% 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_316__5370686_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:08.841

% Could-be-implicit typings (10)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    poly_poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    poly_poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    poly_poly_a : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Set__Oset_It__Real__Oreal_J, type,
    set_real : $tType).
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (53)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Nat__Onat, type,
    fundam1567013434ze_nat : poly_nat > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Real__Oreal, type,
    fundam1947011094e_real : poly_real > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001tf__a, type,
    fundam247907092size_a : poly_a > nat).
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__Polynomial__Opoly_It__Nat__Onat_J, type,
    minus_minus_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    minus_181436949y_real : poly_poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    minus_240770701y_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_Itf__a_J, type,
    minus_minus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001tf__a, type,
    minus_minus_a : a > a > a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    zero_z1059985641ly_nat : poly_poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    zero_z1423781445y_real : poly_poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    zero_z2096148049poly_a : poly_poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J, type,
    zero_zero_poly_a : poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
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__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_less_poly_real : poly_real > poly_real > $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__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_le1180086932y_real : poly_real > poly_real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat, type,
    is_zero_nat : poly_nat > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Real__Oreal, type,
    is_zero_real : poly_real > $o).
thf(sy_c_Polynomial_Ois__zero_001tf__a, type,
    is_zero_a : poly_a > $o).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_poly_real2 : poly_poly_real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_poly_a2 : poly_poly_a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opoly_001tf__a, type,
    poly_a2 : poly_a > a > a).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Nat__Onat, type,
    poly_cutoff_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Real__Oreal, type,
    poly_cutoff_real : nat > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly__cutoff_001tf__a, type,
    poly_cutoff_a : nat > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly__shift_001t__Nat__Onat, type,
    poly_shift_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__shift_001t__Real__Oreal, type,
    poly_shift_real : nat > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly__shift_001tf__a, type,
    poly_shift_a : nat > poly_a > poly_a).
thf(sy_c_Polynomial_Oreflect__poly_001t__Nat__Onat, type,
    reflect_poly_nat : poly_nat > poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    reflec781175074ly_nat : poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    reflec1522834046y_real : poly_poly_real > poly_poly_real).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_Itf__a_J, type,
    reflect_poly_poly_a : poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Oreflect__poly_001t__Real__Oreal, type,
    reflect_poly_real : poly_real > poly_real).
thf(sy_c_Polynomial_Oreflect__poly_001tf__a, type,
    reflect_poly_a : poly_a > poly_a).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001tf__a, type,
    real_V1022479215norm_a : a > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_e, type,
    e : real).
thf(sy_v_p, type,
    p : poly_a).
thf(sy_v_z, type,
    z : a).

% Relevant facts (237)
thf(fact_0_ep, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % ep
thf(fact_1_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_2_zero__less__norm__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X3)) = (~ ((X3 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_3_zero__less__norm__iff, axiom,
    ((![X3 : a]: ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ X3)) = (~ ((X3 = zero_zero_a))))))). % zero_less_norm_iff
thf(fact_4_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_5_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_6_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_7_norm__eq__zero, axiom,
    ((![X3 : a]: (((real_V1022479215norm_a @ X3) = zero_zero_real) = (X3 = zero_zero_a))))). % norm_eq_zero
thf(fact_8_diff__gt__0__iff__gt, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (minus_240770701y_real @ A @ B)) = (ord_less_poly_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_9_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_10_poly__diff, axiom,
    ((![P2 : poly_poly_real, Q : poly_poly_real, X3 : poly_real]: ((poly_poly_real2 @ (minus_181436949y_real @ P2 @ Q) @ X3) = (minus_240770701y_real @ (poly_poly_real2 @ P2 @ X3) @ (poly_poly_real2 @ Q @ X3)))))). % poly_diff
thf(fact_11_poly__diff, axiom,
    ((![P2 : poly_real, Q : poly_real, X3 : real]: ((poly_real2 @ (minus_240770701y_real @ P2 @ Q) @ X3) = (minus_minus_real @ (poly_real2 @ P2 @ X3) @ (poly_real2 @ Q @ X3)))))). % poly_diff
thf(fact_12_poly__0, axiom,
    ((![X3 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X3) = zero_zero_poly_nat)))). % poly_0
thf(fact_13_poly__0, axiom,
    ((![X3 : poly_real]: ((poly_poly_real2 @ zero_z1423781445y_real @ X3) = zero_zero_poly_real)))). % poly_0
thf(fact_14_poly__0, axiom,
    ((![X3 : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X3) = zero_zero_poly_a)))). % poly_0
thf(fact_15_poly__0, axiom,
    ((![X3 : a]: ((poly_a2 @ zero_zero_poly_a @ X3) = zero_zero_a)))). % poly_0
thf(fact_16_poly__0, axiom,
    ((![X3 : real]: ((poly_real2 @ zero_zero_poly_real @ X3) = zero_zero_real)))). % poly_0
thf(fact_17_poly__0, axiom,
    ((![X3 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))). % poly_0
thf(fact_18_diff__self, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % diff_self
thf(fact_19_diff__self, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ A) = zero_zero_poly_real)))). % diff_self
thf(fact_20_diff__self, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % diff_self
thf(fact_21_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_22_diff__0__right, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_0_right
thf(fact_23_diff__0__right, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ zero_zero_poly_real) = A)))). % diff_0_right
thf(fact_24_diff__0__right, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_0_right
thf(fact_25_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_26_zero__diff, axiom,
    ((![A : nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % zero_diff
thf(fact_27_diff__zero, axiom,
    ((![A : poly_nat]: ((minus_minus_poly_nat @ A @ zero_zero_poly_nat) = A)))). % diff_zero
thf(fact_28_diff__zero, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_zero
thf(fact_29_diff__zero, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_zero
thf(fact_30_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_31_diff__zero, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A)))). % diff_zero
thf(fact_32_diff__zero, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ zero_zero_poly_real) = A)))). % diff_zero
thf(fact_33_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_nat]: ((minus_minus_poly_nat @ A @ A) = zero_zero_poly_nat)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_34_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_35_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % 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 : nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_38_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ A) = zero_zero_poly_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_39_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_40_poly__IVT__pos, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P2 @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ B)) => (?[X : real]: ((ord_less_real @ A @ X) & ((ord_less_real @ X @ B) & ((poly_real2 @ P2 @ X) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_41_poly__IVT__neg, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ A)) => ((ord_less_real @ (poly_real2 @ P2 @ B) @ zero_zero_real) => (?[X : real]: ((ord_less_real @ A @ X) & ((ord_less_real @ X @ B) & ((poly_real2 @ P2 @ X) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_42_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_43_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_44_zero__reorient, axiom,
    ((![X3 : a]: ((zero_zero_a = X3) = (X3 = zero_zero_a))))). % zero_reorient
thf(fact_45_zero__reorient, axiom,
    ((![X3 : poly_nat]: ((zero_zero_poly_nat = X3) = (X3 = zero_zero_poly_nat))))). % zero_reorient
thf(fact_46_zero__reorient, axiom,
    ((![X3 : poly_real]: ((zero_zero_poly_real = X3) = (X3 = zero_zero_poly_real))))). % zero_reorient
thf(fact_47_zero__reorient, axiom,
    ((![X3 : poly_a]: ((zero_zero_poly_a = X3) = (X3 = zero_zero_poly_a))))). % zero_reorient
thf(fact_48_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : a, C : a, B : a]: ((minus_minus_a @ (minus_minus_a @ A @ C) @ B) = (minus_minus_a @ (minus_minus_a @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_49_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_50_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : nat, C : nat, B : nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ C) @ B) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_51_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((minus_240770701y_real @ (minus_240770701y_real @ A @ C) @ B) = (minus_240770701y_real @ (minus_240770701y_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_52_diff__eq__diff__eq, axiom,
    ((![A : a, B : a, C : a, D : a]: (((minus_minus_a @ A @ B) = (minus_minus_a @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_53_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_54_diff__eq__diff__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_55_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_real, Q : poly_real]: (((poly_real2 @ P2) = (poly_real2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_56_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_57_gr__implies__not__zero, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_58_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_59_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_60_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_a]: (^[Z2 : poly_a]: (Y2 = Z2))) = (^[A2 : poly_a]: (^[B2 : poly_a]: ((minus_minus_poly_a @ A2 @ B2) = zero_zero_poly_a)))))). % eq_iff_diff_eq_0
thf(fact_61_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : a]: (^[Z2 : a]: (Y2 = Z2))) = (^[A2 : a]: (^[B2 : a]: ((minus_minus_a @ A2 @ B2) = zero_zero_a)))))). % eq_iff_diff_eq_0
thf(fact_62_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_63_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_real]: (^[Z2 : poly_real]: (Y2 = Z2))) = (^[A2 : poly_real]: (^[B2 : poly_real]: ((minus_240770701y_real @ A2 @ B2) = zero_zero_poly_real)))))). % eq_iff_diff_eq_0
thf(fact_64_diff__strict__right__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_less_poly_real @ A @ B) => (ord_less_poly_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ C)))))). % diff_strict_right_mono
thf(fact_65_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_66_diff__strict__left__mono, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: ((ord_less_poly_real @ B @ A) => (ord_less_poly_real @ (minus_240770701y_real @ C @ A) @ (minus_240770701y_real @ C @ B)))))). % diff_strict_left_mono
thf(fact_67_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_68_diff__eq__diff__less, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((ord_less_poly_real @ A @ B) = (ord_less_poly_real @ C @ D)))))). % diff_eq_diff_less
thf(fact_69_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_70_diff__strict__mono, axiom,
    ((![A : poly_real, B : poly_real, D : poly_real, C : poly_real]: ((ord_less_poly_real @ A @ B) => ((ord_less_poly_real @ D @ C) => (ord_less_poly_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ D))))))). % diff_strict_mono
thf(fact_71_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_72_norm__minus__commute, axiom,
    ((![A : a, B : a]: ((real_V1022479215norm_a @ (minus_minus_a @ A @ B)) = (real_V1022479215norm_a @ (minus_minus_a @ B @ A)))))). % norm_minus_commute
thf(fact_73_norm__minus__commute, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (minus_minus_real @ A @ B)) = (real_V646646907m_real @ (minus_minus_real @ B @ A)))))). % norm_minus_commute
thf(fact_74_poly__all__0__iff__0, axiom,
    ((![P2 : poly_real]: ((![X2 : real]: ((poly_real2 @ P2 @ X2) = zero_zero_real)) = (P2 = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_75_poly__all__0__iff__0, axiom,
    ((![P2 : poly_poly_real]: ((![X2 : poly_real]: ((poly_poly_real2 @ P2 @ X2) = zero_zero_poly_real)) = (P2 = zero_z1423781445y_real))))). % poly_all_0_iff_0
thf(fact_76_less__iff__diff__less__0, axiom,
    ((ord_less_poly_real = (^[A2 : poly_real]: (^[B2 : poly_real]: (ord_less_poly_real @ (minus_240770701y_real @ A2 @ B2) @ zero_zero_poly_real)))))). % less_iff_diff_less_0
thf(fact_77_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_78_norm__not__less__zero, axiom,
    ((![X3 : a]: (~ ((ord_less_real @ (real_V1022479215norm_a @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_79_norm__not__less__zero, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_80_field__lbound__gt__zero, axiom,
    ((![D1 : real, D2 : real]: ((ord_less_real @ zero_zero_real @ D1) => ((ord_less_real @ zero_zero_real @ D2) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ D1) & (ord_less_real @ E @ D2))))))))). % field_lbound_gt_zero
thf(fact_81_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real))))). % less_numeral_extra(3)
thf(fact_82_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_83_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_84_psize__eq__0__iff, axiom,
    ((![P2 : poly_nat]: (((fundam1567013434ze_nat @ P2) = zero_zero_nat) = (P2 = zero_zero_poly_nat))))). % psize_eq_0_iff
thf(fact_85_psize__eq__0__iff, axiom,
    ((![P2 : poly_real]: (((fundam1947011094e_real @ P2) = zero_zero_nat) = (P2 = zero_zero_poly_real))))). % psize_eq_0_iff
thf(fact_86_psize__eq__0__iff, axiom,
    ((![P2 : poly_a]: (((fundam247907092size_a @ P2) = zero_zero_nat) = (P2 = zero_zero_poly_a))))). % psize_eq_0_iff
thf(fact_87_is__zero__null, axiom,
    ((is_zero_nat = (^[P3 : poly_nat]: (P3 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_88_is__zero__null, axiom,
    ((is_zero_real = (^[P3 : poly_real]: (P3 = zero_zero_poly_real))))). % is_zero_null
thf(fact_89_is__zero__null, axiom,
    ((is_zero_a = (^[P3 : poly_a]: (P3 = zero_zero_poly_a))))). % is_zero_null
thf(fact_90_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_91_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_real @ N @ zero_zero_poly_real) = zero_zero_poly_real)))). % poly_cutoff_0
thf(fact_92_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_cutoff_0
thf(fact_93_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_real]: (((poly_real2 @ (reflect_poly_real @ P2) @ zero_zero_real) = zero_zero_real) = (P2 = zero_zero_poly_real))))). % reflect_poly_at_0_eq_0_iff
thf(fact_94_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_nat]: (((poly_nat2 @ (reflect_poly_nat @ P2) @ zero_zero_nat) = zero_zero_nat) = (P2 = zero_zero_poly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_95_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_a]: (((poly_a2 @ (reflect_poly_a @ P2) @ zero_zero_a) = zero_zero_a) = (P2 = zero_zero_poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_96_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_poly_nat]: (((poly_poly_nat2 @ (reflec781175074ly_nat @ P2) @ zero_zero_poly_nat) = zero_zero_poly_nat) = (P2 = zero_z1059985641ly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_97_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_poly_real]: (((poly_poly_real2 @ (reflec1522834046y_real @ P2) @ zero_zero_poly_real) = zero_zero_poly_real) = (P2 = zero_z1423781445y_real))))). % reflect_poly_at_0_eq_0_iff
thf(fact_98_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P2 : poly_poly_a]: (((poly_poly_a2 @ (reflect_poly_poly_a @ P2) @ zero_zero_poly_a) = zero_zero_poly_a) = (P2 = zero_z2096148049poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_99_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_a]: (?[M2 : real]: ((ord_less_real @ zero_zero_real @ M2) & (![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ R) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ P2 @ Z)) @ M2)))))))). % poly_bound_exists
thf(fact_100_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_real]: (?[M2 : real]: ((ord_less_real @ zero_zero_real @ M2) & (![Z : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P2 @ Z)) @ M2)))))))). % poly_bound_exists
thf(fact_101_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_102_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_real @ N @ zero_zero_poly_real) = zero_zero_poly_real)))). % poly_shift_0
thf(fact_103_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_shift_0
thf(fact_104_norm__le__zero__iff, axiom,
    ((![X3 : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ X3) @ zero_zero_real) = (X3 = zero_zero_a))))). % norm_le_zero_iff
thf(fact_105_norm__le__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X3) @ zero_zero_real) = (X3 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_106_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_107_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_108_Collect__mem__eq, axiom,
    ((![A3 : set_real]: ((collect_real @ (^[X2 : real]: (member_real @ X2 @ A3))) = A3)))). % Collect_mem_eq
thf(fact_109_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_110_reflect__poly__0, axiom,
    (((reflect_poly_real @ zero_zero_poly_real) = zero_zero_poly_real))). % reflect_poly_0
thf(fact_111_reflect__poly__0, axiom,
    (((reflect_poly_a @ zero_zero_poly_a) = zero_zero_poly_a))). % reflect_poly_0
thf(fact_112_diff__ge__0__iff__ge, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ (minus_240770701y_real @ A @ B)) = (ord_le1180086932y_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_113_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_114_complete__real, axiom,
    ((![S2 : set_real]: ((?[X4 : real]: (member_real @ X4 @ S2)) => ((?[Z : real]: (![X : real]: ((member_real @ X @ S2) => (ord_less_eq_real @ X @ Z)))) => (?[Y3 : real]: ((![X4 : real]: ((member_real @ X4 @ S2) => (ord_less_eq_real @ X4 @ Y3))) & (![Z : real]: ((![X : real]: ((member_real @ X @ S2) => (ord_less_eq_real @ X @ Z))) => (ord_less_eq_real @ Y3 @ Z)))))))))). % complete_real
thf(fact_115_le__numeral__extra_I3_J, axiom,
    ((ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real))). % le_numeral_extra(3)
thf(fact_116_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_117_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat))). % le_numeral_extra(3)
thf(fact_118_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y4 : real]: (((ord_less_real @ X2 @ Y4)) | ((X2 = Y4)))))))). % less_eq_real_def
thf(fact_119_zero__le, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X3)))). % zero_le
thf(fact_120_diff__mono, axiom,
    ((![A : poly_real, B : poly_real, D : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => ((ord_le1180086932y_real @ D @ C) => (ord_le1180086932y_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ D))))))). % diff_mono
thf(fact_121_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_122_diff__left__mono, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: ((ord_le1180086932y_real @ B @ A) => (ord_le1180086932y_real @ (minus_240770701y_real @ C @ A) @ (minus_240770701y_real @ C @ B)))))). % diff_left_mono
thf(fact_123_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_124_diff__right__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ C)))))). % diff_right_mono
thf(fact_125_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_126_diff__eq__diff__less__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((ord_le1180086932y_real @ A @ B) = (ord_le1180086932y_real @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_127_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_128_le__iff__diff__le__0, axiom,
    ((ord_le1180086932y_real = (^[A2 : poly_real]: (^[B2 : poly_real]: (ord_le1180086932y_real @ (minus_240770701y_real @ A2 @ B2) @ zero_zero_poly_real)))))). % le_iff_diff_le_0
thf(fact_129_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_130_norm__triangle__ineq2, axiom,
    ((![A : a, B : a]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022479215norm_a @ A) @ (real_V1022479215norm_a @ B)) @ (real_V1022479215norm_a @ (minus_minus_a @ A @ B)))))). % norm_triangle_ineq2
thf(fact_131_norm__triangle__ineq2, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)) @ (real_V646646907m_real @ (minus_minus_real @ A @ B)))))). % norm_triangle_ineq2
thf(fact_132_norm__ge__zero, axiom,
    ((![X3 : a]: (ord_less_eq_real @ zero_zero_real @ (real_V1022479215norm_a @ X3))))). % norm_ge_zero
thf(fact_133_norm__ge__zero, axiom,
    ((![X3 : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X3))))). % norm_ge_zero
thf(fact_134_Bolzano, axiom,
    ((![A : real, B : real, P : real > real > $o]: ((ord_less_eq_real @ A @ B) => ((![A4 : real, B3 : real, C2 : real]: ((P @ A4 @ B3) => ((P @ B3 @ C2) => ((ord_less_eq_real @ A4 @ B3) => ((ord_less_eq_real @ B3 @ C2) => (P @ A4 @ C2)))))) => ((![X : real]: ((ord_less_eq_real @ A @ X) => ((ord_less_eq_real @ X @ B) => (?[D3 : real]: ((ord_less_real @ zero_zero_real @ D3) & (![A4 : real, B3 : real]: (((ord_less_eq_real @ A4 @ X) & ((ord_less_eq_real @ X @ B3) & (ord_less_real @ (minus_minus_real @ B3 @ A4) @ D3))) => (P @ A4 @ B3)))))))) => (P @ A @ B))))))). % Bolzano
thf(fact_135_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_136_diff__0__eq__0, axiom,
    ((![N : nat]: ((minus_minus_nat @ zero_zero_nat @ N) = zero_zero_nat)))). % diff_0_eq_0
thf(fact_137_diff__self__eq__0, axiom,
    ((![M : nat]: ((minus_minus_nat @ M @ M) = zero_zero_nat)))). % diff_self_eq_0
thf(fact_138_zero__less__diff, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ N @ M)) = (ord_less_nat @ M @ N))))). % zero_less_diff
thf(fact_139_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_140_le0, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % le0
thf(fact_141_bot__nat__0_Oextremum, axiom,
    ((![A : nat]: (ord_less_eq_nat @ zero_zero_nat @ A)))). % bot_nat_0.extremum
thf(fact_142_diff__diff__cancel, axiom,
    ((![I : nat, N : nat]: ((ord_less_eq_nat @ I @ N) => ((minus_minus_nat @ N @ (minus_minus_nat @ N @ I)) = I))))). % diff_diff_cancel
thf(fact_143_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_144_diff__is__0__eq, axiom,
    ((![M : nat, N : nat]: (((minus_minus_nat @ M @ N) = zero_zero_nat) = (ord_less_eq_nat @ M @ N))))). % diff_is_0_eq
thf(fact_145_diff__is__0__eq_H, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => ((minus_minus_nat @ M @ N) = zero_zero_nat))))). % diff_is_0_eq'
thf(fact_146_less__eq__nat_Osimps_I1_J, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % less_eq_nat.simps(1)
thf(fact_147_le__0__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_0_eq
thf(fact_148_eq__diff__iff, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_eq_nat @ K @ M) => ((ord_less_eq_nat @ K @ N) => (((minus_minus_nat @ M @ K) = (minus_minus_nat @ N @ K)) = (M = N))))))). % eq_diff_iff
thf(fact_149_le__diff__iff, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_eq_nat @ K @ M) => ((ord_less_eq_nat @ K @ N) => ((ord_less_eq_nat @ (minus_minus_nat @ M @ K) @ (minus_minus_nat @ N @ K)) = (ord_less_eq_nat @ M @ N))))))). % le_diff_iff
thf(fact_150_nat__less__le, axiom,
    ((ord_less_nat = (^[M3 : nat]: (^[N2 : nat]: (((ord_less_eq_nat @ M3 @ N2)) & ((~ ((M3 = N2)))))))))). % nat_less_le
thf(fact_151_diff__commute, axiom,
    ((![I : nat, J : nat, K : nat]: ((minus_minus_nat @ (minus_minus_nat @ I @ J) @ K) = (minus_minus_nat @ (minus_minus_nat @ I @ K) @ J))))). % diff_commute
thf(fact_152_Nat_Odiff__diff__eq, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_eq_nat @ K @ M) => ((ord_less_eq_nat @ K @ N) => ((minus_minus_nat @ (minus_minus_nat @ M @ K) @ (minus_minus_nat @ N @ K)) = (minus_minus_nat @ M @ N))))))). % Nat.diff_diff_eq
thf(fact_153_diff__le__mono, axiom,
    ((![M : nat, N : nat, L : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ (minus_minus_nat @ M @ L) @ (minus_minus_nat @ N @ L)))))). % diff_le_mono
thf(fact_154_diff__le__self, axiom,
    ((![M : nat, N : nat]: (ord_less_eq_nat @ (minus_minus_nat @ M @ N) @ M)))). % diff_le_self
thf(fact_155_le__diff__iff_H, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ C @ A) @ (minus_minus_nat @ C @ B)) = (ord_less_eq_nat @ B @ A))))))). % le_diff_iff'
thf(fact_156_diff__le__mono2, axiom,
    ((![M : nat, N : nat, L : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ (minus_minus_nat @ L @ N) @ (minus_minus_nat @ L @ M)))))). % diff_le_mono2
thf(fact_157_less__diff__iff, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_eq_nat @ K @ M) => ((ord_less_eq_nat @ K @ N) => ((ord_less_nat @ (minus_minus_nat @ M @ K) @ (minus_minus_nat @ N @ K)) = (ord_less_nat @ M @ N))))))). % less_diff_iff
thf(fact_158_diff__less__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))))). % diff_less_mono
thf(fact_159_diff__less__mono2, axiom,
    ((![M : nat, N : nat, L : nat]: ((ord_less_nat @ M @ N) => ((ord_less_nat @ M @ L) => (ord_less_nat @ (minus_minus_nat @ L @ N) @ (minus_minus_nat @ L @ M))))))). % diff_less_mono2
thf(fact_160_ex__least__nat__le, axiom,
    ((![P : nat > $o, N : nat]: ((P @ N) => ((~ ((P @ zero_zero_nat))) => (?[K2 : nat]: ((ord_less_eq_nat @ K2 @ N) & ((![I2 : nat]: ((ord_less_nat @ I2 @ K2) => (~ ((P @ I2))))) & (P @ K2))))))))). % ex_least_nat_le
thf(fact_161_less__imp__le__nat, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (ord_less_eq_nat @ M @ N))))). % less_imp_le_nat
thf(fact_162_le__eq__less__or__eq, axiom,
    ((ord_less_eq_nat = (^[M3 : nat]: (^[N2 : nat]: (((ord_less_nat @ M3 @ N2)) | ((M3 = N2)))))))). % le_eq_less_or_eq
thf(fact_163_less__or__eq__imp__le, axiom,
    ((![M : nat, N : nat]: (((ord_less_nat @ M @ N) | (M = N)) => (ord_less_eq_nat @ M @ N))))). % less_or_eq_imp_le
thf(fact_164_less__imp__diff__less, axiom,
    ((![J : nat, K : nat, N : nat]: ((ord_less_nat @ J @ K) => (ord_less_nat @ (minus_minus_nat @ J @ N) @ K))))). % less_imp_diff_less
thf(fact_165_le__neq__implies__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => ((~ ((M = N))) => (ord_less_nat @ M @ N)))))). % le_neq_implies_less
thf(fact_166_less__mono__imp__le__mono, axiom,
    ((![F : nat > nat, I : nat, J : nat]: ((![I3 : nat, J2 : nat]: ((ord_less_nat @ I3 @ J2) => (ord_less_nat @ (F @ I3) @ (F @ J2)))) => ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (F @ I) @ (F @ J))))))). % less_mono_imp_le_mono
thf(fact_167_bot__nat__0_Oextremum__unique, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat))))). % bot_nat_0.extremum_unique
thf(fact_168_bot__nat__0_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat))))). % bot_nat_0.extremum_uniqueI
thf(fact_169_linorder__neqE__nat, axiom,
    ((![X3 : nat, Y5 : nat]: ((~ ((X3 = Y5))) => ((~ ((ord_less_nat @ X3 @ Y5))) => (ord_less_nat @ Y5 @ X3)))))). % linorder_neqE_nat
thf(fact_170_infinite__descent, axiom,
    ((![P : nat > $o, N : nat]: ((![N3 : nat]: ((~ ((P @ N3))) => (?[M4 : nat]: ((ord_less_nat @ M4 @ N3) & (~ ((P @ M4))))))) => (P @ N))))). % infinite_descent
thf(fact_171_nat__less__induct, axiom,
    ((![P : nat > $o, N : nat]: ((![N3 : nat]: ((![M4 : nat]: ((ord_less_nat @ M4 @ N3) => (P @ M4))) => (P @ N3))) => (P @ N))))). % nat_less_induct
thf(fact_172_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_173_less__not__refl3, axiom,
    ((![S3 : nat, T : nat]: ((ord_less_nat @ S3 @ T) => (~ ((S3 = T))))))). % less_not_refl3
thf(fact_174_less__not__refl2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ N @ M) => (~ ((M = N))))))). % less_not_refl2
thf(fact_175_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_176_nat__neq__iff, axiom,
    ((![M : nat, N : nat]: ((~ ((M = N))) = (((ord_less_nat @ M @ N)) | ((ord_less_nat @ N @ M))))))). % nat_neq_iff
thf(fact_177_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_178_infinite__descent0, axiom,
    ((![P : nat > $o, N : nat]: ((P @ zero_zero_nat) => ((![N3 : nat]: ((ord_less_nat @ zero_zero_nat @ N3) => ((~ ((P @ N3))) => (?[M4 : nat]: ((ord_less_nat @ M4 @ N3) & (~ ((P @ M4)))))))) => (P @ N)))))). % infinite_descent0
thf(fact_179_minus__nat_Odiff__0, axiom,
    ((![M : nat]: ((minus_minus_nat @ M @ zero_zero_nat) = M)))). % minus_nat.diff_0
thf(fact_180_diffs0__imp__equal, axiom,
    ((![M : nat, N : nat]: (((minus_minus_nat @ M @ N) = zero_zero_nat) => (((minus_minus_nat @ N @ M) = zero_zero_nat) => (M = N)))))). % diffs0_imp_equal
thf(fact_181_gr__implies__not0, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_182_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_183_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_184_diff__less, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_nat @ zero_zero_nat @ M) => (ord_less_nat @ (minus_minus_nat @ M @ N) @ M)))))). % diff_less
thf(fact_185_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_186_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_187_order__refl, axiom,
    ((![X3 : real]: (ord_less_eq_real @ X3 @ X3)))). % order_refl
thf(fact_188_order__refl, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ X3 @ X3)))). % order_refl
thf(fact_189_complete__interval, axiom,
    ((![A : real, B : real, P : real > $o]: ((ord_less_real @ A @ B) => ((P @ A) => ((~ ((P @ B))) => (?[C2 : real]: ((ord_less_eq_real @ A @ C2) & ((ord_less_eq_real @ C2 @ B) & ((![X4 : real]: (((ord_less_eq_real @ A @ X4) & (ord_less_real @ X4 @ C2)) => (P @ X4))) & (![D3 : real]: ((![X : real]: (((ord_less_eq_real @ A @ X) & (ord_less_real @ X @ D3)) => (P @ X))) => (ord_less_eq_real @ D3 @ C2))))))))))))). % complete_interval
thf(fact_190_complete__interval, axiom,
    ((![A : nat, B : nat, P : nat > $o]: ((ord_less_nat @ A @ B) => ((P @ A) => ((~ ((P @ B))) => (?[C2 : nat]: ((ord_less_eq_nat @ A @ C2) & ((ord_less_eq_nat @ C2 @ B) & ((![X4 : nat]: (((ord_less_eq_nat @ A @ X4) & (ord_less_nat @ X4 @ C2)) => (P @ X4))) & (![D3 : nat]: ((![X : nat]: (((ord_less_eq_nat @ A @ X) & (ord_less_nat @ X @ D3)) => (P @ X))) => (ord_less_eq_nat @ D3 @ C2))))))))))))). % complete_interval
thf(fact_191_order_Onot__eq__order__implies__strict, axiom,
    ((![A : real, B : real]: ((~ ((A = B))) => ((ord_less_eq_real @ A @ B) => (ord_less_real @ A @ B)))))). % order.not_eq_order_implies_strict
thf(fact_192_order_Onot__eq__order__implies__strict, axiom,
    ((![A : nat, B : nat]: ((~ ((A = B))) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B)))))). % order.not_eq_order_implies_strict
thf(fact_193_dual__order_Ostrict__implies__order, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (ord_less_eq_real @ B @ A))))). % dual_order.strict_implies_order
thf(fact_194_dual__order_Ostrict__implies__order, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (ord_less_eq_nat @ B @ A))))). % dual_order.strict_implies_order
thf(fact_195_Nat_Oex__has__greatest__nat, axiom,
    ((![P : nat > $o, K : nat, B : nat]: ((P @ K) => ((![Y3 : nat]: ((P @ Y3) => (ord_less_eq_nat @ Y3 @ B))) => (?[X : nat]: ((P @ X) & (![Y : nat]: ((P @ Y) => (ord_less_eq_nat @ Y @ X)))))))))). % Nat.ex_has_greatest_nat
thf(fact_196_nat__le__linear, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) | (ord_less_eq_nat @ N @ M))))). % nat_le_linear
thf(fact_197_le__antisym, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => ((ord_less_eq_nat @ N @ M) => (M = N)))))). % le_antisym
thf(fact_198_eq__imp__le, axiom,
    ((![M : nat, N : nat]: ((M = N) => (ord_less_eq_nat @ M @ N))))). % eq_imp_le
thf(fact_199_le__trans, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ J @ K) => (ord_less_eq_nat @ I @ K)))))). % le_trans
thf(fact_200_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_201_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_202_dual__order_Oantisym, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_203_dual__order_Oeq__iff, axiom,
    (((^[Y2 : real]: (^[Z2 : real]: (Y2 = Z2))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A2)) & ((ord_less_eq_real @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_204_dual__order_Oeq__iff, axiom,
    (((^[Y2 : nat]: (^[Z2 : nat]: (Y2 = Z2))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A2)) & ((ord_less_eq_nat @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_205_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_206_dual__order_Otrans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))))). % dual_order.trans
thf(fact_207_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B3 : real]: ((ord_less_eq_real @ A4 @ B3) => (P @ A4 @ B3))) => ((![A4 : real, B3 : real]: ((P @ B3 @ A4) => (P @ A4 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_208_linorder__wlog, axiom,
    ((![P : nat > nat > $o, A : nat, B : nat]: ((![A4 : nat, B3 : nat]: ((ord_less_eq_nat @ A4 @ B3) => (P @ A4 @ B3))) => ((![A4 : nat, B3 : nat]: ((P @ B3 @ A4) => (P @ A4 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_209_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_210_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_211_order__trans, axiom,
    ((![X3 : real, Y5 : real, Z3 : real]: ((ord_less_eq_real @ X3 @ Y5) => ((ord_less_eq_real @ Y5 @ Z3) => (ord_less_eq_real @ X3 @ Z3)))))). % order_trans
thf(fact_212_order__trans, axiom,
    ((![X3 : nat, Y5 : nat, Z3 : nat]: ((ord_less_eq_nat @ X3 @ Y5) => ((ord_less_eq_nat @ Y5 @ Z3) => (ord_less_eq_nat @ X3 @ Z3)))))). % order_trans
thf(fact_213_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_214_order__class_Oorder_Oantisym, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_215_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_216_ord__le__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C)))))). % ord_le_eq_trans
thf(fact_217_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_218_ord__eq__le__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % ord_eq_le_trans
thf(fact_219_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y2 : real]: (^[Z2 : real]: (Y2 = Z2))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ A2 @ B2)) & ((ord_less_eq_real @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_220_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y2 : nat]: (^[Z2 : nat]: (Y2 = Z2))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A2 @ B2)) & ((ord_less_eq_nat @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_221_antisym__conv, axiom,
    ((![Y5 : real, X3 : real]: ((ord_less_eq_real @ Y5 @ X3) => ((ord_less_eq_real @ X3 @ Y5) = (X3 = Y5)))))). % antisym_conv
thf(fact_222_antisym__conv, axiom,
    ((![Y5 : nat, X3 : nat]: ((ord_less_eq_nat @ Y5 @ X3) => ((ord_less_eq_nat @ X3 @ Y5) = (X3 = Y5)))))). % antisym_conv
thf(fact_223_le__cases3, axiom,
    ((![X3 : real, Y5 : real, Z3 : real]: (((ord_less_eq_real @ X3 @ Y5) => (~ ((ord_less_eq_real @ Y5 @ Z3)))) => (((ord_less_eq_real @ Y5 @ X3) => (~ ((ord_less_eq_real @ X3 @ Z3)))) => (((ord_less_eq_real @ X3 @ Z3) => (~ ((ord_less_eq_real @ Z3 @ Y5)))) => (((ord_less_eq_real @ Z3 @ Y5) => (~ ((ord_less_eq_real @ Y5 @ X3)))) => (((ord_less_eq_real @ Y5 @ Z3) => (~ ((ord_less_eq_real @ Z3 @ X3)))) => (~ (((ord_less_eq_real @ Z3 @ X3) => (~ ((ord_less_eq_real @ X3 @ Y5)))))))))))))). % le_cases3
thf(fact_224_le__cases3, axiom,
    ((![X3 : nat, Y5 : nat, Z3 : nat]: (((ord_less_eq_nat @ X3 @ Y5) => (~ ((ord_less_eq_nat @ Y5 @ Z3)))) => (((ord_less_eq_nat @ Y5 @ X3) => (~ ((ord_less_eq_nat @ X3 @ Z3)))) => (((ord_less_eq_nat @ X3 @ Z3) => (~ ((ord_less_eq_nat @ Z3 @ Y5)))) => (((ord_less_eq_nat @ Z3 @ Y5) => (~ ((ord_less_eq_nat @ Y5 @ X3)))) => (((ord_less_eq_nat @ Y5 @ Z3) => (~ ((ord_less_eq_nat @ Z3 @ X3)))) => (~ (((ord_less_eq_nat @ Z3 @ X3) => (~ ((ord_less_eq_nat @ X3 @ Y5)))))))))))))). % le_cases3
thf(fact_225_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_226_order_Otrans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % order.trans
thf(fact_227_le__cases, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((ord_less_eq_real @ X3 @ Y5))) => (ord_less_eq_real @ Y5 @ X3))))). % le_cases
thf(fact_228_le__cases, axiom,
    ((![X3 : nat, Y5 : nat]: ((~ ((ord_less_eq_nat @ X3 @ Y5))) => (ord_less_eq_nat @ Y5 @ X3))))). % le_cases
thf(fact_229_eq__refl, axiom,
    ((![X3 : real, Y5 : real]: ((X3 = Y5) => (ord_less_eq_real @ X3 @ Y5))))). % eq_refl
thf(fact_230_eq__refl, axiom,
    ((![X3 : nat, Y5 : nat]: ((X3 = Y5) => (ord_less_eq_nat @ X3 @ Y5))))). % eq_refl
thf(fact_231_linear, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_eq_real @ X3 @ Y5) | (ord_less_eq_real @ Y5 @ X3))))). % linear
thf(fact_232_linear, axiom,
    ((![X3 : nat, Y5 : nat]: ((ord_less_eq_nat @ X3 @ Y5) | (ord_less_eq_nat @ Y5 @ X3))))). % linear
thf(fact_233_antisym, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_eq_real @ X3 @ Y5) => ((ord_less_eq_real @ Y5 @ X3) => (X3 = Y5)))))). % antisym
thf(fact_234_antisym, axiom,
    ((![X3 : nat, Y5 : nat]: ((ord_less_eq_nat @ X3 @ Y5) => ((ord_less_eq_nat @ Y5 @ X3) => (X3 = Y5)))))). % antisym
thf(fact_235_eq__iff, axiom,
    (((^[Y2 : real]: (^[Z2 : real]: (Y2 = Z2))) = (^[X2 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X2 @ Y4)) & ((ord_less_eq_real @ Y4 @ X2)))))))). % eq_iff
thf(fact_236_eq__iff, axiom,
    (((^[Y2 : nat]: (^[Z2 : nat]: (Y2 = Z2))) = (^[X2 : nat]: (^[Y4 : nat]: (((ord_less_eq_nat @ X2 @ Y4)) & ((ord_less_eq_nat @ Y4 @ X2)))))))). % eq_iff

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[D3 : real]: ((ord_less_real @ zero_zero_real @ D3) & (![W : a]: (((~ ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ (minus_minus_a @ W @ z))))) | (~ ((ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ W @ z)) @ D3)))) | (ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ (poly_a2 @ p @ W) @ (poly_a2 @ p @ z))) @ e))))))).
