% 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_354__5370986_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:30.330

% Could-be-implicit typings (3)
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_tf__a, type,
    a : $tType).

% Explicit typings (22)
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__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_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__Real__Oreal, type,
    ord_less_real : real > 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_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_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_w____, type,
    w : a).
thf(sy_v_z, type,
    z : a).

% Relevant facts (153)
thf(fact_0_ep, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % ep
thf(fact_1_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_2_H_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ da))). % H(1)
thf(fact_3_H_I2_J, axiom,
    ((ord_less_real @ da @ one_one_real))). % H(2)
thf(fact_4_H_I4_J, axiom,
    ((~ ((w = z))))). % H(4)
thf(fact_5_H_I3_J, axiom,
    ((ord_less_real @ da @ (divide_divide_real @ e @ m)))). % H(3)
thf(fact_6_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_7_d_I2_J, axiom,
    ((ord_less_real @ d @ one_one_real))). % d(2)
thf(fact_8_H_I5_J, axiom,
    ((ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ w @ z)) @ da))). % H(5)
thf(fact_9_d1_I2_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ da))). % d1(2)
thf(fact_10_d1_I1_J, axiom,
    ((ord_less_eq_real @ (real_V1022479215norm_a @ (minus_minus_a @ w @ z)) @ one_one_real))). % d1(1)
thf(fact_11_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_12_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_13_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_14_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_15_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_16_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_17_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_18_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_19_pCons_Ohyps_I2_J, axiom,
    ((?[D2 : real]: ((ord_less_real @ zero_zero_real @ D2) & (![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)) @ D2)) => (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_20_one0, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % one0
thf(fact_21_norm__ge__zero, axiom,
    ((![X : a]: (ord_less_eq_real @ zero_zero_real @ (real_V1022479215norm_a @ X))))). % norm_ge_zero
thf(fact_22_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_23_d_I3_J, axiom,
    ((ord_less_real @ d @ (divide_divide_real @ e @ m)))). % d(3)
thf(fact_24_em0, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ e @ m)))). % em0
thf(fact_25_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_26_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_27_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_28_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_29_diff__zero, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_zero
thf(fact_30_diff__zero, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_zero
thf(fact_31_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_32_diff__0__right, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_0_right
thf(fact_33_diff__0__right, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_0_right
thf(fact_34_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_35_diff__self, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % diff_self
thf(fact_36_diff__self, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % diff_self
thf(fact_37__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_38__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,
    ((~ ((![D2 : real]: ((ord_less_real @ zero_zero_real @ D2) => ((ord_less_real @ D2 @ one_one_real) => (~ ((ord_less_real @ D2 @ (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_39__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_40__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_41_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_42_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_43_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_44_norm__eq__zero, axiom,
    ((![X : a]: (((real_V1022479215norm_a @ X) = zero_zero_real) = (X = zero_zero_a))))). % norm_eq_zero
thf(fact_45_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_46_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_47_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_48_norm__one, axiom,
    (((real_V1022479215norm_a @ one_one_a) = one_one_real))). % norm_one
thf(fact_49_zero__less__norm__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X)) = (~ ((X = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_50_zero__less__norm__iff, axiom,
    ((![X : a]: ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ X)) = (~ ((X = zero_zero_a))))))). % zero_less_norm_iff
thf(fact_51_norm__le__zero__iff, axiom,
    ((![X : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X) @ zero_zero_real) = (X = zero_zero_real))))). % norm_le_zero_iff
thf(fact_52_norm__le__zero__iff, axiom,
    ((![X : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ X) @ zero_zero_real) = (X = zero_zero_a))))). % norm_le_zero_iff
thf(fact_53_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_54_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_55_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_56_zero__reorient, axiom,
    ((![X : poly_a]: ((zero_zero_poly_a = X) = (X = zero_zero_poly_a))))). % zero_reorient
thf(fact_57_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X2 : real, Y : real]: ((ord_less_real @ X2 @ Y) => (ord_less_real @ (F @ X2) @ (F @ Y)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_58_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X2 : real, Y : real]: ((ord_less_real @ X2 @ Y) => (ord_less_real @ (F @ X2) @ (F @ Y)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_59_order__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X2 : real, Y : real]: ((ord_less_real @ X2 @ Y) => (ord_less_real @ (F @ X2) @ (F @ Y)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_60_order__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X2 : real, Y : real]: ((ord_less_real @ X2 @ Y) => (ord_less_real @ (F @ X2) @ (F @ Y)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_61_lt__ex, axiom,
    ((![X : real]: (?[Y : real]: (ord_less_real @ Y @ X))))). % lt_ex
thf(fact_62_gt__ex, axiom,
    ((![X : real]: (?[X_1 : real]: (ord_less_real @ X @ X_1))))). % gt_ex
thf(fact_63_neqE, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) => ((~ ((ord_less_real @ X @ Y2))) => (ord_less_real @ Y2 @ X)))))). % neqE
thf(fact_64_neq__iff, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) = (((ord_less_real @ X @ Y2)) | ((ord_less_real @ Y2 @ X))))))). % neq_iff
thf(fact_65_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_66_dense, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (?[Z3 : real]: ((ord_less_real @ X @ Z3) & (ord_less_real @ Z3 @ Y2))))))). % dense
thf(fact_67_less__imp__neq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_neq
thf(fact_68_less__asym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_asym
thf(fact_69_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_70_less__trans, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_real @ X @ Y2) => ((ord_less_real @ Y2 @ Z2) => (ord_less_real @ X @ Z2)))))). % less_trans
thf(fact_71_less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) | ((X = Y2) | (ord_less_real @ Y2 @ X)))))). % less_linear
thf(fact_72_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_73_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_74_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_75_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_76_less__imp__not__eq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_not_eq
thf(fact_77_less__not__sym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_not_sym
thf(fact_78_antisym__conv3, axiom,
    ((![Y2 : real, X : real]: ((~ ((ord_less_real @ Y2 @ X))) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv3
thf(fact_79_less__imp__not__eq2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((Y2 = X))))))). % less_imp_not_eq2
thf(fact_80_less__imp__triv, axiom,
    ((![X : real, Y2 : real, P : $o]: ((ord_less_real @ X @ Y2) => ((ord_less_real @ Y2 @ X) => P))))). % less_imp_triv
thf(fact_81_linorder__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((~ ((X = Y2))) => (ord_less_real @ Y2 @ X)))))). % linorder_cases
thf(fact_82_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_83_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_84_less__imp__not__less, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_imp_not_less
thf(fact_85_linorder__less__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A2 : real, B2 : real]: ((ord_less_real @ A2 @ B2) => (P @ A2 @ B2))) => ((![A2 : real]: (P @ A2 @ A2)) => ((![A2 : real, B2 : real]: ((P @ B2 @ A2) => (P @ A2 @ B2))) => (P @ A @ B))))))). % linorder_less_wlog
thf(fact_86_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_87_not__less__iff__gr__or__eq, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) = (((ord_less_real @ Y2 @ X)) | ((X = Y2))))))). % not_less_iff_gr_or_eq
thf(fact_88_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_89_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_90_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_91_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_92_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_93_norm__not__less__zero, axiom,
    ((![X : a]: (~ ((ord_less_real @ (real_V1022479215norm_a @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_94_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_12 : real]: (P @ X_12)) => ((?[Z : real]: (![X2 : real]: ((P @ X2) => (ord_less_real @ X2 @ Z)))) => (?[S : real]: (![Y3 : real]: ((?[X3 : real]: (((P @ X3)) & ((ord_less_real @ Y3 @ X3)))) = (ord_less_real @ Y3 @ S))))))))). % real_sup_exists
thf(fact_95_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_96_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_97_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_98_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[B3 : real]: (^[A3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((~ ((A3 = B3)))))))))). % dual_order.strict_iff_order
thf(fact_99_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[B3 : real]: (^[A3 : real]: (((ord_less_real @ B3 @ A3)) | ((A3 = B3)))))))). % dual_order.order_iff_strict
thf(fact_100_order_Ostrict__implies__order, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B))))). % order.strict_implies_order
thf(fact_101_dense__le__bounded, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_real @ X @ Y2) => ((![W2 : real]: ((ord_less_real @ X @ W2) => ((ord_less_real @ W2 @ Y2) => (ord_less_eq_real @ W2 @ Z2)))) => (ord_less_eq_real @ Y2 @ Z2)))))). % dense_le_bounded
thf(fact_102_dense__ge__bounded, axiom,
    ((![Z2 : real, X : real, Y2 : real]: ((ord_less_real @ Z2 @ X) => ((![W2 : real]: ((ord_less_real @ Z2 @ W2) => ((ord_less_real @ W2 @ X) => (ord_less_eq_real @ Y2 @ W2)))) => (ord_less_eq_real @ Y2 @ Z2)))))). % dense_ge_bounded
thf(fact_103_dual__order_Ostrict__trans2, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans2
thf(fact_104_dual__order_Ostrict__trans1, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans1
thf(fact_105_order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ A3 @ B3)) & ((~ ((A3 = B3)))))))))). % order.strict_iff_order
thf(fact_106_order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[A3 : real]: (^[B3 : real]: (((ord_less_real @ A3 @ B3)) | ((A3 = B3)))))))). % order.order_iff_strict
thf(fact_107_order_Ostrict__trans2, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans2
thf(fact_108_order_Ostrict__trans1, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans1
thf(fact_109_not__le__imp__less, axiom,
    ((![Y2 : real, X : real]: ((~ ((ord_less_eq_real @ Y2 @ X))) => (ord_less_real @ X @ Y2))))). % not_le_imp_less
thf(fact_110_less__le__not__le, axiom,
    ((ord_less_real = (^[X3 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X3 @ Y4)) & ((~ ((ord_less_eq_real @ Y4 @ X3)))))))))). % less_le_not_le
thf(fact_111_le__imp__less__or__eq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_real @ X @ Y2) | (X = Y2)))))). % le_imp_less_or_eq
thf(fact_112_le__less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) | (ord_less_real @ Y2 @ X))))). % le_less_linear
thf(fact_113_dense__le, axiom,
    ((![Y2 : real, Z2 : real]: ((![X2 : real]: ((ord_less_real @ X2 @ Y2) => (ord_less_eq_real @ X2 @ Z2))) => (ord_less_eq_real @ Y2 @ Z2))))). % dense_le
thf(fact_114_dense__ge, axiom,
    ((![Z2 : real, Y2 : real]: ((![X2 : real]: ((ord_less_real @ Z2 @ X2) => (ord_less_eq_real @ Y2 @ X2))) => (ord_less_eq_real @ Y2 @ Z2))))). % dense_ge
thf(fact_115_less__le__trans, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ Z2) => (ord_less_real @ X @ Z2)))))). % less_le_trans
thf(fact_116_le__less__trans, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_real @ Y2 @ Z2) => (ord_less_real @ X @ Z2)))))). % le_less_trans
thf(fact_117_less__imp__le, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (ord_less_eq_real @ X @ Y2))))). % less_imp_le
thf(fact_118_antisym__conv2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv2
thf(fact_119_antisym__conv1, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((ord_less_eq_real @ X @ Y2) = (X = Y2)))))). % antisym_conv1
thf(fact_120_le__neq__trans, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((~ ((A = B))) => (ord_less_real @ A @ B)))))). % le_neq_trans
thf(fact_121_not__less, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) = (ord_less_eq_real @ Y2 @ X))))). % not_less
thf(fact_122_not__le, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_eq_real @ X @ Y2))) = (ord_less_real @ Y2 @ X))))). % not_le
thf(fact_123_order__less__le__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X2 : real, Y : real]: ((ord_less_real @ X2 @ Y) => (ord_less_real @ (F @ X2) @ (F @ Y)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_le_subst2
thf(fact_124_order__less__le__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) => (ord_less_eq_real @ (F @ X2) @ (F @ Y)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_le_subst1
thf(fact_125_order__le__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) => (ord_less_eq_real @ (F @ X2) @ (F @ Y)))) => (ord_less_real @ (F @ A) @ C))))))). % order_le_less_subst2
thf(fact_126_order__le__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X2 : real, Y : real]: ((ord_less_real @ X2 @ Y) => (ord_less_real @ (F @ X2) @ (F @ Y)))) => (ord_less_real @ A @ (F @ C)))))))). % order_le_less_subst1
thf(fact_127_less__le, axiom,
    ((ord_less_real = (^[X3 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X3 @ Y4)) & ((~ ((X3 = Y4)))))))))). % less_le
thf(fact_128_le__less, axiom,
    ((ord_less_eq_real = (^[X3 : real]: (^[Y4 : real]: (((ord_less_real @ X3 @ Y4)) | ((X3 = Y4)))))))). % le_less
thf(fact_129_leI, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % leI
thf(fact_130_leD, axiom,
    ((![Y2 : real, X : real]: ((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_real @ X @ Y2))))))). % leD
thf(fact_131_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_132_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_133_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_134_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_135_eq__iff__diff__eq__0, axiom,
    (((^[Y5 : real]: (^[Z4 : real]: (Y5 = Z4))) = (^[A3 : real]: (^[B3 : real]: ((minus_minus_real @ A3 @ B3) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_136_eq__iff__diff__eq__0, axiom,
    (((^[Y5 : poly_a]: (^[Z4 : poly_a]: (Y5 = Z4))) = (^[A3 : poly_a]: (^[B3 : poly_a]: ((minus_minus_poly_a @ A3 @ B3) = zero_zero_poly_a)))))). % eq_iff_diff_eq_0
thf(fact_137_eq__iff__diff__eq__0, axiom,
    (((^[Y5 : a]: (^[Z4 : a]: (Y5 = Z4))) = (^[A3 : a]: (^[B3 : a]: ((minus_minus_a @ A3 @ B3) = zero_zero_a)))))). % eq_iff_diff_eq_0
thf(fact_138_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_139_dual__order_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z4 : real]: (Y5 = Z4))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((ord_less_eq_real @ A3 @ B3)))))))). % dual_order.eq_iff
thf(fact_140_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_141_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A2 : real, B2 : real]: ((ord_less_eq_real @ A2 @ B2) => (P @ A2 @ B2))) => ((![A2 : real, B2 : real]: ((P @ B2 @ A2) => (P @ A2 @ B2))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_142_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_143_order__trans, axiom,
    ((![X : real, Y2 : real, Z2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ Z2) => (ord_less_eq_real @ X @ Z2)))))). % order_trans
thf(fact_144_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_145_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_146_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_147_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z4 : real]: (Y5 = Z4))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ A3 @ B3)) & ((ord_less_eq_real @ B3 @ A3)))))))). % order_class.order.eq_iff
thf(fact_148_antisym__conv, axiom,
    ((![Y2 : real, X : real]: ((ord_less_eq_real @ Y2 @ X) => ((ord_less_eq_real @ X @ Y2) = (X = Y2)))))). % antisym_conv
thf(fact_149_le__cases3, axiom,
    ((![X : real, Y2 : real, Z2 : real]: (((ord_less_eq_real @ X @ Y2) => (~ ((ord_less_eq_real @ Y2 @ Z2)))) => (((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_eq_real @ X @ Z2)))) => (((ord_less_eq_real @ X @ Z2) => (~ ((ord_less_eq_real @ Z2 @ Y2)))) => (((ord_less_eq_real @ Z2 @ Y2) => (~ ((ord_less_eq_real @ Y2 @ X)))) => (((ord_less_eq_real @ Y2 @ Z2) => (~ ((ord_less_eq_real @ Z2 @ X)))) => (~ (((ord_less_eq_real @ Z2 @ X) => (~ ((ord_less_eq_real @ X @ Y2)))))))))))))). % le_cases3
thf(fact_150_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_151_le__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_eq_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % le_cases
thf(fact_152_eq__refl, axiom,
    ((![X : real, Y2 : real]: ((X = Y2) => (ord_less_eq_real @ X @ Y2))))). % eq_refl

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (real_V1022479215norm_a @ (minus_minus_a @ w @ z)) @ da))).
