% 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_346__5370904_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:26.258

% Could-be-implicit typings (7)
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_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_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 (45)
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_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    one_one_poly_real : poly_real).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Oone__class_Oone_001tf__a, type,
    one_one_a : a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    times_775122617y_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_Itf__a_J, type,
    times_times_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Otimes__class_Otimes_001tf__a, type,
    times_times_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__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_Polynomial_Odegree_001t__Real__Oreal, type,
    degree_real : poly_real > nat).
thf(sy_c_Polynomial_Odegree_001tf__a, type,
    degree_a : poly_a > nat).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    pCons_poly_real : poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_Itf__a_J, type,
    pCons_poly_a : poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_OpCons_001t__Real__Oreal, type,
    pCons_real : real > poly_real > poly_real).
thf(sy_c_Polynomial_OpCons_001tf__a, type,
    pCons_a : a > poly_a > poly_a).
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_Opos__poly_001t__Real__Oreal, type,
    pos_poly_real : poly_real > $o).
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_Rings_Odivide__class_Odivide_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    divide1727078534y_real : poly_real > poly_real > poly_real).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_c_Rings_Odivide__class_Odivide_001tf__a, type,
    divide_divide_a : a > a > a).
thf(sy_v_c____, type,
    c : a).
thf(sy_v_cs____, type,
    cs : poly_a).
thf(sy_v_d____, type,
    d : real).
thf(sy_v_e, type,
    e : real).
thf(sy_v_m____, type,
    m : real).
thf(sy_v_p, type,
    p : poly_a).
thf(sy_v_q____, type,
    q : poly_a).
thf(sy_v_z, type,
    z : a).

% Relevant facts (187)
thf(fact_0_ep, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % ep
thf(fact_1_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_2_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_3_pCons_Ohyps_I2_J, axiom,
    ((?[D : real]: ((ord_less_real @ zero_zero_real @ D) & (![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)) @ D)) => (ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ (poly_a2 @ cs @ (minus_minus_a @ W @ z)) @ (poly_a2 @ cs @ (minus_minus_a @ z @ z)))) @ e))))))). % pCons.hyps(2)
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_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_6_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_7_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_8_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_9_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_10_norm__eq__zero, axiom,
    ((![X3 : a]: (((real_V1022479215norm_a @ X3) = zero_zero_real) = (X3 = zero_zero_a))))). % norm_eq_zero
thf(fact_11_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_12_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_13_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_14_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_15_poly__0, axiom,
    ((![X3 : real]: ((poly_real2 @ zero_zero_poly_real @ X3) = zero_zero_real)))). % poly_0
thf(fact_16_poly__0, axiom,
    ((![X3 : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X3) = zero_zero_poly_a)))). % poly_0
thf(fact_17_poly__0, axiom,
    ((![X3 : a]: ((poly_a2 @ zero_zero_poly_a @ X3) = zero_zero_a)))). % poly_0
thf(fact_18_diff__pCons, axiom,
    ((![A : a, P2 : poly_a, B : a, Q : poly_a]: ((minus_minus_poly_a @ (pCons_a @ A @ P2) @ (pCons_a @ B @ Q)) = (pCons_a @ (minus_minus_a @ A @ B) @ (minus_minus_poly_a @ P2 @ Q)))))). % diff_pCons
thf(fact_19_diff__pCons, axiom,
    ((![A : poly_real, P2 : poly_poly_real, B : poly_real, Q : poly_poly_real]: ((minus_181436949y_real @ (pCons_poly_real @ A @ P2) @ (pCons_poly_real @ B @ Q)) = (pCons_poly_real @ (minus_240770701y_real @ A @ B) @ (minus_181436949y_real @ P2 @ Q)))))). % diff_pCons
thf(fact_20_diff__pCons, axiom,
    ((![A : real, P2 : poly_real, B : real, Q : poly_real]: ((minus_240770701y_real @ (pCons_real @ A @ P2) @ (pCons_real @ B @ Q)) = (pCons_real @ (minus_minus_real @ A @ B) @ (minus_240770701y_real @ P2 @ Q)))))). % diff_pCons
thf(fact_21_pCons__0__0, axiom,
    (((pCons_real @ zero_zero_real @ zero_zero_poly_real) = zero_zero_poly_real))). % pCons_0_0
thf(fact_22_pCons__0__0, axiom,
    (((pCons_a @ zero_zero_a @ zero_zero_poly_a) = zero_zero_poly_a))). % pCons_0_0
thf(fact_23_pCons__0__0, axiom,
    (((pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % pCons_0_0
thf(fact_24_pCons__eq__0__iff, axiom,
    ((![A : real, P2 : poly_real]: (((pCons_real @ A @ P2) = zero_zero_poly_real) = (((A = zero_zero_real)) & ((P2 = zero_zero_poly_real))))))). % pCons_eq_0_iff
thf(fact_25_pCons__eq__0__iff, axiom,
    ((![A : poly_a, P2 : poly_poly_a]: (((pCons_poly_a @ A @ P2) = zero_z2096148049poly_a) = (((A = zero_zero_poly_a)) & ((P2 = zero_z2096148049poly_a))))))). % pCons_eq_0_iff
thf(fact_26_pCons__eq__0__iff, axiom,
    ((![A : a, P2 : poly_a]: (((pCons_a @ A @ P2) = zero_zero_poly_a) = (((A = zero_zero_a)) & ((P2 = zero_zero_poly_a))))))). % pCons_eq_0_iff
thf(fact_27_diff__self, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % diff_self
thf(fact_28_diff__self, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % diff_self
thf(fact_29_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_30_diff__self, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ A) = zero_zero_poly_real)))). % diff_self
thf(fact_31_diff__0__right, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_0_right
thf(fact_32_diff__0__right, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_0_right
thf(fact_33_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_34_diff__0__right, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ zero_zero_poly_real) = A)))). % diff_0_right
thf(fact_35_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_36_pCons__eq__iff, axiom,
    ((![A : a, P2 : poly_a, B : a, Q : poly_a]: (((pCons_a @ A @ P2) = (pCons_a @ B @ Q)) = (((A = B)) & ((P2 = Q))))))). % pCons_eq_iff
thf(fact_37_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_38_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_39_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_40_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_41_diff__zero, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_zero
thf(fact_42_diff__zero, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_zero
thf(fact_43_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_44_diff__zero, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ zero_zero_poly_real) = A)))). % diff_zero
thf(fact_45_d_I2_J, axiom,
    ((ord_less_real @ d @ one_one_real))). % d(2)
thf(fact_46_d_I3_J, axiom,
    ((ord_less_real @ d @ (divide_divide_real @ e @ m)))). % d(3)
thf(fact_47_poly__induct2, axiom,
    ((![P : poly_a > poly_a > $o, P2 : poly_a, Q : poly_a]: ((P @ zero_zero_poly_a @ zero_zero_poly_a) => ((![A2 : a, P3 : poly_a, B2 : a, Q2 : poly_a]: ((P @ P3 @ Q2) => (P @ (pCons_a @ A2 @ P3) @ (pCons_a @ B2 @ Q2)))) => (P @ P2 @ Q)))))). % poly_induct2
thf(fact_48_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_49_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_50_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_51_zero__reorient, axiom,
    ((![X3 : a]: ((zero_zero_a = X3) = (X3 = zero_zero_a))))). % zero_reorient
thf(fact_52_zero__reorient, axiom,
    ((![X3 : poly_a]: ((zero_zero_poly_a = X3) = (X3 = zero_zero_poly_a))))). % zero_reorient
thf(fact_53_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_54_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_55_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_56_diff__eq__diff__eq, axiom,
    ((![A : a, B : a, C : a, D2 : a]: (((minus_minus_a @ A @ B) = (minus_minus_a @ C @ D2)) => ((A = B) = (C = D2)))))). % diff_eq_diff_eq
thf(fact_57_diff__eq__diff__eq, axiom,
    ((![A : real, B : real, C : real, D2 : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D2)) => ((A = B) = (C = D2)))))). % diff_eq_diff_eq
thf(fact_58_diff__eq__diff__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D2 : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D2)) => ((A = B) = (C = D2)))))). % diff_eq_diff_eq
thf(fact_59_pCons__cases, axiom,
    ((![P2 : poly_a]: (~ ((![A2 : a, Q2 : poly_a]: (~ ((P2 = (pCons_a @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_60_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_61_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_a]: (^[Z2 : poly_a]: (Y2 = Z2))) = (^[A3 : poly_a]: (^[B3 : poly_a]: ((minus_minus_poly_a @ A3 @ B3) = zero_zero_poly_a)))))). % eq_iff_diff_eq_0
thf(fact_62_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : a]: (^[Z2 : a]: (Y2 = Z2))) = (^[A3 : a]: (^[B3 : a]: ((minus_minus_a @ A3 @ B3) = zero_zero_a)))))). % eq_iff_diff_eq_0
thf(fact_63_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : real]: (^[Z2 : real]: (Y2 = Z2))) = (^[A3 : real]: (^[B3 : real]: ((minus_minus_real @ A3 @ B3) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_64_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_real]: (^[Z2 : poly_real]: (Y2 = Z2))) = (^[A3 : poly_real]: (^[B3 : poly_real]: ((minus_240770701y_real @ A3 @ B3) = zero_zero_poly_real)))))). % eq_iff_diff_eq_0
thf(fact_65_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_66_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_67_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_68_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_69_diff__eq__diff__less, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D2 : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D2)) => ((ord_less_poly_real @ A @ B) = (ord_less_poly_real @ C @ D2)))))). % diff_eq_diff_less
thf(fact_70_diff__eq__diff__less, axiom,
    ((![A : real, B : real, C : real, D2 : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D2)) => ((ord_less_real @ A @ B) = (ord_less_real @ C @ D2)))))). % diff_eq_diff_less
thf(fact_71_diff__strict__mono, axiom,
    ((![A : poly_real, B : poly_real, D2 : poly_real, C : poly_real]: ((ord_less_poly_real @ A @ B) => ((ord_less_poly_real @ D2 @ C) => (ord_less_poly_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ D2))))))). % diff_strict_mono
thf(fact_72_diff__strict__mono, axiom,
    ((![A : real, B : real, D2 : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ D2 @ C) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D2))))))). % diff_strict_mono
thf(fact_73_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_74_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_75_pCons__induct, axiom,
    ((![P : poly_real > $o, P2 : poly_real]: ((P @ zero_zero_poly_real) => ((![A2 : real, P3 : poly_real]: (((~ ((A2 = zero_zero_real))) | (~ ((P3 = zero_zero_poly_real)))) => ((P @ P3) => (P @ (pCons_real @ A2 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_76_pCons__induct, axiom,
    ((![P : poly_poly_a > $o, P2 : poly_poly_a]: ((P @ zero_z2096148049poly_a) => ((![A2 : poly_a, P3 : poly_poly_a]: (((~ ((A2 = zero_zero_poly_a))) | (~ ((P3 = zero_z2096148049poly_a)))) => ((P @ P3) => (P @ (pCons_poly_a @ A2 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_77_pCons__induct, axiom,
    ((![P : poly_a > $o, P2 : poly_a]: ((P @ zero_zero_poly_a) => ((![A2 : a, P3 : poly_a]: (((~ ((A2 = zero_zero_a))) | (~ ((P3 = zero_zero_poly_a)))) => ((P @ P3) => (P @ (pCons_a @ A2 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_78_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_79_less__iff__diff__less__0, axiom,
    ((ord_less_poly_real = (^[A3 : poly_real]: (^[B3 : poly_real]: (ord_less_poly_real @ (minus_240770701y_real @ A3 @ B3) @ zero_zero_poly_real)))))). % less_iff_diff_less_0
thf(fact_80_less__iff__diff__less__0, axiom,
    ((ord_less_real = (^[A3 : real]: (^[B3 : real]: (ord_less_real @ (minus_minus_real @ A3 @ B3) @ zero_zero_real)))))). % less_iff_diff_less_0
thf(fact_81_norm__not__less__zero, axiom,
    ((![X3 : a]: (~ ((ord_less_real @ (real_V1022479215norm_a @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_82_norm__not__less__zero, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_83_dm_I2_J, axiom,
    ((ord_less_real @ (times_times_real @ d @ m) @ e))). % dm(2)
thf(fact_84_dm_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ (times_times_real @ d @ m)))). % dm(1)
thf(fact_85_em0, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ e @ m)))). % em0
thf(fact_86_th, axiom,
    ((![W2 : a]: ((poly_a2 @ q @ (minus_minus_a @ W2 @ z)) = (poly_a2 @ p @ W2))))). % th
thf(fact_87_one0, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % one0
thf(fact_88_field__lbound__gt__zero, axiom,
    ((![D1 : real, D22 : real]: ((ord_less_real @ zero_zero_real @ D1) => ((ord_less_real @ zero_zero_real @ D22) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ D1) & (ord_less_real @ E @ D22))))))))). % field_lbound_gt_zero
thf(fact_89_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_90_pos__poly__pCons, axiom,
    ((![A : real, P2 : poly_real]: ((pos_poly_real @ (pCons_real @ A @ P2)) = (((pos_poly_real @ P2)) | ((((P2 = zero_zero_poly_real)) & ((ord_less_real @ zero_zero_real @ A))))))))). % pos_poly_pCons
thf(fact_91_mult_Oleft__neutral, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % mult.left_neutral
thf(fact_92_mult_Oright__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.right_neutral
thf(fact_93__092_060open_062_092_060exists_062ea_0620_O_Aea_A_060_A1_A_092_060and_062_Aea_A_060_Ae_A_P_Am_092_060close_062, axiom,
    ((?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ one_one_real) & (ord_less_real @ E @ (divide_divide_real @ e @ m))))))). % \<open>\<exists>ea>0. ea < 1 \<and> ea < e / m\<close>
thf(fact_94__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_A_092_060lbrakk_0620_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![D : real]: ((ord_less_real @ zero_zero_real @ D) => ((ord_less_real @ D @ one_one_real) => (~ ((ord_less_real @ D @ (divide_divide_real @ e @ m))))))))))). % \<open>\<And>thesis. (\<And>d. \<lbrakk>0 < d; d < 1; d < e / m\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_95_poly__mult, axiom,
    ((![P2 : poly_a, Q : poly_a, X3 : a]: ((poly_a2 @ (times_times_poly_a @ P2 @ Q) @ X3) = (times_times_a @ (poly_a2 @ P2 @ X3) @ (poly_a2 @ Q @ X3)))))). % poly_mult
thf(fact_96_poly__mult, axiom,
    ((![P2 : poly_real, Q : poly_real, X3 : real]: ((poly_real2 @ (times_775122617y_real @ P2 @ Q) @ X3) = (times_times_real @ (poly_real2 @ P2 @ X3) @ (poly_real2 @ Q @ X3)))))). % poly_mult
thf(fact_97_poly__1, axiom,
    ((![X3 : real]: ((poly_real2 @ one_one_poly_real @ X3) = one_one_real)))). % poly_1
thf(fact_98_diff__numeral__special_I9_J, axiom,
    (((minus_minus_a @ one_one_a @ one_one_a) = zero_zero_a))). % diff_numeral_special(9)
thf(fact_99_diff__numeral__special_I9_J, axiom,
    (((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real))). % diff_numeral_special(9)
thf(fact_100_diff__numeral__special_I9_J, axiom,
    (((minus_240770701y_real @ one_one_poly_real @ one_one_poly_real) = zero_zero_poly_real))). % diff_numeral_special(9)
thf(fact_101_norm__one, axiom,
    (((real_V1022479215norm_a @ one_one_a) = one_one_real))). % norm_one
thf(fact_102_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_103_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_real = (pCons_real @ one_one_real @ zero_zero_poly_real)))). % one_poly_eq_simps(1)
thf(fact_104_one__poly__eq__simps_I2_J, axiom,
    (((pCons_real @ one_one_real @ zero_zero_poly_real) = one_one_poly_real))). % one_poly_eq_simps(2)
thf(fact_105_q_I1_J, axiom,
    (((degree_a @ q) = (degree_a @ p)))). % q(1)
thf(fact_106_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_107_one__reorient, axiom,
    ((![X3 : real]: ((one_one_real = X3) = (X3 = one_one_real))))). % one_reorient
thf(fact_108_norm__divide, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_divide
thf(fact_109_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_110_mult_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.assoc
thf(fact_111_mult_Ocommute, axiom,
    ((times_times_real = (^[A3 : real]: (^[B3 : real]: (times_times_real @ B3 @ A3)))))). % mult.commute
thf(fact_112_mult_Ocomm__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.comm_neutral
thf(fact_113_mult_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((times_times_real @ B @ (times_times_real @ A @ C)) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.left_commute
thf(fact_114_norm__mult, axiom,
    ((![X3 : a, Y3 : a]: ((real_V1022479215norm_a @ (times_times_a @ X3 @ Y3)) = (times_times_real @ (real_V1022479215norm_a @ X3) @ (real_V1022479215norm_a @ Y3)))))). % norm_mult
thf(fact_115_norm__mult, axiom,
    ((![X3 : real, Y3 : real]: ((real_V646646907m_real @ (times_times_real @ X3 @ Y3)) = (times_times_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y3)))))). % norm_mult
thf(fact_116_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_117_nonzero__norm__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B))))))). % nonzero_norm_divide
thf(fact_118_norm__mult__less, axiom,
    ((![X3 : a, R : real, Y3 : a, S2 : real]: ((ord_less_real @ (real_V1022479215norm_a @ X3) @ R) => ((ord_less_real @ (real_V1022479215norm_a @ Y3) @ S2) => (ord_less_real @ (real_V1022479215norm_a @ (times_times_a @ X3 @ Y3)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_119_norm__mult__less, axiom,
    ((![X3 : real, R : real, Y3 : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X3) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y3) @ S2) => (ord_less_real @ (real_V646646907m_real @ (times_times_real @ X3 @ Y3)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_120_pCons__one, axiom,
    (((pCons_real @ one_one_real @ zero_zero_poly_real) = one_one_poly_real))). % pCons_one
thf(fact_121_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_122_less__poly__def, axiom,
    ((ord_less_poly_real = (^[X2 : poly_real]: (^[Y4 : poly_real]: (pos_poly_real @ (minus_240770701y_real @ Y4 @ X2))))))). % less_poly_def
thf(fact_123_poly__IVT, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ (poly_real2 @ P2 @ A) @ (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
thf(fact_124_nonzero__divide__mult__cancel__left, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ B)))))). % nonzero_divide_mult_cancel_left
thf(fact_125_nonzero__divide__mult__cancel__right, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((divide_divide_real @ B @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ A)))))). % nonzero_divide_mult_cancel_right
thf(fact_126_divide__less__0__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % divide_less_0_1_iff
thf(fact_127_divide__less__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B)))))). % divide_less_eq_1_neg
thf(fact_128_divide__less__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)))))). % divide_less_eq_1_pos
thf(fact_129_division__ring__divide__zero, axiom,
    ((![A : a]: ((divide_divide_a @ A @ zero_zero_a) = zero_zero_a)))). % division_ring_divide_zero
thf(fact_130_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_131_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_132_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_133_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_134_times__divide__eq__left, axiom,
    ((![B : real, C : real, A : real]: ((times_times_real @ (divide_divide_real @ B @ C) @ A) = (divide_divide_real @ (times_times_real @ B @ A) @ C))))). % times_divide_eq_left
thf(fact_135_divide__divide__eq__left, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ B @ C)))))). % divide_divide_eq_left
thf(fact_136_divide__divide__eq__right, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ C) @ B))))). % divide_divide_eq_right
thf(fact_137_times__divide__eq__right, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ B) @ C))))). % times_divide_eq_right
thf(fact_138_degree__0, axiom,
    (((degree_a @ zero_zero_poly_a) = zero_zero_nat))). % degree_0
thf(fact_139_nonzero__mult__divide__mult__cancel__right2, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ A @ C) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right2
thf(fact_140_nonzero__mult__divide__mult__cancel__right, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right
thf(fact_141_nonzero__mult__divide__mult__cancel__left2, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ B @ C)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left2
thf(fact_142_nonzero__mult__divide__mult__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left
thf(fact_143_mult__divide__mult__cancel__left__if, axiom,
    ((![C : real, A : real, B : real]: (((C = zero_zero_real) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = zero_zero_real)) & ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B))))))). % mult_divide_mult_cancel_left_if
thf(fact_144_zero__eq__1__divide__iff, axiom,
    ((![A : real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real))))). % zero_eq_1_divide_iff
thf(fact_145_one__divide__eq__0__iff, axiom,
    ((![A : real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % one_divide_eq_0_iff
thf(fact_146_eq__divide__eq__1, axiom,
    ((![B : real, A : real]: ((one_one_real = (divide_divide_real @ B @ A)) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % eq_divide_eq_1
thf(fact_147_divide__eq__eq__1, axiom,
    ((![B : real, A : real]: (((divide_divide_real @ B @ A) = one_one_real) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % divide_eq_eq_1
thf(fact_148_divide__self__if, axiom,
    ((![A : a]: (((A = zero_zero_a) => ((divide_divide_a @ A @ A) = zero_zero_a)) & ((~ ((A = zero_zero_a))) => ((divide_divide_a @ A @ A) = one_one_a)))))). % divide_self_if
thf(fact_149_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_150_divide__self, axiom,
    ((![A : a]: ((~ ((A = zero_zero_a))) => ((divide_divide_a @ A @ A) = one_one_a))))). % divide_self
thf(fact_151_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_152_one__eq__divide__iff, axiom,
    ((![A : real, B : real]: ((one_one_real = (divide_divide_real @ A @ B)) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_153_divide__eq__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = one_one_real) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_154_zero__less__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_divide_1_iff
thf(fact_155_less__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)))))). % less_divide_eq_1_pos
thf(fact_156_less__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)))))). % less_divide_eq_1_neg
thf(fact_157_degree__mult__eq__0, axiom,
    ((![P2 : poly_a, Q : poly_a]: (((degree_a @ (times_times_poly_a @ P2 @ Q)) = zero_zero_nat) = (((P2 = zero_zero_poly_a)) | ((((Q = zero_zero_poly_a)) | ((((~ ((P2 = zero_zero_poly_a)))) & ((((~ ((Q = zero_zero_poly_a)))) & (((((degree_a @ P2) = zero_zero_nat)) & (((degree_a @ Q) = zero_zero_nat))))))))))))))). % degree_mult_eq_0
thf(fact_158_mult__poly__0__left, axiom,
    ((![Q : poly_a]: ((times_times_poly_a @ zero_zero_poly_a @ Q) = zero_zero_poly_a)))). % mult_poly_0_left
thf(fact_159_mult__poly__0__right, axiom,
    ((![P2 : poly_a]: ((times_times_poly_a @ P2 @ zero_zero_poly_a) = zero_zero_poly_a)))). % mult_poly_0_right
thf(fact_160_degree__diff__less, axiom,
    ((![P2 : poly_a, N : nat, Q : poly_a]: ((ord_less_nat @ (degree_a @ P2) @ N) => ((ord_less_nat @ (degree_a @ Q) @ N) => (ord_less_nat @ (degree_a @ (minus_minus_poly_a @ P2 @ Q)) @ N)))))). % degree_diff_less
thf(fact_161_degree__diff__less, axiom,
    ((![P2 : poly_real, N : nat, Q : poly_real]: ((ord_less_nat @ (degree_real @ P2) @ N) => ((ord_less_nat @ (degree_real @ Q) @ N) => (ord_less_nat @ (degree_real @ (minus_240770701y_real @ P2 @ Q)) @ N)))))). % degree_diff_less
thf(fact_162_poly__div__diff__left, axiom,
    ((![X3 : poly_real, Y3 : poly_real, Z3 : poly_real]: ((divide1727078534y_real @ (minus_240770701y_real @ X3 @ Y3) @ Z3) = (minus_240770701y_real @ (divide1727078534y_real @ X3 @ Z3) @ (divide1727078534y_real @ Y3 @ Z3)))))). % poly_div_diff_left
thf(fact_163_degree__pCons__0, axiom,
    ((![A : a]: ((degree_a @ (pCons_a @ A @ zero_zero_poly_a)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_164_degree__eq__zeroE, axiom,
    ((![P2 : poly_a]: (((degree_a @ P2) = zero_zero_nat) => (~ ((![A2 : a]: (~ ((P2 = (pCons_a @ A2 @ zero_zero_poly_a))))))))))). % degree_eq_zeroE
thf(fact_165_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % linordered_field_no_ub
thf(fact_166_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y5 : real]: (ord_less_real @ Y5 @ X4))))). % linordered_field_no_lb
thf(fact_167_times__divide__times__eq, axiom,
    ((![X3 : real, Y3 : real, Z3 : real, W2 : real]: ((times_times_real @ (divide_divide_real @ X3 @ Y3) @ (divide_divide_real @ Z3 @ W2)) = (divide_divide_real @ (times_times_real @ X3 @ Z3) @ (times_times_real @ Y3 @ W2)))))). % times_divide_times_eq
thf(fact_168_divide__divide__times__eq, axiom,
    ((![X3 : real, Y3 : real, Z3 : real, W2 : real]: ((divide_divide_real @ (divide_divide_real @ X3 @ Y3) @ (divide_divide_real @ Z3 @ W2)) = (divide_divide_real @ (times_times_real @ X3 @ W2) @ (times_times_real @ Y3 @ Z3)))))). % divide_divide_times_eq
thf(fact_169_divide__divide__eq__left_H, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ C @ B)))))). % divide_divide_eq_left'
thf(fact_170_diff__divide__distrib, axiom,
    ((![A : a, B : a, C : a]: ((divide_divide_a @ (minus_minus_a @ A @ B) @ C) = (minus_minus_a @ (divide_divide_a @ A @ C) @ (divide_divide_a @ B @ C)))))). % diff_divide_distrib
thf(fact_171_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_172_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_173_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_174_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_175_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_176_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_177_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_178_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_179_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_180_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_181_nonzero__eq__divide__eq, axiom,
    ((![C : a, A : a, B : a]: ((~ ((C = zero_zero_a))) => ((A = (divide_divide_a @ B @ C)) = ((times_times_a @ A @ C) = B)))))). % nonzero_eq_divide_eq
thf(fact_182_nonzero__eq__divide__eq, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((A = (divide_divide_real @ B @ C)) = ((times_times_real @ A @ C) = B)))))). % nonzero_eq_divide_eq
thf(fact_183_nonzero__divide__eq__eq, axiom,
    ((![C : a, B : a, A : a]: ((~ ((C = zero_zero_a))) => (((divide_divide_a @ B @ C) = A) = (B = (times_times_a @ A @ C))))))). % nonzero_divide_eq_eq
thf(fact_184_nonzero__divide__eq__eq, axiom,
    ((![C : real, B : real, A : real]: ((~ ((C = zero_zero_real))) => (((divide_divide_real @ B @ C) = A) = (B = (times_times_real @ A @ C))))))). % nonzero_divide_eq_eq
thf(fact_185_eq__divide__imp, axiom,
    ((![C : a, A : a, B : a]: ((~ ((C = zero_zero_a))) => (((times_times_a @ A @ C) = B) => (A = (divide_divide_a @ B @ C))))))). % eq_divide_imp
thf(fact_186_eq__divide__imp, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => (((times_times_real @ A @ C) = B) => (A = (divide_divide_real @ B @ C))))))). % eq_divide_imp

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[D3 : real]: ((ord_less_real @ zero_zero_real @ D3) & (![W3 : a]: (((~ ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ (minus_minus_a @ W3 @ z))))) | (~ ((ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ W3 @ z)) @ D3)))) | (ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ (poly_a2 @ (pCons_a @ c @ cs) @ (minus_minus_a @ W3 @ z)) @ (poly_a2 @ (pCons_a @ c @ cs) @ (minus_minus_a @ z @ z)))) @ e))))))).
