% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Fundamental_Theorem_Algebra/prob_296__5370454_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:00.224

% 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 (41)
thf(sy_c_Complex_Ocomplex_OIm, type,
    im : complex > real).
thf(sy_c_Complex_Ocomplex_ORe, type,
    re : complex > real).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex, type,
    abs_abs_complex : complex > complex).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint, type,
    abs_abs_int : int > int).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint, type,
    minus_minus_int : int > int > int).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__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_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
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_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint, type,
    ord_less_int : int > int > $o).
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_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint, type,
    ord_less_eq_int : int > int > $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).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat, type,
    order_769474267at_nat : (nat > nat) > $o).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
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).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_v_e____, type,
    e : real).
thf(sy_v_f____, type,
    f : nat > nat).
thf(sy_v_g____, type,
    g : nat > nat).
thf(sy_v_r, type,
    r : real).
thf(sy_v_s, type,
    s : nat > complex).
thf(sy_v_thesis____, type,
    thesis : $o).
thf(sy_v_x____, type,
    x : real).
thf(sy_v_y____, type,
    y : real).

% Relevant facts (238)
thf(fact_0__092_060open_062_092_060exists_062n0_O_A_092_060forall_062n_092_060ge_062n0_O_A_092_060bar_062Re_A_Is_A_If_An_J_J_A_N_Ax_092_060bar_062_A_060_Ae_A_P_A2_092_060close_062, axiom,
    ((?[N0 : nat]: (![N : nat]: ((ord_less_eq_nat @ N0 @ N) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ (re @ (s @ (f @ N))) @ x)) @ (divide_divide_real @ e @ (numeral_numeral_real @ (bit0 @ one))))))))). % \<open>\<exists>n0. \<forall>n\<ge>n0. \<bar>Re (s (f n)) - x\<bar> < e / 2\<close>
thf(fact_1_f_I1_J, axiom,
    ((order_769474267at_nat @ f))). % f(1)
thf(fact_2_g_I1_J, axiom,
    ((order_769474267at_nat @ g))). % g(1)
thf(fact_3__092_060open_062_092_060exists_062n0_O_A_092_060forall_062n_092_060ge_062n0_O_A_092_060bar_062Im_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_092_060bar_062_A_060_Ae_A_P_A2_092_060close_062, axiom,
    ((?[N0 : nat]: (![N : nat]: ((ord_less_eq_nat @ N0 @ N) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ (im @ (s @ (f @ (g @ N)))) @ y)) @ (divide_divide_real @ e @ (numeral_numeral_real @ (bit0 @ one))))))))). % \<open>\<exists>n0. \<forall>n\<ge>n0. \<bar>Im (s (f (g n))) - y\<bar> < e / 2\<close>
thf(fact_4_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_5_y, axiom,
    ((![R : real]: ((ord_less_real @ zero_zero_real @ R) => (?[N0 : nat]: (![N : nat]: ((ord_less_eq_nat @ N0 @ N) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ (im @ (s @ (f @ (g @ N)))) @ y)) @ R)))))))). % y
thf(fact_6_x, axiom,
    ((![R : real]: ((ord_less_real @ zero_zero_real @ R) => (?[N0 : nat]: (![N : nat]: ((ord_less_eq_nat @ N0 @ N) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ (re @ (s @ (f @ N))) @ x)) @ R)))))))). % x
thf(fact_7_e2, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ e @ (numeral_numeral_real @ (bit0 @ one)))))). % e2
thf(fact_8_abs__divide, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_divide
thf(fact_9_abs__divide, axiom,
    ((![A : complex, B : complex]: ((abs_abs_complex @ (divide1210191872omplex @ A @ B)) = (divide1210191872omplex @ (abs_abs_complex @ A) @ (abs_abs_complex @ B)))))). % abs_divide
thf(fact_10_abs__numeral, axiom,
    ((![N2 : num]: ((abs_abs_real @ (numeral_numeral_real @ N2)) = (numeral_numeral_real @ N2))))). % abs_numeral
thf(fact_11_abs__numeral, axiom,
    ((![N2 : num]: ((abs_abs_int @ (numeral_numeral_int @ N2)) = (numeral_numeral_int @ N2))))). % abs_numeral
thf(fact_12_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_13_semiring__norm_I83_J, axiom,
    ((![N2 : num]: (~ ((one = (bit0 @ N2))))))). % semiring_norm(83)
thf(fact_14_numeral__less__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N2)) = (ord_less_num @ M @ N2))))). % numeral_less_iff
thf(fact_15_numeral__less__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N2)) = (ord_less_num @ M @ N2))))). % numeral_less_iff
thf(fact_16_numeral__less__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N2)) = (ord_less_num @ M @ N2))))). % numeral_less_iff
thf(fact_17_numeral__le__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N2)) = (ord_less_eq_num @ M @ N2))))). % numeral_le_iff
thf(fact_18_numeral__le__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_eq_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N2)) = (ord_less_eq_num @ M @ N2))))). % numeral_le_iff
thf(fact_19_numeral__le__iff, axiom,
    ((![M : num, N2 : num]: ((ord_less_eq_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N2)) = (ord_less_eq_num @ M @ N2))))). % numeral_le_iff
thf(fact_20_numeral__Bit0__div__2, axiom,
    ((![N2 : num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit0 @ N2)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ N2))))). % numeral_Bit0_div_2
thf(fact_21_numeral__Bit0__div__2, axiom,
    ((![N2 : num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ N2)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ N2))))). % numeral_Bit0_div_2
thf(fact_22_abs__triangle__ineq2, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B)))))). % abs_triangle_ineq2
thf(fact_23_abs__triangle__ineq2, axiom,
    ((![A : int, B : int]: (ord_less_eq_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) @ (abs_abs_int @ (minus_minus_int @ A @ B)))))). % abs_triangle_ineq2
thf(fact_24_abs__triangle__ineq3, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B)))))). % abs_triangle_ineq3
thf(fact_25_abs__triangle__ineq3, axiom,
    ((![A : int, B : int]: (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))) @ (abs_abs_int @ (minus_minus_int @ A @ B)))))). % abs_triangle_ineq3
thf(fact_26_numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N2)) = (M = N2))))). % numeral_eq_iff
thf(fact_27_numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N2)) = (M = N2))))). % numeral_eq_iff
thf(fact_28_numeral__eq__iff, axiom,
    ((![M : num, N2 : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N2)) = (M = N2))))). % numeral_eq_iff
thf(fact_29_semiring__norm_I87_J, axiom,
    ((![M : num, N2 : num]: (((bit0 @ M) = (bit0 @ N2)) = (M = N2))))). % semiring_norm(87)
thf(fact_30_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_31_abs__idempotent, axiom,
    ((![A : int]: ((abs_abs_int @ (abs_abs_int @ A)) = (abs_abs_int @ A))))). % abs_idempotent
thf(fact_32_le__zero__eq, axiom,
    ((![N2 : nat]: ((ord_less_eq_nat @ N2 @ zero_zero_nat) = (N2 = zero_zero_nat))))). % le_zero_eq
thf(fact_33_not__gr__zero, axiom,
    ((![N2 : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N2))) = (N2 = zero_zero_nat))))). % not_gr_zero
thf(fact_34_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_35_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : int]: ((minus_minus_int @ A @ A) = zero_zero_int)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_36_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_37_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_38_diff__zero, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A)))). % diff_zero
thf(fact_39_diff__zero, axiom,
    ((![A : int]: ((minus_minus_int @ A @ zero_zero_int) = A)))). % diff_zero
thf(fact_40_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_41_diff__zero, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_zero
thf(fact_42_zero__diff, axiom,
    ((![A : nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % zero_diff
thf(fact_43_diff__0__right, axiom,
    ((![A : int]: ((minus_minus_int @ A @ zero_zero_int) = A)))). % diff_0_right
thf(fact_44_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_45_diff__0__right, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_0_right
thf(fact_46_diff__self, axiom,
    ((![A : int]: ((minus_minus_int @ A @ A) = zero_zero_int)))). % diff_self
thf(fact_47_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_48_diff__self, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % diff_self
thf(fact_49_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_50_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_51_divide__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((divide_divide_real @ A @ C) = (divide_divide_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_right
thf(fact_52_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_53_divide__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((divide_divide_real @ C @ A) = (divide_divide_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_left
thf(fact_54_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_55_divide__eq__0__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % divide_eq_0_iff
thf(fact_56_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_57_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_58_abs__zero, axiom,
    (((abs_abs_int @ zero_zero_int) = zero_zero_int))). % abs_zero
thf(fact_59_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_60_abs__eq__0, axiom,
    ((![A : int]: (((abs_abs_int @ A) = zero_zero_int) = (A = zero_zero_int))))). % abs_eq_0
thf(fact_61_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_62_abs__0__eq, axiom,
    ((![A : int]: ((zero_zero_int = (abs_abs_int @ A)) = (A = zero_zero_int))))). % abs_0_eq
thf(fact_63_semiring__norm_I78_J, axiom,
    ((![M : num, N2 : num]: ((ord_less_num @ (bit0 @ M) @ (bit0 @ N2)) = (ord_less_num @ M @ N2))))). % semiring_norm(78)
thf(fact_64_semiring__norm_I71_J, axiom,
    ((![M : num, N2 : num]: ((ord_less_eq_num @ (bit0 @ M) @ (bit0 @ N2)) = (ord_less_eq_num @ M @ N2))))). % semiring_norm(71)
thf(fact_65_semiring__norm_I75_J, axiom,
    ((![M : num]: (~ ((ord_less_num @ M @ one)))))). % semiring_norm(75)
thf(fact_66_semiring__norm_I68_J, axiom,
    ((![N2 : num]: (ord_less_eq_num @ one @ N2)))). % semiring_norm(68)
thf(fact_67_diff__ge__0__iff__ge, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_68_diff__ge__0__iff__ge, axiom,
    ((![A : int, B : int]: ((ord_less_eq_int @ zero_zero_int @ (minus_minus_int @ A @ B)) = (ord_less_eq_int @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_69_diff__gt__0__iff__gt, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_70_diff__gt__0__iff__gt, axiom,
    ((![A : int, B : int]: ((ord_less_int @ zero_zero_int @ (minus_minus_int @ A @ B)) = (ord_less_int @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_71_abs__le__zero__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real))))). % abs_le_zero_iff
thf(fact_72_abs__le__zero__iff, axiom,
    ((![A : int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ zero_zero_int) = (A = zero_zero_int))))). % abs_le_zero_iff
thf(fact_73_abs__le__self__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % abs_le_self_iff
thf(fact_74_abs__le__self__iff, axiom,
    ((![A : int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ A) = (ord_less_eq_int @ zero_zero_int @ A))))). % abs_le_self_iff
thf(fact_75_abs__of__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_nonneg
thf(fact_76_abs__of__nonneg, axiom,
    ((![A : int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((abs_abs_int @ A) = A))))). % abs_of_nonneg
thf(fact_77_zero__less__abs__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ A)) = (~ ((A = zero_zero_real))))))). % zero_less_abs_iff
thf(fact_78_zero__less__abs__iff, axiom,
    ((![A : int]: ((ord_less_int @ zero_zero_int @ (abs_abs_int @ A)) = (~ ((A = zero_zero_int))))))). % zero_less_abs_iff
thf(fact_79_semiring__norm_I76_J, axiom,
    ((![N2 : num]: (ord_less_num @ one @ (bit0 @ N2))))). % semiring_norm(76)
thf(fact_80_semiring__norm_I69_J, axiom,
    ((![M : num]: (~ ((ord_less_eq_num @ (bit0 @ M) @ one)))))). % semiring_norm(69)
thf(fact_81_rp, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % rp
thf(fact_82_zero__le__divide__abs__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ (abs_abs_real @ B))) = (((ord_less_eq_real @ zero_zero_real @ A)) | ((B = zero_zero_real))))))). % zero_le_divide_abs_iff
thf(fact_83_divide__le__0__abs__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ (abs_abs_real @ B)) @ zero_zero_real) = (((ord_less_eq_real @ A @ zero_zero_real)) | ((B = zero_zero_real))))))). % divide_le_0_abs_iff
thf(fact_84_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_85_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_86_zero__reorient, axiom,
    ((![X3 : int]: ((zero_zero_int = X3) = (X3 = zero_zero_int))))). % zero_reorient
thf(fact_87_zero__reorient, axiom,
    ((![X3 : complex]: ((zero_zero_complex = X3) = (X3 = zero_zero_complex))))). % zero_reorient
thf(fact_88_le__num__One__iff, axiom,
    ((![X3 : num]: ((ord_less_eq_num @ X3 @ one) = (X3 = one))))). % le_num_One_iff
thf(fact_89_div__le__dividend, axiom,
    ((![M : nat, N2 : nat]: (ord_less_eq_nat @ (divide_divide_nat @ M @ N2) @ M)))). % div_le_dividend
thf(fact_90_div__le__mono, axiom,
    ((![M : nat, N2 : nat, K : nat]: ((ord_less_eq_nat @ M @ N2) => (ord_less_eq_nat @ (divide_divide_nat @ M @ K) @ (divide_divide_nat @ N2 @ K)))))). % div_le_mono
thf(fact_91_zero__le, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X3)))). % zero_le
thf(fact_92_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat))). % le_numeral_extra(3)
thf(fact_93_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_94_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_int @ zero_zero_int @ zero_zero_int))). % le_numeral_extra(3)
thf(fact_95_zero__less__iff__neq__zero, axiom,
    ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) = (~ ((N2 = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_96_gr__implies__not__zero, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ M @ N2) => (~ ((N2 = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_97_not__less__zero, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ zero_zero_nat)))))). % not_less_zero
thf(fact_98_gr__zeroI, axiom,
    ((![N2 : nat]: ((~ ((N2 = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N2))))). % gr_zeroI
thf(fact_99_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_100_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_101_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_numeral_extra(3)
thf(fact_102_zero__neq__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N2))))))). % zero_neq_numeral
thf(fact_103_zero__neq__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_real = (numeral_numeral_real @ N2))))))). % zero_neq_numeral
thf(fact_104_zero__neq__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_complex = (numera632737353omplex @ N2))))))). % zero_neq_numeral
thf(fact_105_zero__neq__numeral, axiom,
    ((![N2 : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N2))))))). % zero_neq_numeral
thf(fact_106_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : int]: (^[Z2 : int]: (Y2 = Z2))) = (^[A2 : int]: (^[B2 : int]: ((minus_minus_int @ A2 @ B2) = zero_zero_int)))))). % eq_iff_diff_eq_0
thf(fact_107_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : real]: (^[Z2 : real]: (Y2 = Z2))) = (^[A2 : real]: (^[B2 : real]: ((minus_minus_real @ A2 @ B2) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_108_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : complex]: (^[Z2 : complex]: (Y2 = Z2))) = (^[A2 : complex]: (^[B2 : complex]: ((minus_minus_complex @ A2 @ B2) = zero_zero_complex)))))). % eq_iff_diff_eq_0
thf(fact_109_not__numeral__le__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_eq_nat @ (numeral_numeral_nat @ N2) @ zero_zero_nat)))))). % not_numeral_le_zero
thf(fact_110_not__numeral__le__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_eq_real @ (numeral_numeral_real @ N2) @ zero_zero_real)))))). % not_numeral_le_zero
thf(fact_111_not__numeral__le__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_eq_int @ (numeral_numeral_int @ N2) @ zero_zero_int)))))). % not_numeral_le_zero
thf(fact_112_zero__le__numeral, axiom,
    ((![N2 : num]: (ord_less_eq_nat @ zero_zero_nat @ (numeral_numeral_nat @ N2))))). % zero_le_numeral
thf(fact_113_zero__le__numeral, axiom,
    ((![N2 : num]: (ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ N2))))). % zero_le_numeral
thf(fact_114_zero__le__numeral, axiom,
    ((![N2 : num]: (ord_less_eq_int @ zero_zero_int @ (numeral_numeral_int @ N2))))). % zero_le_numeral
thf(fact_115_le__iff__diff__le__0, axiom,
    ((ord_less_eq_real = (^[A2 : real]: (^[B2 : real]: (ord_less_eq_real @ (minus_minus_real @ A2 @ B2) @ zero_zero_real)))))). % le_iff_diff_le_0
thf(fact_116_le__iff__diff__le__0, axiom,
    ((ord_less_eq_int = (^[A2 : int]: (^[B2 : int]: (ord_less_eq_int @ (minus_minus_int @ A2 @ B2) @ zero_zero_int)))))). % le_iff_diff_le_0
thf(fact_117_not__numeral__less__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N2) @ zero_zero_nat)))))). % not_numeral_less_zero
thf(fact_118_not__numeral__less__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N2) @ zero_zero_real)))))). % not_numeral_less_zero
thf(fact_119_not__numeral__less__zero, axiom,
    ((![N2 : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N2) @ zero_zero_int)))))). % not_numeral_less_zero
thf(fact_120_zero__less__numeral, axiom,
    ((![N2 : num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ N2))))). % zero_less_numeral
thf(fact_121_zero__less__numeral, axiom,
    ((![N2 : num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ N2))))). % zero_less_numeral
thf(fact_122_zero__less__numeral, axiom,
    ((![N2 : num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ N2))))). % zero_less_numeral
thf(fact_123_less__iff__diff__less__0, axiom,
    ((ord_less_real = (^[A2 : real]: (^[B2 : real]: (ord_less_real @ (minus_minus_real @ A2 @ B2) @ zero_zero_real)))))). % less_iff_diff_less_0
thf(fact_124_less__iff__diff__less__0, axiom,
    ((ord_less_int = (^[A2 : int]: (^[B2 : int]: (ord_less_int @ (minus_minus_int @ A2 @ B2) @ zero_zero_int)))))). % less_iff_diff_less_0
thf(fact_125_divide__right__mono__neg, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C))))))). % divide_right_mono_neg
thf(fact_126_divide__nonpos__nonpos, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ Y3 @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y3))))))). % divide_nonpos_nonpos
thf(fact_127_divide__nonpos__nonneg, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ Y3) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Y3) @ zero_zero_real)))))). % divide_nonpos_nonneg
thf(fact_128_divide__nonneg__nonpos, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ Y3 @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Y3) @ zero_zero_real)))))). % divide_nonneg_nonpos
thf(fact_129_divide__nonneg__nonneg, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y3) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y3))))))). % divide_nonneg_nonneg
thf(fact_130_zero__le__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ zero_zero_real))))))))). % zero_le_divide_iff
thf(fact_131_divide__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_right_mono
thf(fact_132_divide__le__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ zero_zero_real)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B))))))))). % divide_le_0_iff
thf(fact_133_divide__strict__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono_neg
thf(fact_134_divide__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono
thf(fact_135_zero__less__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ zero_zero_real @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real))))))))). % zero_less_divide_iff
thf(fact_136_divide__less__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A)))) & ((~ ((C = zero_zero_real))))))))))). % divide_less_cancel
thf(fact_137_divide__less__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ zero_zero_real)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B))))))))). % divide_less_0_iff
thf(fact_138_divide__pos__pos, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y3))))))). % divide_pos_pos
thf(fact_139_divide__pos__neg, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X3 @ Y3) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_140_divide__neg__pos, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_real @ (divide_divide_real @ X3 @ Y3) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_141_divide__neg__neg, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y3))))))). % divide_neg_neg
thf(fact_142_abs__ge__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A))))). % abs_ge_zero
thf(fact_143_abs__ge__zero, axiom,
    ((![A : int]: (ord_less_eq_int @ zero_zero_int @ (abs_abs_int @ A))))). % abs_ge_zero
thf(fact_144_abs__not__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (abs_abs_real @ A) @ zero_zero_real)))))). % abs_not_less_zero
thf(fact_145_abs__not__less__zero, axiom,
    ((![A : int]: (~ ((ord_less_int @ (abs_abs_int @ A) @ zero_zero_int)))))). % abs_not_less_zero
thf(fact_146_abs__of__pos, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_pos
thf(fact_147_abs__of__pos, axiom,
    ((![A : int]: ((ord_less_int @ zero_zero_int @ A) => ((abs_abs_int @ A) = A))))). % abs_of_pos
thf(fact_148_nonzero__abs__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((abs_abs_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))))). % nonzero_abs_divide
thf(fact_149_divide__nonpos__pos, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Y3) @ zero_zero_real)))))). % divide_nonpos_pos
thf(fact_150_divide__nonpos__neg, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y3))))))). % divide_nonpos_neg
thf(fact_151_divide__nonneg__pos, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y3))))))). % divide_nonneg_pos
thf(fact_152_divide__nonneg__neg, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Y3) @ zero_zero_real)))))). % divide_nonneg_neg
thf(fact_153_divide__le__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ A))))))))). % divide_le_cancel
thf(fact_154_frac__less2, axiom,
    ((![X3 : real, Y3 : real, W : real, Z3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ X3 @ Y3) => ((ord_less_real @ zero_zero_real @ W) => ((ord_less_real @ W @ Z3) => (ord_less_real @ (divide_divide_real @ X3 @ Z3) @ (divide_divide_real @ Y3 @ W))))))))). % frac_less2
thf(fact_155_frac__less, axiom,
    ((![X3 : real, Y3 : real, W : real, Z3 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_real @ X3 @ Y3) => ((ord_less_real @ zero_zero_real @ W) => ((ord_less_eq_real @ W @ Z3) => (ord_less_real @ (divide_divide_real @ X3 @ Z3) @ (divide_divide_real @ Y3 @ W))))))))). % frac_less
thf(fact_156_frac__le, axiom,
    ((![Y3 : real, X3 : real, W : real, Z3 : real]: ((ord_less_eq_real @ zero_zero_real @ Y3) => ((ord_less_eq_real @ X3 @ Y3) => ((ord_less_real @ zero_zero_real @ W) => ((ord_less_eq_real @ W @ Z3) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Z3) @ (divide_divide_real @ Y3 @ W))))))))). % frac_le
thf(fact_157_dense__eq0__I, axiom,
    ((![X3 : real]: ((![E : real]: ((ord_less_real @ zero_zero_real @ E) => (ord_less_eq_real @ (abs_abs_real @ X3) @ E))) => (X3 = zero_zero_real))))). % dense_eq0_I
thf(fact_158_abs__div__pos, axiom,
    ((![Y3 : real, X3 : real]: ((ord_less_real @ zero_zero_real @ Y3) => ((divide_divide_real @ (abs_abs_real @ X3) @ Y3) = (abs_abs_real @ (divide_divide_real @ X3 @ Y3))))))). % abs_div_pos
thf(fact_159_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % linordered_field_no_ub
thf(fact_160_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y4 : real]: (ord_less_real @ Y4 @ X4))))). % linordered_field_no_lb
thf(fact_161_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (minus_minus_real @ A @ C) @ B) = (minus_minus_real @ (minus_minus_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_162_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ C) @ B) = (minus_minus_complex @ (minus_minus_complex @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_163_diff__eq__diff__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_164_diff__eq__diff__eq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: (((minus_minus_complex @ A @ B) = (minus_minus_complex @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_165_half__gt__zero__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) = (ord_less_real @ zero_zero_real @ A))))). % half_gt_zero_iff
thf(fact_166_half__gt__zero, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))))))). % half_gt_zero
thf(fact_167_diff__eq__diff__less__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_168_diff__eq__diff__less__eq, axiom,
    ((![A : int, B : int, C : int, D : int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_169_diff__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_right_mono
thf(fact_170_diff__right__mono, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)))))). % diff_right_mono
thf(fact_171_diff__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_left_mono
thf(fact_172_diff__left__mono, axiom,
    ((![B : int, A : int, C : int]: ((ord_less_eq_int @ B @ A) => (ord_less_eq_int @ (minus_minus_int @ C @ A) @ (minus_minus_int @ C @ B)))))). % diff_left_mono
thf(fact_173_diff__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ D @ C) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_mono
thf(fact_174_diff__mono, axiom,
    ((![A : int, B : int, D : int, C : int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ D @ C) => (ord_less_eq_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ D))))))). % diff_mono
thf(fact_175_diff__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_strict_right_mono
thf(fact_176_diff__strict__right__mono, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_int @ A @ B) => (ord_less_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)))))). % diff_strict_right_mono
thf(fact_177_diff__strict__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => (ord_less_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_strict_left_mono
thf(fact_178_diff__strict__left__mono, axiom,
    ((![B : int, A : int, C : int]: ((ord_less_int @ B @ A) => (ord_less_int @ (minus_minus_int @ C @ A) @ (minus_minus_int @ C @ B)))))). % diff_strict_left_mono
thf(fact_179_diff__eq__diff__less, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_real @ A @ B) = (ord_less_real @ C @ D)))))). % diff_eq_diff_less
thf(fact_180_diff__eq__diff__less, axiom,
    ((![A : int, B : int, C : int, D : int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((ord_less_int @ A @ B) = (ord_less_int @ C @ D)))))). % diff_eq_diff_less
thf(fact_181_diff__strict__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ D @ C) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_strict_mono
thf(fact_182_diff__strict__mono, axiom,
    ((![A : int, B : int, D : int, C : int]: ((ord_less_int @ A @ B) => ((ord_less_int @ D @ C) => (ord_less_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ D))))))). % diff_strict_mono
thf(fact_183_diff__divide__distrib, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)))))). % diff_divide_distrib
thf(fact_184_diff__divide__distrib, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (divide1210191872omplex @ A @ C) @ (divide1210191872omplex @ B @ C)))))). % diff_divide_distrib
thf(fact_185_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_186_abs__ge__self, axiom,
    ((![A : int]: (ord_less_eq_int @ A @ (abs_abs_int @ A))))). % abs_ge_self
thf(fact_187_abs__le__D1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B))))). % abs_le_D1
thf(fact_188_abs__le__D1, axiom,
    ((![A : int, B : int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ B) => (ord_less_eq_int @ A @ B))))). % abs_le_D1
thf(fact_189_abs__minus__commute, axiom,
    ((![A : int, B : int]: ((abs_abs_int @ (minus_minus_int @ A @ B)) = (abs_abs_int @ (minus_minus_int @ B @ A)))))). % abs_minus_commute
thf(fact_190_abs__minus__commute, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A)))))). % abs_minus_commute
thf(fact_191_divide__numeral__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A)))). % divide_numeral_1
thf(fact_192_divide__numeral__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ (numera632737353omplex @ one)) = A)))). % divide_numeral_1
thf(fact_193_abs__triangle__ineq2__sym, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A)))))). % abs_triangle_ineq2_sym
thf(fact_194_abs__triangle__ineq2__sym, axiom,
    ((![A : int, B : int]: (ord_less_eq_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) @ (abs_abs_int @ (minus_minus_int @ B @ A)))))). % abs_triangle_ineq2_sym
thf(fact_195_Im__divide__numeral, axiom,
    ((![Z3 : complex, W : num]: ((im @ (divide1210191872omplex @ Z3 @ (numera632737353omplex @ W))) = (divide_divide_real @ (im @ Z3) @ (numeral_numeral_real @ W)))))). % Im_divide_numeral
thf(fact_196_Re__divide__numeral, axiom,
    ((![Z3 : complex, W : num]: ((re @ (divide1210191872omplex @ Z3 @ (numera632737353omplex @ W))) = (divide_divide_real @ (re @ Z3) @ (numeral_numeral_real @ W)))))). % Re_divide_numeral
thf(fact_197_complex__Re__numeral, axiom,
    ((![V : num]: ((re @ (numera632737353omplex @ V)) = (numeral_numeral_real @ V))))). % complex_Re_numeral
thf(fact_198_complex__Im__numeral, axiom,
    ((![V : num]: ((im @ (numera632737353omplex @ V)) = zero_zero_real)))). % complex_Im_numeral
thf(fact_199_abs__0, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_0
thf(fact_200_abs__0, axiom,
    (((abs_abs_int @ zero_zero_int) = zero_zero_int))). % abs_0
thf(fact_201_abs__0, axiom,
    (((abs_abs_complex @ zero_zero_complex) = zero_zero_complex))). % abs_0
thf(fact_202_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_203_bits__div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % bits_div_by_0
thf(fact_204_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_205_bits__div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % bits_div_0
thf(fact_206_div__by__0, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % div_by_0
thf(fact_207_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_208_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_209_div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % div_by_0
thf(fact_210_div__0, axiom,
    ((![A : real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real)))). % div_0
thf(fact_211_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_212_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_213_div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % div_0
thf(fact_214_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_215_abs__abs, axiom,
    ((![A : complex]: ((abs_abs_complex @ (abs_abs_complex @ A)) = (abs_abs_complex @ A))))). % abs_abs
thf(fact_216_abs__abs, axiom,
    ((![A : int]: ((abs_abs_int @ (abs_abs_int @ A)) = (abs_abs_int @ A))))). % abs_abs
thf(fact_217_div__less, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ M @ N2) => ((divide_divide_nat @ M @ N2) = zero_zero_nat))))). % div_less
thf(fact_218_half__nonnegative__int__iff, axiom,
    ((![K : int]: ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ K @ (numeral_numeral_int @ (bit0 @ one)))) = (ord_less_eq_int @ zero_zero_int @ K))))). % half_nonnegative_int_iff
thf(fact_219_half__negative__int__iff, axiom,
    ((![K : int]: ((ord_less_int @ (divide_divide_int @ K @ (numeral_numeral_int @ (bit0 @ one))) @ zero_zero_int) = (ord_less_int @ K @ zero_zero_int))))). % half_negative_int_iff
thf(fact_220_r, axiom,
    ((![N : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (s @ N)) @ r)))). % r
thf(fact_221_Euclidean__Division_Odiv__eq__0__iff, axiom,
    ((![M : nat, N2 : nat]: (((divide_divide_nat @ M @ N2) = zero_zero_nat) = (((ord_less_nat @ M @ N2)) | ((N2 = zero_zero_nat))))))). % Euclidean_Division.div_eq_0_iff
thf(fact_222_div__greater__zero__iff, axiom,
    ((![M : nat, N2 : nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ M @ N2)) = (((ord_less_eq_nat @ N2 @ M)) & ((ord_less_nat @ zero_zero_nat @ N2))))))). % div_greater_zero_iff
thf(fact_223_div__le__mono2, axiom,
    ((![M : nat, N2 : nat, K : nat]: ((ord_less_nat @ zero_zero_nat @ M) => ((ord_less_eq_nat @ M @ N2) => (ord_less_eq_nat @ (divide_divide_nat @ K @ N2) @ (divide_divide_nat @ K @ M))))))). % div_le_mono2
thf(fact_224_zero__complex_Osimps_I1_J, axiom,
    (((re @ zero_zero_complex) = zero_zero_real))). % zero_complex.simps(1)
thf(fact_225_zero__complex_Osimps_I2_J, axiom,
    (((im @ zero_zero_complex) = zero_zero_real))). % zero_complex.simps(2)
thf(fact_226_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y3 : real]: ((~ ((X3 = Y3))) => ((~ ((ord_less_real @ X3 @ Y3))) => (ord_less_real @ Y3 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_227_linorder__neqE__linordered__idom, axiom,
    ((![X3 : int, Y3 : int]: ((~ ((X3 = Y3))) => ((~ ((ord_less_int @ X3 @ Y3))) => (ord_less_int @ Y3 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_228_abs__eq__0__iff, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0_iff
thf(fact_229_abs__eq__0__iff, axiom,
    ((![A : int]: (((abs_abs_int @ A) = zero_zero_int) = (A = zero_zero_int))))). % abs_eq_0_iff
thf(fact_230_abs__eq__0__iff, axiom,
    ((![A : complex]: (((abs_abs_complex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % abs_eq_0_iff
thf(fact_231_complex__eqI, axiom,
    ((![X3 : complex, Y3 : complex]: (((re @ X3) = (re @ Y3)) => (((im @ X3) = (im @ Y3)) => (X3 = Y3)))))). % complex_eqI
thf(fact_232_complex_Oexpand, axiom,
    ((![Complex : complex, Complex2 : complex]: ((((re @ Complex) = (re @ Complex2)) & ((im @ Complex) = (im @ Complex2))) => (Complex = Complex2))))). % complex.expand
thf(fact_233_complex__eq__iff, axiom,
    (((^[Y2 : complex]: (^[Z2 : complex]: (Y2 = Z2))) = (^[X2 : complex]: (^[Y5 : complex]: ((((re @ X2) = (re @ Y5))) & (((im @ X2) = (im @ Y5))))))))). % complex_eq_iff
thf(fact_234_complex_Ocoinduct__strong, axiom,
    ((![R2 : complex > complex > $o, Complex : complex, Complex2 : complex]: ((R2 @ Complex @ Complex2) => ((![Complex3 : complex, Complex4 : complex]: ((R2 @ Complex3 @ Complex4) => (((re @ Complex3) = (re @ Complex4)) & ((im @ Complex3) = (im @ Complex4))))) => (Complex = Complex2)))))). % complex.coinduct_strong
thf(fact_235_minus__complex_Osimps_I1_J, axiom,
    ((![X3 : complex, Y3 : complex]: ((re @ (minus_minus_complex @ X3 @ Y3)) = (minus_minus_real @ (re @ X3) @ (re @ Y3)))))). % minus_complex.simps(1)
thf(fact_236_minus__complex_Osimps_I2_J, axiom,
    ((![X3 : complex, Y3 : complex]: ((im @ (minus_minus_complex @ X3 @ Y3)) = (minus_minus_real @ (im @ X3) @ (im @ Y3)))))). % minus_complex.simps(2)
thf(fact_237_lemma__interval, axiom,
    ((![A : real, X3 : real, B : real]: ((ord_less_real @ A @ X3) => ((ord_less_real @ X3 @ B) => (?[D2 : real]: ((ord_less_real @ zero_zero_real @ D2) & (![Y : real]: ((ord_less_real @ (abs_abs_real @ (minus_minus_real @ X3 @ Y)) @ D2) => ((ord_less_eq_real @ A @ Y) & (ord_less_eq_real @ Y @ B))))))))))). % lemma_interval

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![N1 : nat, N22 : nat]: ((![N3 : nat]: ((ord_less_eq_nat @ N1 @ N3) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ (re @ (s @ (f @ N3))) @ x)) @ (divide_divide_real @ e @ (numeral_numeral_real @ (bit0 @ one)))))) => ((![N3 : nat]: ((ord_less_eq_nat @ N22 @ N3) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ (im @ (s @ (f @ (g @ N3)))) @ y)) @ (divide_divide_real @ e @ (numeral_numeral_real @ (bit0 @ one)))))) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
