% 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/FFT/prob_136__3224106_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:25.117

% Could-be-implicit typings (5)
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Int__Oint, type,
    int : $tType).

% Explicit typings (43)
thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal, type,
    archim1371465213g_real : real > int).
thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal, type,
    archim1031974863r_real : real > int).
thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal, type,
    archim619457678d_real : real > int).
thf(sy_c_Complex_Oarg, type,
    arg : complex > real).
thf(sy_c_Complex_Ocsqrt, type,
    csqrt : complex > complex).
thf(sy_c_Complex_Orcis, type,
    rcis : real > real > complex).
thf(sy_c_FFT__Mirabelle__ulikgskiun_Oroot, type,
    fFT_Mirabelle_root : nat > complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint, type,
    one_one_int : int).
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__Int__Oint, type,
    plus_plus_int : int > int > int).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum, type,
    plus_plus_num : num > num > num).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint, type,
    uminus_uminus_int : int > int).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_real : real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint, type,
    zero_zero_int : int).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Num_Oinc, type,
    inc : num > num).
thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex, type,
    neg_nu1648888445omplex : complex > complex).
thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint, type,
    neg_numeral_dbl_int : int > int).
thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal, type,
    neg_numeral_dbl_real : real > real).
thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex, type,
    neg_nu972282243omplex : complex > complex).
thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint, type,
    neg_nu493100289ec_int : int > int).
thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal, type,
    neg_nu533782273c_real : real > real).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex, type,
    neg_nu484426047omplex : complex > complex).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint, type,
    neg_nu1877376189nc_int : int > int).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal, type,
    neg_nu1973887165c_real : real > real).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex, type,
    numera632737353omplex : num > complex).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint, type,
    numeral_numeral_int : num > int).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > real).
thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal, type,
    arcosh_real : real > real).
thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal, type,
    arsinh_real : real > real).
thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal, type,
    artanh_real : real > real).
thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex, type,
    cot_complex : complex > complex).
thf(sy_c_Transcendental_Ocot_001t__Real__Oreal, type,
    cot_real : real > real).
thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal, type,
    ln_ln_real : real > real).
thf(sy_c_Transcendental_Opowr_001t__Real__Oreal, type,
    powr_real : real > real > real).
thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex, type,
    tanh_complex : complex > complex).
thf(sy_c_Transcendental_Otanh_001t__Real__Oreal, type,
    tanh_real : real > real).
thf(sy_v_n, type,
    n : nat).

% Relevant facts (245)
thf(fact_0_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_1_zero__reorient, axiom,
    ((![X : int]: ((zero_zero_int = X) = (X = zero_zero_int))))). % zero_reorient
thf(fact_2_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_3_arsinh__0, axiom,
    (((arsinh_real @ zero_zero_real) = zero_zero_real))). % arsinh_0
thf(fact_4_artanh__0, axiom,
    (((artanh_real @ zero_zero_real) = zero_zero_real))). % artanh_0
thf(fact_5_csqrt__0, axiom,
    (((csqrt @ zero_zero_complex) = zero_zero_complex))). % csqrt_0
thf(fact_6_csqrt__eq__0, axiom,
    ((![Z : complex]: (((csqrt @ Z) = zero_zero_complex) = (Z = zero_zero_complex))))). % csqrt_eq_0
thf(fact_7_dbl__simps_I2_J, axiom,
    (((neg_nu1648888445omplex @ zero_zero_complex) = zero_zero_complex))). % dbl_simps(2)
thf(fact_8_dbl__simps_I2_J, axiom,
    (((neg_numeral_dbl_int @ zero_zero_int) = zero_zero_int))). % dbl_simps(2)
thf(fact_9_dbl__simps_I2_J, axiom,
    (((neg_numeral_dbl_real @ zero_zero_real) = zero_zero_real))). % dbl_simps(2)
thf(fact_10_cot__zero, axiom,
    (((cot_complex @ zero_zero_complex) = zero_zero_complex))). % cot_zero
thf(fact_11_cot__zero, axiom,
    (((cot_real @ zero_zero_real) = zero_zero_real))). % cot_zero
thf(fact_12_powr__0, axiom,
    ((![Z : real]: ((powr_real @ zero_zero_real @ Z) = zero_zero_real)))). % powr_0
thf(fact_13_powr__eq__0__iff, axiom,
    ((![W : real, Z : real]: (((powr_real @ W @ Z) = zero_zero_real) = (W = zero_zero_real))))). % powr_eq_0_iff
thf(fact_14_tanh__0, axiom,
    (((tanh_complex @ zero_zero_complex) = zero_zero_complex))). % tanh_0
thf(fact_15_tanh__0, axiom,
    (((tanh_real @ zero_zero_real) = zero_zero_real))). % tanh_0
thf(fact_16_round__0, axiom,
    (((archim619457678d_real @ zero_zero_real) = zero_zero_int))). % round_0
thf(fact_17_zero__integer_Orsp, axiom,
    ((zero_zero_int = zero_zero_int))). % zero_integer.rsp
thf(fact_18_powr__zero__eq__one, axiom,
    ((![X : real]: (((X = zero_zero_real) => ((powr_real @ X @ zero_zero_real) = zero_zero_real)) & ((~ ((X = zero_zero_real))) => ((powr_real @ X @ zero_zero_real) = one_one_real)))))). % powr_zero_eq_one
thf(fact_19_rcis__eq__zero__iff, axiom,
    ((![R : real, A : real]: (((rcis @ R @ A) = zero_zero_complex) = (R = zero_zero_real))))). % rcis_eq_zero_iff
thf(fact_20_rcis__zero__mod, axiom,
    ((![A : real]: ((rcis @ zero_zero_real @ A) = zero_zero_complex)))). % rcis_zero_mod
thf(fact_21_ceiling__zero, axiom,
    (((archim1371465213g_real @ zero_zero_real) = zero_zero_int))). % ceiling_zero
thf(fact_22_arg__zero, axiom,
    (((arg @ zero_zero_complex) = zero_zero_real))). % arg_zero
thf(fact_23_floor__zero, axiom,
    (((archim1031974863r_real @ zero_zero_real) = zero_zero_int))). % floor_zero
thf(fact_24_csqrt__1, axiom,
    (((csqrt @ one_one_complex) = one_one_complex))). % csqrt_1
thf(fact_25_csqrt__eq__1, axiom,
    ((![Z : complex]: (((csqrt @ Z) = one_one_complex) = (Z = one_one_complex))))). % csqrt_eq_1
thf(fact_26_cot__minus, axiom,
    ((![X : complex]: ((cot_complex @ (uminus1204672759omplex @ X)) = (uminus1204672759omplex @ (cot_complex @ X)))))). % cot_minus
thf(fact_27_cot__minus, axiom,
    ((![X : real]: ((cot_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (cot_real @ X)))))). % cot_minus
thf(fact_28_add_Oinverse__inverse, axiom,
    ((![A : int]: ((uminus_uminus_int @ (uminus_uminus_int @ A)) = A)))). % add.inverse_inverse
thf(fact_29_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_30_neg__equal__iff__equal, axiom,
    ((![A : int, B : int]: (((uminus_uminus_int @ A) = (uminus_uminus_int @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_31_neg__equal__iff__equal, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_32_tanh__real__zero__iff, axiom,
    ((![X : real]: (((tanh_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % tanh_real_zero_iff
thf(fact_33_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_34_add_Oinverse__neutral, axiom,
    (((uminus_uminus_int @ zero_zero_int) = zero_zero_int))). % add.inverse_neutral
thf(fact_35_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_36_neg__0__equal__iff__equal, axiom,
    ((![A : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A)) = (zero_zero_complex = A))))). % neg_0_equal_iff_equal
thf(fact_37_neg__0__equal__iff__equal, axiom,
    ((![A : int]: ((zero_zero_int = (uminus_uminus_int @ A)) = (zero_zero_int = A))))). % neg_0_equal_iff_equal
thf(fact_38_neg__0__equal__iff__equal, axiom,
    ((![A : real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A))))). % neg_0_equal_iff_equal
thf(fact_39_neg__equal__0__iff__equal, axiom,
    ((![A : complex]: (((uminus1204672759omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_40_neg__equal__0__iff__equal, axiom,
    ((![A : int]: (((uminus_uminus_int @ A) = zero_zero_int) = (A = zero_zero_int))))). % neg_equal_0_iff_equal
thf(fact_41_neg__equal__0__iff__equal, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % neg_equal_0_iff_equal
thf(fact_42_equal__neg__zero, axiom,
    ((![A : int]: ((A = (uminus_uminus_int @ A)) = (A = zero_zero_int))))). % equal_neg_zero
thf(fact_43_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_44_neg__equal__zero, axiom,
    ((![A : int]: (((uminus_uminus_int @ A) = A) = (A = zero_zero_int))))). % neg_equal_zero
thf(fact_45_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_46_powr__one__eq__one, axiom,
    ((![A : real]: ((powr_real @ one_one_real @ A) = one_one_real)))). % powr_one_eq_one
thf(fact_47_tanh__minus, axiom,
    ((![X : real]: ((tanh_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (tanh_real @ X)))))). % tanh_minus
thf(fact_48_rcis__Ex, axiom,
    ((![Z : complex]: (?[R2 : real, A2 : real]: (Z = (rcis @ R2 @ A2)))))). % rcis_Ex
thf(fact_49_one__reorient, axiom,
    ((![X : complex]: ((one_one_complex = X) = (X = one_one_complex))))). % one_reorient
thf(fact_50_one__reorient, axiom,
    ((![X : int]: ((one_one_int = X) = (X = one_one_int))))). % one_reorient
thf(fact_51_ceiling__def, axiom,
    ((archim1371465213g_real = (^[X2 : real]: (uminus_uminus_int @ (archim1031974863r_real @ (uminus_uminus_real @ X2))))))). % ceiling_def
thf(fact_52_floor__minus, axiom,
    ((![X : real]: ((archim1031974863r_real @ (uminus_uminus_real @ X)) = (uminus_uminus_int @ (archim1371465213g_real @ X)))))). % floor_minus
thf(fact_53_ceiling__minus, axiom,
    ((![X : real]: ((archim1371465213g_real @ (uminus_uminus_real @ X)) = (uminus_uminus_int @ (archim1031974863r_real @ X)))))). % ceiling_minus
thf(fact_54_one__neq__neg__one, axiom,
    ((~ ((one_one_complex = (uminus1204672759omplex @ one_one_complex)))))). % one_neq_neg_one
thf(fact_55_one__neq__neg__one, axiom,
    ((~ ((one_one_int = (uminus_uminus_int @ one_one_int)))))). % one_neq_neg_one
thf(fact_56_one__neq__neg__one, axiom,
    ((~ ((one_one_real = (uminus_uminus_real @ one_one_real)))))). % one_neq_neg_one
thf(fact_57_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_complex = (uminus1204672759omplex @ one_one_complex)))))). % zero_neq_neg_one
thf(fact_58_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_int = (uminus_uminus_int @ one_one_int)))))). % zero_neq_neg_one
thf(fact_59_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_real = (uminus_uminus_real @ one_one_real)))))). % zero_neq_neg_one
thf(fact_60_equation__minus__iff, axiom,
    ((![A : int, B : int]: ((A = (uminus_uminus_int @ B)) = (B = (uminus_uminus_int @ A)))))). % equation_minus_iff
thf(fact_61_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_62_minus__equation__iff, axiom,
    ((![A : int, B : int]: (((uminus_uminus_int @ A) = B) = ((uminus_uminus_int @ B) = A))))). % minus_equation_iff
thf(fact_63_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_64_arcosh__1, axiom,
    (((arcosh_real @ one_one_real) = zero_zero_real))). % arcosh_1
thf(fact_65_dbl__dec__simps_I2_J, axiom,
    (((neg_nu972282243omplex @ zero_zero_complex) = (uminus1204672759omplex @ one_one_complex)))). % dbl_dec_simps(2)
thf(fact_66_dbl__dec__simps_I2_J, axiom,
    (((neg_nu493100289ec_int @ zero_zero_int) = (uminus_uminus_int @ one_one_int)))). % dbl_dec_simps(2)
thf(fact_67_dbl__dec__simps_I2_J, axiom,
    (((neg_nu533782273c_real @ zero_zero_real) = (uminus_uminus_real @ one_one_real)))). % dbl_dec_simps(2)
thf(fact_68_verit__minus__simplify_I4_J, axiom,
    ((![B : int]: ((uminus_uminus_int @ (uminus_uminus_int @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_69_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_70_ln__one, axiom,
    (((ln_ln_real @ one_one_real) = zero_zero_real))). % ln_one
thf(fact_71_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_72_zero__neq__one, axiom,
    ((~ ((zero_zero_int = one_one_int))))). % zero_neq_one
thf(fact_73_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_74_dbl__inc__simps_I4_J, axiom,
    (((neg_nu484426047omplex @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ one_one_complex)))). % dbl_inc_simps(4)
thf(fact_75_dbl__inc__simps_I4_J, axiom,
    (((neg_nu1877376189nc_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))). % dbl_inc_simps(4)
thf(fact_76_dbl__inc__simps_I4_J, axiom,
    (((neg_nu1973887165c_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ one_one_real)))). % dbl_inc_simps(4)
thf(fact_77_tanh__real__eq__iff, axiom,
    ((![X : real, Y : real]: (((tanh_real @ X) = (tanh_real @ Y)) = (X = Y))))). % tanh_real_eq_iff
thf(fact_78_dbl__dec__simps_I3_J, axiom,
    (((neg_nu972282243omplex @ one_one_complex) = one_one_complex))). % dbl_dec_simps(3)
thf(fact_79_dbl__dec__simps_I3_J, axiom,
    (((neg_nu493100289ec_int @ one_one_int) = one_one_int))). % dbl_dec_simps(3)
thf(fact_80_dbl__inc__simps_I2_J, axiom,
    (((neg_nu484426047omplex @ zero_zero_complex) = one_one_complex))). % dbl_inc_simps(2)
thf(fact_81_dbl__inc__simps_I2_J, axiom,
    (((neg_nu1877376189nc_int @ zero_zero_int) = one_one_int))). % dbl_inc_simps(2)
thf(fact_82_dbl__inc__simps_I2_J, axiom,
    (((neg_nu1973887165c_real @ zero_zero_real) = one_one_real))). % dbl_inc_simps(2)
thf(fact_83_one__integer_Orsp, axiom,
    ((one_one_int = one_one_int))). % one_integer.rsp
thf(fact_84_artanh__tanh__real, axiom,
    ((![X : real]: ((artanh_real @ (tanh_real @ X)) = X)))). % artanh_tanh_real
thf(fact_85_verit__negate__coefficient_I3_J, axiom,
    ((![A : int, B : int]: ((A = B) => ((uminus_uminus_int @ A) = (uminus_uminus_int @ B)))))). % verit_negate_coefficient(3)
thf(fact_86_verit__negate__coefficient_I3_J, axiom,
    ((![A : real, B : real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B)))))). % verit_negate_coefficient(3)
thf(fact_87_uminus__int__code_I1_J, axiom,
    (((uminus_uminus_int @ zero_zero_int) = zero_zero_int))). % uminus_int_code(1)
thf(fact_88_dbl__dec__simps_I1_J, axiom,
    ((![K : num]: ((neg_nu493100289ec_int @ (uminus_uminus_int @ (numeral_numeral_int @ K))) = (uminus_uminus_int @ (neg_nu1877376189nc_int @ (numeral_numeral_int @ K))))))). % dbl_dec_simps(1)
thf(fact_89_dbl__dec__simps_I1_J, axiom,
    ((![K : num]: ((neg_nu533782273c_real @ (uminus_uminus_real @ (numeral_numeral_real @ K))) = (uminus_uminus_real @ (neg_nu1973887165c_real @ (numeral_numeral_real @ K))))))). % dbl_dec_simps(1)
thf(fact_90_dbl__inc__simps_I1_J, axiom,
    ((![K : num]: ((neg_nu1877376189nc_int @ (uminus_uminus_int @ (numeral_numeral_int @ K))) = (uminus_uminus_int @ (neg_nu493100289ec_int @ (numeral_numeral_int @ K))))))). % dbl_inc_simps(1)
thf(fact_91_dbl__inc__simps_I1_J, axiom,
    ((![K : num]: ((neg_nu1973887165c_real @ (uminus_uminus_real @ (numeral_numeral_real @ K))) = (uminus_uminus_real @ (neg_nu533782273c_real @ (numeral_numeral_real @ K))))))). % dbl_inc_simps(1)
thf(fact_92_add__neg__numeral__special_I7_J, axiom,
    (((plus_plus_complex @ one_one_complex @ (uminus1204672759omplex @ one_one_complex)) = zero_zero_complex))). % add_neg_numeral_special(7)
thf(fact_93_add__neg__numeral__special_I7_J, axiom,
    (((plus_plus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = zero_zero_int))). % add_neg_numeral_special(7)
thf(fact_94_add__neg__numeral__special_I7_J, axiom,
    (((plus_plus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = zero_zero_real))). % add_neg_numeral_special(7)
thf(fact_95_add__neg__numeral__special_I8_J, axiom,
    (((plus_plus_complex @ (uminus1204672759omplex @ one_one_complex) @ one_one_complex) = zero_zero_complex))). % add_neg_numeral_special(8)
thf(fact_96_add__neg__numeral__special_I8_J, axiom,
    (((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = zero_zero_int))). % add_neg_numeral_special(8)
thf(fact_97_add__neg__numeral__special_I8_J, axiom,
    (((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = zero_zero_real))). % add_neg_numeral_special(8)
thf(fact_98_add__left__cancel, axiom,
    ((![A : int, B : int, C : int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_99_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_100_add__right__cancel, axiom,
    ((![B : int, A : int, C : int]: (((plus_plus_int @ B @ A) = (plus_plus_int @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_101_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_102_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_103_add_Oleft__neutral, axiom,
    ((![A : int]: ((plus_plus_int @ zero_zero_int @ A) = A)))). % add.left_neutral
thf(fact_104_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_105_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_106_add_Oright__neutral, axiom,
    ((![A : int]: ((plus_plus_int @ A @ zero_zero_int) = A)))). % add.right_neutral
thf(fact_107_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_108_double__zero, axiom,
    ((![A : int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int))))). % double_zero
thf(fact_109_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_110_double__zero__sym, axiom,
    ((![A : int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int))))). % double_zero_sym
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 : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) = (B = zero_zero_complex))))). % add_cancel_left_left
thf(fact_113_add__cancel__left__left, axiom,
    ((![B : int, A : int]: (((plus_plus_int @ B @ A) = A) = (B = zero_zero_int))))). % add_cancel_left_left
thf(fact_114_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_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__left__right, axiom,
    ((![A : int, B : int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int))))). % add_cancel_left_right
thf(fact_117_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_118_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_119_add__cancel__right__left, axiom,
    ((![A : int, B : int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int))))). % add_cancel_right_left
thf(fact_120_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_121_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_122_add__cancel__right__right, axiom,
    ((![A : int, B : int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int))))). % add_cancel_right_right
thf(fact_123_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_124_add__numeral__left, axiom,
    ((![V : num, W : num, Z : int]: ((plus_plus_int @ (numeral_numeral_int @ V) @ (plus_plus_int @ (numeral_numeral_int @ W) @ Z)) = (plus_plus_int @ (numeral_numeral_int @ (plus_plus_num @ V @ W)) @ Z))))). % add_numeral_left
thf(fact_125_add__numeral__left, axiom,
    ((![V : num, W : num, Z : real]: ((plus_plus_real @ (numeral_numeral_real @ V) @ (plus_plus_real @ (numeral_numeral_real @ W) @ Z)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ V @ W)) @ Z))))). % add_numeral_left
thf(fact_126_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N)) = (numeral_numeral_int @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_127_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_128_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus_uminus_int @ (numeral_numeral_int @ M)) = (uminus_uminus_int @ (numeral_numeral_int @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_129_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_130_add__minus__cancel, axiom,
    ((![A : int, B : int]: ((plus_plus_int @ A @ (plus_plus_int @ (uminus_uminus_int @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_131_add__minus__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ A @ (plus_plus_real @ (uminus_uminus_real @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_132_minus__add__cancel, axiom,
    ((![A : int, B : int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ (plus_plus_int @ A @ B)) = B)))). % minus_add_cancel
thf(fact_133_minus__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ (plus_plus_real @ A @ B)) = B)))). % minus_add_cancel
thf(fact_134_minus__add__distrib, axiom,
    ((![A : int, B : int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)))))). % minus_add_distrib
thf(fact_135_minus__add__distrib, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)))))). % minus_add_distrib
thf(fact_136_add_Oright__inverse, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ (uminus1204672759omplex @ A)) = zero_zero_complex)))). % add.right_inverse
thf(fact_137_add_Oright__inverse, axiom,
    ((![A : int]: ((plus_plus_int @ A @ (uminus_uminus_int @ A)) = zero_zero_int)))). % add.right_inverse
thf(fact_138_add_Oright__inverse, axiom,
    ((![A : real]: ((plus_plus_real @ A @ (uminus_uminus_real @ A)) = zero_zero_real)))). % add.right_inverse
thf(fact_139_add_Oleft__inverse, axiom,
    ((![A : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ A) = zero_zero_complex)))). % add.left_inverse
thf(fact_140_add_Oleft__inverse, axiom,
    ((![A : int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int)))). % add.left_inverse
thf(fact_141_add_Oleft__inverse, axiom,
    ((![A : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real)))). % add.left_inverse
thf(fact_142_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ M)) @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (uminus_uminus_int @ (plus_plus_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N))))))). % add_neg_numeral_simps(3)
thf(fact_143_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_real @ (plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N))))))). % add_neg_numeral_simps(3)
thf(fact_144_ceiling__add__numeral, axiom,
    ((![X : real, V : num]: ((archim1371465213g_real @ (plus_plus_real @ X @ (numeral_numeral_real @ V))) = (plus_plus_int @ (archim1371465213g_real @ X) @ (numeral_numeral_int @ V)))))). % ceiling_add_numeral
thf(fact_145_dbl__simps_I1_J, axiom,
    ((![K : num]: ((neg_nu1648888445omplex @ (uminus1204672759omplex @ (numera632737353omplex @ K))) = (uminus1204672759omplex @ (neg_nu1648888445omplex @ (numera632737353omplex @ K))))))). % dbl_simps(1)
thf(fact_146_dbl__simps_I1_J, axiom,
    ((![K : num]: ((neg_numeral_dbl_int @ (uminus_uminus_int @ (numeral_numeral_int @ K))) = (uminus_uminus_int @ (neg_numeral_dbl_int @ (numeral_numeral_int @ K))))))). % dbl_simps(1)
thf(fact_147_dbl__simps_I1_J, axiom,
    ((![K : num]: ((neg_numeral_dbl_real @ (uminus_uminus_real @ (numeral_numeral_real @ K))) = (uminus_uminus_real @ (neg_numeral_dbl_real @ (numeral_numeral_real @ K))))))). % dbl_simps(1)
thf(fact_148_ceiling__add__one, axiom,
    ((![X : real]: ((archim1371465213g_real @ (plus_plus_real @ X @ one_one_real)) = (plus_plus_int @ (archim1371465213g_real @ X) @ one_one_int))))). % ceiling_add_one
thf(fact_149_floor__neg__numeral, axiom,
    ((![V : num]: ((archim1031974863r_real @ (uminus_uminus_real @ (numeral_numeral_real @ V))) = (uminus_uminus_int @ (numeral_numeral_int @ V)))))). % floor_neg_numeral
thf(fact_150_ceiling__neg__numeral, axiom,
    ((![V : num]: ((archim1371465213g_real @ (uminus_uminus_real @ (numeral_numeral_real @ V))) = (uminus_uminus_int @ (numeral_numeral_int @ V)))))). % ceiling_neg_numeral
thf(fact_151_round__neg__numeral, axiom,
    ((![N : num]: ((archim619457678d_real @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_int @ (numeral_numeral_int @ N)))))). % round_neg_numeral
thf(fact_152_one__plus__numeral__commute, axiom,
    ((![X : num]: ((plus_plus_complex @ one_one_complex @ (numera632737353omplex @ X)) = (plus_plus_complex @ (numera632737353omplex @ X) @ one_one_complex))))). % one_plus_numeral_commute
thf(fact_153_one__plus__numeral__commute, axiom,
    ((![X : num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ X)) = (plus_plus_int @ (numeral_numeral_int @ X) @ one_one_int))))). % one_plus_numeral_commute
thf(fact_154_one__plus__numeral__commute, axiom,
    ((![X : num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ X)) = (plus_plus_real @ (numeral_numeral_real @ X) @ one_one_real))))). % one_plus_numeral_commute
thf(fact_155_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : int, B : int, C : int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_156_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_157_is__num__normalize_I1_J, axiom,
    ((![A : int, B : int, C : int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C)))))). % is_num_normalize(1)
thf(fact_158_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_159_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : int, J : int, K : int, L : int]: (((I = J) & (K = L)) => ((plus_plus_int @ I @ K) = (plus_plus_int @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_160_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_161_group__cancel_Oadd1, axiom,
    ((![A3 : int, K : int, A : int, B : int]: ((A3 = (plus_plus_int @ K @ A)) => ((plus_plus_int @ A3 @ B) = (plus_plus_int @ K @ (plus_plus_int @ A @ B))))))). % group_cancel.add1
thf(fact_162_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_163_group__cancel_Oadd2, axiom,
    ((![B2 : int, K : int, B : int, A : int]: ((B2 = (plus_plus_int @ K @ B)) => ((plus_plus_int @ A @ B2) = (plus_plus_int @ K @ (plus_plus_int @ A @ B))))))). % group_cancel.add2
thf(fact_164_group__cancel_Oadd2, axiom,
    ((![B2 : real, K : real, B : real, A : real]: ((B2 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B2) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_165_add_Oassoc, axiom,
    ((![A : int, B : int, C : int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C)))))). % add.assoc
thf(fact_166_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_167_add_Oleft__cancel, axiom,
    ((![A : int, B : int, C : int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_168_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_169_add_Oright__cancel, axiom,
    ((![B : int, A : int, C : int]: (((plus_plus_int @ B @ A) = (plus_plus_int @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_170_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_171_add_Ocommute, axiom,
    ((plus_plus_int = (^[A4 : int]: (^[B3 : int]: (plus_plus_int @ B3 @ A4)))))). % add.commute
thf(fact_172_add_Ocommute, axiom,
    ((plus_plus_real = (^[A4 : real]: (^[B3 : real]: (plus_plus_real @ B3 @ A4)))))). % add.commute
thf(fact_173_add_Oleft__commute, axiom,
    ((![B : int, A : int, C : int]: ((plus_plus_int @ B @ (plus_plus_int @ A @ C)) = (plus_plus_int @ A @ (plus_plus_int @ B @ C)))))). % add.left_commute
thf(fact_174_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_175_add__left__imp__eq, axiom,
    ((![A : int, B : int, C : int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_176_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_177_add__right__imp__eq, axiom,
    ((![B : int, A : int, C : int]: (((plus_plus_int @ B @ A) = (plus_plus_int @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_178_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_179_plus__int__code_I2_J, axiom,
    ((![L : int]: ((plus_plus_int @ zero_zero_int @ L) = L)))). % plus_int_code(2)
thf(fact_180_plus__int__code_I1_J, axiom,
    ((![K : int]: ((plus_plus_int @ K @ zero_zero_int) = K)))). % plus_int_code(1)
thf(fact_181_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N))))))). % zero_neq_numeral
thf(fact_182_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N))))))). % zero_neq_numeral
thf(fact_183_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_real = (numeral_numeral_real @ N))))))). % zero_neq_numeral
thf(fact_184_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_185_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : int]: ((plus_plus_int @ zero_zero_int @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_186_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_187_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_188_add_Ocomm__neutral, axiom,
    ((![A : int]: ((plus_plus_int @ A @ zero_zero_int) = A)))). % add.comm_neutral
thf(fact_189_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_190_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_191_add_Ogroup__left__neutral, axiom,
    ((![A : int]: ((plus_plus_int @ zero_zero_int @ A) = A)))). % add.group_left_neutral
thf(fact_192_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_193_verit__sum__simplify, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % verit_sum_simplify
thf(fact_194_verit__sum__simplify, axiom,
    ((![A : int]: ((plus_plus_int @ A @ zero_zero_int) = A)))). % verit_sum_simplify
thf(fact_195_verit__sum__simplify, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % verit_sum_simplify
thf(fact_196_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus_uminus_int @ (numeral_numeral_int @ M)) = (numeral_numeral_int @ N))))))). % neg_numeral_neq_numeral
thf(fact_197_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (numeral_numeral_real @ N))))))). % neg_numeral_neq_numeral
thf(fact_198_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numeral_numeral_int @ M) = (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % numeral_neq_neg_numeral
thf(fact_199_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numeral_numeral_real @ M) = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % numeral_neq_neg_numeral
thf(fact_200_is__num__normalize_I8_J, axiom,
    ((![A : int, B : int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)))))). % is_num_normalize(8)
thf(fact_201_is__num__normalize_I8_J, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % is_num_normalize(8)
thf(fact_202_group__cancel_Oneg1, axiom,
    ((![A3 : int, K : int, A : int]: ((A3 = (plus_plus_int @ K @ A)) => ((uminus_uminus_int @ A3) = (plus_plus_int @ (uminus_uminus_int @ K) @ (uminus_uminus_int @ A))))))). % group_cancel.neg1
thf(fact_203_group__cancel_Oneg1, axiom,
    ((![A3 : real, K : real, A : real]: ((A3 = (plus_plus_real @ K @ A)) => ((uminus_uminus_real @ A3) = (plus_plus_real @ (uminus_uminus_real @ K) @ (uminus_uminus_real @ A))))))). % group_cancel.neg1
thf(fact_204_add_Oinverse__distrib__swap, axiom,
    ((![A : int, B : int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)))))). % add.inverse_distrib_swap
thf(fact_205_add_Oinverse__distrib__swap, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % add.inverse_distrib_swap
thf(fact_206_odd__nonzero, axiom,
    ((![Z : int]: (~ (((plus_plus_int @ (plus_plus_int @ one_one_int @ Z) @ Z) = zero_zero_int)))))). % odd_nonzero
thf(fact_207_one__add__floor, axiom,
    ((![X : real]: ((plus_plus_int @ (archim1031974863r_real @ X) @ one_one_int) = (archim1031974863r_real @ (plus_plus_real @ X @ one_one_real)))))). % one_add_floor
thf(fact_208_dbl__def, axiom,
    ((neg_numeral_dbl_real = (^[X2 : real]: (plus_plus_real @ X2 @ X2))))). % dbl_def
thf(fact_209_dbl__def, axiom,
    ((neg_numeral_dbl_int = (^[X2 : int]: (plus_plus_int @ X2 @ X2))))). % dbl_def
thf(fact_210_dbl__def, axiom,
    ((neg_nu1648888445omplex = (^[X2 : complex]: (plus_plus_complex @ X2 @ X2))))). % dbl_def
thf(fact_211_zero__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % zero_neq_neg_numeral
thf(fact_212_zero__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % zero_neq_neg_numeral
thf(fact_213_zero__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_real = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % zero_neq_neg_numeral
thf(fact_214_add__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) = (B = (uminus1204672759omplex @ A)))))). % add_eq_0_iff
thf(fact_215_add__eq__0__iff, axiom,
    ((![A : int, B : int]: (((plus_plus_int @ A @ B) = zero_zero_int) = (B = (uminus_uminus_int @ A)))))). % add_eq_0_iff
thf(fact_216_add__eq__0__iff, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = zero_zero_real) = (B = (uminus_uminus_real @ A)))))). % add_eq_0_iff
thf(fact_217_ab__group__add__class_Oab__left__minus, axiom,
    ((![A : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ A) = zero_zero_complex)))). % ab_group_add_class.ab_left_minus
thf(fact_218_ab__group__add__class_Oab__left__minus, axiom,
    ((![A : int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int)))). % ab_group_add_class.ab_left_minus
thf(fact_219_ab__group__add__class_Oab__left__minus, axiom,
    ((![A : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real)))). % ab_group_add_class.ab_left_minus
thf(fact_220_add_Oinverse__unique, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) => ((uminus1204672759omplex @ A) = B))))). % add.inverse_unique
thf(fact_221_add_Oinverse__unique, axiom,
    ((![A : int, B : int]: (((plus_plus_int @ A @ B) = zero_zero_int) => ((uminus_uminus_int @ A) = B))))). % add.inverse_unique
thf(fact_222_add_Oinverse__unique, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = zero_zero_real) => ((uminus_uminus_real @ A) = B))))). % add.inverse_unique
thf(fact_223_eq__neg__iff__add__eq__0, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = ((plus_plus_complex @ A @ B) = zero_zero_complex))))). % eq_neg_iff_add_eq_0
thf(fact_224_eq__neg__iff__add__eq__0, axiom,
    ((![A : int, B : int]: ((A = (uminus_uminus_int @ B)) = ((plus_plus_int @ A @ B) = zero_zero_int))))). % eq_neg_iff_add_eq_0
thf(fact_225_eq__neg__iff__add__eq__0, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = ((plus_plus_real @ A @ B) = zero_zero_real))))). % eq_neg_iff_add_eq_0
thf(fact_226_neg__eq__iff__add__eq__0, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((plus_plus_complex @ A @ B) = zero_zero_complex))))). % neg_eq_iff_add_eq_0
thf(fact_227_neg__eq__iff__add__eq__0, axiom,
    ((![A : int, B : int]: (((uminus_uminus_int @ A) = B) = ((plus_plus_int @ A @ B) = zero_zero_int))))). % neg_eq_iff_add_eq_0
thf(fact_228_neg__eq__iff__add__eq__0, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((plus_plus_real @ A @ B) = zero_zero_real))))). % neg_eq_iff_add_eq_0
thf(fact_229_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numera632737353omplex @ N) = (uminus1204672759omplex @ one_one_complex))))))). % numeral_neq_neg_one
thf(fact_230_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numeral_numeral_int @ N) = (uminus_uminus_int @ one_one_int))))))). % numeral_neq_neg_one
thf(fact_231_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numeral_numeral_real @ N) = (uminus_uminus_real @ one_one_real))))))). % numeral_neq_neg_one
thf(fact_232_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_complex = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % one_neq_neg_numeral
thf(fact_233_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_int = (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % one_neq_neg_numeral
thf(fact_234_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_real = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % one_neq_neg_numeral
thf(fact_235_dbl__inc__def, axiom,
    ((neg_nu484426047omplex = (^[X2 : complex]: (plus_plus_complex @ (plus_plus_complex @ X2 @ X2) @ one_one_complex))))). % dbl_inc_def
thf(fact_236_dbl__inc__def, axiom,
    ((neg_nu1877376189nc_int = (^[X2 : int]: (plus_plus_int @ (plus_plus_int @ X2 @ X2) @ one_one_int))))). % dbl_inc_def
thf(fact_237_dbl__inc__def, axiom,
    ((neg_nu1973887165c_real = (^[X2 : real]: (plus_plus_real @ (plus_plus_real @ X2 @ X2) @ one_one_real))))). % dbl_inc_def
thf(fact_238_semiring__norm_I168_J, axiom,
    ((![V : num, W : num, Y : int]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ V)) @ (plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ W)) @ Y)) = (plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ V @ W))) @ Y))))). % semiring_norm(168)
thf(fact_239_semiring__norm_I168_J, axiom,
    ((![V : num, W : num, Y : real]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ V)) @ (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ W)) @ Y)) = (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ V @ W))) @ Y))))). % semiring_norm(168)
thf(fact_240_real__add__minus__iff, axiom,
    ((![X : real, A : real]: (((plus_plus_real @ X @ (uminus_uminus_real @ A)) = zero_zero_real) = (X = A))))). % real_add_minus_iff
thf(fact_241_add__neg__numeral__special_I5_J, axiom,
    ((![N : num]: ((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ N))) = (uminus_uminus_int @ (numeral_numeral_int @ (inc @ N))))))). % add_neg_numeral_special(5)
thf(fact_242_add__neg__numeral__special_I5_J, axiom,
    ((![N : num]: ((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_real @ (numeral_numeral_real @ (inc @ N))))))). % add_neg_numeral_special(5)
thf(fact_243_arsinh__minus__real, axiom,
    ((![X : real]: ((arsinh_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (arsinh_real @ X)))))). % arsinh_minus_real
thf(fact_244_add__inc, axiom,
    ((![X : num, Y : num]: ((plus_plus_num @ X @ (inc @ Y)) = (inc @ (plus_plus_num @ X @ Y)))))). % add_inc

% Conjectures (1)
thf(conj_0, conjecture,
    ((~ (((fFT_Mirabelle_root @ n) = zero_zero_complex))))).
