% 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_419__5371618_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:59.025

% Could-be-implicit typings (3)
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (21)
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__Real__Oreal, type,
    minus_minus_real : 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_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $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__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_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Real__Oreal, type,
    order_952716343t_real : (nat > real) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Nat__Onat, type,
    order_297469111al_nat : (real > nat) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Real__Oreal, type,
    order_1818878995l_real : (real > real) > $o).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_v_d____, type,
    d : real).
thf(sy_v_f____, type,
    f : nat > nat).
thf(sy_v_g____, type,
    g : nat > complex).
thf(sy_v_r, type,
    r : real).
thf(sy_v_thesis____, type,
    thesis : $o).
thf(sy_v_z____, type,
    z : complex).

% Relevant facts (219)
thf(fact_0_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_1_fz_I2_J, axiom,
    ((![E : real]: ((ord_less_real @ zero_zero_real @ E) => (?[N : nat]: (![N2 : nat]: ((ord_less_eq_nat @ N @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N2)) @ z)) @ E)))))))). % fz(2)
thf(fact_2_fz_I1_J, axiom,
    ((order_769474267at_nat @ f))). % fz(1)
thf(fact_3_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_4__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) => (?[N : nat]: (![N2 : nat]: ((ord_less_eq_nat @ N @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (F @ N2)) @ 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_5__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) => (?[N : nat]: (![N2 : nat]: ((ord_less_eq_nat @ N @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (F @ N2)) @ 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_6_order__refl, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ X3 @ X3)))). % order_refl
thf(fact_7_order__refl, axiom,
    ((![X3 : real]: (ord_less_eq_real @ X3 @ X3)))). % order_refl
thf(fact_8_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_9_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_10_diff__strict__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ D @ C) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_strict_mono
thf(fact_11_diff__eq__diff__less, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_real @ A @ B) = (ord_less_real @ C @ D)))))). % diff_eq_diff_less
thf(fact_12_diff__strict__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => (ord_less_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_strict_left_mono
thf(fact_13_diff__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_strict_right_mono
thf(fact_14_diff__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ D @ C) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_mono
thf(fact_15_diff__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_left_mono
thf(fact_16_diff__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_right_mono
thf(fact_17_True, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % True
thf(fact_18_le__zero__eq, axiom,
    ((![N3 : nat]: ((ord_less_eq_nat @ N3 @ zero_zero_nat) = (N3 = zero_zero_nat))))). % le_zero_eq
thf(fact_19_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_20_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_21_diff__zero, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_zero
thf(fact_22_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_23_diff__0__right, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_0_right
thf(fact_24_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_25_diff__self, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % diff_self
thf(fact_26_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_27_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_28_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_29_norm__le__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X3) @ zero_zero_real) = (X3 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_30_norm__le__zero__iff, axiom,
    ((![X3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X3) @ zero_zero_real) = (X3 = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_31_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_32_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_33_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_34_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_35_g_I1_J, axiom,
    ((![N2 : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (g @ N2)) @ r)))). % g(1)
thf(fact_36_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_37_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_38_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_39_strict__mono__eq, axiom,
    ((![F2 : nat > nat, X3 : nat, Y2 : nat]: ((order_769474267at_nat @ F2) => (((F2 @ X3) = (F2 @ Y2)) = (X3 = Y2)))))). % strict_mono_eq
thf(fact_40_norm__ge__zero, axiom,
    ((![X3 : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X3))))). % norm_ge_zero
thf(fact_41_strict__mono__less__eq, axiom,
    ((![F2 : real > nat, X3 : real, Y2 : real]: ((order_297469111al_nat @ F2) => ((ord_less_eq_nat @ (F2 @ X3) @ (F2 @ Y2)) = (ord_less_eq_real @ X3 @ Y2)))))). % strict_mono_less_eq
thf(fact_42_strict__mono__less__eq, axiom,
    ((![F2 : nat > real, X3 : nat, Y2 : nat]: ((order_952716343t_real @ F2) => ((ord_less_eq_real @ (F2 @ X3) @ (F2 @ Y2)) = (ord_less_eq_nat @ X3 @ Y2)))))). % strict_mono_less_eq
thf(fact_43_strict__mono__less__eq, axiom,
    ((![F2 : real > real, X3 : real, Y2 : real]: ((order_1818878995l_real @ F2) => ((ord_less_eq_real @ (F2 @ X3) @ (F2 @ Y2)) = (ord_less_eq_real @ X3 @ Y2)))))). % strict_mono_less_eq
thf(fact_44_strict__mono__less__eq, axiom,
    ((![F2 : nat > nat, X3 : nat, Y2 : nat]: ((order_769474267at_nat @ F2) => ((ord_less_eq_nat @ (F2 @ X3) @ (F2 @ Y2)) = (ord_less_eq_nat @ X3 @ Y2)))))). % strict_mono_less_eq
thf(fact_45_strict__mono__less, axiom,
    ((![F2 : real > real, X3 : real, Y2 : real]: ((order_1818878995l_real @ F2) => ((ord_less_real @ (F2 @ X3) @ (F2 @ Y2)) = (ord_less_real @ X3 @ Y2)))))). % strict_mono_less
thf(fact_46_strict__mono__less, axiom,
    ((![F2 : nat > nat, X3 : nat, Y2 : nat]: ((order_769474267at_nat @ F2) => ((ord_less_nat @ (F2 @ X3) @ (F2 @ Y2)) = (ord_less_nat @ X3 @ Y2)))))). % strict_mono_less
thf(fact_47_strict__mono__def, axiom,
    ((order_1818878995l_real = (^[F3 : real > real]: (![X2 : real]: (![Y3 : real]: (((ord_less_real @ X2 @ Y3)) => ((ord_less_real @ (F3 @ X2) @ (F3 @ Y3)))))))))). % strict_mono_def
thf(fact_48_strict__mono__def, axiom,
    ((order_769474267at_nat = (^[F3 : nat > nat]: (![X2 : nat]: (![Y3 : nat]: (((ord_less_nat @ X2 @ Y3)) => ((ord_less_nat @ (F3 @ X2) @ (F3 @ Y3)))))))))). % strict_mono_def
thf(fact_49_strict__monoI, axiom,
    ((![F2 : real > real]: ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F2 @ X) @ (F2 @ Y4)))) => (order_1818878995l_real @ F2))))). % strict_monoI
thf(fact_50_strict__monoI, axiom,
    ((![F2 : nat > nat]: ((![X : nat, Y4 : nat]: ((ord_less_nat @ X @ Y4) => (ord_less_nat @ (F2 @ X) @ (F2 @ Y4)))) => (order_769474267at_nat @ F2))))). % strict_monoI
thf(fact_51_strict__monoD, axiom,
    ((![F2 : real > real, X3 : real, Y2 : real]: ((order_1818878995l_real @ F2) => ((ord_less_real @ X3 @ Y2) => (ord_less_real @ (F2 @ X3) @ (F2 @ Y2))))))). % strict_monoD
thf(fact_52_strict__monoD, axiom,
    ((![F2 : nat > nat, X3 : nat, Y2 : nat]: ((order_769474267at_nat @ F2) => ((ord_less_nat @ X3 @ Y2) => (ord_less_nat @ (F2 @ X3) @ (F2 @ Y2))))))). % strict_monoD
thf(fact_53_norm__triangle__ineq2, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)) @ (real_V646646907m_real @ (minus_minus_real @ A @ B)))))). % norm_triangle_ineq2
thf(fact_54_norm__triangle__ineq2, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)) @ (real_V638595069omplex @ (minus_minus_complex @ A @ B)))))). % norm_triangle_ineq2
thf(fact_55_zero__le, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X3)))). % zero_le
thf(fact_56_eq__iff__diff__eq__0, axiom,
    (((^[Y5 : complex]: (^[Z3 : complex]: (Y5 = Z3))) = (^[A2 : complex]: (^[B2 : complex]: ((minus_minus_complex @ A2 @ B2) = zero_zero_complex)))))). % eq_iff_diff_eq_0
thf(fact_57_eq__iff__diff__eq__0, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[A2 : real]: (^[B2 : real]: ((minus_minus_real @ A2 @ B2) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_58_Bolzano__Weierstrass__complex__disc, axiom,
    ((![S2 : nat > complex, R : real]: ((![N4 : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (S2 @ N4)) @ R)) => (?[F : nat > nat, Z2 : complex]: ((order_769474267at_nat @ F) & (![E : real]: ((ord_less_real @ zero_zero_real @ E) => (?[N : nat]: (![N2 : nat]: ((ord_less_eq_nat @ N @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (S2 @ (F @ N2)) @ Z2)) @ E)))))))))))). % Bolzano_Weierstrass_complex_disc
thf(fact_59_dual__order_Oantisym, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_60_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_61_dual__order_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z3 : nat]: (Y5 = Z3))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A2)) & ((ord_less_eq_nat @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_62_dual__order_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A2)) & ((ord_less_eq_real @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_63_dual__order_Otrans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))))). % dual_order.trans
thf(fact_64_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_65_linorder__wlog, axiom,
    ((![P : nat > nat > $o, A : nat, B : nat]: ((![A3 : nat, B3 : nat]: ((ord_less_eq_nat @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : nat, B3 : nat]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_66_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A3 : real, B3 : real]: ((ord_less_eq_real @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : real, B3 : real]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_67_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_68_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_69_order__trans, axiom,
    ((![X3 : nat, Y2 : nat, Z4 : nat]: ((ord_less_eq_nat @ X3 @ Y2) => ((ord_less_eq_nat @ Y2 @ Z4) => (ord_less_eq_nat @ X3 @ Z4)))))). % order_trans
thf(fact_70_order__trans, axiom,
    ((![X3 : real, Y2 : real, Z4 : real]: ((ord_less_eq_real @ X3 @ Y2) => ((ord_less_eq_real @ Y2 @ Z4) => (ord_less_eq_real @ X3 @ Z4)))))). % order_trans
thf(fact_71_order__class_Oorder_Oantisym, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_72_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_73_ord__le__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C)))))). % ord_le_eq_trans
thf(fact_74_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_75_ord__eq__le__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % ord_eq_le_trans
thf(fact_76_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_77_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z3 : nat]: (Y5 = Z3))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A2 @ B2)) & ((ord_less_eq_nat @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_78_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ A2 @ B2)) & ((ord_less_eq_real @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_79_antisym__conv, axiom,
    ((![Y2 : nat, X3 : nat]: ((ord_less_eq_nat @ Y2 @ X3) => ((ord_less_eq_nat @ X3 @ Y2) = (X3 = Y2)))))). % antisym_conv
thf(fact_80_antisym__conv, axiom,
    ((![Y2 : real, X3 : real]: ((ord_less_eq_real @ Y2 @ X3) => ((ord_less_eq_real @ X3 @ Y2) = (X3 = Y2)))))). % antisym_conv
thf(fact_81_le__cases3, axiom,
    ((![X3 : nat, Y2 : nat, Z4 : nat]: (((ord_less_eq_nat @ X3 @ Y2) => (~ ((ord_less_eq_nat @ Y2 @ Z4)))) => (((ord_less_eq_nat @ Y2 @ X3) => (~ ((ord_less_eq_nat @ X3 @ Z4)))) => (((ord_less_eq_nat @ X3 @ Z4) => (~ ((ord_less_eq_nat @ Z4 @ Y2)))) => (((ord_less_eq_nat @ Z4 @ Y2) => (~ ((ord_less_eq_nat @ Y2 @ X3)))) => (((ord_less_eq_nat @ Y2 @ Z4) => (~ ((ord_less_eq_nat @ Z4 @ X3)))) => (~ (((ord_less_eq_nat @ Z4 @ X3) => (~ ((ord_less_eq_nat @ X3 @ Y2)))))))))))))). % le_cases3
thf(fact_82_le__cases3, axiom,
    ((![X3 : real, Y2 : real, Z4 : real]: (((ord_less_eq_real @ X3 @ Y2) => (~ ((ord_less_eq_real @ Y2 @ Z4)))) => (((ord_less_eq_real @ Y2 @ X3) => (~ ((ord_less_eq_real @ X3 @ Z4)))) => (((ord_less_eq_real @ X3 @ Z4) => (~ ((ord_less_eq_real @ Z4 @ Y2)))) => (((ord_less_eq_real @ Z4 @ Y2) => (~ ((ord_less_eq_real @ Y2 @ X3)))) => (((ord_less_eq_real @ Y2 @ Z4) => (~ ((ord_less_eq_real @ Z4 @ X3)))) => (~ (((ord_less_eq_real @ Z4 @ X3) => (~ ((ord_less_eq_real @ X3 @ Y2)))))))))))))). % le_cases3
thf(fact_83_order_Otrans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % order.trans
thf(fact_84_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_85_le__cases, axiom,
    ((![X3 : nat, Y2 : nat]: ((~ ((ord_less_eq_nat @ X3 @ Y2))) => (ord_less_eq_nat @ Y2 @ X3))))). % le_cases
thf(fact_86_le__cases, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_eq_real @ X3 @ Y2))) => (ord_less_eq_real @ Y2 @ X3))))). % le_cases
thf(fact_87_eq__refl, axiom,
    ((![X3 : nat, Y2 : nat]: ((X3 = Y2) => (ord_less_eq_nat @ X3 @ Y2))))). % eq_refl
thf(fact_88_eq__refl, axiom,
    ((![X3 : real, Y2 : real]: ((X3 = Y2) => (ord_less_eq_real @ X3 @ Y2))))). % eq_refl
thf(fact_89_linear, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ Y2) | (ord_less_eq_nat @ Y2 @ X3))))). % linear
thf(fact_90_linear, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) | (ord_less_eq_real @ Y2 @ X3))))). % linear
thf(fact_91_antisym, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ Y2) => ((ord_less_eq_nat @ Y2 @ X3) => (X3 = Y2)))))). % antisym
thf(fact_92_antisym, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => ((ord_less_eq_real @ Y2 @ X3) => (X3 = Y2)))))). % antisym
thf(fact_93_eq__iff, axiom,
    (((^[Y5 : nat]: (^[Z3 : nat]: (Y5 = Z3))) = (^[X2 : nat]: (^[Y3 : nat]: (((ord_less_eq_nat @ X2 @ Y3)) & ((ord_less_eq_nat @ Y3 @ X2)))))))). % eq_iff
thf(fact_94_eq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[X2 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X2 @ Y3)) & ((ord_less_eq_real @ Y3 @ X2)))))))). % eq_iff
thf(fact_95_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (((F2 @ B) = C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_96_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > real, C : real]: ((ord_less_eq_nat @ A @ B) => (((F2 @ B) = C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_97_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F2 : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => (((F2 @ B) = C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_98_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F2 @ B) = C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_99_ord__eq__le__subst, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((A = (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_100_ord__eq__le__subst, axiom,
    ((![A : real, F2 : nat > real, B : nat, C : nat]: ((A = (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_101_ord__eq__le__subst, axiom,
    ((![A : nat, F2 : real > nat, B : real, C : real]: ((A = (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_102_ord__eq__le__subst, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((A = (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_103_order__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_104_order__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > real, C : real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (F2 @ B) @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_105_order__subst2, axiom,
    ((![A : real, B : real, F2 : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_106_order__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F2 @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_107_order__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_108_order__subst1, axiom,
    ((![A : nat, F2 : real > nat, B : real, C : real]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_109_order__subst1, axiom,
    ((![A : real, F2 : nat > real, B : nat, C : nat]: ((ord_less_eq_real @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_110_order__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_111_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_112_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_113_not__less__iff__gr__or__eq, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_real @ X3 @ Y2))) = (((ord_less_real @ Y2 @ X3)) | ((X3 = Y2))))))). % not_less_iff_gr_or_eq
thf(fact_114_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_115_linorder__less__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A3 : real, B3 : real]: ((ord_less_real @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : real]: (P @ A3 @ A3)) => ((![A3 : real, B3 : real]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B))))))). % linorder_less_wlog
thf(fact_116_less__imp__not__less, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((ord_less_real @ Y2 @ X3))))))). % less_imp_not_less
thf(fact_117_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_118_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_119_linorder__cases, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_real @ X3 @ Y2))) => ((~ ((X3 = Y2))) => (ord_less_real @ Y2 @ X3)))))). % linorder_cases
thf(fact_120_less__imp__triv, axiom,
    ((![X3 : real, Y2 : real, P : $o]: ((ord_less_real @ X3 @ Y2) => ((ord_less_real @ Y2 @ X3) => P))))). % less_imp_triv
thf(fact_121_less__imp__not__eq2, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((Y2 = X3))))))). % less_imp_not_eq2
thf(fact_122_antisym__conv3, axiom,
    ((![Y2 : real, X3 : real]: ((~ ((ord_less_real @ Y2 @ X3))) => ((~ ((ord_less_real @ X3 @ Y2))) = (X3 = Y2)))))). % antisym_conv3
thf(fact_123_less__not__sym, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((ord_less_real @ Y2 @ X3))))))). % less_not_sym
thf(fact_124_less__imp__not__eq, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((X3 = Y2))))))). % less_imp_not_eq
thf(fact_125_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_126_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_127_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_128_less__irrefl, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ X3 @ X3)))))). % less_irrefl
thf(fact_129_less__linear, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) | ((X3 = Y2) | (ord_less_real @ Y2 @ X3)))))). % less_linear
thf(fact_130_less__trans, axiom,
    ((![X3 : real, Y2 : real, Z4 : real]: ((ord_less_real @ X3 @ Y2) => ((ord_less_real @ Y2 @ Z4) => (ord_less_real @ X3 @ Z4)))))). % less_trans
thf(fact_131_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_132_less__asym, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((ord_less_real @ Y2 @ X3))))))). % less_asym
thf(fact_133_less__imp__neq, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((X3 = Y2))))))). % less_imp_neq
thf(fact_134_dense, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (?[Z2 : real]: ((ord_less_real @ X3 @ Z2) & (ord_less_real @ Z2 @ Y2))))))). % dense
thf(fact_135_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_136_neq__iff, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) = (((ord_less_real @ X3 @ Y2)) | ((ord_less_real @ Y2 @ X3))))))). % neq_iff
thf(fact_137_neqE, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) => ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_real @ Y2 @ X3)))))). % neqE
thf(fact_138_gt__ex, axiom,
    ((![X3 : real]: (?[X_12 : real]: (ord_less_real @ X3 @ X_12))))). % gt_ex
thf(fact_139_lt__ex, axiom,
    ((![X3 : real]: (?[Y4 : real]: (ord_less_real @ Y4 @ X3))))). % lt_ex
thf(fact_140_order__less__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F2 @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_less_subst2
thf(fact_141_order__less__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_real @ A @ (F2 @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_less_subst1
thf(fact_142_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_real @ A @ B) => (((F2 @ B) = C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ (F2 @ A) @ C))))))). % ord_less_eq_subst
thf(fact_143_ord__eq__less__subst, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((A = (F2 @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ A @ (F2 @ C)))))))). % ord_eq_less_subst
thf(fact_144_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ C) @ B) = (minus_minus_complex @ (minus_minus_complex @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_145_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (minus_minus_real @ A @ C) @ B) = (minus_minus_real @ (minus_minus_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_146_diff__eq__diff__eq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: (((minus_minus_complex @ A @ B) = (minus_minus_complex @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_147_diff__eq__diff__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_148_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_149_less__iff__diff__less__0, axiom,
    ((ord_less_real = (^[A2 : real]: (^[B2 : real]: (ord_less_real @ (minus_minus_real @ A2 @ B2) @ zero_zero_real)))))). % less_iff_diff_less_0
thf(fact_150_norm__not__less__zero, axiom,
    ((![X3 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_151_order_Onot__eq__order__implies__strict, axiom,
    ((![A : nat, B : nat]: ((~ ((A = B))) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B)))))). % order.not_eq_order_implies_strict
thf(fact_152_order_Onot__eq__order__implies__strict, axiom,
    ((![A : real, B : real]: ((~ ((A = B))) => ((ord_less_eq_real @ A @ B) => (ord_less_real @ A @ B)))))). % order.not_eq_order_implies_strict
thf(fact_153_dual__order_Ostrict__implies__order, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (ord_less_eq_nat @ B @ A))))). % dual_order.strict_implies_order
thf(fact_154_dual__order_Ostrict__implies__order, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (ord_less_eq_real @ B @ A))))). % dual_order.strict_implies_order
thf(fact_155_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_nat = (^[B2 : nat]: (^[A2 : nat]: (((ord_less_eq_nat @ B2 @ A2)) & ((~ ((A2 = B2)))))))))). % dual_order.strict_iff_order
thf(fact_156_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[B2 : real]: (^[A2 : real]: (((ord_less_eq_real @ B2 @ A2)) & ((~ ((A2 = B2)))))))))). % dual_order.strict_iff_order
thf(fact_157_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_nat = (^[B2 : nat]: (^[A2 : nat]: (((ord_less_nat @ B2 @ A2)) | ((A2 = B2)))))))). % dual_order.order_iff_strict
thf(fact_158_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[B2 : real]: (^[A2 : real]: (((ord_less_real @ B2 @ A2)) | ((A2 = B2)))))))). % dual_order.order_iff_strict
thf(fact_159_order_Ostrict__implies__order, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B))))). % order.strict_implies_order
thf(fact_160_order_Ostrict__implies__order, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B))))). % order.strict_implies_order
thf(fact_161_dense__le__bounded, axiom,
    ((![X3 : real, Y2 : real, Z4 : real]: ((ord_less_real @ X3 @ Y2) => ((![W : real]: ((ord_less_real @ X3 @ W) => ((ord_less_real @ W @ Y2) => (ord_less_eq_real @ W @ Z4)))) => (ord_less_eq_real @ Y2 @ Z4)))))). % dense_le_bounded
thf(fact_162_dense__ge__bounded, axiom,
    ((![Z4 : real, X3 : real, Y2 : real]: ((ord_less_real @ Z4 @ X3) => ((![W : real]: ((ord_less_real @ Z4 @ W) => ((ord_less_real @ W @ X3) => (ord_less_eq_real @ Y2 @ W)))) => (ord_less_eq_real @ Y2 @ Z4)))))). % dense_ge_bounded
thf(fact_163_dual__order_Ostrict__trans2, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_nat @ B @ A) => ((ord_less_eq_nat @ C @ B) => (ord_less_nat @ C @ A)))))). % dual_order.strict_trans2
thf(fact_164_dual__order_Ostrict__trans2, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans2
thf(fact_165_dual__order_Ostrict__trans1, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))))). % dual_order.strict_trans1
thf(fact_166_dual__order_Ostrict__trans1, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans1
thf(fact_167_order_Ostrict__iff__order, axiom,
    ((ord_less_nat = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A2 @ B2)) & ((~ ((A2 = B2)))))))))). % order.strict_iff_order
thf(fact_168_order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ A2 @ B2)) & ((~ ((A2 = B2)))))))))). % order.strict_iff_order
thf(fact_169_order_Oorder__iff__strict, axiom,
    ((ord_less_eq_nat = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_nat @ A2 @ B2)) | ((A2 = B2)))))))). % order.order_iff_strict
thf(fact_170_order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[A2 : real]: (^[B2 : real]: (((ord_less_real @ A2 @ B2)) | ((A2 = B2)))))))). % order.order_iff_strict
thf(fact_171_order_Ostrict__trans2, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C)))))). % order.strict_trans2
thf(fact_172_order_Ostrict__trans2, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans2
thf(fact_173_order_Ostrict__trans1, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))))). % order.strict_trans1
thf(fact_174_order_Ostrict__trans1, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans1
thf(fact_175_not__le__imp__less, axiom,
    ((![Y2 : nat, X3 : nat]: ((~ ((ord_less_eq_nat @ Y2 @ X3))) => (ord_less_nat @ X3 @ Y2))))). % not_le_imp_less
thf(fact_176_not__le__imp__less, axiom,
    ((![Y2 : real, X3 : real]: ((~ ((ord_less_eq_real @ Y2 @ X3))) => (ord_less_real @ X3 @ Y2))))). % not_le_imp_less
thf(fact_177_less__le__not__le, axiom,
    ((ord_less_nat = (^[X2 : nat]: (^[Y3 : nat]: (((ord_less_eq_nat @ X2 @ Y3)) & ((~ ((ord_less_eq_nat @ Y3 @ X2)))))))))). % less_le_not_le
thf(fact_178_less__le__not__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X2 @ Y3)) & ((~ ((ord_less_eq_real @ Y3 @ X2)))))))))). % less_le_not_le
thf(fact_179_le__imp__less__or__eq, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ Y2) => ((ord_less_nat @ X3 @ Y2) | (X3 = Y2)))))). % le_imp_less_or_eq
thf(fact_180_le__imp__less__or__eq, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => ((ord_less_real @ X3 @ Y2) | (X3 = Y2)))))). % le_imp_less_or_eq
thf(fact_181_le__less__linear, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ Y2) | (ord_less_nat @ Y2 @ X3))))). % le_less_linear
thf(fact_182_le__less__linear, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) | (ord_less_real @ Y2 @ X3))))). % le_less_linear
thf(fact_183_dense__le, axiom,
    ((![Y2 : real, Z4 : real]: ((![X : real]: ((ord_less_real @ X @ Y2) => (ord_less_eq_real @ X @ Z4))) => (ord_less_eq_real @ Y2 @ Z4))))). % dense_le
thf(fact_184_dense__ge, axiom,
    ((![Z4 : real, Y2 : real]: ((![X : real]: ((ord_less_real @ Z4 @ X) => (ord_less_eq_real @ Y2 @ X))) => (ord_less_eq_real @ Y2 @ Z4))))). % dense_ge
thf(fact_185_less__le__trans, axiom,
    ((![X3 : nat, Y2 : nat, Z4 : nat]: ((ord_less_nat @ X3 @ Y2) => ((ord_less_eq_nat @ Y2 @ Z4) => (ord_less_nat @ X3 @ Z4)))))). % less_le_trans
thf(fact_186_less__le__trans, axiom,
    ((![X3 : real, Y2 : real, Z4 : real]: ((ord_less_real @ X3 @ Y2) => ((ord_less_eq_real @ Y2 @ Z4) => (ord_less_real @ X3 @ Z4)))))). % less_le_trans
thf(fact_187_le__less__trans, axiom,
    ((![X3 : nat, Y2 : nat, Z4 : nat]: ((ord_less_eq_nat @ X3 @ Y2) => ((ord_less_nat @ Y2 @ Z4) => (ord_less_nat @ X3 @ Z4)))))). % le_less_trans
thf(fact_188_le__less__trans, axiom,
    ((![X3 : real, Y2 : real, Z4 : real]: ((ord_less_eq_real @ X3 @ Y2) => ((ord_less_real @ Y2 @ Z4) => (ord_less_real @ X3 @ Z4)))))). % le_less_trans
thf(fact_189_less__imp__le, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_nat @ X3 @ Y2) => (ord_less_eq_nat @ X3 @ Y2))))). % less_imp_le
thf(fact_190_less__imp__le, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_eq_real @ X3 @ Y2))))). % less_imp_le
thf(fact_191_antisym__conv2, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ Y2) => ((~ ((ord_less_nat @ X3 @ Y2))) = (X3 = Y2)))))). % antisym_conv2
thf(fact_192_antisym__conv2, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => ((~ ((ord_less_real @ X3 @ Y2))) = (X3 = Y2)))))). % antisym_conv2
thf(fact_193_antisym__conv1, axiom,
    ((![X3 : nat, Y2 : nat]: ((~ ((ord_less_nat @ X3 @ Y2))) => ((ord_less_eq_nat @ X3 @ Y2) = (X3 = Y2)))))). % antisym_conv1
thf(fact_194_antisym__conv1, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_real @ X3 @ Y2))) => ((ord_less_eq_real @ X3 @ Y2) = (X3 = Y2)))))). % antisym_conv1
thf(fact_195_le__neq__trans, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((~ ((A = B))) => (ord_less_nat @ A @ B)))))). % le_neq_trans
thf(fact_196_le__neq__trans, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((~ ((A = B))) => (ord_less_real @ A @ B)))))). % le_neq_trans
thf(fact_197_not__less, axiom,
    ((![X3 : nat, Y2 : nat]: ((~ ((ord_less_nat @ X3 @ Y2))) = (ord_less_eq_nat @ Y2 @ X3))))). % not_less
thf(fact_198_not__less, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_real @ X3 @ Y2))) = (ord_less_eq_real @ Y2 @ X3))))). % not_less
thf(fact_199_not__le, axiom,
    ((![X3 : nat, Y2 : nat]: ((~ ((ord_less_eq_nat @ X3 @ Y2))) = (ord_less_nat @ Y2 @ X3))))). % not_le
thf(fact_200_not__le, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_eq_real @ X3 @ Y2))) = (ord_less_real @ Y2 @ X3))))). % not_le
thf(fact_201_order__less__le__subst2, axiom,
    ((![A : real, B : real, F2 : real > nat, C : nat]: ((ord_less_real @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % order_less_le_subst2
thf(fact_202_order__less__le__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F2 @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_less_le_subst2
thf(fact_203_order__less__le__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_nat @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % order_less_le_subst1
thf(fact_204_order__less__le__subst1, axiom,
    ((![A : real, F2 : nat > real, B : nat, C : nat]: ((ord_less_real @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_less_le_subst1
thf(fact_205_order__less__le__subst1, axiom,
    ((![A : nat, F2 : real > nat, B : real, C : real]: ((ord_less_nat @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % order_less_le_subst1
thf(fact_206_order__less__le__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_real @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_less_le_subst1
thf(fact_207_order__le__less__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (F2 @ B) @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % order_le_less_subst2
thf(fact_208_order__le__less__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > real, C : real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_real @ (F2 @ B) @ C) => ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_le_less_subst2
thf(fact_209_order__le__less__subst2, axiom,
    ((![A : real, B : real, F2 : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_nat @ (F2 @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % order_le_less_subst2
thf(fact_210_order__le__less__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F2 @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_le_less_subst2
thf(fact_211_order__le__less__subst1, axiom,
    ((![A : nat, F2 : real > nat, B : real, C : real]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_nat @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % order_le_less_subst1
thf(fact_212_order__le__less__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F2 @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F2 @ X) @ (F2 @ Y4)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_le_less_subst1
thf(fact_213_less__le, axiom,
    ((ord_less_nat = (^[X2 : nat]: (^[Y3 : nat]: (((ord_less_eq_nat @ X2 @ Y3)) & ((~ ((X2 = Y3)))))))))). % less_le
thf(fact_214_less__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X2 @ Y3)) & ((~ ((X2 = Y3)))))))))). % less_le
thf(fact_215_le__less, axiom,
    ((ord_less_eq_nat = (^[X2 : nat]: (^[Y3 : nat]: (((ord_less_nat @ X2 @ Y3)) | ((X2 = Y3)))))))). % le_less
thf(fact_216_le__less, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y3 : real]: (((ord_less_real @ X2 @ Y3)) | ((X2 = Y3)))))))). % le_less
thf(fact_217_leI, axiom,
    ((![X3 : nat, Y2 : nat]: ((~ ((ord_less_nat @ X3 @ Y2))) => (ord_less_eq_nat @ Y2 @ X3))))). % leI
thf(fact_218_leI, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_eq_real @ Y2 @ X3))))). % leI

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![N1 : nat]: ((![N4 : nat]: ((ord_less_eq_nat @ N1 @ N4) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N4)) @ z)) @ d))) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
