% 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_213__3224800_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:56.647

% Could-be-implicit typings (3)
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).

% Explicit typings (20)
thf(sy_c_FFT__Mirabelle__ulikgskiun_Oroot, type,
    fFT_Mirabelle_root : nat > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : 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__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__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_Nat_OSuc, type,
    suc : 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__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__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum, type,
    ord_less_num : num > num > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum, type,
    ord_less_eq_num : num > num > $o).

% Relevant facts (121)
thf(fact_0_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_1_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ one_one_complex)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_2_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_3_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_4_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_5_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_6_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_7_semiring__norm_I83_J, axiom,
    ((![N : num]: (~ ((one = (bit0 @ N))))))). % semiring_norm(83)
thf(fact_8_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_9_uminus__numeral__One, axiom,
    (((uminus1204672759omplex @ (numera632737353omplex @ one)) = (uminus1204672759omplex @ one_one_complex)))). % uminus_numeral_One
thf(fact_10_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numera632737353omplex @ N) = (uminus1204672759omplex @ one_one_complex))))))). % numeral_neq_neg_one
thf(fact_11_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_complex = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % one_neq_neg_numeral
thf(fact_12_numeral__One, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numeral_One
thf(fact_13_numeral__One, axiom,
    (((numera632737353omplex @ one) = one_one_complex))). % numeral_One
thf(fact_14_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_15_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_16_semiring__norm_I87_J, axiom,
    ((![M : num, N : num]: (((bit0 @ M) = (bit0 @ N)) = (M = N))))). % semiring_norm(87)
thf(fact_17_root1, axiom,
    (((fFT_Mirabelle_root @ one_one_nat) = one_one_complex))). % root1
thf(fact_18_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_19_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numera632737353omplex @ M) = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % numeral_neq_neg_numeral
thf(fact_20_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (numera632737353omplex @ N))))))). % neg_numeral_neq_numeral
thf(fact_21_one__neq__neg__one, axiom,
    ((~ ((one_one_complex = (uminus1204672759omplex @ one_one_complex)))))). % one_neq_neg_one
thf(fact_22_dbl__simps_I4_J, axiom,
    (((neg_nu1648888445omplex @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ (numera632737353omplex @ (bit0 @ one)))))). % dbl_simps(4)
thf(fact_23_dbl__simps_I3_J, axiom,
    (((neg_nu1648888445omplex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % dbl_simps(3)
thf(fact_24_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_25_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_26_verit__minus__simplify_I4_J, axiom,
    ((![B : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_27_verit__eq__simplify_I8_J, axiom,
    ((![X2 : num, Y2 : num]: (((bit0 @ X2) = (bit0 @ Y2)) = (X2 = Y2))))). % verit_eq_simplify(8)
thf(fact_28_dbl__simps_I5_J, axiom,
    ((![K : num]: ((neg_nu1648888445omplex @ (numera632737353omplex @ K)) = (numera632737353omplex @ (bit0 @ K)))))). % dbl_simps(5)
thf(fact_29_dbl__simps_I1_J, axiom,
    ((![K : num]: ((neg_nu1648888445omplex @ (uminus1204672759omplex @ (numera632737353omplex @ K))) = (uminus1204672759omplex @ (neg_nu1648888445omplex @ (numera632737353omplex @ K))))))). % dbl_simps(1)
thf(fact_30_one__reorient, axiom,
    ((![X : complex]: ((one_one_complex = X) = (X = one_one_complex))))). % one_reorient
thf(fact_31_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_32_equation__minus__iff, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = (B = (uminus1204672759omplex @ A)))))). % equation_minus_iff
thf(fact_33_minus__equation__iff, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((uminus1204672759omplex @ B) = A))))). % minus_equation_iff
thf(fact_34_verit__eq__simplify_I10_J, axiom,
    ((![X2 : num]: (~ ((one = (bit0 @ X2))))))). % verit_eq_simplify(10)
thf(fact_35_dbl__inc__simps_I4_J, axiom,
    (((neg_nu484426047omplex @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ one_one_complex)))). % dbl_inc_simps(4)
thf(fact_36_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_37_diff__numeral__special_I11_J, axiom,
    (((minus_minus_complex @ one_one_complex @ (uminus1204672759omplex @ one_one_complex)) = (numera632737353omplex @ (bit0 @ one))))). % diff_numeral_special(11)
thf(fact_38_diff__numeral__special_I10_J, axiom,
    (((minus_minus_complex @ (uminus1204672759omplex @ one_one_complex) @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ (bit0 @ one)))))). % diff_numeral_special(10)
thf(fact_39_Suc__1, axiom,
    (((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % Suc_1
thf(fact_40_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_41_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_42_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_43_semiring__norm_I78_J, axiom,
    ((![M : num, N : num]: ((ord_less_num @ (bit0 @ M) @ (bit0 @ N)) = (ord_less_num @ M @ N))))). % semiring_norm(78)
thf(fact_44_semiring__norm_I71_J, axiom,
    ((![M : num, N : num]: ((ord_less_eq_num @ (bit0 @ M) @ (bit0 @ N)) = (ord_less_eq_num @ M @ N))))). % semiring_norm(71)
thf(fact_45_semiring__norm_I75_J, axiom,
    ((![M : num]: (~ ((ord_less_num @ M @ one)))))). % semiring_norm(75)
thf(fact_46_semiring__norm_I68_J, axiom,
    ((![N : num]: (ord_less_eq_num @ one @ N)))). % semiring_norm(68)
thf(fact_47_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_48_add__le__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_49_add__le__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_left
thf(fact_50_numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (ord_less_num @ M @ N))))). % numeral_less_iff
thf(fact_51_add__less__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_nat @ A @ B))))). % add_less_cancel_right
thf(fact_52_add__less__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ B))))). % add_less_cancel_left
thf(fact_53_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_54_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_55_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_56_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_57_add__diff__cancel__right_H, axiom,
    ((![A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_58_add__diff__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (minus_minus_nat @ A @ B))))). % add_diff_cancel_right
thf(fact_59_add__diff__cancel__left_H, axiom,
    ((![A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_60_add__diff__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ B))))). % add_diff_cancel_left
thf(fact_61_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_62_minus__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ (plus_plus_complex @ A @ B)) = B)))). % minus_add_cancel
thf(fact_63_add__minus__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1204672759omplex @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_64_minus__diff__eq, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ B @ A))))). % minus_diff_eq
thf(fact_65_semiring__norm_I2_J, axiom,
    (((plus_plus_num @ one @ one) = (bit0 @ one)))). % semiring_norm(2)
thf(fact_66_semiring__norm_I76_J, axiom,
    ((![N : num]: (ord_less_num @ one @ (bit0 @ N))))). % semiring_norm(76)
thf(fact_67_semiring__norm_I69_J, axiom,
    ((![M : num]: (~ ((ord_less_eq_num @ (bit0 @ M) @ one)))))). % semiring_norm(69)
thf(fact_68_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_69_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_70_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((minus_minus_complex @ (numera632737353omplex @ M) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (numera632737353omplex @ (plus_plus_num @ M @ N)))))). % diff_numeral_simps(2)
thf(fact_71_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((minus_minus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ M @ N))))))). % diff_numeral_simps(3)
thf(fact_72_diff__minus__eq__add, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ A @ (uminus1204672759omplex @ B)) = (plus_plus_complex @ A @ B))))). % diff_minus_eq_add
thf(fact_73_uminus__add__conv__diff, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ B) = (minus_minus_complex @ B @ A))))). % uminus_add_conv_diff
thf(fact_74_Suc__numeral, axiom,
    ((![N : num]: ((suc @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ N @ one)))))). % Suc_numeral
thf(fact_75_numeral__le__one__iff, axiom,
    ((![N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ N) @ one_one_nat) = (ord_less_eq_num @ N @ one))))). % numeral_le_one_iff
thf(fact_76_one__less__numeral__iff, axiom,
    ((![N : num]: ((ord_less_nat @ one_one_nat @ (numeral_numeral_nat @ N)) = (ord_less_num @ one @ N))))). % one_less_numeral_iff
thf(fact_77_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_78_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_79_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_80_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_81_add__2__eq__Suc_H, axiom,
    ((![N : nat]: ((plus_plus_nat @ N @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ N)))))). % add_2_eq_Suc'
thf(fact_82_add__2__eq__Suc, axiom,
    ((![N : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N) = (suc @ (suc @ N)))))). % add_2_eq_Suc
thf(fact_83_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_84_one__add__one, axiom,
    (((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % one_add_one
thf(fact_85_diff__numeral__special_I3_J, axiom,
    ((![N : num]: ((minus_minus_complex @ one_one_complex @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (numera632737353omplex @ (plus_plus_num @ one @ N)))))). % diff_numeral_special(3)
thf(fact_86_diff__numeral__special_I4_J, axiom,
    ((![M : num]: ((minus_minus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ M @ one))))))). % diff_numeral_special(4)
thf(fact_87_group__cancel_Osub2, axiom,
    ((![B2 : complex, K : complex, B : complex, A : complex]: ((B2 = (plus_plus_complex @ K @ B)) => ((minus_minus_complex @ A @ B2) = (plus_plus_complex @ (uminus1204672759omplex @ K) @ (minus_minus_complex @ A @ B))))))). % group_cancel.sub2
thf(fact_88_diff__conv__add__uminus, axiom,
    ((minus_minus_complex = (^[A2 : complex]: (^[B3 : complex]: (plus_plus_complex @ A2 @ (uminus1204672759omplex @ B3))))))). % diff_conv_add_uminus
thf(fact_89_ab__group__add__class_Oab__diff__conv__add__uminus, axiom,
    ((minus_minus_complex = (^[A2 : complex]: (^[B3 : complex]: (plus_plus_complex @ A2 @ (uminus1204672759omplex @ B3))))))). % ab_group_add_class.ab_diff_conv_add_uminus
thf(fact_90_add__less__imp__less__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) => (ord_less_nat @ A @ B))))). % add_less_imp_less_right
thf(fact_91_add__less__imp__less__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ B))))). % add_less_imp_less_left
thf(fact_92_add__strict__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)))))). % add_strict_right_mono
thf(fact_93_add__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)))))). % add_strict_left_mono
thf(fact_94_add__le__imp__le__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_right
thf(fact_95_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))))))). % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
thf(fact_96_add__le__imp__le__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_left
thf(fact_97_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B))))). % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
thf(fact_98_add__less__le__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_less_le_mono
thf(fact_99_add__le__less__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_le_less_mono
thf(fact_100_add__strict__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_strict_mono
thf(fact_101_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)))))). % ordered_cancel_comm_monoid_diff_class.diff_diff_right
thf(fact_102_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C)))))). % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
thf(fact_103_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)))))). % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
thf(fact_104_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A))))))). % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
thf(fact_105_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A)))))). % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
thf(fact_106_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B)))))). % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
thf(fact_107_le__add__diff, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)))))). % le_add_diff
thf(fact_108_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A2 : nat]: (^[B3 : nat]: (?[C2 : nat]: (B3 = (plus_plus_nat @ A2 @ C2)))))))). % le_iff_add
thf(fact_109_diff__add, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B))))). % diff_add
thf(fact_110_add__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)))))). % add_right_mono
thf(fact_111_less__eqE, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => (~ ((![C3 : nat]: (~ ((B = (plus_plus_nat @ A @ C3))))))))))). % less_eqE
thf(fact_112_add__implies__diff, axiom,
    ((![C : nat, B : nat, A : nat]: (((plus_plus_nat @ C @ B) = A) => (C = (minus_minus_nat @ A @ B)))))). % add_implies_diff
thf(fact_113_add__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)))))). % add_left_mono
thf(fact_114_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_115_diff__diff__add, axiom,
    ((![A : nat, B : nat, C : nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C)))))). % diff_diff_add
thf(fact_116_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_117_add__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_mono
thf(fact_118_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_119_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B3 : nat]: (plus_plus_nat @ B3 @ A2)))))). % add.commute
thf(fact_120_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

% Conjectures (1)
thf(conj_0, conjecture,
    (((fFT_Mirabelle_root @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1204672759omplex @ one_one_complex)))).
