% 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_132__5368194_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:27:17.677

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

% Explicit typings (18)
thf(sy_c_Complex_Oimaginary__unit, type,
    imaginary_unit : complex).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex, type,
    abs_abs_complex : complex > complex).
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__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_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__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex, type,
    real_V306493662omplex : real > complex).
thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal, type,
    real_V1205483228l_real : real > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_z, type,
    z : complex).

% Relevant facts (188)
thf(fact_0_md, axiom,
    (((real_V638595069omplex @ z) = one_one_real))). % md
thf(fact_1_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_2_norm__ii, axiom,
    (((real_V638595069omplex @ imaginary_unit) = one_one_real))). % norm_ii
thf(fact_3_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_4_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_5_add__diff__cancel, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_6_add__diff__cancel, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_7_diff__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_8_diff__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_9_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_10_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_11_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_12_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_13_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_14_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_15_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_16_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_17_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_18_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_19_norm__add__less, axiom,
    ((![X3 : complex, R : real, Y2 : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X3) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y2) @ S2) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ (plus_plus_real @ R @ S2))))))). % norm_add_less
thf(fact_20_norm__add__less, axiom,
    ((![X3 : real, R : real, Y2 : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X3) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S2) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ (plus_plus_real @ R @ S2))))))). % norm_add_less
thf(fact_21_norm__triangle__lt, axiom,
    ((![X3 : complex, Y2 : complex, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_22_norm__triangle__lt, axiom,
    ((![X3 : real, Y2 : real, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_23_add__right__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_24_add__right__cancel, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_25_add__left__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_26_add__left__cancel, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_27_norm__diff__triangle__less, axiom,
    ((![X3 : complex, Y2 : complex, E1 : real, Z2 : complex, E2 : real]: ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Y2)) @ E1) => ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Y2 @ Z2)) @ E2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Z2)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_28_norm__diff__triangle__less, axiom,
    ((![X3 : real, Y2 : real, E1 : real, Z2 : real, E2 : real]: ((ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Y2)) @ E1) => ((ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ Y2 @ Z2)) @ E2) => (ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Z2)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_29_add__right__imp__eq, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_30_add__right__imp__eq, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_31_add__left__imp__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_32_add__left__imp__eq, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_33_add_Oleft__commute, axiom,
    ((![B : complex, A : complex, C : complex]: ((plus_plus_complex @ B @ (plus_plus_complex @ A @ C)) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.left_commute
thf(fact_34_add_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((plus_plus_real @ B @ (plus_plus_real @ A @ C)) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % add.left_commute
thf(fact_35_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_36_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_37_add_Oright__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_38_add_Oright__cancel, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_39_add_Oleft__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_40_add_Oleft__cancel, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_41_add_Oassoc, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.assoc
thf(fact_42_add_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % add.assoc
thf(fact_43_group__cancel_Oadd2, axiom,
    ((![B3 : complex, K : complex, B : complex, A : complex]: ((B3 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B3) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_44_group__cancel_Oadd2, axiom,
    ((![B3 : real, K : real, B : real, A : real]: ((B3 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B3) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_45_group__cancel_Oadd1, axiom,
    ((![A3 : complex, K : complex, A : complex, B : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A3 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_46_group__cancel_Oadd1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A3 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_47_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (K = L)) => ((plus_plus_real @ I @ K) = (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_48_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_49_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_50_one__reorient, axiom,
    ((![X3 : complex]: ((one_one_complex = X3) = (X3 = one_one_complex))))). % one_reorient
thf(fact_51_one__reorient, axiom,
    ((![X3 : real]: ((one_one_real = X3) = (X3 = one_one_real))))). % one_reorient
thf(fact_52_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_53_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_54_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_55_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_56_add__less__imp__less__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_imp_less_right
thf(fact_57_add__less__imp__less__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_imp_less_left
thf(fact_58_add__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_strict_right_mono
thf(fact_59_add__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_strict_left_mono
thf(fact_60_add__strict__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_strict_mono
thf(fact_61_add__mono__thms__linordered__field_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (K = L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(1)
thf(fact_62_add__mono__thms__linordered__field_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(2)
thf(fact_63_add__mono__thms__linordered__field_I5_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(5)
thf(fact_64_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_65_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_66_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_67_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_68_add__implies__diff, axiom,
    ((![C : complex, B : complex, A : complex]: (((plus_plus_complex @ C @ B) = A) => (C = (minus_minus_complex @ A @ B)))))). % add_implies_diff
thf(fact_69_add__implies__diff, axiom,
    ((![C : real, B : real, A : real]: (((plus_plus_real @ C @ B) = A) => (C = (minus_minus_real @ A @ B)))))). % add_implies_diff
thf(fact_70_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_71_Collect__mem__eq, axiom,
    ((![A3 : set_real]: ((collect_real @ (^[X2 : real]: (member_real @ X2 @ A3))) = A3)))). % Collect_mem_eq
thf(fact_72_diff__diff__add, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ A @ (plus_plus_complex @ B @ C)))))). % diff_diff_add
thf(fact_73_diff__diff__add, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C)))))). % diff_diff_add
thf(fact_74_diff__add__eq__diff__diff__swap, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ A @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ (minus_minus_complex @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_75_diff__add__eq__diff__diff__swap, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_76_diff__add__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B))))). % diff_add_eq
thf(fact_77_diff__add__eq, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B))))). % diff_add_eq
thf(fact_78_diff__diff__eq2, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_79_diff__diff__eq2, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_80_add__diff__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ B) @ C))))). % add_diff_eq
thf(fact_81_add__diff__eq, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C))))). % add_diff_eq
thf(fact_82_eq__diff__eq, axiom,
    ((![A : complex, C : complex, B : complex]: ((A = (minus_minus_complex @ C @ B)) = ((plus_plus_complex @ A @ B) = C))))). % eq_diff_eq
thf(fact_83_eq__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((A = (minus_minus_real @ C @ B)) = ((plus_plus_real @ A @ B) = C))))). % eq_diff_eq
thf(fact_84_diff__eq__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((minus_minus_complex @ A @ B) = C) = (A = (plus_plus_complex @ C @ B)))))). % diff_eq_eq
thf(fact_85_diff__eq__eq, axiom,
    ((![A : real, B : real, C : real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B)))))). % diff_eq_eq
thf(fact_86_group__cancel_Osub1, axiom,
    ((![A3 : complex, K : complex, A : complex, B : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((minus_minus_complex @ A3 @ B) = (plus_plus_complex @ K @ (minus_minus_complex @ A @ B))))))). % group_cancel.sub1
thf(fact_87_group__cancel_Osub1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((minus_minus_real @ A3 @ B) = (plus_plus_real @ K @ (minus_minus_real @ A @ B))))))). % group_cancel.sub1
thf(fact_88_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_89_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_90_complex__i__not__one, axiom,
    ((~ ((imaginary_unit = one_one_complex))))). % complex_i_not_one
thf(fact_91_less__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ A @ (minus_minus_real @ C @ B)) = (ord_less_real @ (plus_plus_real @ A @ B) @ C))))). % less_diff_eq
thf(fact_92_diff__less__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_real @ A @ (plus_plus_real @ C @ B)))))). % diff_less_eq
thf(fact_93_linordered__semidom__class_Oadd__diff__inverse, axiom,
    ((![A : real, B : real]: ((~ ((ord_less_real @ A @ B))) => ((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A))))). % linordered_semidom_class.add_diff_inverse
thf(fact_94_add__mono1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ one_one_real) @ (plus_plus_real @ B @ one_one_real)))))). % add_mono1
thf(fact_95_less__add__one, axiom,
    ((![A : real]: (ord_less_real @ A @ (plus_plus_real @ A @ one_one_real))))). % less_add_one
thf(fact_96_add__diff__add, axiom,
    ((![A : complex, C : complex, B : complex, D : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ C) @ (plus_plus_complex @ B @ D)) = (plus_plus_complex @ (minus_minus_complex @ A @ B) @ (minus_minus_complex @ C @ D)))))). % add_diff_add
thf(fact_97_add__diff__add, axiom,
    ((![A : real, C : real, B : real, D : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) = (plus_plus_real @ (minus_minus_real @ A @ B) @ (minus_minus_real @ C @ D)))))). % add_diff_add
thf(fact_98_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_99_norm__diff__triangle__ineq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ D))) @ (plus_plus_real @ (real_V638595069omplex @ (minus_minus_complex @ A @ C)) @ (real_V638595069omplex @ (minus_minus_complex @ B @ D))))))). % norm_diff_triangle_ineq
thf(fact_100_norm__diff__triangle__ineq, axiom,
    ((![A : real, B : real, C : real, D : real]: (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (real_V646646907m_real @ (minus_minus_real @ A @ C)) @ (real_V646646907m_real @ (minus_minus_real @ B @ D))))))). % norm_diff_triangle_ineq
thf(fact_101_complex__mod__triangle__sub, axiom,
    ((![W : complex, Z2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W @ Z2)) @ (real_V638595069omplex @ Z2)))))). % complex_mod_triangle_sub
thf(fact_102_norm__less__p1, axiom,
    ((![X3 : complex]: (ord_less_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ (plus_plus_complex @ (real_V306493662omplex @ (real_V638595069omplex @ X3)) @ one_one_complex)))))). % norm_less_p1
thf(fact_103_norm__less__p1, axiom,
    ((![X3 : real]: (ord_less_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ (plus_plus_real @ (real_V1205483228l_real @ (real_V646646907m_real @ X3)) @ one_one_real)))))). % norm_less_p1
thf(fact_104_eq__diff__eq_H, axiom,
    ((![X3 : real, Y2 : real, Z2 : real]: ((X3 = (minus_minus_real @ Y2 @ Z2)) = (Y2 = (plus_plus_real @ X3 @ Z2)))))). % eq_diff_eq'
thf(fact_105_add__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_left
thf(fact_106_add__le__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_right
thf(fact_107_le__add__diff__inverse, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A))))). % le_add_diff_inverse
thf(fact_108_le__add__diff__inverse2, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))))). % le_add_diff_inverse2
thf(fact_109_of__real__1, axiom,
    (((real_V306493662omplex @ one_one_real) = one_one_complex))). % of_real_1
thf(fact_110_of__real__1, axiom,
    (((real_V1205483228l_real @ one_one_real) = one_one_real))). % of_real_1
thf(fact_111_of__real__eq__1__iff, axiom,
    ((![X3 : real]: (((real_V306493662omplex @ X3) = one_one_complex) = (X3 = one_one_real))))). % of_real_eq_1_iff
thf(fact_112_of__real__eq__1__iff, axiom,
    ((![X3 : real]: (((real_V1205483228l_real @ X3) = one_one_real) = (X3 = one_one_real))))). % of_real_eq_1_iff
thf(fact_113_of__real__add, axiom,
    ((![X3 : real, Y2 : real]: ((real_V306493662omplex @ (plus_plus_real @ X3 @ Y2)) = (plus_plus_complex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2)))))). % of_real_add
thf(fact_114_of__real__add, axiom,
    ((![X3 : real, Y2 : real]: ((real_V1205483228l_real @ (plus_plus_real @ X3 @ Y2)) = (plus_plus_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2)))))). % of_real_add
thf(fact_115_of__real__diff, axiom,
    ((![X3 : real, Y2 : real]: ((real_V306493662omplex @ (minus_minus_real @ X3 @ Y2)) = (minus_minus_complex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2)))))). % of_real_diff
thf(fact_116_of__real__diff, axiom,
    ((![X3 : real, Y2 : real]: ((real_V1205483228l_real @ (minus_minus_real @ X3 @ Y2)) = (minus_minus_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2)))))). % of_real_diff
thf(fact_117_complete__real, axiom,
    ((![S3 : set_real]: ((?[X4 : real]: (member_real @ X4 @ S3)) => ((?[Z : real]: (![X : real]: ((member_real @ X @ S3) => (ord_less_eq_real @ X @ Z)))) => (?[Y3 : real]: ((![X4 : real]: ((member_real @ X4 @ S3) => (ord_less_eq_real @ X4 @ Y3))) & (![Z : real]: ((![X : real]: ((member_real @ X @ S3) => (ord_less_eq_real @ X @ Z))) => (ord_less_eq_real @ Y3 @ Z)))))))))). % complete_real
thf(fact_118_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_119_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y4 : real]: (((ord_less_real @ X2 @ Y4)) | ((X2 = Y4)))))))). % less_eq_real_def
thf(fact_120_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (K = L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_121_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_122_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_123_add__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_mono
thf(fact_124_add__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_left_mono
thf(fact_125_add__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_right_mono
thf(fact_126_add__le__imp__le__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_left
thf(fact_127_add__le__imp__le__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_right
thf(fact_128_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_129_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_130_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_131_diff__eq__diff__less__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_132_add__le__imp__le__diff, axiom,
    ((![I : real, K : real, N : real]: ((ord_less_eq_real @ (plus_plus_real @ I @ K) @ N) => (ord_less_eq_real @ I @ (minus_minus_real @ N @ K)))))). % add_le_imp_le_diff
thf(fact_133_add__le__add__imp__diff__le, axiom,
    ((![I : real, K : real, N : real, J : real]: ((ord_less_eq_real @ (plus_plus_real @ I @ K) @ N) => ((ord_less_eq_real @ N @ (plus_plus_real @ J @ K)) => ((ord_less_eq_real @ (plus_plus_real @ I @ K) @ N) => ((ord_less_eq_real @ N @ (plus_plus_real @ J @ K)) => (ord_less_eq_real @ (minus_minus_real @ N @ K) @ J)))))))). % add_le_add_imp_diff_le
thf(fact_134_add__mono__thms__linordered__field_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(4)
thf(fact_135_add__mono__thms__linordered__field_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(3)
thf(fact_136_add__le__less__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_le_less_mono
thf(fact_137_add__less__le__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_less_le_mono
thf(fact_138_diff__le__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B)))))). % diff_le_eq
thf(fact_139_le__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) = (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))))). % le_diff_eq
thf(fact_140_norm__diff__ineq, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)) @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)))))). % norm_diff_ineq
thf(fact_141_norm__diff__ineq, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)) @ (real_V646646907m_real @ (plus_plus_real @ A @ B)))))). % norm_diff_ineq
thf(fact_142_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_143_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_144_complex__mod__triangle__ineq2, axiom,
    ((![B : complex, A : complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V638595069omplex @ (plus_plus_complex @ B @ A)) @ (real_V638595069omplex @ B)) @ (real_V638595069omplex @ A))))). % complex_mod_triangle_ineq2
thf(fact_145_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) => ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_real @ Y2 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_146_is__num__normalize_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % is_num_normalize(1)
thf(fact_147_is__num__normalize_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % is_num_normalize(1)
thf(fact_148_norm__add__leD, axiom,
    ((![A : complex, B : complex, C : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ C) => (ord_less_eq_real @ (real_V638595069omplex @ B) @ (plus_plus_real @ (real_V638595069omplex @ A) @ C)))))). % norm_add_leD
thf(fact_149_norm__add__leD, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ C) => (ord_less_eq_real @ (real_V646646907m_real @ B) @ (plus_plus_real @ (real_V646646907m_real @ A) @ C)))))). % norm_add_leD
thf(fact_150_norm__triangle__le, axiom,
    ((![X3 : complex, Y2 : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ E))))). % norm_triangle_le
thf(fact_151_norm__triangle__le, axiom,
    ((![X3 : real, Y2 : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ E))))). % norm_triangle_le
thf(fact_152_norm__triangle__ineq, axiom,
    ((![X3 : complex, Y2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)))))). % norm_triangle_ineq
thf(fact_153_norm__triangle__ineq, axiom,
    ((![X3 : real, Y2 : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)))))). % norm_triangle_ineq
thf(fact_154_norm__triangle__mono, axiom,
    ((![A : complex, R : real, B : complex, S2 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ A) @ R) => ((ord_less_eq_real @ (real_V638595069omplex @ B) @ S2) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ R @ S2))))))). % norm_triangle_mono
thf(fact_155_norm__triangle__mono, axiom,
    ((![A : real, R : real, B : real, S2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ A) @ R) => ((ord_less_eq_real @ (real_V646646907m_real @ B) @ S2) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ R @ S2))))))). % norm_triangle_mono
thf(fact_156_norm__triangle__sub, axiom,
    ((![X3 : complex, Y2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ X3) @ (plus_plus_real @ (real_V638595069omplex @ Y2) @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Y2))))))). % norm_triangle_sub
thf(fact_157_norm__triangle__sub, axiom,
    ((![X3 : real, Y2 : real]: (ord_less_eq_real @ (real_V646646907m_real @ X3) @ (plus_plus_real @ (real_V646646907m_real @ Y2) @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Y2))))))). % norm_triangle_sub
thf(fact_158_norm__triangle__ineq4, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ A @ B)) @ (plus_plus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_triangle_ineq4
thf(fact_159_norm__triangle__ineq4, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_triangle_ineq4
thf(fact_160_norm__diff__triangle__le, axiom,
    ((![X3 : complex, Y2 : complex, E1 : real, Z2 : complex, E2 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Y2)) @ E1) => ((ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ Y2 @ Z2)) @ E2) => (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Z2)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_le
thf(fact_161_norm__diff__triangle__le, axiom,
    ((![X3 : real, Y2 : real, E1 : real, Z2 : real, E2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Y2)) @ E1) => ((ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ Y2 @ Z2)) @ E2) => (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Z2)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_le
thf(fact_162_norm__triangle__le__diff, axiom,
    ((![X3 : complex, Y2 : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Y2)) @ E))))). % norm_triangle_le_diff
thf(fact_163_norm__triangle__le__diff, axiom,
    ((![X3 : real, Y2 : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Y2)) @ E))))). % norm_triangle_le_diff
thf(fact_164_order__refl, axiom,
    ((![X3 : real]: (ord_less_eq_real @ X3 @ X3)))). % order_refl
thf(fact_165_norm__of__real__add1, axiom,
    ((![X3 : real]: ((real_V638595069omplex @ (plus_plus_complex @ (real_V306493662omplex @ X3) @ one_one_complex)) = (abs_abs_real @ (plus_plus_real @ X3 @ one_one_real)))))). % norm_of_real_add1
thf(fact_166_norm__of__real__add1, axiom,
    ((![X3 : real]: ((real_V646646907m_real @ (plus_plus_real @ (real_V1205483228l_real @ X3) @ one_one_real)) = (abs_abs_real @ (plus_plus_real @ X3 @ one_one_real)))))). % norm_of_real_add1
thf(fact_167_minf_I8_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => (~ ((ord_less_eq_real @ T @ X4))))))))). % minf(8)
thf(fact_168_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_169_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_170_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_171_abs__1, axiom,
    (((abs_abs_complex @ one_one_complex) = one_one_complex))). % abs_1
thf(fact_172_abs__1, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_1
thf(fact_173_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_174_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_175_norm__of__real, axiom,
    ((![R : real]: ((real_V638595069omplex @ (real_V306493662omplex @ R)) = (abs_abs_real @ R))))). % norm_of_real
thf(fact_176_norm__of__real, axiom,
    ((![R : real]: ((real_V646646907m_real @ (real_V1205483228l_real @ R)) = (abs_abs_real @ R))))). % norm_of_real
thf(fact_177_abs__le__D1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B))))). % abs_le_D1
thf(fact_178_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_179_abs__one, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_one
thf(fact_180_abs__minus__commute, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A)))))). % abs_minus_commute
thf(fact_181_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_182_abs__triangle__ineq, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_triangle_ineq
thf(fact_183_abs__triangle__ineq2__sym, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A)))))). % abs_triangle_ineq2_sym
thf(fact_184_abs__triangle__ineq3, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B)))))). % abs_triangle_ineq3
thf(fact_185_abs__triangle__ineq2, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B)))))). % abs_triangle_ineq2
thf(fact_186_abs__diff__triangle__ineq, axiom,
    ((![A : real, B : real, C : real, D : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ C)) @ (abs_abs_real @ (minus_minus_real @ B @ D))))))). % abs_diff_triangle_ineq
thf(fact_187_abs__triangle__ineq4, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_triangle_ineq4

% Conjectures (1)
thf(conj_0, conjecture,
    (((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ z @ one_one_complex)) @ one_one_real) | ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ z @ one_one_complex)) @ one_one_real) | ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ z @ imaginary_unit)) @ one_one_real) | (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ z @ imaginary_unit)) @ one_one_real)))))).
