% 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_134__5368250_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:27:19.192

% Could-be-implicit typings (2)
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).

% Explicit typings (19)
thf(sy_c_Complex_Ocis, type,
    cis : real > complex).
thf(sy_c_Complex_Ocomplex_OComplex, type,
    complex2 : real > real > complex).
thf(sy_c_Complex_Ocomplex_OIm, type,
    im : complex > real).
thf(sy_c_Complex_Ocomplex_ORe, type,
    re : complex > real).
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_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_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
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_Transcendental_Oarcosh_001t__Real__Oreal, type,
    arcosh_real : real > real).
thf(sy_v_thesis____, type,
    thesis : $o).
thf(sy_v_z, type,
    z : complex).

% Relevant facts (155)
thf(fact_0_complex_Oinject, axiom,
    ((![X1 : real, X2 : real, Y1 : real, Y2 : real]: (((complex2 @ X1 @ X2) = (complex2 @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % complex.inject
thf(fact_1_md, axiom,
    (((real_V638595069omplex @ z) = one_one_real))). % md
thf(fact_2_complex_Oexhaust, axiom,
    ((![Y : complex]: (~ ((![X12 : real, X22 : real]: (~ ((Y = (complex2 @ X12 @ X22)))))))))). % complex.exhaust
thf(fact_3_complex_Osel_I1_J, axiom,
    ((![X1 : real, X2 : real]: ((re @ (complex2 @ X1 @ X2)) = X1)))). % complex.sel(1)
thf(fact_4_complex_Osel_I2_J, axiom,
    ((![X1 : real, X2 : real]: ((im @ (complex2 @ X1 @ X2)) = X2)))). % complex.sel(2)
thf(fact_5_complex__surj, axiom,
    ((![Z : complex]: ((complex2 @ (re @ Z) @ (im @ Z)) = Z)))). % complex_surj
thf(fact_6_complex_Ocollapse, axiom,
    ((![Complex : complex]: ((complex2 @ (re @ Complex) @ (im @ Complex)) = Complex)))). % complex.collapse
thf(fact_7_complex__eqI, axiom,
    ((![X : complex, Y : complex]: (((re @ X) = (re @ Y)) => (((im @ X) = (im @ Y)) => (X = Y)))))). % complex_eqI
thf(fact_8_complex_Oexpand, axiom,
    ((![Complex : complex, Complex2 : complex]: ((((re @ Complex) = (re @ Complex2)) & ((im @ Complex) = (im @ Complex2))) => (Complex = Complex2))))). % complex.expand
thf(fact_9_complex__eq__iff, axiom,
    (((^[Y3 : complex]: (^[Z2 : complex]: (Y3 = Z2))) = (^[X3 : complex]: (^[Y4 : complex]: ((((re @ X3) = (re @ Y4))) & (((im @ X3) = (im @ Y4))))))))). % complex_eq_iff
thf(fact_10_complex_Oexhaust__sel, axiom,
    ((![Complex : complex]: (Complex = (complex2 @ (re @ Complex) @ (im @ Complex)))))). % complex.exhaust_sel
thf(fact_11_complex_Ocoinduct__strong, axiom,
    ((![R : complex > complex > $o, Complex : complex, Complex2 : complex]: ((R @ Complex @ Complex2) => ((![Complex3 : complex, Complex4 : complex]: ((R @ Complex3 @ Complex4) => (((re @ Complex3) = (re @ Complex4)) & ((im @ Complex3) = (im @ Complex4))))) => (Complex = Complex2)))))). % complex.coinduct_strong
thf(fact_12_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_13_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_14_norm__cis, axiom,
    ((![A : real]: ((real_V638595069omplex @ (cis @ A)) = one_one_real)))). % norm_cis
thf(fact_15_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_16_one__reorient, axiom,
    ((![X : complex]: ((one_one_complex = X) = (X = one_one_complex))))). % one_reorient
thf(fact_17_norm__ii, axiom,
    (((real_V638595069omplex @ imaginary_unit) = one_one_real))). % norm_ii
thf(fact_18_imaginary__unit_Osimps_I2_J, axiom,
    (((im @ imaginary_unit) = one_one_real))). % imaginary_unit.simps(2)
thf(fact_19_complex__Re__le__cmod, axiom,
    ((![X : complex]: (ord_less_eq_real @ (re @ X) @ (real_V638595069omplex @ X))))). % complex_Re_le_cmod
thf(fact_20_one__complex_Osimps_I1_J, axiom,
    (((re @ one_one_complex) = one_one_real))). % one_complex.simps(1)
thf(fact_21_Im__eq__0, axiom,
    ((![Z : complex]: (((abs_abs_real @ (re @ Z)) = (real_V638595069omplex @ Z)) => ((im @ Z) = zero_zero_real))))). % Im_eq_0
thf(fact_22_cmod__eq__Im, axiom,
    ((![Z : complex]: (((re @ Z) = zero_zero_real) => ((real_V638595069omplex @ Z) = (abs_abs_real @ (im @ Z))))))). % cmod_eq_Im
thf(fact_23_cmod__eq__Re, axiom,
    ((![Z : complex]: (((im @ Z) = zero_zero_real) => ((real_V638595069omplex @ Z) = (abs_abs_real @ (re @ Z))))))). % cmod_eq_Re
thf(fact_24_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_25_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_26_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_27_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_28_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_29_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_30_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_31_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_32_abs__of__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_nonneg
thf(fact_33_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_34_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_35_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_36_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_37_cis__zero, axiom,
    (((cis @ zero_zero_real) = one_one_complex))). % cis_zero
thf(fact_38_norm__le__zero__iff, axiom,
    ((![X : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X) @ zero_zero_real) = (X = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_39_norm__le__zero__iff, axiom,
    ((![X : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X) @ zero_zero_real) = (X = zero_zero_real))))). % norm_le_zero_iff
thf(fact_40_complex__i__not__one, axiom,
    ((~ ((imaginary_unit = one_one_complex))))). % complex_i_not_one
thf(fact_41_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_42_norm__ge__zero, axiom,
    ((![X : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X))))). % norm_ge_zero
thf(fact_43_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_44_abs__ge__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A))))). % abs_ge_zero
thf(fact_45_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_46_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_47_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_48_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_49_one__complex_Osimps_I2_J, axiom,
    (((im @ one_one_complex) = zero_zero_real))). % one_complex.simps(2)
thf(fact_50_imaginary__unit_Osimps_I1_J, axiom,
    (((re @ imaginary_unit) = zero_zero_real))). % imaginary_unit.simps(1)
thf(fact_51_abs__Re__le__cmod, axiom,
    ((![X : complex]: (ord_less_eq_real @ (abs_abs_real @ (re @ X)) @ (real_V638595069omplex @ X))))). % abs_Re_le_cmod
thf(fact_52_abs__Im__le__cmod, axiom,
    ((![X : complex]: (ord_less_eq_real @ (abs_abs_real @ (im @ X)) @ (real_V638595069omplex @ X))))). % abs_Im_le_cmod
thf(fact_53_one__complex_Ocode, axiom,
    ((one_one_complex = (complex2 @ one_one_real @ zero_zero_real)))). % one_complex.code
thf(fact_54_Complex__eq__1, axiom,
    ((![A : real, B : real]: (((complex2 @ A @ B) = one_one_complex) = (((A = one_one_real)) & ((B = zero_zero_real))))))). % Complex_eq_1
thf(fact_55_imaginary__unit_Ocode, axiom,
    ((imaginary_unit = (complex2 @ zero_zero_real @ one_one_real)))). % imaginary_unit.code
thf(fact_56_Complex__eq__i, axiom,
    ((![X : real, Y : real]: (((complex2 @ X @ Y) = imaginary_unit) = (((X = zero_zero_real)) & ((Y = one_one_real))))))). % Complex_eq_i
thf(fact_57_cmod__Re__le__iff, axiom,
    ((![X : complex, Y : complex]: (((im @ X) = (im @ Y)) => ((ord_less_eq_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)) = (ord_less_eq_real @ (abs_abs_real @ (re @ X)) @ (abs_abs_real @ (re @ Y)))))))). % cmod_Re_le_iff
thf(fact_58_cmod__Im__le__iff, axiom,
    ((![X : complex, Y : complex]: (((re @ X) = (re @ Y)) => ((ord_less_eq_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)) = (ord_less_eq_real @ (abs_abs_real @ (im @ X)) @ (abs_abs_real @ (im @ Y)))))))). % cmod_Im_le_iff
thf(fact_59_abs__1, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_1
thf(fact_60_abs__1, axiom,
    (((abs_abs_complex @ one_one_complex) = one_one_complex))). % abs_1
thf(fact_61_abs__0, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_0
thf(fact_62_abs__0, axiom,
    (((abs_abs_complex @ zero_zero_complex) = zero_zero_complex))). % abs_0
thf(fact_63_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_64_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_65_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_66_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_67_abs__one, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_one
thf(fact_68_complex__i__not__zero, axiom,
    ((~ ((imaginary_unit = zero_zero_complex))))). % complex_i_not_zero
thf(fact_69_cis__neq__zero, axiom,
    ((![A : real]: (~ (((cis @ A) = zero_zero_complex)))))). % cis_neq_zero
thf(fact_70_zero__complex_Osimps_I1_J, axiom,
    (((re @ zero_zero_complex) = zero_zero_real))). % zero_complex.simps(1)
thf(fact_71_zero__complex_Osimps_I2_J, axiom,
    (((im @ zero_zero_complex) = zero_zero_real))). % zero_complex.simps(2)
thf(fact_72_Complex__eq__0, axiom,
    ((![A : real, B : real]: (((complex2 @ A @ B) = zero_zero_complex) = (((A = zero_zero_real)) & ((B = zero_zero_real))))))). % Complex_eq_0
thf(fact_73_zero__complex_Ocode, axiom,
    ((zero_zero_complex = (complex2 @ zero_zero_real @ zero_zero_real)))). % zero_complex.code
thf(fact_74_order__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y5 : real]: ((ord_less_eq_real @ X4 @ Y5) => (ord_less_eq_real @ (F @ X4) @ (F @ Y5)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_75_order__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X4 : real, Y5 : real]: ((ord_less_eq_real @ X4 @ Y5) => (ord_less_eq_real @ (F @ X4) @ (F @ Y5)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_76_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y5 : real]: ((ord_less_eq_real @ X4 @ Y5) => (ord_less_eq_real @ (F @ X4) @ (F @ Y5)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_77_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X4 : real, Y5 : real]: ((ord_less_eq_real @ X4 @ Y5) => (ord_less_eq_real @ (F @ X4) @ (F @ Y5)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_78_eq__iff, axiom,
    (((^[Y3 : real]: (^[Z2 : real]: (Y3 = Z2))) = (^[X3 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X3 @ Y4)) & ((ord_less_eq_real @ Y4 @ X3)))))))). % eq_iff
thf(fact_79_antisym, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) => ((ord_less_eq_real @ Y @ X) => (X = Y)))))). % antisym
thf(fact_80_linear, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) | (ord_less_eq_real @ Y @ X))))). % linear
thf(fact_81_eq__refl, axiom,
    ((![X : real, Y : real]: ((X = Y) => (ord_less_eq_real @ X @ Y))))). % eq_refl
thf(fact_82_le__cases, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_eq_real @ X @ Y))) => (ord_less_eq_real @ Y @ X))))). % le_cases
thf(fact_83_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_84_le__cases3, axiom,
    ((![X : real, Y : real, Z : real]: (((ord_less_eq_real @ X @ Y) => (~ ((ord_less_eq_real @ Y @ Z)))) => (((ord_less_eq_real @ Y @ X) => (~ ((ord_less_eq_real @ X @ Z)))) => (((ord_less_eq_real @ X @ Z) => (~ ((ord_less_eq_real @ Z @ Y)))) => (((ord_less_eq_real @ Z @ Y) => (~ ((ord_less_eq_real @ Y @ X)))) => (((ord_less_eq_real @ Y @ Z) => (~ ((ord_less_eq_real @ Z @ X)))) => (~ (((ord_less_eq_real @ Z @ X) => (~ ((ord_less_eq_real @ X @ Y)))))))))))))). % le_cases3
thf(fact_85_antisym__conv, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ Y @ X) => ((ord_less_eq_real @ X @ Y) = (X = Y)))))). % antisym_conv
thf(fact_86_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : real]: (^[Z2 : real]: (Y3 = Z2))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ A2 @ B2)) & ((ord_less_eq_real @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_87_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_88_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_89_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_90_order__trans, axiom,
    ((![X : real, Y : real, Z : real]: ((ord_less_eq_real @ X @ Y) => ((ord_less_eq_real @ Y @ Z) => (ord_less_eq_real @ X @ Z)))))). % order_trans
thf(fact_91_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_92_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_93_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_94_dual__order_Oeq__iff, axiom,
    (((^[Y3 : real]: (^[Z2 : real]: (Y3 = Z2))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A2)) & ((ord_less_eq_real @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_95_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_96_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_97_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_98_abs__eq__0__iff, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0_iff
thf(fact_99_abs__eq__0__iff, axiom,
    ((![A : complex]: (((abs_abs_complex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % abs_eq_0_iff
thf(fact_100_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_101_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_102_cmod__le, axiom,
    ((![Z : complex]: (ord_less_eq_real @ (real_V638595069omplex @ Z) @ (plus_plus_real @ (abs_abs_real @ (re @ Z)) @ (abs_abs_real @ (im @ Z))))))). % cmod_le
thf(fact_103_arcosh__1, axiom,
    (((arcosh_real @ one_one_real) = zero_zero_real))). % arcosh_1
thf(fact_104_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_105_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_106_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_107_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_108_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_109_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_110_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_111_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_112_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_113_add__cancel__left__left, axiom,
    ((![B : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) = (B = zero_zero_complex))))). % add_cancel_left_left
thf(fact_114_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_115_add__cancel__left__right, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex))))). % add_cancel_left_right
thf(fact_116_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_117_add__cancel__right__left, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex))))). % add_cancel_right_left
thf(fact_118_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_119_add__cancel__right__right, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex))))). % add_cancel_right_right
thf(fact_120_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_121_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_122_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_123_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_124_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_125_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_126_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_127_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_128_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_129_norm__triangle__mono, axiom,
    ((![A : complex, R2 : real, B : complex, S : real]: ((ord_less_eq_real @ (real_V638595069omplex @ A) @ R2) => ((ord_less_eq_real @ (real_V638595069omplex @ B) @ S) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ R2 @ S))))))). % norm_triangle_mono
thf(fact_130_norm__triangle__mono, axiom,
    ((![A : real, R2 : real, B : real, S : real]: ((ord_less_eq_real @ (real_V646646907m_real @ A) @ R2) => ((ord_less_eq_real @ (real_V646646907m_real @ B) @ S) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ R2 @ S))))))). % norm_triangle_mono
thf(fact_131_norm__triangle__ineq, axiom,
    ((![X : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X @ Y)) @ (plus_plus_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)))))). % norm_triangle_ineq
thf(fact_132_norm__triangle__ineq, axiom,
    ((![X : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y)) @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_triangle_ineq
thf(fact_133_norm__triangle__le, axiom,
    ((![X : complex, Y : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X @ Y)) @ E))))). % norm_triangle_le
thf(fact_134_norm__triangle__le, axiom,
    ((![X : real, Y : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y)) @ E))))). % norm_triangle_le
thf(fact_135_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_136_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_137_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_138_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_139_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_140_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_141_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_142_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_143_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_144_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_145_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_146_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_147_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_148_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_149_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_150_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_151_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_152_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_153_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_154_group__cancel_Oadd1, axiom,
    ((![A4 : real, K : real, A : real, B : real]: ((A4 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A4 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![X5 : real, Y6 : real]: ((z = (complex2 @ X5 @ Y6)) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
