% 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_357__5371018_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:31.691

% Could-be-implicit typings (6)
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 (39)
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__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__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_Odegree_001tf__a, type,
    degree_a : poly_a > nat).
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_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__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_da____, type,
    da : 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_w____, type,
    w : a).
thf(sy_v_z, type,
    z : a).

% Relevant facts (158)
thf(fact_0_dme, axiom,
    ((ord_less_real @ (times_times_real @ da @ m) @ e))). % dme
thf(fact_1_H_I4_J, axiom,
    ((~ ((w = z))))). % H(4)
thf(fact_2_H_I5_J, axiom,
    ((ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ w @ z)) @ da))). % H(5)
thf(fact_3__092_060open_062norm_A_Iw_A_N_Az_J_A_K_Anorm_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_092_060le_062_Ad_A_K_Am_092_060close_062, axiom,
    ((ord_less_eq_real @ (times_times_real @ (real_V1022479215norm_a @ (minus_minus_a @ w @ z)) @ (real_V1022479215norm_a @ (poly_a2 @ cs @ (minus_minus_a @ w @ z)))) @ (times_times_real @ da @ m)))). % \<open>norm (w - z) * norm (poly cs (w - z)) \<le> d * m\<close>
thf(fact_4_ep, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % ep
thf(fact_5_H_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ da))). % H(1)
thf(fact_6_H_I2_J, axiom,
    ((ord_less_real @ da @ one_one_real))). % H(2)
thf(fact_7_th, axiom,
    ((ord_less_eq_real @ (real_V1022479215norm_a @ (minus_minus_a @ w @ z)) @ da))). % th
thf(fact_8_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_9_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_10_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_11_dm_I2_J, axiom,
    ((ord_less_real @ (times_times_real @ d @ m) @ e))). % dm(2)
thf(fact_12_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_13_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_14_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_15_H_I3_J, axiom,
    ((ord_less_real @ da @ (divide_divide_real @ e @ m)))). % H(3)
thf(fact_16_norm__mult__less, axiom,
    ((![X3 : real, R : real, Y2 : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X3) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S2) => (ord_less_real @ (real_V646646907m_real @ (times_times_real @ X3 @ Y2)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_17_norm__mult__less, axiom,
    ((![X3 : a, R : real, Y2 : a, S2 : real]: ((ord_less_real @ (real_V1022479215norm_a @ X3) @ R) => ((ord_less_real @ (real_V1022479215norm_a @ Y2) @ S2) => (ord_less_real @ (real_V1022479215norm_a @ (times_times_a @ X3 @ Y2)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_18_d1_I1_J, axiom,
    ((ord_less_eq_real @ (real_V1022479215norm_a @ (minus_minus_a @ w @ z)) @ one_one_real))). % d1(1)
thf(fact_19_norm__mult, axiom,
    ((![X3 : real, Y2 : real]: ((real_V646646907m_real @ (times_times_real @ X3 @ Y2)) = (times_times_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)))))). % norm_mult
thf(fact_20_norm__mult, axiom,
    ((![X3 : a, Y2 : a]: ((real_V1022479215norm_a @ (times_times_a @ X3 @ Y2)) = (times_times_real @ (real_V1022479215norm_a @ X3) @ (real_V1022479215norm_a @ Y2)))))). % norm_mult
thf(fact_21__092_060open_062_092_060And_062w_O_Apoly_Ap_Aw_A_061_Apoly_Aq_A_Iw_A_N_Az_J_092_060close_062, axiom,
    ((![W2 : a]: ((poly_a2 @ p @ W2) = (poly_a2 @ q @ (minus_minus_a @ W2 @ z)))))). % \<open>\<And>w. poly p w = poly q (w - z)\<close>
thf(fact_22_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_23_inf__period_I2_J, axiom,
    ((![P : real > $o, D2 : real, Q2 : real > $o]: ((![X : real, K : real]: ((P @ X) = (P @ (minus_minus_real @ X @ (times_times_real @ K @ D2))))) => ((![X : real, K : real]: ((Q2 @ X) = (Q2 @ (minus_minus_real @ X @ (times_times_real @ K @ D2))))) => (![X4 : real, K2 : real]: ((((P @ X4)) | ((Q2 @ X4))) = (((P @ (minus_minus_real @ X4 @ (times_times_real @ K2 @ D2)))) | ((Q2 @ (minus_minus_real @ X4 @ (times_times_real @ K2 @ D2)))))))))))). % inf_period(2)
thf(fact_24_inf__period_I1_J, axiom,
    ((![P : real > $o, D2 : real, Q2 : real > $o]: ((![X : real, K : real]: ((P @ X) = (P @ (minus_minus_real @ X @ (times_times_real @ K @ D2))))) => ((![X : real, K : real]: ((Q2 @ X) = (Q2 @ (minus_minus_real @ X @ (times_times_real @ K @ D2))))) => (![X4 : real, K2 : real]: ((((P @ X4)) & ((Q2 @ X4))) = (((P @ (minus_minus_real @ X4 @ (times_times_real @ K2 @ D2)))) & ((Q2 @ (minus_minus_real @ X4 @ (times_times_real @ K2 @ D2)))))))))))). % inf_period(1)
thf(fact_25_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_26_d_I2_J, axiom,
    ((ord_less_real @ d @ one_one_real))). % d(2)
thf(fact_27_one0, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % one0
thf(fact_28_d1_I2_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ da))). % d1(2)
thf(fact_29_d_I3_J, axiom,
    ((ord_less_real @ d @ (divide_divide_real @ e @ m)))). % d(3)
thf(fact_30_em0, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ e @ m)))). % em0
thf(fact_31_dm_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ (times_times_real @ d @ m)))). % dm(1)
thf(fact_32__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_33__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_34_poly__0, axiom,
    ((![X3 : real]: ((poly_real2 @ zero_zero_poly_real @ X3) = zero_zero_real)))). % poly_0
thf(fact_35_poly__0, axiom,
    ((![X3 : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X3) = zero_zero_poly_a)))). % poly_0
thf(fact_36_poly__0, axiom,
    ((![X3 : a]: ((poly_a2 @ zero_zero_poly_a @ X3) = zero_zero_a)))). % poly_0
thf(fact_37_poly__1, axiom,
    ((![X3 : real]: ((poly_real2 @ one_one_poly_real @ X3) = one_one_real)))). % poly_1
thf(fact_38__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_092_060lbrakk_0620_A_060_Am_059_A_092_060And_062z_O_Anorm_Az_A_092_060le_062_A1_A_092_060Longrightarrow_062_Anorm_A_Ipoly_Acs_Az_J_A_092_060le_062_Am_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![M : real]: ((ord_less_real @ zero_zero_real @ M) => (~ ((![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ one_one_real) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ M))))))))))). % \<open>\<And>thesis. (\<And>m. \<lbrakk>0 < m; \<And>z. norm z \<le> 1 \<Longrightarrow> norm (poly cs z) \<le> m\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_39__092_060open_062_092_060exists_062m_0620_O_A_092_060forall_062z_O_Anorm_Az_A_092_060le_062_A1_A_092_060longrightarrow_062_Anorm_A_Ipoly_Acs_Az_J_A_092_060le_062_Am_092_060close_062, axiom,
    ((?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ one_one_real) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ M))))))). % \<open>\<exists>m>0. \<forall>z. norm z \<le> 1 \<longrightarrow> norm (poly cs z) \<le> m\<close>
thf(fact_40_m_I2_J, axiom,
    ((![Z2 : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z2) @ one_one_real) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z2)) @ m))))). % m(2)
thf(fact_41_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_42_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_43_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_44_norm__eq__zero, axiom,
    ((![X3 : a]: (((real_V1022479215norm_a @ X3) = zero_zero_real) = (X3 = zero_zero_a))))). % norm_eq_zero
thf(fact_45_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_46_norm__one, axiom,
    (((real_V1022479215norm_a @ one_one_a) = one_one_real))). % norm_one
thf(fact_47_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_48_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_49_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_50_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_51_q_I1_J, axiom,
    (((degree_a @ q) = (degree_a @ p)))). % q(1)
thf(fact_52_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_53_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_54_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_55_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_56_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_57_norm__ge__zero, axiom,
    ((![X3 : a]: (ord_less_eq_real @ zero_zero_real @ (real_V1022479215norm_a @ X3))))). % norm_ge_zero
thf(fact_58_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_59_norm__not__less__zero, axiom,
    ((![X3 : a]: (~ ((ord_less_real @ (real_V1022479215norm_a @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_60_pinf_I6_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ Z3 @ X4) => (~ ((ord_less_eq_real @ X4 @ T))))))))). % pinf(6)
thf(fact_61_pinf_I8_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ Z3 @ X4) => (ord_less_eq_real @ T @ X4))))))). % pinf(8)
thf(fact_62_minf_I6_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => (ord_less_eq_real @ X4 @ T))))))). % minf(6)
thf(fact_63_minf_I8_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => (~ ((ord_less_eq_real @ T @ X4))))))))). % minf(8)
thf(fact_64_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_real]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_65_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_a]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ R) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_66_pinf_I1_J, axiom,
    ((![P : real > $o, P3 : real > $o, Q2 : real > $o, Q3 : real > $o]: ((?[Z : real]: (![X : real]: ((ord_less_real @ Z @ X) => ((P @ X) = (P3 @ X))))) => ((?[Z : real]: (![X : real]: ((ord_less_real @ Z @ X) => ((Q2 @ X) = (Q3 @ X))))) => (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ Z3 @ X4) => ((((P @ X4)) & ((Q2 @ X4))) = (((P3 @ X4)) & ((Q3 @ X4)))))))))))). % pinf(1)
thf(fact_67_pinf_I2_J, axiom,
    ((![P : real > $o, P3 : real > $o, Q2 : real > $o, Q3 : real > $o]: ((?[Z : real]: (![X : real]: ((ord_less_real @ Z @ X) => ((P @ X) = (P3 @ X))))) => ((?[Z : real]: (![X : real]: ((ord_less_real @ Z @ X) => ((Q2 @ X) = (Q3 @ X))))) => (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ Z3 @ X4) => ((((P @ X4)) | ((Q2 @ X4))) = (((P3 @ X4)) | ((Q3 @ X4)))))))))))). % pinf(2)
thf(fact_68_pinf_I3_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ Z3 @ X4) => (~ ((X4 = T))))))))). % pinf(3)
thf(fact_69_pinf_I4_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ Z3 @ X4) => (~ ((X4 = T))))))))). % pinf(4)
thf(fact_70_pinf_I5_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ Z3 @ X4) => (~ ((ord_less_real @ X4 @ T))))))))). % pinf(5)
thf(fact_71_pinf_I7_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ Z3 @ X4) => (ord_less_real @ T @ X4))))))). % pinf(7)
thf(fact_72_minf_I1_J, axiom,
    ((![P : real > $o, P3 : real > $o, Q2 : real > $o, Q3 : real > $o]: ((?[Z : real]: (![X : real]: ((ord_less_real @ X @ Z) => ((P @ X) = (P3 @ X))))) => ((?[Z : real]: (![X : real]: ((ord_less_real @ X @ Z) => ((Q2 @ X) = (Q3 @ X))))) => (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => ((((P @ X4)) & ((Q2 @ X4))) = (((P3 @ X4)) & ((Q3 @ X4)))))))))))). % minf(1)
thf(fact_73_minf_I2_J, axiom,
    ((![P : real > $o, P3 : real > $o, Q2 : real > $o, Q3 : real > $o]: ((?[Z : real]: (![X : real]: ((ord_less_real @ X @ Z) => ((P @ X) = (P3 @ X))))) => ((?[Z : real]: (![X : real]: ((ord_less_real @ X @ Z) => ((Q2 @ X) = (Q3 @ X))))) => (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => ((((P @ X4)) | ((Q2 @ X4))) = (((P3 @ X4)) | ((Q3 @ X4)))))))))))). % minf(2)
thf(fact_74_minf_I3_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => (~ ((X4 = T))))))))). % minf(3)
thf(fact_75_minf_I4_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => (~ ((X4 = T))))))))). % minf(4)
thf(fact_76_minf_I5_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => (ord_less_real @ X4 @ T))))))). % minf(5)
thf(fact_77_minf_I7_J, axiom,
    ((![T : real]: (?[Z3 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z3) => (~ ((ord_less_real @ T @ X4))))))))). % minf(7)
thf(fact_78_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_79_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_80_norm__mult__ineq, axiom,
    ((![X3 : real, Y2 : real]: (ord_less_eq_real @ (real_V646646907m_real @ (times_times_real @ X3 @ Y2)) @ (times_times_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)))))). % norm_mult_ineq
thf(fact_81_norm__mult__ineq, axiom,
    ((![X3 : a, Y2 : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (times_times_a @ X3 @ Y2)) @ (times_times_real @ (real_V1022479215norm_a @ X3) @ (real_V1022479215norm_a @ Y2)))))). % norm_mult_ineq
thf(fact_82_divide__le__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B)))))). % divide_le_eq_1_neg
thf(fact_83_divide__le__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A)))))). % divide_le_eq_1_pos
thf(fact_84_le__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ B @ A)))))). % le_divide_eq_1_neg
thf(fact_85_le__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B)))))). % le_divide_eq_1_pos
thf(fact_86_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_87_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_88_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_89_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_90_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_91_division__ring__divide__zero, axiom,
    ((![A : a]: ((divide_divide_a @ A @ zero_zero_a) = zero_zero_a)))). % division_ring_divide_zero
thf(fact_92_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_93_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_94_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_95_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_96_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_97_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_98_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_99_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_100_degree__0, axiom,
    (((degree_a @ zero_zero_poly_a) = zero_zero_nat))). % degree_0
thf(fact_101_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_102_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_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_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_111_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_112_divide__self, axiom,
    ((![A : a]: ((~ ((A = zero_zero_a))) => ((divide_divide_a @ A @ A) = one_one_a))))). % divide_self
thf(fact_113_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_114_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_115_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_116_zero__le__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_divide_1_iff
thf(fact_117_divide__le__0__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % divide_le_0_1_iff
thf(fact_118_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_119_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_120_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_121_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_122_degree__diff__le, axiom,
    ((![P2 : poly_a, N : nat, Q : poly_a]: ((ord_less_eq_nat @ (degree_a @ P2) @ N) => ((ord_less_eq_nat @ (degree_a @ Q) @ N) => (ord_less_eq_nat @ (degree_a @ (minus_minus_poly_a @ P2 @ Q)) @ N)))))). % degree_diff_le
thf(fact_123_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_124_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_125_degree__mult__right__le, axiom,
    ((![Q : poly_a, P2 : poly_a]: ((~ ((Q = zero_zero_poly_a))) => (ord_less_eq_nat @ (degree_a @ P2) @ (degree_a @ (times_times_poly_a @ P2 @ Q))))))). % degree_mult_right_le
thf(fact_126_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_127_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_128_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y3 : real]: (ord_less_real @ Y3 @ X4))))). % linordered_field_no_lb
thf(fact_129_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % linordered_field_no_ub
thf(fact_130_times__divide__times__eq, axiom,
    ((![X3 : real, Y2 : real, Z2 : real, W2 : real]: ((times_times_real @ (divide_divide_real @ X3 @ Y2) @ (divide_divide_real @ Z2 @ W2)) = (divide_divide_real @ (times_times_real @ X3 @ Z2) @ (times_times_real @ Y2 @ W2)))))). % times_divide_times_eq
thf(fact_131_divide__divide__times__eq, axiom,
    ((![X3 : real, Y2 : real, Z2 : real, W2 : real]: ((divide_divide_real @ (divide_divide_real @ X3 @ Y2) @ (divide_divide_real @ Z2 @ W2)) = (divide_divide_real @ (times_times_real @ X3 @ W2) @ (times_times_real @ Y2 @ Z2)))))). % divide_divide_times_eq
thf(fact_132_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_133_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_134_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_135_divide__right__mono__neg, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C))))))). % divide_right_mono_neg
thf(fact_136_divide__nonpos__nonpos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ Y2 @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_nonpos_nonpos
thf(fact_137_divide__nonpos__nonneg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ Y2) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_nonpos_nonneg
thf(fact_138_divide__nonneg__nonpos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ Y2 @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_nonneg_nonpos
thf(fact_139_divide__nonneg__nonneg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y2) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_nonneg_nonneg
thf(fact_140_zero__le__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ zero_zero_real))))))))). % zero_le_divide_iff
thf(fact_141_divide__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_right_mono
thf(fact_142_divide__le__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ zero_zero_real)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B))))))))). % divide_le_0_iff
thf(fact_143_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_144_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_145_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_146_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_147_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_148_divide__pos__pos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y2) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_pos_pos
thf(fact_149_divide__pos__neg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ Y2 @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_150_divide__neg__pos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y2) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_151_divide__neg__neg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ Y2 @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_neg_neg
thf(fact_152_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_153_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_154_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_155_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_156_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_157_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,
    ((ord_less_real @ (times_times_real @ (real_V1022479215norm_a @ (minus_minus_a @ w @ z)) @ (real_V1022479215norm_a @ (poly_a2 @ cs @ (minus_minus_a @ w @ z)))) @ e))).
