% 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_423__5371658_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:01.909

% Could-be-implicit typings (5)
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $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).

% Explicit typings (40)
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__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum, type,
    plus_plus_num : num > num > num).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_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__Real__Oreal, type,
    uminus_uminus_real : real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__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__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__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__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_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum, type,
    ord_less_eq_num : num > num > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat, type,
    order_769474267at_nat : (nat > nat) > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > 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_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_N1____, type,
    n1 : nat).
thf(sy_v_N2____, type,
    n2 : nat).
thf(sy_v_d____, type,
    d : real).
thf(sy_v_f____, type,
    f : nat > nat).
thf(sy_v_g____, type,
    g : nat > complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_s____, type,
    s : real).
thf(sy_v_z____, type,
    z : complex).

% Relevant facts (200)
thf(fact_0_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_1_fz_I1_J, axiom,
    ((order_769474267at_nat @ f))). % fz(1)
thf(fact_2__092_060open_062N1_A_092_060le_062_AN1_A_L_AN2_A_092_060Longrightarrow_062_Acmod_A_Ig_A_If_A_IN1_A_L_AN2_J_J_A_N_Az_J_A_060_Ad_092_060close_062, axiom,
    (((ord_less_eq_nat @ n1 @ (plus_plus_nat @ n1 @ n2)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ (plus_plus_nat @ n1 @ n2))) @ z)) @ d)))). % \<open>N1 \<le> N1 + N2 \<Longrightarrow> cmod (g (f (N1 + N2)) - z) < d\<close>
thf(fact_3_N1, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ n1 @ N) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N)) @ z)) @ d))))). % N1
thf(fact_4_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_5_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_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062N1_O_A_092_060forall_062n_092_060ge_062N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![N1 : nat]: (~ ((![N : nat]: ((ord_less_eq_nat @ N1 @ N) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N)) @ z)) @ d)))))))))). % \<open>\<And>thesis. (\<And>N1. \<forall>n\<ge>N1. cmod (g (f n) - z) < d \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_7_N2, axiom,
    ((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 @ n2)))). % N2
thf(fact_8_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_9_fz_I2_J, axiom,
    ((![E : real]: ((ord_less_real @ zero_zero_real @ E) => (?[N2 : nat]: (![N : nat]: ((ord_less_eq_nat @ N2 @ N) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N)) @ z)) @ E)))))))). % fz(2)
thf(fact_10_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_11__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_12__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_13_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_14_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_15_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_16__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,
    ((?[N3 : 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 @ N3))))). % \<open>\<exists>n. 2 / \<bar>cmod (poly p z) - - s\<bar> < real n\<close>
thf(fact_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062N2_O_A2_A_P_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_060_Areal_AN2_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![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))))))))). % \<open>\<And>thesis. (\<And>N2. 2 / \<bar>cmod (poly p z) - - s\<bar> < real N2 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_18_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_19_norm__neg__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (uminus1204672759omplex @ (numera632737353omplex @ W))) = (numeral_numeral_real @ W))))). % norm_neg_numeral
thf(fact_20_norm__numeral, axiom,
    ((![W : num]: ((real_V646646907m_real @ (numeral_numeral_real @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_21_norm__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (numera632737353omplex @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_22_abs__neg__numeral, axiom,
    ((![N4 : num]: ((abs_abs_real @ (uminus_uminus_real @ (numeral_numeral_real @ N4))) = (numeral_numeral_real @ N4))))). % abs_neg_numeral
thf(fact_23_diff__minus__eq__add, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ A @ (uminus1204672759omplex @ B)) = (plus_plus_complex @ A @ B))))). % diff_minus_eq_add
thf(fact_24_diff__minus__eq__add, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ A @ (uminus_uminus_real @ B)) = (plus_plus_real @ A @ B))))). % diff_minus_eq_add
thf(fact_25_uminus__add__conv__diff, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ B) = (minus_minus_complex @ B @ A))))). % uminus_add_conv_diff
thf(fact_26_uminus__add__conv__diff, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ B) = (minus_minus_real @ B @ A))))). % uminus_add_conv_diff
thf(fact_27_semiring__norm_I168_J, axiom,
    ((![V : num, W : num, Y2 : real]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ V)) @ (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ W)) @ Y2)) = (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ V @ W))) @ Y2))))). % semiring_norm(168)
thf(fact_28_add__right__cancel, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_29_add__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_30_numeral__eq__iff, axiom,
    ((![M : num, N4 : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N4)) = (M = N4))))). % numeral_eq_iff
thf(fact_31_semiring__norm_I87_J, axiom,
    ((![M : num, N4 : num]: (((bit0 @ M) = (bit0 @ N4)) = (M = N4))))). % semiring_norm(87)
thf(fact_32_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_33_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_34_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_35_le__zero__eq, axiom,
    ((![N4 : nat]: ((ord_less_eq_nat @ N4 @ zero_zero_nat) = (N4 = zero_zero_nat))))). % le_zero_eq
thf(fact_36_zero__eq__add__iff__both__eq__0, axiom,
    ((![X3 : nat, Y2 : nat]: ((zero_zero_nat = (plus_plus_nat @ X3 @ Y2)) = (((X3 = zero_zero_nat)) & ((Y2 = zero_zero_nat))))))). % zero_eq_add_iff_both_eq_0
thf(fact_37_add__eq__0__iff__both__eq__0, axiom,
    ((![X3 : nat, Y2 : nat]: (((plus_plus_nat @ X3 @ Y2) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y2 = zero_zero_nat))))))). % add_eq_0_iff_both_eq_0
thf(fact_38_add__cancel__right__right, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat))))). % add_cancel_right_right
thf(fact_39_add__cancel__right__right, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real))))). % add_cancel_right_right
thf(fact_40_add__cancel__right__left, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat))))). % add_cancel_right_left
thf(fact_41_add__cancel__right__left, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real))))). % add_cancel_right_left
thf(fact_42_add__cancel__left__right, axiom,
    ((![A : nat, B : nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat))))). % add_cancel_left_right
thf(fact_43_add__cancel__left__right, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real))))). % add_cancel_left_right
thf(fact_44_add__cancel__left__left, axiom,
    ((![B : nat, A : nat]: (((plus_plus_nat @ B @ A) = A) = (B = zero_zero_nat))))). % add_cancel_left_left
thf(fact_45_add__cancel__left__left, axiom,
    ((![B : real, A : real]: (((plus_plus_real @ B @ A) = A) = (B = zero_zero_real))))). % add_cancel_left_left
thf(fact_46_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_47_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_48_add_Oright__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.right_neutral
thf(fact_49_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_50_add_Oleft__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % add.left_neutral
thf(fact_51_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_52_add__le__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_53_add__le__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_left
thf(fact_54_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_55_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_56_diff__zero, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_zero
thf(fact_57_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_58_diff__0__right, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_0_right
thf(fact_59_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_60_diff__self, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % diff_self
thf(fact_61_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_62_numeral__le__iff, axiom,
    ((![M : num, N4 : num]: ((ord_less_eq_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N4)) = (ord_less_eq_num @ M @ N4))))). % numeral_le_iff
thf(fact_63_numeral__le__iff, axiom,
    ((![M : num, N4 : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N4)) = (ord_less_eq_num @ M @ N4))))). % numeral_le_iff
thf(fact_64_add__less__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_nat @ A @ B))))). % add_less_cancel_right
thf(fact_65_add__less__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_real @ A @ B))))). % add_less_cancel_right
thf(fact_66_add__less__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ B))))). % add_less_cancel_left
thf(fact_67_add__less__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_real @ A @ B))))). % add_less_cancel_left
thf(fact_68_numeral__less__iff, axiom,
    ((![M : num, N4 : num]: ((ord_less_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N4)) = (ord_less_num @ M @ N4))))). % numeral_less_iff
thf(fact_69_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_70_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_71_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_72_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_73_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_74_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_75_add__diff__cancel__right_H, axiom,
    ((![A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_76_add__diff__cancel__right_H, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_77_add__diff__cancel__right_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_78_add__diff__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (minus_minus_nat @ A @ B))))). % add_diff_cancel_right
thf(fact_79_add__diff__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ C) @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_right
thf(fact_80_add__diff__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_right
thf(fact_81_add__diff__cancel__left_H, axiom,
    ((![A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_82_add__diff__cancel__left_H, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_83_add__diff__cancel__left_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_84_add__diff__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ B))))). % add_diff_cancel_left
thf(fact_85_add__diff__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ C @ A) @ (plus_plus_complex @ C @ B)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_left
thf(fact_86_add__diff__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_left
thf(fact_87_diff__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_88_diff__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_89_add__diff__cancel, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_90_add__diff__cancel, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_91_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_92_minus__add__distrib, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)))))). % minus_add_distrib
thf(fact_93_minus__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ (plus_plus_real @ A @ B)) = B)))). % minus_add_cancel
thf(fact_94_add__minus__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ A @ (plus_plus_real @ (uminus_uminus_real @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_95_neg__numeral__eq__iff, axiom,
    ((![M : num, N4 : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N4))) = (M = N4))))). % neg_numeral_eq_iff
thf(fact_96_minus__diff__eq, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ B @ A))))). % minus_diff_eq
thf(fact_97_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_98_semiring__norm_I83_J, axiom,
    ((![N4 : num]: (~ ((one = (bit0 @ N4))))))). % semiring_norm(83)
thf(fact_99_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_100_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_101_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_102_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_103_of__nat__numeral, axiom,
    ((![N4 : num]: ((semiri2110766477t_real @ (numeral_numeral_nat @ N4)) = (numeral_numeral_real @ N4))))). % of_nat_numeral
thf(fact_104_abs__add__abs, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_add_abs
thf(fact_105_abs__numeral, axiom,
    ((![N4 : num]: ((abs_abs_real @ (numeral_numeral_real @ N4)) = (numeral_numeral_real @ N4))))). % abs_numeral
thf(fact_106_abs__minus__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus_cancel
thf(fact_107_norm__minus__cancel, axiom,
    ((![X3 : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X3)) = (real_V646646907m_real @ X3))))). % norm_minus_cancel
thf(fact_108_norm__minus__cancel, axiom,
    ((![X3 : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X3)) = (real_V638595069omplex @ X3))))). % norm_minus_cancel
thf(fact_109_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_110__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062f_Az_O_A_092_060lbrakk_062strict__mono_Af_059_A_092_060forall_062e_0620_O_A_092_060exists_062N_O_A_092_060forall_062n_092_060ge_062N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ae_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![F : nat > nat]: ((order_769474267at_nat @ F) => (![Z2 : complex]: (~ ((![E : real]: ((ord_less_real @ zero_zero_real @ E) => (?[N2 : nat]: (![N : nat]: ((ord_less_eq_nat @ N2 @ N) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (F @ N)) @ Z2)) @ E))))))))))))))). % \<open>\<And>thesis. (\<And>f z. \<lbrakk>strict_mono f; \<forall>e>0. \<exists>N. \<forall>n\<ge>N. cmod (g (f n) - z) < e\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_111__092_060open_062_092_060exists_062f_Az_O_Astrict__mono_Af_A_092_060and_062_A_I_092_060forall_062e_0620_O_A_092_060exists_062N_O_A_092_060forall_062n_092_060ge_062N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ae_J_092_060close_062, axiom,
    ((?[F : nat > nat, Z2 : complex]: ((order_769474267at_nat @ F) & (![E : real]: ((ord_less_real @ zero_zero_real @ E) => (?[N2 : nat]: (![N : nat]: ((ord_less_eq_nat @ N2 @ N) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (F @ N)) @ Z2)) @ E)))))))))). % \<open>\<exists>f z. strict_mono f \<and> (\<forall>e>0. \<exists>N. \<forall>n\<ge>N. cmod (g (f n) - z) < e)\<close>
thf(fact_112_semiring__norm_I6_J, axiom,
    ((![M : num, N4 : num]: ((plus_plus_num @ (bit0 @ M) @ (bit0 @ N4)) = (bit0 @ (plus_plus_num @ M @ N4)))))). % semiring_norm(6)
thf(fact_113_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_114_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_115_le__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel2
thf(fact_116_le__add__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_eq_nat @ zero_zero_nat @ B))))). % le_add_same_cancel2
thf(fact_117_le__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel1
thf(fact_118_le__add__same__cancel1, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_eq_nat @ zero_zero_nat @ B))))). % le_add_same_cancel1
thf(fact_119_add__le__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel2
thf(fact_120_add__le__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat))))). % add_le_same_cancel2
thf(fact_121_add__le__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel1
thf(fact_122_add__le__same__cancel1, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat))))). % add_le_same_cancel1
thf(fact_123_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_124_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_125_less__add__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B))))). % less_add_same_cancel2
thf(fact_126_less__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel2
thf(fact_127_less__add__same__cancel1, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B))))). % less_add_same_cancel1
thf(fact_128_less__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel1
thf(fact_129_add__less__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat))))). % add_less_same_cancel2
thf(fact_130_add__less__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel2
thf(fact_131_add__less__same__cancel1, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ B) = (ord_less_nat @ A @ zero_zero_nat))))). % add_less_same_cancel1
thf(fact_132_add__less__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel1
thf(fact_133_diff__ge__0__iff__ge, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_134_diff__gt__0__iff__gt, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_135_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_136_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_137_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_138_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_139_diff__add__zero, axiom,
    ((![A : nat, B : nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat)))). % diff_add_zero
thf(fact_140_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_141_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_142_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_143_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_144_add_Oright__inverse, axiom,
    ((![A : real]: ((plus_plus_real @ A @ (uminus_uminus_real @ A)) = zero_zero_real)))). % add.right_inverse
thf(fact_145_add_Oleft__inverse, axiom,
    ((![A : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real)))). % add.left_inverse
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 : real]: ((minus_minus_real @ zero_zero_real @ A) = (uminus_uminus_real @ A))))). % diff_0
thf(fact_148_neg__numeral__le__iff, axiom,
    ((![M : num, N4 : num]: ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N4))) = (ord_less_eq_num @ N4 @ M))))). % neg_numeral_le_iff
thf(fact_149_neg__numeral__less__iff, axiom,
    ((![M : num, N4 : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N4))) = (ord_less_num @ N4 @ M))))). % neg_numeral_less_iff
thf(fact_150_abs__le__zero__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real))))). % abs_le_zero_iff
thf(fact_151_abs__le__self__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % abs_le_self_iff
thf(fact_152_abs__of__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_nonneg
thf(fact_153_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N4 : num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N4))) = (uminus_uminus_real @ (plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N4))))))). % add_neg_numeral_simps(3)
thf(fact_154_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_155_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_156_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_157_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_158_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_159_numeral__plus__numeral, axiom,
    ((![M : num, N4 : num]: ((plus_plus_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N4)) = (numeral_numeral_nat @ (plus_plus_num @ M @ N4)))))). % numeral_plus_numeral
thf(fact_160_numeral__plus__numeral, axiom,
    ((![M : num, N4 : num]: ((plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N4)) = (numeral_numeral_real @ (plus_plus_num @ M @ N4)))))). % numeral_plus_numeral
thf(fact_161_add__numeral__left, axiom,
    ((![V : num, W : num, Z3 : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ (numeral_numeral_nat @ W) @ Z3)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ V @ W)) @ Z3))))). % add_numeral_left
thf(fact_162_add__numeral__left, axiom,
    ((![V : num, W : num, Z3 : real]: ((plus_plus_real @ (numeral_numeral_real @ V) @ (plus_plus_real @ (numeral_numeral_real @ W) @ Z3)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ V @ W)) @ Z3))))). % add_numeral_left
thf(fact_163_norm__of__nat, axiom,
    ((![N4 : nat]: ((real_V646646907m_real @ (semiri2110766477t_real @ N4)) = (semiri2110766477t_real @ N4))))). % norm_of_nat
thf(fact_164_norm__of__nat, axiom,
    ((![N4 : nat]: ((real_V638595069omplex @ (semiri356525583omplex @ N4)) = (semiri2110766477t_real @ N4))))). % norm_of_nat
thf(fact_165_semiring__norm_I2_J, axiom,
    (((plus_plus_num @ one @ one) = (bit0 @ one)))). % semiring_norm(2)
thf(fact_166_abs__of__nonpos, axiom,
    ((![A : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((abs_abs_real @ A) = (uminus_uminus_real @ A)))))). % abs_of_nonpos
thf(fact_167_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_168_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_169_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N4 : num]: ((minus_minus_complex @ (numera632737353omplex @ M) @ (uminus1204672759omplex @ (numera632737353omplex @ N4))) = (numera632737353omplex @ (plus_plus_num @ M @ N4)))))). % diff_numeral_simps(2)
thf(fact_170_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N4 : num]: ((minus_minus_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N4))) = (numeral_numeral_real @ (plus_plus_num @ M @ N4)))))). % diff_numeral_simps(2)
thf(fact_171_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N4 : num]: ((minus_minus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (numera632737353omplex @ N4)) = (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ M @ N4))))))). % diff_numeral_simps(3)
thf(fact_172_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N4 : num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N4)) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ M @ N4))))))). % diff_numeral_simps(3)
thf(fact_173_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_174_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat))). % le_numeral_extra(3)
thf(fact_175_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_176_zero__le, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X3)))). % zero_le
thf(fact_177_add__nonpos__eq__0__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ Y2 @ zero_zero_real) => (((plus_plus_real @ X3 @ Y2) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y2 = zero_zero_real))))))))). % add_nonpos_eq_0_iff
thf(fact_178_add__nonpos__eq__0__iff, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ zero_zero_nat) => ((ord_less_eq_nat @ Y2 @ zero_zero_nat) => (((plus_plus_nat @ X3 @ Y2) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y2 = zero_zero_nat))))))))). % add_nonpos_eq_0_iff
thf(fact_179_add__nonneg__eq__0__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y2) => (((plus_plus_real @ X3 @ Y2) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y2 = zero_zero_real))))))))). % add_nonneg_eq_0_iff
thf(fact_180_add__nonneg__eq__0__iff, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ zero_zero_nat @ X3) => ((ord_less_eq_nat @ zero_zero_nat @ Y2) => (((plus_plus_nat @ X3 @ Y2) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y2 = zero_zero_nat))))))))). % add_nonneg_eq_0_iff
thf(fact_181_add__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_nonpos
thf(fact_182_add__nonpos__nonpos, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_nonpos_nonpos
thf(fact_183_add__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_184_add__nonneg__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_nonneg_nonneg
thf(fact_185_add__increasing2, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing2
thf(fact_186_add__increasing2, axiom,
    ((![C : nat, B : nat, A : nat]: ((ord_less_eq_nat @ zero_zero_nat @ C) => ((ord_less_eq_nat @ B @ A) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C))))))). % add_increasing2
thf(fact_187_add__decreasing2, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ C @ zero_zero_real) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_188_add__decreasing2, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ C @ zero_zero_nat) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ B)))))). % add_decreasing2
thf(fact_189_add__increasing, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing
thf(fact_190_add__increasing, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C))))))). % add_increasing
thf(fact_191_add__decreasing, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_192_add__decreasing, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ B)))))). % add_decreasing
thf(fact_193_not__numeral__le__zero, axiom,
    ((![N4 : num]: (~ ((ord_less_eq_real @ (numeral_numeral_real @ N4) @ zero_zero_real)))))). % not_numeral_le_zero
thf(fact_194_not__numeral__le__zero, axiom,
    ((![N4 : num]: (~ ((ord_less_eq_nat @ (numeral_numeral_nat @ N4) @ zero_zero_nat)))))). % not_numeral_le_zero
thf(fact_195_zero__le__numeral, axiom,
    ((![N4 : num]: (ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ N4))))). % zero_le_numeral
thf(fact_196_zero__le__numeral, axiom,
    ((![N4 : num]: (ord_less_eq_nat @ zero_zero_nat @ (numeral_numeral_nat @ N4))))). % zero_le_numeral
thf(fact_197_le__iff__diff__le__0, axiom,
    ((ord_less_eq_real = (^[A2 : real]: (^[B2 : real]: (ord_less_eq_real @ (minus_minus_real @ A2 @ B2) @ zero_zero_real)))))). % le_iff_diff_le_0
thf(fact_198_abs__ge__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A))))). % abs_ge_zero
thf(fact_199_add__One__commute, axiom,
    ((![N4 : num]: ((plus_plus_num @ one @ N4) = (plus_plus_num @ N4 @ one))))). % add_One_commute

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2)))) @ (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)))))).
