% 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_217__3224852_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:57.902

% Could-be-implicit typings (4)
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $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 (28)
thf(sy_c_Complex_Oimaginary__unit, type,
    imaginary_unit : complex).
thf(sy_c_FFT__Mirabelle__ulikgskiun_Oroot, type,
    fFT_Mirabelle_root : nat > complex).
thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex, type,
    semiri1865663904omplex : nat > complex).
thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint, type,
    semiri688227102ct_int : nat > int).
thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat, type,
    semiri50953410ct_nat : nat > nat).
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__Nat__Onat, type,
    one_one_nat : nat).
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__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum, type,
    plus_plus_num : num > num > num).
thf(sy_c_Groups_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_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__Nat__Onat, type,
    zero_zero_nat : nat).
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__inc_001t__Complex__Ocomplex, type,
    neg_nu484426047omplex : complex > complex).
thf(sy_c_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex, type,
    numera632737353omplex : num > complex).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint, type,
    numeral_numeral_int : num > int).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint, type,
    divide_divide_int : int > int > int).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat, type,
    divide_divide_nat : nat > nat > nat).

% Relevant facts (196)
thf(fact_0_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_1_semiring__norm_I83_J, axiom,
    ((![N : num]: (~ ((one = (bit0 @ N))))))). % semiring_norm(83)
thf(fact_2_verit__eq__simplify_I8_J, axiom,
    ((![X2 : num, Y2 : num]: (((bit0 @ X2) = (bit0 @ Y2)) = (X2 = Y2))))). % verit_eq_simplify(8)
thf(fact_3_semiring__norm_I87_J, axiom,
    ((![M : num, N : num]: (((bit0 @ M) = (bit0 @ N)) = (M = N))))). % semiring_norm(87)
thf(fact_4_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_5_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_6_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_7_verit__eq__simplify_I10_J, axiom,
    ((![X2 : num]: (~ ((one = (bit0 @ X2))))))). % verit_eq_simplify(10)
thf(fact_8_fact__2, axiom,
    (((semiri50953410ct_nat @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ (bit0 @ one))))). % fact_2
thf(fact_9_fact__2, axiom,
    (((semiri688227102ct_int @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_int @ (bit0 @ one))))). % fact_2
thf(fact_10_fact__2, axiom,
    (((semiri1865663904omplex @ (numeral_numeral_nat @ (bit0 @ one))) = (numera632737353omplex @ (bit0 @ one))))). % fact_2
thf(fact_11_dbl__simps_I5_J, axiom,
    ((![K : num]: ((neg_numeral_dbl_int @ (numeral_numeral_int @ K)) = (numeral_numeral_int @ (bit0 @ K)))))). % dbl_simps(5)
thf(fact_12_dbl__simps_I5_J, axiom,
    ((![K : num]: ((neg_nu1648888445omplex @ (numera632737353omplex @ K)) = (numera632737353omplex @ (bit0 @ K)))))). % dbl_simps(5)
thf(fact_13_root2, axiom,
    (((fFT_Mirabelle_root @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1204672759omplex @ one_one_complex)))). % root2
thf(fact_14_numeral__Bit0__div__2, axiom,
    ((![N : num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ N)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ N))))). % numeral_Bit0_div_2
thf(fact_15_numeral__Bit0__div__2, axiom,
    ((![N : num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit0 @ N)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ N))))). % numeral_Bit0_div_2
thf(fact_16_verit__minus__simplify_I4_J, axiom,
    ((![B : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_17_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_18_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_19_div__minus__minus, axiom,
    ((![A : int, B : int]: ((divide_divide_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (divide_divide_int @ A @ B))))). % div_minus_minus
thf(fact_20_fact__1, axiom,
    (((semiri1865663904omplex @ one_one_nat) = one_one_complex))). % fact_1
thf(fact_21_fact__1, axiom,
    (((semiri688227102ct_int @ one_one_nat) = one_one_int))). % fact_1
thf(fact_22_fact__1, axiom,
    (((semiri50953410ct_nat @ one_one_nat) = one_one_nat))). % fact_1
thf(fact_23_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_24_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_int = (numeral_numeral_int @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_25_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_26_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_27_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_int @ N) = one_one_int) = (N = one))))). % numeral_eq_one_iff
thf(fact_28_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_29_div__minus1__right, axiom,
    ((![A : int]: ((divide_divide_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ A))))). % div_minus1_right
thf(fact_30_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_31_dbl__simps_I1_J, axiom,
    ((![K : num]: ((neg_nu1648888445omplex @ (uminus1204672759omplex @ (numera632737353omplex @ K))) = (uminus1204672759omplex @ (neg_nu1648888445omplex @ (numera632737353omplex @ K))))))). % dbl_simps(1)
thf(fact_32_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus_uminus_int @ (numeral_numeral_int @ N)) = (uminus_uminus_int @ one_one_int)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_33_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ one_one_complex)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_34_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus_uminus_int @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_35_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_36_dbl__simps_I3_J, axiom,
    (((neg_numeral_dbl_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one))))). % dbl_simps(3)
thf(fact_37_dbl__simps_I3_J, axiom,
    (((neg_nu1648888445omplex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % dbl_simps(3)
thf(fact_38_dbl__simps_I4_J, axiom,
    (((neg_numeral_dbl_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one)))))). % dbl_simps(4)
thf(fact_39_dbl__simps_I4_J, axiom,
    (((neg_nu1648888445omplex @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ (numera632737353omplex @ (bit0 @ one)))))). % dbl_simps(4)
thf(fact_40_one__neq__neg__one, axiom,
    ((~ ((one_one_complex = (uminus1204672759omplex @ one_one_complex)))))). % one_neq_neg_one
thf(fact_41_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numeral_numeral_int @ N) = (uminus_uminus_int @ one_one_int))))))). % numeral_neq_neg_one
thf(fact_42_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numera632737353omplex @ N) = (uminus1204672759omplex @ one_one_complex))))))). % numeral_neq_neg_one
thf(fact_43_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_int = (uminus_uminus_int @ (numeral_numeral_int @ N)))))))). % one_neq_neg_numeral
thf(fact_44_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_complex = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % one_neq_neg_numeral
thf(fact_45_div__minus__right, axiom,
    ((![A : int, B : int]: ((divide_divide_int @ A @ (uminus_uminus_int @ B)) = (divide_divide_int @ (uminus_uminus_int @ A) @ B))))). % div_minus_right
thf(fact_46_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_47_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numera632737353omplex @ M) = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % numeral_neq_neg_numeral
thf(fact_48_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_49_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (numera632737353omplex @ N))))))). % neg_numeral_neq_numeral
thf(fact_50_uminus__numeral__One, axiom,
    (((uminus_uminus_int @ (numeral_numeral_int @ one)) = (uminus_uminus_int @ one_one_int)))). % uminus_numeral_One
thf(fact_51_uminus__numeral__One, axiom,
    (((uminus1204672759omplex @ (numera632737353omplex @ one)) = (uminus1204672759omplex @ one_one_complex)))). % uminus_numeral_One
thf(fact_52_divide__numeral__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ (numera632737353omplex @ one)) = A)))). % divide_numeral_1
thf(fact_53_numeral__One, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numeral_One
thf(fact_54_numeral__One, axiom,
    (((numeral_numeral_int @ one) = one_one_int))). % numeral_One
thf(fact_55_numeral__One, axiom,
    (((numera632737353omplex @ one) = one_one_complex))). % numeral_One
thf(fact_56_minus__1__div__2__eq, axiom,
    (((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (uminus_uminus_int @ one_one_int)))). % minus_1_div_2_eq
thf(fact_57_divide__minus1, axiom,
    ((![X : complex]: ((divide1210191872omplex @ X @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ X))))). % divide_minus1
thf(fact_58_div__by__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ one_one_complex) = A)))). % div_by_1
thf(fact_59_div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % div_by_1
thf(fact_60_div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % div_by_1
thf(fact_61_bits__div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % bits_div_by_1
thf(fact_62_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_63_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_64_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_65_zdiv__numeral__Bit0, axiom,
    ((![V : num, W : num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ V)) @ (numeral_numeral_int @ (bit0 @ W))) = (divide_divide_int @ (numeral_numeral_int @ V) @ (numeral_numeral_int @ W)))))). % zdiv_numeral_Bit0
thf(fact_66_root1, axiom,
    (((fFT_Mirabelle_root @ one_one_nat) = one_one_complex))). % root1
thf(fact_67_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_68_one__reorient, axiom,
    ((![X : complex]: ((one_one_complex = X) = (X = one_one_complex))))). % one_reorient
thf(fact_69_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_70_minus__equation__iff, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((uminus1204672759omplex @ B) = A))))). % minus_equation_iff
thf(fact_71_equation__minus__iff, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = (B = (uminus1204672759omplex @ A)))))). % equation_minus_iff
thf(fact_72_minus__divide__left, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (divide1210191872omplex @ A @ B)) = (divide1210191872omplex @ (uminus1204672759omplex @ A) @ B))))). % minus_divide_left
thf(fact_73_minus__divide__divide, axiom,
    ((![A : complex, B : complex]: ((divide1210191872omplex @ (uminus1204672759omplex @ A) @ (uminus1204672759omplex @ B)) = (divide1210191872omplex @ A @ B))))). % minus_divide_divide
thf(fact_74_minus__divide__right, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (divide1210191872omplex @ A @ B)) = (divide1210191872omplex @ A @ (uminus1204672759omplex @ B)))))). % minus_divide_right
thf(fact_75_complex__i__not__neg__numeral, axiom,
    ((![W : num]: (~ ((imaginary_unit = (uminus1204672759omplex @ (numera632737353omplex @ W)))))))). % complex_i_not_neg_numeral
thf(fact_76_complex__i__not__one, axiom,
    ((~ ((imaginary_unit = one_one_complex))))). % complex_i_not_one
thf(fact_77_bits__1__div__2, axiom,
    (((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))). % bits_1_div_2
thf(fact_78_bits__1__div__2, axiom,
    (((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % bits_1_div_2
thf(fact_79_one__div__two__eq__zero, axiom,
    (((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))). % one_div_two_eq_zero
thf(fact_80_one__div__two__eq__zero, axiom,
    (((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % one_div_two_eq_zero
thf(fact_81_dbl__inc__simps_I4_J, axiom,
    (((neg_nu484426047omplex @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ one_one_complex)))). % dbl_inc_simps(4)
thf(fact_82_add__neg__numeral__special_I9_J, axiom,
    (((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one)))))). % add_neg_numeral_special(9)
thf(fact_83_add__neg__numeral__special_I9_J, axiom,
    (((plus_plus_complex @ (uminus1204672759omplex @ one_one_complex) @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ (numera632737353omplex @ (bit0 @ one)))))). % add_neg_numeral_special(9)
thf(fact_84_add__right__cancel, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_85_add__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_86_semiring__norm_I6_J, axiom,
    ((![M : num, N : num]: ((plus_plus_num @ (bit0 @ M) @ (bit0 @ N)) = (bit0 @ (plus_plus_num @ M @ N)))))). % semiring_norm(6)
thf(fact_87_zero__eq__add__iff__both__eq__0, axiom,
    ((![X : nat, Y : nat]: ((zero_zero_nat = (plus_plus_nat @ X @ Y)) = (((X = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % zero_eq_add_iff_both_eq_0
thf(fact_88_add__eq__0__iff__both__eq__0, axiom,
    ((![X : nat, Y : nat]: (((plus_plus_nat @ X @ Y) = zero_zero_nat) = (((X = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % add_eq_0_iff_both_eq_0
thf(fact_89_add__cancel__right__right, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat))))). % add_cancel_right_right
thf(fact_90_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_91_add__cancel__right__left, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat))))). % add_cancel_right_left
thf(fact_92_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_93_add__cancel__left__right, axiom,
    ((![A : nat, B : nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat))))). % add_cancel_left_right
thf(fact_94_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_95_add__cancel__left__left, axiom,
    ((![B : nat, A : nat]: (((plus_plus_nat @ B @ A) = A) = (B = zero_zero_nat))))). % add_cancel_left_left
thf(fact_96_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_97_add_Oright__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.right_neutral
thf(fact_98_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_99_add_Oleft__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % add.left_neutral
thf(fact_100_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_101_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_102_div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % div_0
thf(fact_103_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_104_divide__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % divide_eq_0_iff
thf(fact_105_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_106_div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % div_by_0
thf(fact_107_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_108_divide__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((divide1210191872omplex @ C @ A) = (divide1210191872omplex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_left
thf(fact_109_bits__div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % bits_div_0
thf(fact_110_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_111_divide__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_right
thf(fact_112_bits__div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % bits_div_by_0
thf(fact_113_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_114_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_115_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_116_neg__0__equal__iff__equal, axiom,
    ((![A : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A)) = (zero_zero_complex = A))))). % neg_0_equal_iff_equal
thf(fact_117_neg__equal__0__iff__equal, axiom,
    ((![A : complex]: (((uminus1204672759omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_118_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_119_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_120_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_complex @ (numera632737353omplex @ M) @ (numera632737353omplex @ N)) = (numera632737353omplex @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_121_add__numeral__left, axiom,
    ((![V : num, W : num, Z : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ (numeral_numeral_nat @ W) @ Z)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ V @ W)) @ Z))))). % add_numeral_left
thf(fact_122_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_123_add__numeral__left, axiom,
    ((![V : num, W : num, Z : complex]: ((plus_plus_complex @ (numera632737353omplex @ V) @ (plus_plus_complex @ (numera632737353omplex @ W) @ Z)) = (plus_plus_complex @ (numera632737353omplex @ (plus_plus_num @ V @ W)) @ Z))))). % add_numeral_left
thf(fact_124_add__minus__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1204672759omplex @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_125_minus__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ (plus_plus_complex @ A @ B)) = B)))). % minus_add_cancel
thf(fact_126_minus__add__distrib, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1204672759omplex @ A) @ (uminus1204672759omplex @ B)))))). % minus_add_distrib
thf(fact_127_semiring__norm_I2_J, axiom,
    (((plus_plus_num @ one @ one) = (bit0 @ one)))). % semiring_norm(2)
thf(fact_128_fact__0, axiom,
    (((semiri1865663904omplex @ zero_zero_nat) = one_one_complex))). % fact_0
thf(fact_129_fact__0, axiom,
    (((semiri688227102ct_int @ zero_zero_nat) = one_one_int))). % fact_0
thf(fact_130_fact__0, axiom,
    (((semiri50953410ct_nat @ zero_zero_nat) = one_one_nat))). % fact_0
thf(fact_131_dbl__simps_I2_J, axiom,
    (((neg_nu1648888445omplex @ zero_zero_complex) = zero_zero_complex))). % dbl_simps(2)
thf(fact_132_dbl__simps_I2_J, axiom,
    (((neg_numeral_dbl_int @ zero_zero_int) = zero_zero_int))). % dbl_simps(2)
thf(fact_133_root0, axiom,
    (((fFT_Mirabelle_root @ zero_zero_nat) = one_one_complex))). % root0
thf(fact_134_add_Oleft__inverse, axiom,
    ((![A : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ A) = zero_zero_complex)))). % add.left_inverse
thf(fact_135_add_Oright__inverse, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ (uminus1204672759omplex @ A)) = zero_zero_complex)))). % add.right_inverse
thf(fact_136_divide__eq__1__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = one_one_complex) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_137_div__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % div_self
thf(fact_138_div__self, axiom,
    ((![A : int]: ((~ ((A = zero_zero_int))) => ((divide_divide_int @ A @ A) = one_one_int))))). % div_self
thf(fact_139_div__self, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ A @ A) = one_one_nat))))). % div_self
thf(fact_140_one__eq__divide__iff, axiom,
    ((![A : complex, B : complex]: ((one_one_complex = (divide1210191872omplex @ A @ B)) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_141_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_142_divide__self__if, axiom,
    ((![A : complex]: (((A = zero_zero_complex) => ((divide1210191872omplex @ A @ A) = zero_zero_complex)) & ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex)))))). % divide_self_if
thf(fact_143_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_144_semiring__norm_I168_J, axiom,
    ((![V : num, W : num, Y : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ V)) @ (plus_plus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ W)) @ Y)) = (plus_plus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ V @ W))) @ Y))))). % semiring_norm(168)
thf(fact_145_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_146_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((plus_plus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (uminus1204672759omplex @ (plus_plus_complex @ (numera632737353omplex @ M) @ (numera632737353omplex @ N))))))). % add_neg_numeral_simps(3)
thf(fact_147_add__self__div__2, axiom,
    ((![M : nat]: ((divide_divide_nat @ (plus_plus_nat @ M @ M) @ (numeral_numeral_nat @ (bit0 @ one))) = M)))). % add_self_div_2
thf(fact_148_dbl__inc__simps_I2_J, axiom,
    (((neg_nu484426047omplex @ zero_zero_complex) = one_one_complex))). % dbl_inc_simps(2)
thf(fact_149_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_150_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_151_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_152_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ N)) = (numeral_numeral_int @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_153_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_complex @ one_one_complex @ (numera632737353omplex @ N)) = (numera632737353omplex @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_154_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_nat @ (numeral_numeral_nat @ N) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_155_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_int @ (numeral_numeral_int @ N) @ one_one_int) = (numeral_numeral_int @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_156_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_complex @ (numera632737353omplex @ N) @ one_one_complex) = (numera632737353omplex @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_157_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_158_one__add__one, axiom,
    (((plus_plus_int @ one_one_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one))))). % one_add_one
thf(fact_159_one__add__one, axiom,
    (((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % one_add_one
thf(fact_160_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_161_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_162_add_Oinverse__unique, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) => ((uminus1204672759omplex @ A) = B))))). % add.inverse_unique
thf(fact_163_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_164_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_165_add__right__imp__eq, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_166_add__left__imp__eq, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_167_add_Oleft__commute, axiom,
    ((![B : nat, A : nat, C : nat]: ((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.left_commute
thf(fact_168_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_169_add_Ocomm__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.comm_neutral
thf(fact_170_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_171_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B2 : nat]: (plus_plus_nat @ B2 @ A2)))))). % add.commute
thf(fact_172_add_Oassoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.assoc
thf(fact_173_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_174_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_175_group__cancel_Oadd2, axiom,
    ((![B3 : nat, K : nat, B : nat, A : nat]: ((B3 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B3) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_176_group__cancel_Oadd1, axiom,
    ((![A3 : nat, K : nat, A : nat, B : nat]: ((A3 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A3 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_177_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_178_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_179_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (K = L)) => ((plus_plus_nat @ I @ K) = (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_180_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_181_dbl__inc__def, axiom,
    ((neg_nu484426047omplex = (^[X3 : complex]: (plus_plus_complex @ (plus_plus_complex @ X3 @ X3) @ one_one_complex))))). % dbl_inc_def
thf(fact_182_complex__i__not__zero, axiom,
    ((~ ((imaginary_unit = zero_zero_complex))))). % complex_i_not_zero
thf(fact_183_verit__sum__simplify, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % verit_sum_simplify
thf(fact_184_verit__sum__simplify, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % verit_sum_simplify
thf(fact_185_div__add__self1, axiom,
    ((![B : int, A : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ B @ A) @ B) = (plus_plus_int @ (divide_divide_int @ A @ B) @ one_one_int)))))). % div_add_self1
thf(fact_186_div__add__self1, axiom,
    ((![B : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ B @ A) @ B) = (plus_plus_nat @ (divide_divide_nat @ A @ B) @ one_one_nat)))))). % div_add_self1
thf(fact_187_div__add__self2, axiom,
    ((![B : int, A : int]: ((~ ((B = zero_zero_int))) => ((divide_divide_int @ (plus_plus_int @ A @ B) @ B) = (plus_plus_int @ (divide_divide_int @ A @ B) @ one_one_int)))))). % div_add_self2
thf(fact_188_div__add__self2, axiom,
    ((![B : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ A @ B) @ B) = (plus_plus_nat @ (divide_divide_nat @ A @ B) @ one_one_nat)))))). % div_add_self2
thf(fact_189_is__num__normalize_I8_J, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1204672759omplex @ B) @ (uminus1204672759omplex @ A)))))). % is_num_normalize(8)
thf(fact_190_group__cancel_Oneg1, axiom,
    ((![A3 : complex, K : complex, A : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((uminus1204672759omplex @ A3) = (plus_plus_complex @ (uminus1204672759omplex @ K) @ (uminus1204672759omplex @ A))))))). % group_cancel.neg1
thf(fact_191_add_Oinverse__distrib__swap, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1204672759omplex @ B) @ (uminus1204672759omplex @ A)))))). % add.inverse_distrib_swap
thf(fact_192_add__One__commute, axiom,
    ((![N : num]: ((plus_plus_num @ one @ N) = (plus_plus_num @ N @ one))))). % add_One_commute
thf(fact_193_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_194_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N))))))). % zero_neq_numeral
thf(fact_195_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N))))))). % zero_neq_numeral

% Conjectures (1)
thf(conj_0, conjecture,
    (((fFT_Mirabelle_root @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = imaginary_unit))).
