% 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_393__5371342_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:47.866

% Could-be-implicit typings (5)
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (24)
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    one_one_poly_complex : poly_complex).
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_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    uminus1138659839omplex : poly_complex > poly_complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    uminus1613791741y_real : poly_real > poly_real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_real : real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
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__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex, type,
    neg_nu972282243omplex : complex > complex).
thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal, type,
    neg_nu533782273c_real : real > real).
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_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_r, type,
    r : real).
thf(sy_v_s____, type,
    s : real).
thf(sy_v_y____, type,
    y : real).

% Relevant facts (142)
thf(fact_0__092_060open_062_092_060And_062b_O_A_I_N_Ay_A_060_Ab_J_A_061_A_I_N_Ab_A_060_Ay_J_092_060close_062, axiom,
    ((![B : real]: ((ord_less_real @ (uminus_uminus_real @ y) @ B) = (ord_less_real @ (uminus_uminus_real @ B) @ y))))). % \<open>\<And>b. (- y < b) = (- b < y)\<close>
thf(fact_1_s, axiom,
    ((![Y : real]: ((?[X : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X)))))) & ((ord_less_real @ Y @ X)))) = (ord_less_real @ Y @ s))))). % s
thf(fact_2_True, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % True
thf(fact_3_mth1, axiom,
    ((?[X2 : real, Z2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z2) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ Z2)) = (uminus_uminus_real @ X2)))))). % mth1
thf(fact_4__092_060open_062_092_060exists_062s_O_A_092_060forall_062y_O_A_I_092_060exists_062x_O_A_I_092_060exists_062z_O_Acmod_Az_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_092_060and_062_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_092_060close_062, axiom,
    ((?[S : real]: (![Y : real]: ((?[X : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X)))))) & ((ord_less_real @ Y @ X)))) = (ord_less_real @ Y @ S)))))). % \<open>\<exists>s. \<forall>y. (\<exists>x. (\<exists>z. cmod z \<le> r \<and> cmod (poly p z) = - x) \<and> y < x) = (y < s)\<close>
thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060forall_062y_O_A_I_092_060exists_062x_O_A_I_092_060exists_062z_O_Acmod_Az_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_092_060and_062_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![S : real]: (~ ((![Y : real]: ((?[X : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X)))))) & ((ord_less_real @ Y @ X)))) = (ord_less_real @ Y @ S)))))))))). % \<open>\<And>thesis. (\<And>s. \<forall>y. (\<exists>x. (\<exists>z. cmod z \<le> r \<and> cmod (poly p z) = - x) \<and> y < x) = (y < s) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_6_mth2, axiom,
    ((?[Z2 : real]: (![X3 : real]: ((?[Za : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Za) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ Za)) = (uminus_uminus_real @ X3)))) => (ord_less_real @ X3 @ Z2)))))). % mth2
thf(fact_7__092_060open_062_I_092_060exists_062x_O_A_I_092_060exists_062z_O_Acmod_Az_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_092_060and_062_A_N_Ay_A_060_Ax_J_A_061_A_I_N_Ay_A_060_As_J_092_060close_062, axiom,
    (((?[X : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X)))))) & ((ord_less_real @ (uminus_uminus_real @ y) @ X)))) = (ord_less_real @ (uminus_uminus_real @ y) @ s)))). % \<open>(\<exists>x. (\<exists>z. cmod z \<le> r \<and> cmod (poly p z) = - x) \<and> - y < x) = (- y < s)\<close>
thf(fact_8_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z3 : real]: (![X2 : real]: ((P @ X2) => (ord_less_real @ X2 @ Z3)))) => (?[S : real]: (![Y : real]: ((?[X : real]: (((P @ X)) & ((ord_less_real @ Y @ X)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_9__092_060open_062_092_060And_062z_Ax_O_A_092_060lbrakk_062cmod_Az_A_092_060le_062_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_092_060not_062_Ax_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((![Z4 : complex, X4 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ Z4) @ r) => (((real_V638595069omplex @ (poly_complex2 @ p @ Z4)) = (uminus_uminus_real @ X4)) => (ord_less_real @ X4 @ one_one_real)))))). % \<open>\<And>z x. \<lbrakk>cmod z \<le> r; cmod (poly p z) = - x; \<not> x < 1\<rbrakk> \<Longrightarrow> False\<close>
thf(fact_10__092_060open_062cmod_A0_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_092_060close_062, axiom,
    (((ord_less_eq_real @ (real_V638595069omplex @ zero_zero_complex) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ zero_zero_complex)) = (uminus_uminus_real @ (uminus_uminus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ zero_zero_complex)))))))). % \<open>cmod 0 \<le> r \<and> cmod (poly p 0) = - (- cmod (poly p 0))\<close>
thf(fact_11_poly__minus, axiom,
    ((![P2 : poly_complex, X4 : complex]: ((poly_complex2 @ (uminus1138659839omplex @ P2) @ X4) = (uminus1204672759omplex @ (poly_complex2 @ P2 @ X4)))))). % poly_minus
thf(fact_12_poly__minus, axiom,
    ((![P2 : poly_real, X4 : real]: ((poly_real2 @ (uminus1613791741y_real @ P2) @ X4) = (uminus_uminus_real @ (poly_real2 @ P2 @ X4)))))). % poly_minus
thf(fact_13_norm__minus__cancel, axiom,
    ((![X4 : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X4)) = (real_V646646907m_real @ X4))))). % norm_minus_cancel
thf(fact_14_norm__minus__cancel, axiom,
    ((![X4 : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X4)) = (real_V638595069omplex @ X4))))). % norm_minus_cancel
thf(fact_15_neg__less__iff__less, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ B))))). % neg_less_iff_less
thf(fact_16_neg__le__iff__le, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ B))))). % neg_le_iff_le
thf(fact_17_complex__mod__minus__le__complex__mod, axiom,
    ((![X4 : complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V638595069omplex @ X4)) @ (real_V638595069omplex @ X4))))). % complex_mod_minus_le_complex_mod
thf(fact_18_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_19_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_20_neg__equal__iff__equal, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_21_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_22_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_23_neg__equal__0__iff__equal, axiom,
    ((![A : complex]: (((uminus1204672759omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_24_neg__equal__0__iff__equal, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % neg_equal_0_iff_equal
thf(fact_25_neg__0__equal__iff__equal, axiom,
    ((![A : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A)) = (zero_zero_complex = A))))). % neg_0_equal_iff_equal
thf(fact_26_neg__0__equal__iff__equal, axiom,
    ((![A : real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A))))). % neg_0_equal_iff_equal
thf(fact_27_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_28_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_29_poly__0, axiom,
    ((![X4 : real]: ((poly_real2 @ zero_zero_poly_real @ X4) = zero_zero_real)))). % poly_0
thf(fact_30_poly__0, axiom,
    ((![X4 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X4) = zero_zero_complex)))). % poly_0
thf(fact_31_poly__1, axiom,
    ((![X4 : complex]: ((poly_complex2 @ one_one_poly_complex @ X4) = one_one_complex)))). % poly_1
thf(fact_32_poly__1, axiom,
    ((![X4 : real]: ((poly_real2 @ one_one_poly_real @ X4) = one_one_real)))). % poly_1
thf(fact_33_neg__less__eq__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % neg_less_eq_nonneg
thf(fact_34_less__eq__neg__nonpos, axiom,
    ((![A : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real))))). % less_eq_neg_nonpos
thf(fact_35_neg__le__0__iff__le, axiom,
    ((![A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_eq_real @ zero_zero_real @ A))))). % neg_le_0_iff_le
thf(fact_36_neg__0__le__iff__le, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real))))). % neg_0_le_iff_le
thf(fact_37_neg__less__0__iff__less, axiom,
    ((![A : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_real @ zero_zero_real @ A))))). % neg_less_0_iff_less
thf(fact_38_neg__0__less__iff__less, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real))))). % neg_0_less_iff_less
thf(fact_39_neg__less__pos, axiom,
    ((![A : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ A) = (ord_less_real @ zero_zero_real @ A))))). % neg_less_pos
thf(fact_40_less__neg__neg, axiom,
    ((![A : real]: ((ord_less_real @ A @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real))))). % less_neg_neg
thf(fact_41_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_42_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_43_norm__eq__zero, axiom,
    ((![X4 : real]: (((real_V646646907m_real @ X4) = zero_zero_real) = (X4 = zero_zero_real))))). % norm_eq_zero
thf(fact_44_norm__eq__zero, axiom,
    ((![X4 : complex]: (((real_V638595069omplex @ X4) = zero_zero_real) = (X4 = zero_zero_complex))))). % 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_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_47_zero__less__norm__iff, axiom,
    ((![X4 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X4)) = (~ ((X4 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_48_zero__less__norm__iff, axiom,
    ((![X4 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X4)) = (~ ((X4 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_49_norm__le__zero__iff, axiom,
    ((![X4 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X4) @ zero_zero_real) = (X4 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_50_norm__le__zero__iff, axiom,
    ((![X4 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X4) @ zero_zero_real) = (X4 = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_51_one__reorient, axiom,
    ((![X4 : real]: ((one_one_real = X4) = (X4 = one_one_real))))). % one_reorient
thf(fact_52_zero__reorient, axiom,
    ((![X4 : real]: ((zero_zero_real = X4) = (X4 = zero_zero_real))))). % zero_reorient
thf(fact_53_zero__reorient, axiom,
    ((![X4 : complex]: ((zero_zero_complex = X4) = (X4 = zero_zero_complex))))). % zero_reorient
thf(fact_54_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) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P2 @ X2) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_55_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)) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P2 @ X2) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_56_poly__all__0__iff__0, axiom,
    ((![P2 : poly_real]: ((![X : real]: ((poly_real2 @ P2 @ X) = zero_zero_real)) = (P2 = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_57_poly__all__0__iff__0, axiom,
    ((![P2 : poly_complex]: ((![X : complex]: ((poly_complex2 @ P2 @ X) = zero_zero_complex)) = (P2 = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_58_norm__not__less__zero, axiom,
    ((![X4 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X4) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_59_norm__ge__zero, axiom,
    ((![X4 : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X4))))). % norm_ge_zero
thf(fact_60_verit__la__disequality, axiom,
    ((![A : real, B : real]: ((A = B) | ((~ ((ord_less_eq_real @ A @ B))) | (~ ((ord_less_eq_real @ B @ A)))))))). % verit_la_disequality
thf(fact_61_verit__comp__simplify1_I1_J, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_62_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_63_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_64_verit__negate__coefficient_I3_J, axiom,
    ((![A : real, B : real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B)))))). % verit_negate_coefficient(3)
thf(fact_65_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_complex, Q : poly_complex]: (((poly_complex2 @ P2) = (poly_complex2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_66_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_67_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_real]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z3) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P2 @ Z3)) @ M)))))))). % poly_bound_exists
thf(fact_68_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_complex]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P2 @ Z3)) @ M)))))))). % poly_bound_exists
thf(fact_69_verit__comp__simplify1_I3_J, axiom,
    ((![B2 : real, A2 : real]: ((~ ((ord_less_eq_real @ B2 @ A2))) = (ord_less_real @ A2 @ B2))))). % verit_comp_simplify1(3)
thf(fact_70_le__imp__neg__le, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % le_imp_neg_le
thf(fact_71_minus__le__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ A))))). % minus_le_iff
thf(fact_72_le__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A)))))). % le_minus_iff
thf(fact_73_minus__less__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ B) = (ord_less_real @ (uminus_uminus_real @ B) @ A))))). % minus_less_iff
thf(fact_74_less__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ (uminus_uminus_real @ A)))))). % less_minus_iff
thf(fact_75_verit__negate__coefficient_I2_J, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % verit_negate_coefficient(2)
thf(fact_76_less__minus__one__simps_I1_J, axiom,
    ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real))). % less_minus_one_simps(1)
thf(fact_77_less__minus__one__simps_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))))). % less_minus_one_simps(3)
thf(fact_78_le__minus__one__simps_I1_J, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real))). % le_minus_one_simps(1)
thf(fact_79_le__minus__one__simps_I3_J, axiom,
    ((~ ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))))). % le_minus_one_simps(3)
thf(fact_80_less__minus__one__simps_I2_J, axiom,
    ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ one_one_real))). % less_minus_one_simps(2)
thf(fact_81_less__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))))). % less_minus_one_simps(4)
thf(fact_82_le__minus__one__simps_I2_J, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ one_one_real))). % le_minus_one_simps(2)
thf(fact_83_le__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))))). % le_minus_one_simps(4)
thf(fact_84_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_complex = (uminus1204672759omplex @ one_one_complex)))))). % zero_neq_neg_one
thf(fact_85_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_real = (uminus_uminus_real @ one_one_real)))))). % zero_neq_neg_one
thf(fact_86_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_87_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_88_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_89_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_90_one__neq__neg__one, axiom,
    ((~ ((one_one_real = (uminus_uminus_real @ one_one_real)))))). % one_neq_neg_one
thf(fact_91_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_92_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_93_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_94_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_95_linorder__neqE__linordered__idom, axiom,
    ((![X4 : real, Y2 : real]: ((~ ((X4 = Y2))) => ((~ ((ord_less_real @ X4 @ Y2))) => (ord_less_real @ Y2 @ X4)))))). % linorder_neqE_linordered_idom
thf(fact_96_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_97_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_98_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_99_dbl__dec__simps_I2_J, axiom,
    (((neg_nu972282243omplex @ zero_zero_complex) = (uminus1204672759omplex @ one_one_complex)))). % dbl_dec_simps(2)
thf(fact_100_dbl__dec__simps_I2_J, axiom,
    (((neg_nu533782273c_real @ zero_zero_real) = (uminus_uminus_real @ one_one_real)))). % dbl_dec_simps(2)
thf(fact_101_order__refl, axiom,
    ((![X4 : real]: (ord_less_eq_real @ X4 @ X4)))). % order_refl
thf(fact_102_dbl__dec__simps_I3_J, axiom,
    (((neg_nu533782273c_real @ one_one_real) = one_one_real))). % dbl_dec_simps(3)
thf(fact_103_order__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X2 : real, Y3 : real]: ((ord_less_eq_real @ X2 @ Y3) => (ord_less_eq_real @ (F @ X2) @ (F @ Y3)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_104_order__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X2 : real, Y3 : real]: ((ord_less_eq_real @ X2 @ Y3) => (ord_less_eq_real @ (F @ X2) @ (F @ Y3)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_105_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X2 : real, Y3 : real]: ((ord_less_eq_real @ X2 @ Y3) => (ord_less_eq_real @ (F @ X2) @ (F @ Y3)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_106_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X2 : real, Y3 : real]: ((ord_less_eq_real @ X2 @ Y3) => (ord_less_eq_real @ (F @ X2) @ (F @ Y3)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_107_eq__iff, axiom,
    (((^[Y4 : real]: (^[Z5 : real]: (Y4 = Z5))) = (^[X : real]: (^[Y5 : real]: (((ord_less_eq_real @ X @ Y5)) & ((ord_less_eq_real @ Y5 @ X)))))))). % eq_iff
thf(fact_108_antisym, axiom,
    ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => ((ord_less_eq_real @ Y2 @ X4) => (X4 = Y2)))))). % antisym
thf(fact_109_linear, axiom,
    ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) | (ord_less_eq_real @ Y2 @ X4))))). % linear
thf(fact_110_eq__refl, axiom,
    ((![X4 : real, Y2 : real]: ((X4 = Y2) => (ord_less_eq_real @ X4 @ Y2))))). % eq_refl
thf(fact_111_le__cases, axiom,
    ((![X4 : real, Y2 : real]: ((~ ((ord_less_eq_real @ X4 @ Y2))) => (ord_less_eq_real @ Y2 @ X4))))). % le_cases
thf(fact_112_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_113_le__cases3, axiom,
    ((![X4 : real, Y2 : real, Z4 : real]: (((ord_less_eq_real @ X4 @ Y2) => (~ ((ord_less_eq_real @ Y2 @ Z4)))) => (((ord_less_eq_real @ Y2 @ X4) => (~ ((ord_less_eq_real @ X4 @ Z4)))) => (((ord_less_eq_real @ X4 @ Z4) => (~ ((ord_less_eq_real @ Z4 @ Y2)))) => (((ord_less_eq_real @ Z4 @ Y2) => (~ ((ord_less_eq_real @ Y2 @ X4)))) => (((ord_less_eq_real @ Y2 @ Z4) => (~ ((ord_less_eq_real @ Z4 @ X4)))) => (~ (((ord_less_eq_real @ Z4 @ X4) => (~ ((ord_less_eq_real @ X4 @ Y2)))))))))))))). % le_cases3
thf(fact_114_antisym__conv, axiom,
    ((![Y2 : real, X4 : real]: ((ord_less_eq_real @ Y2 @ X4) => ((ord_less_eq_real @ X4 @ Y2) = (X4 = Y2)))))). % antisym_conv
thf(fact_115_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y4 : real]: (^[Z5 : real]: (Y4 = Z5))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ A3 @ B3)) & ((ord_less_eq_real @ B3 @ A3)))))))). % order_class.order.eq_iff
thf(fact_116_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_117_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_118_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_119_order__trans, axiom,
    ((![X4 : real, Y2 : real, Z4 : real]: ((ord_less_eq_real @ X4 @ Y2) => ((ord_less_eq_real @ Y2 @ Z4) => (ord_less_eq_real @ X4 @ Z4)))))). % order_trans
thf(fact_120_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_121_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B4 : real]: ((ord_less_eq_real @ A4 @ B4) => (P @ A4 @ B4))) => ((![A4 : real, B4 : real]: ((P @ B4 @ A4) => (P @ A4 @ B4))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_122_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_123_dual__order_Oeq__iff, axiom,
    (((^[Y4 : real]: (^[Z5 : real]: (Y4 = Z5))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((ord_less_eq_real @ A3 @ B3)))))))). % dual_order.eq_iff
thf(fact_124_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_125_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X2 : real, Y3 : real]: ((ord_less_real @ X2 @ Y3) => (ord_less_real @ (F @ X2) @ (F @ Y3)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_126_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X2 : real, Y3 : real]: ((ord_less_real @ X2 @ Y3) => (ord_less_real @ (F @ X2) @ (F @ Y3)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_127_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, Y3 : real]: ((ord_less_real @ X2 @ Y3) => (ord_less_real @ (F @ X2) @ (F @ Y3)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_128_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, Y3 : real]: ((ord_less_real @ X2 @ Y3) => (ord_less_real @ (F @ X2) @ (F @ Y3)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_129_lt__ex, axiom,
    ((![X4 : real]: (?[Y3 : real]: (ord_less_real @ Y3 @ X4))))). % lt_ex
thf(fact_130_gt__ex, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % gt_ex
thf(fact_131_neqE, axiom,
    ((![X4 : real, Y2 : real]: ((~ ((X4 = Y2))) => ((~ ((ord_less_real @ X4 @ Y2))) => (ord_less_real @ Y2 @ X4)))))). % neqE
thf(fact_132_neq__iff, axiom,
    ((![X4 : real, Y2 : real]: ((~ ((X4 = Y2))) = (((ord_less_real @ X4 @ Y2)) | ((ord_less_real @ Y2 @ X4))))))). % neq_iff
thf(fact_133_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_134_dense, axiom,
    ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (?[Z2 : real]: ((ord_less_real @ X4 @ Z2) & (ord_less_real @ Z2 @ Y2))))))). % dense
thf(fact_135_less__imp__neq, axiom,
    ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (~ ((X4 = Y2))))))). % less_imp_neq
thf(fact_136_less__asym, axiom,
    ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (~ ((ord_less_real @ Y2 @ X4))))))). % less_asym
thf(fact_137_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_138_less__trans, axiom,
    ((![X4 : real, Y2 : real, Z4 : real]: ((ord_less_real @ X4 @ Y2) => ((ord_less_real @ Y2 @ Z4) => (ord_less_real @ X4 @ Z4)))))). % less_trans
thf(fact_139_less__linear, axiom,
    ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) | ((X4 = Y2) | (ord_less_real @ Y2 @ X4)))))). % less_linear
thf(fact_140_less__irrefl, axiom,
    ((![X4 : real]: (~ ((ord_less_real @ X4 @ X4)))))). % less_irrefl
thf(fact_141_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

% Conjectures (1)
thf(conj_0, conjecture,
    (((?[Z : complex]: (?[X : a]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & ((ord_less_real @ (uminus_uminus_real @ (uminus_uminus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ Z)))) @ y))))) = (ord_less_real @ (uminus_uminus_real @ s) @ y)))).
