ (semiri2019852685at_int @ B2))))))). % nat_int_comparison(2)
thf(fact_221_gr0I, axiom,
    ((![N2 : nat]: ((~ ((N2 = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N2))))). % gr0I
thf(fact_222_not__gr0, axiom,
    ((![N2 : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N2))) = (N2 = zero_zero_nat))))). % not_gr0
thf(fact_223_diff__less, axiom,
    ((![N2 : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((ord_less_nat @ zero_zero_nat @ M) => (ord_less_nat @ (minus_minus_nat @ M @ N2) @ M)))))). % diff_less
thf(fact_224_not__less0, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ zero_zero_nat)))))). % not_less0
thf(fact_225_less__zeroE, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ zero_zero_nat)))))). % less_zeroE
thf(fact_226_nat__neq__iff, axiom,
    ((![M : nat, N2 : nat]: ((~ ((M = N2))) = (((ord_less_nat @ M @ N2)) | ((ord_less_nat @ N2 @ M))))))). % nat_neq_iff
thf(fact_227_less__not__refl, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ N2)))))). % less_not_refl
thf(fact_228_less__not__refl2, axiom,
    ((![N2 : nat, M : nat]: ((ord_less_nat @ N2 @ M) => (~ ((M = N2))))))). % less_not_refl2
thf(fact_229_less__not__refl3, axiom,
    ((![S2 : nat, T : nat]: ((ord_less_nat @ S2 @ T) => (~ ((S2 = T))))))). % less_not_refl3
thf(fact_230_diff__less__mono2, axiom,
    ((![M : nat, N2 : nat, L : nat]: ((ord_less_nat @ M @ N2) => ((ord_less_nat @ M @ L) => (ord_less_nat @ (minus_minus_nat @ L @ N2) @ (minus_minus_nat @ L @ M))))))). % diff_less_mono2
thf(fact_231_gr__implies__not0, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ M @ N2) => (~ ((N2 = zero_zero_nat))))))). % gr_implies_not0
thf(fact_232_less__irrefl__nat, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ N2)))))). % less_irrefl_nat
thf(fact_233_nat__less__induct, axiom,
    ((![P : nat > $o, N2 : nat]: ((![N : nat]: ((![M2 : nat]: ((ord_less_nat @ M2 @ N) => (P @ M2))) => (P @ N))) => (P @ N2))))). % nat_less_induct
thf(fact_234_diffs0__imp__equal, axiom,
    ((![M : nat, N2 : nat]: (((minus_minus_nat @ M @ N2) = zero_zero_nat) => (((minus_minus_nat @ N2 @ M) = zero_zero_nat) => (M = N2)))))). % diffs0_imp_equal
thf(fact_235_infinite__descent, axiom,
    ((![P : nat > $o, N2 : nat]: ((![N : nat]: ((~ ((P @ N))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N) & (~ ((P @ M2))))))) => (P @ N2))))). % infinite_descent
thf(fact_236_minus__nat_Odiff__0, axiom,
    ((![M : nat]: ((minus_minus_nat @ M @ zero_zero_nat) = M)))). % minus_nat.diff_0
thf(fact_237_infinite__descent0, axiom,
    ((![P : nat > $o, N2 : nat]: ((P @ zero_zero_nat) => ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((~ ((P @ N))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N) & (~ ((P @ M2)))))))) => (P @ N2)))))). % infinite_descent0
thf(fact_238_linorder__neqE__nat, axiom,
    ((![X3 : nat, Y3 : nat]: ((~ ((X3 = Y3))) => ((~ ((ord_less_nat @ X3 @ Y3))) => (ord_less_nat @ Y3 @ X3)))))). % linorder_neqE_nat
thf(fact_239_less__imp__diff__less, axiom,
    ((![J : nat, K : nat, N2 : nat]: ((ord_less_nat @ J @ K) => (ord_less_nat @ (minus_minus_nat @ J @ N2) @ K))))). % less_imp_diff_less
thf(fact_240_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![N22 : nat]: ((ord_less_real @ (divide_divide_real @ (numeral_numeral_real @ (bit0 @ one)) @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s)))) @ (semiri2110766477t_real @ N22)) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
