% 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_655__5374438_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:31:52.979

% Could-be-implicit typings (7)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    poly_poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__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_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (37)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Complex__Ocomplex, type,
    fundam1201687030omplex : poly_complex > complex > poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1307691262omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    fundam534701948y_real : poly_poly_real > poly_real > poly_poly_real).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Real__Oreal, type,
    fundam1552870388y_real : poly_real > real > poly_real).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1956464160omplex : poly_poly_complex > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    fundam1770960798y_real : poly_poly_real > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Real__Oreal, type,
    fundam1947011094e_real : poly_real > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    plus_p1547158847omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    plus_p138939463omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    plus_p639965381y_real : poly_poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    plus_plus_poly_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : 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__Nat__Onat, type,
    zero_zero_nat : nat).
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_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_less_poly_real : poly_real > poly_real > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_le1180086932y_real : poly_real > poly_real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_poly_real2 : poly_poly_real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__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_c____, type,
    c : complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_pa____, type,
    pa : poly_complex).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (248)
thf(fact_0_nc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ p)))))). % nc
thf(fact_1_less_Oprems, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ pa)))))). % less.prems
thf(fact_2__092_060open_062_092_060exists_062q_O_Apsize_Aq_A_061_Apsize_Ap_A_092_060and_062_A_I_092_060forall_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_092_060close_062, axiom,
    ((?[Q : poly_complex]: (((fundam1709708056omplex @ Q) = (fundam1709708056omplex @ pa)) & (![X : complex]: ((poly_complex2 @ Q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))))). % \<open>\<exists>q. psize q = psize p \<and> (\<forall>x. poly q x = poly p (c + x))\<close>
thf(fact_3_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_4_poly__offset, axiom,
    ((![P : poly_poly_real, A : poly_real]: (?[Q : poly_poly_real]: (((fundam1770960798y_real @ Q) = (fundam1770960798y_real @ P)) & (![X : poly_real]: ((poly_poly_real2 @ Q @ X) = (poly_poly_real2 @ P @ (plus_plus_poly_real @ A @ X))))))))). % poly_offset
thf(fact_5_poly__offset, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: (?[Q : poly_poly_complex]: (((fundam1956464160omplex @ Q) = (fundam1956464160omplex @ P)) & (![X : poly_complex]: ((poly_poly_complex2 @ Q @ X) = (poly_poly_complex2 @ P @ (plus_p1547158847omplex @ A @ X))))))))). % poly_offset
thf(fact_6_poly__offset, axiom,
    ((![P : poly_real, A : real]: (?[Q : poly_real]: (((fundam1947011094e_real @ Q) = (fundam1947011094e_real @ P)) & (![X : real]: ((poly_real2 @ Q @ X) = (poly_real2 @ P @ (plus_plus_real @ A @ X))))))))). % poly_offset
thf(fact_7_poly__offset, axiom,
    ((![P : poly_complex, A : complex]: (?[Q : poly_complex]: (((fundam1709708056omplex @ Q) = (fundam1709708056omplex @ P)) & (![X : complex]: ((poly_complex2 @ Q @ X) = (poly_complex2 @ P @ (plus_plus_complex @ A @ X))))))))). % poly_offset
thf(fact_8_poly__add, axiom,
    ((![P : poly_poly_real, Q2 : poly_poly_real, X2 : poly_real]: ((poly_poly_real2 @ (plus_p639965381y_real @ P @ Q2) @ X2) = (plus_plus_poly_real @ (poly_poly_real2 @ P @ X2) @ (poly_poly_real2 @ Q2 @ X2)))))). % poly_add
thf(fact_9_poly__add, axiom,
    ((![P : poly_poly_complex, Q2 : poly_poly_complex, X2 : poly_complex]: ((poly_poly_complex2 @ (plus_p138939463omplex @ P @ Q2) @ X2) = (plus_p1547158847omplex @ (poly_poly_complex2 @ P @ X2) @ (poly_poly_complex2 @ Q2 @ X2)))))). % poly_add
thf(fact_10_poly__add, axiom,
    ((![P : poly_complex, Q2 : poly_complex, X2 : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P @ Q2) @ X2) = (plus_plus_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q2 @ X2)))))). % poly_add
thf(fact_11_poly__add, axiom,
    ((![P : poly_real, Q2 : poly_real, X2 : real]: ((poly_real2 @ (plus_plus_poly_real @ P @ Q2) @ X2) = (plus_plus_real @ (poly_real2 @ P @ X2) @ (poly_real2 @ Q2 @ X2)))))). % poly_add
thf(fact_12_add__left__cancel, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: (((plus_plus_poly_real @ A @ B) = (plus_plus_poly_real @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_13_add__left__cancel, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ A @ B) = (plus_p1547158847omplex @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_14_add__left__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_15_add__left__cancel, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_16_add__right__cancel, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: (((plus_plus_poly_real @ B @ A) = (plus_plus_poly_real @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_17_add__right__cancel, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ B @ A) = (plus_p1547158847omplex @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_18_add__right__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_19_add__right__cancel, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_20_c, axiom,
    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ c)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % c
thf(fact_21_poly__offset__poly, axiom,
    ((![P : poly_poly_real, H : poly_real, X2 : poly_real]: ((poly_poly_real2 @ (fundam534701948y_real @ P @ H) @ X2) = (poly_poly_real2 @ P @ (plus_plus_poly_real @ H @ X2)))))). % poly_offset_poly
thf(fact_22_poly__offset__poly, axiom,
    ((![P : poly_poly_complex, H : poly_complex, X2 : poly_complex]: ((poly_poly_complex2 @ (fundam1307691262omplex @ P @ H) @ X2) = (poly_poly_complex2 @ P @ (plus_p1547158847omplex @ H @ X2)))))). % poly_offset_poly
thf(fact_23_poly__offset__poly, axiom,
    ((![P : poly_complex, H : complex, X2 : complex]: ((poly_complex2 @ (fundam1201687030omplex @ P @ H) @ X2) = (poly_complex2 @ P @ (plus_plus_complex @ H @ X2)))))). % poly_offset_poly
thf(fact_24_poly__offset__poly, axiom,
    ((![P : poly_real, H : real, X2 : real]: ((poly_real2 @ (fundam1552870388y_real @ P @ H) @ X2) = (poly_real2 @ P @ (plus_plus_real @ H @ X2)))))). % poly_offset_poly
thf(fact_25_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q2 : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q2)) = (P = Q2))))). % poly_eq_poly_eq_iff
thf(fact_26_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_real, Q2 : poly_real]: (((poly_real2 @ P) = (poly_real2 @ Q2)) = (P = Q2))))). % poly_eq_poly_eq_iff
thf(fact_27_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_28_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_29_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ (plus_plus_poly_real @ A @ B) @ C) = (plus_plus_poly_real @ A @ (plus_plus_poly_real @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_30_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ (plus_p1547158847omplex @ A @ B) @ C) = (plus_p1547158847omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_31_is__num__normalize_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % is_num_normalize(1)
thf(fact_32_is__num__normalize_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % is_num_normalize(1)
thf(fact_33_is__num__normalize_I1_J, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ (plus_plus_poly_real @ A @ B) @ C) = (plus_plus_poly_real @ A @ (plus_plus_poly_real @ B @ C)))))). % is_num_normalize(1)
thf(fact_34_is__num__normalize_I1_J, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ (plus_p1547158847omplex @ A @ B) @ C) = (plus_p1547158847omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % is_num_normalize(1)
thf(fact_35_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (K = L)) => ((plus_plus_real @ I @ K) = (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_36_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : poly_real, J : poly_real, K : poly_real, L : poly_real]: (((I = J) & (K = L)) => ((plus_plus_poly_real @ I @ K) = (plus_plus_poly_real @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_37_group__cancel_Oadd1, axiom,
    ((![A2 : complex, K : complex, A : complex, B : complex]: ((A2 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A2 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_38_group__cancel_Oadd1, axiom,
    ((![A2 : real, K : real, A : real, B : real]: ((A2 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A2 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_39_group__cancel_Oadd1, axiom,
    ((![A2 : poly_real, K : poly_real, A : poly_real, B : poly_real]: ((A2 = (plus_plus_poly_real @ K @ A)) => ((plus_plus_poly_real @ A2 @ B) = (plus_plus_poly_real @ K @ (plus_plus_poly_real @ A @ B))))))). % group_cancel.add1
thf(fact_40_group__cancel_Oadd1, axiom,
    ((![A2 : poly_complex, K : poly_complex, A : poly_complex, B : poly_complex]: ((A2 = (plus_p1547158847omplex @ K @ A)) => ((plus_p1547158847omplex @ A2 @ B) = (plus_p1547158847omplex @ K @ (plus_p1547158847omplex @ A @ B))))))). % group_cancel.add1
thf(fact_41_group__cancel_Oadd2, axiom,
    ((![B2 : complex, K : complex, B : complex, A : complex]: ((B2 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B2) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_42_group__cancel_Oadd2, axiom,
    ((![B2 : real, K : real, B : real, A : real]: ((B2 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B2) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_43_group__cancel_Oadd2, axiom,
    ((![B2 : poly_real, K : poly_real, B : poly_real, A : poly_real]: ((B2 = (plus_plus_poly_real @ K @ B)) => ((plus_plus_poly_real @ A @ B2) = (plus_plus_poly_real @ K @ (plus_plus_poly_real @ A @ B))))))). % group_cancel.add2
thf(fact_44_group__cancel_Oadd2, axiom,
    ((![B2 : poly_complex, K : poly_complex, B : poly_complex, A : poly_complex]: ((B2 = (plus_p1547158847omplex @ K @ B)) => ((plus_p1547158847omplex @ A @ B2) = (plus_p1547158847omplex @ K @ (plus_p1547158847omplex @ A @ B))))))). % group_cancel.add2
thf(fact_45_add_Oassoc, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.assoc
thf(fact_46_add_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % add.assoc
thf(fact_47_add_Oassoc, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ (plus_plus_poly_real @ A @ B) @ C) = (plus_plus_poly_real @ A @ (plus_plus_poly_real @ B @ C)))))). % add.assoc
thf(fact_48_add_Oassoc, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ (plus_p1547158847omplex @ A @ B) @ C) = (plus_p1547158847omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % add.assoc
thf(fact_49__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_O_A_092_060forall_062w_O_Acmod_A_Ipoly_Ap_Ac_J_A_092_060le_062_Acmod_A_Ipoly_Ap_Aw_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![C2 : complex]: (~ ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ C2)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W))))))))))). % \<open>\<And>thesis. (\<And>c. \<forall>w. cmod (poly p c) \<le> cmod (poly p w) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_50_add__cancel__right__right, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real))))). % add_cancel_right_right
thf(fact_51_add__cancel__right__right, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (plus_plus_poly_real @ A @ B)) = (B = zero_zero_poly_real))))). % add_cancel_right_right
thf(fact_52_add__cancel__right__right, axiom,
    ((![A : poly_complex, B : poly_complex]: ((A = (plus_p1547158847omplex @ A @ B)) = (B = zero_z1746442943omplex))))). % add_cancel_right_right
thf(fact_53_add__cancel__right__right, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex))))). % add_cancel_right_right
thf(fact_54_add__cancel__right__left, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real))))). % add_cancel_right_left
thf(fact_55_add__cancel__right__left, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (plus_plus_poly_real @ B @ A)) = (B = zero_zero_poly_real))))). % add_cancel_right_left
thf(fact_56_add__cancel__right__left, axiom,
    ((![A : poly_complex, B : poly_complex]: ((A = (plus_p1547158847omplex @ B @ A)) = (B = zero_z1746442943omplex))))). % add_cancel_right_left
thf(fact_57_add__cancel__right__left, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex))))). % add_cancel_right_left
thf(fact_58_add__cancel__left__right, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real))))). % add_cancel_left_right
thf(fact_59_add__cancel__left__right, axiom,
    ((![A : poly_real, B : poly_real]: (((plus_plus_poly_real @ A @ B) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_right
thf(fact_60_add__cancel__left__right, axiom,
    ((![A : poly_complex, B : poly_complex]: (((plus_p1547158847omplex @ A @ B) = A) = (B = zero_z1746442943omplex))))). % add_cancel_left_right
thf(fact_61_add__cancel__left__right, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex))))). % add_cancel_left_right
thf(fact_62_add__cancel__left__left, axiom,
    ((![B : real, A : real]: (((plus_plus_real @ B @ A) = A) = (B = zero_zero_real))))). % add_cancel_left_left
thf(fact_63_add__cancel__left__left, axiom,
    ((![B : poly_real, A : poly_real]: (((plus_plus_poly_real @ B @ A) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_left
thf(fact_64_add__cancel__left__left, axiom,
    ((![B : poly_complex, A : poly_complex]: (((plus_p1547158847omplex @ B @ A) = A) = (B = zero_z1746442943omplex))))). % add_cancel_left_left
thf(fact_65_add__cancel__left__left, axiom,
    ((![B : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) = (B = zero_zero_complex))))). % add_cancel_left_left
thf(fact_66_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_67_double__zero__sym, axiom,
    ((![A : poly_real]: ((zero_zero_poly_real = (plus_plus_poly_real @ A @ A)) = (A = zero_zero_poly_real))))). % double_zero_sym
thf(fact_68_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_69_double__zero, axiom,
    ((![A : poly_real]: (((plus_plus_poly_real @ A @ A) = zero_zero_poly_real) = (A = zero_zero_poly_real))))). % double_zero
thf(fact_70_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_71_add_Oright__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ A @ zero_zero_poly_real) = A)))). % add.right_neutral
thf(fact_72_add_Oright__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ A @ zero_z1746442943omplex) = A)))). % add.right_neutral
thf(fact_73_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_74_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_75_add_Oleft__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % add.left_neutral
thf(fact_76_add_Oleft__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ zero_z1746442943omplex @ A) = A)))). % add.left_neutral
thf(fact_77_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_78_add__le__cancel__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)) = (ord_le1180086932y_real @ A @ B))))). % add_le_cancel_right
thf(fact_79_add__le__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_right
thf(fact_80_add__le__cancel__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)) = (ord_le1180086932y_real @ A @ B))))). % add_le_cancel_left
thf(fact_81_add__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_left
thf(fact_82_poly__0, axiom,
    ((![X2 : real]: ((poly_real2 @ zero_zero_poly_real @ X2) = zero_zero_real)))). % poly_0
thf(fact_83_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_84_add__le__same__cancel1, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ B @ A) @ B) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % add_le_same_cancel1
thf(fact_85_add__le__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel1
thf(fact_86_add__le__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ B) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % add_le_same_cancel2
thf(fact_87_add__le__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel2
thf(fact_88_le__add__same__cancel1, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (plus_plus_poly_real @ A @ B)) = (ord_le1180086932y_real @ zero_zero_poly_real @ B))))). % le_add_same_cancel1
thf(fact_89_le__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel1
thf(fact_90_le__add__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (plus_plus_poly_real @ B @ A)) = (ord_le1180086932y_real @ zero_zero_poly_real @ B))))). % le_add_same_cancel2
thf(fact_91_le__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel2
thf(fact_92_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ A) @ zero_zero_poly_real) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_93_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_94_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ A)) = (ord_le1180086932y_real @ zero_zero_poly_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_95_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_96_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_97_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_98_poly__all__0__iff__0, axiom,
    ((![P : poly_real]: ((![X3 : real]: ((poly_real2 @ P @ X3) = zero_zero_real)) = (P = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_99_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X3 : complex]: ((poly_complex2 @ P @ X3) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_100_add__decreasing, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ zero_zero_poly_real) => ((ord_le1180086932y_real @ C @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_101_add__decreasing, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_102_add__increasing, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_le1180086932y_real @ B @ C) => (ord_le1180086932y_real @ B @ (plus_plus_poly_real @ A @ C))))))). % add_increasing
thf(fact_103_add__increasing, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing
thf(fact_104_add__decreasing2, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ C @ zero_zero_poly_real) => ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_105_add__decreasing2, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ C @ zero_zero_real) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_106_add__increasing2, axiom,
    ((![C : poly_real, B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ C) => ((ord_le1180086932y_real @ B @ A) => (ord_le1180086932y_real @ B @ (plus_plus_poly_real @ A @ C))))))). % add_increasing2
thf(fact_107_add__increasing2, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing2
thf(fact_108_add__nonneg__nonneg, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_le1180086932y_real @ zero_zero_poly_real @ B) => (ord_le1180086932y_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_109_add__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_110_add__nonpos__nonpos, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ zero_zero_poly_real) => ((ord_le1180086932y_real @ B @ zero_zero_poly_real) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ zero_zero_poly_real)))))). % add_nonpos_nonpos
thf(fact_111_add__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_nonpos
thf(fact_112_add__nonneg__eq__0__iff, axiom,
    ((![X2 : poly_real, Y : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ X2) => ((ord_le1180086932y_real @ zero_zero_poly_real @ Y) => (((plus_plus_poly_real @ X2 @ Y) = zero_zero_poly_real) = (((X2 = zero_zero_poly_real)) & ((Y = zero_zero_poly_real))))))))). % add_nonneg_eq_0_iff
thf(fact_113_add__nonneg__eq__0__iff, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X2) => ((ord_less_eq_real @ zero_zero_real @ Y) => (((plus_plus_real @ X2 @ Y) = zero_zero_real) = (((X2 = zero_zero_real)) & ((Y = zero_zero_real))))))))). % add_nonneg_eq_0_iff
thf(fact_114_add__nonpos__eq__0__iff, axiom,
    ((![X2 : poly_real, Y : poly_real]: ((ord_le1180086932y_real @ X2 @ zero_zero_poly_real) => ((ord_le1180086932y_real @ Y @ zero_zero_poly_real) => (((plus_plus_poly_real @ X2 @ Y) = zero_zero_poly_real) = (((X2 = zero_zero_poly_real)) & ((Y = zero_zero_poly_real))))))))). % add_nonpos_eq_0_iff
thf(fact_115_add__nonpos__eq__0__iff, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ zero_zero_real) => ((ord_less_eq_real @ Y @ zero_zero_real) => (((plus_plus_real @ X2 @ Y) = zero_zero_real) = (((X2 = zero_zero_real)) & ((Y = zero_zero_real))))))))). % add_nonpos_eq_0_iff
thf(fact_116_complex__mod__triangle__sub, axiom,
    ((![W2 : complex, Z : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W2) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W2 @ Z)) @ (real_V638595069omplex @ Z)))))). % complex_mod_triangle_sub
thf(fact_117_add__le__imp__le__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)) => (ord_le1180086932y_real @ A @ B))))). % add_le_imp_le_right
thf(fact_118_add__le__imp__le__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_right
thf(fact_119_add__le__imp__le__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)) => (ord_le1180086932y_real @ A @ B))))). % add_le_imp_le_left
thf(fact_120_add__le__imp__le__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_left
thf(fact_121_add__right__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)))))). % add_right_mono
thf(fact_122_add__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_right_mono
thf(fact_123_add__left__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)))))). % add_left_mono
thf(fact_124_add__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_left_mono
thf(fact_125_add__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: ((ord_le1180086932y_real @ A @ B) => ((ord_le1180086932y_real @ C @ D) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ D))))))). % add_mono
thf(fact_126_add__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_mono
thf(fact_127_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : poly_real, J : poly_real, K : poly_real, L : poly_real]: (((ord_le1180086932y_real @ I @ J) & (ord_le1180086932y_real @ K @ L)) => (ord_le1180086932y_real @ (plus_plus_poly_real @ I @ K) @ (plus_plus_poly_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_128_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_129_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : poly_real, J : poly_real, K : poly_real, L : poly_real]: (((I = J) & (ord_le1180086932y_real @ K @ L)) => (ord_le1180086932y_real @ (plus_plus_poly_real @ I @ K) @ (plus_plus_poly_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_130_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_131_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : poly_real, J : poly_real, K : poly_real, L : poly_real]: (((ord_le1180086932y_real @ I @ J) & (K = L)) => (ord_le1180086932y_real @ (plus_plus_poly_real @ I @ K) @ (plus_plus_poly_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_132_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (K = L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_133_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_134_add_Ogroup__left__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % add.group_left_neutral
thf(fact_135_add_Ogroup__left__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ zero_z1746442943omplex @ A) = A)))). % add.group_left_neutral
thf(fact_136_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_137_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_138_add_Ocomm__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ A @ zero_zero_poly_real) = A)))). % add.comm_neutral
thf(fact_139_add_Ocomm__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ A @ zero_z1746442943omplex) = A)))). % add.comm_neutral
thf(fact_140_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_141_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_142_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_143_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ zero_z1746442943omplex @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_144_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_145_poly__minimum__modulus__disc, axiom,
    ((![R : real, P : poly_complex]: (?[Z2 : complex]: (![W : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ W) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z2)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W))))))))). % poly_minimum_modulus_disc
thf(fact_146_poly__minimum__modulus, axiom,
    ((![P : poly_complex]: (?[Z2 : complex]: (![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z2)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W)))))))). % poly_minimum_modulus
thf(fact_147_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y2 : complex]: ((F @ X3) = (F @ Y2)))))))). % constant_def
thf(fact_148_add__right__imp__eq, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_149_add__right__imp__eq, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_150_add__right__imp__eq, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: (((plus_plus_poly_real @ B @ A) = (plus_plus_poly_real @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_151_add__right__imp__eq, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ B @ A) = (plus_p1547158847omplex @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_152_add__left__imp__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_153_add__left__imp__eq, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_154_add__left__imp__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: (((plus_plus_poly_real @ A @ B) = (plus_plus_poly_real @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_155_add__left__imp__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ A @ B) = (plus_p1547158847omplex @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_156_add_Oleft__commute, axiom,
    ((![B : complex, A : complex, C : complex]: ((plus_plus_complex @ B @ (plus_plus_complex @ A @ C)) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.left_commute
thf(fact_157_add_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((plus_plus_real @ B @ (plus_plus_real @ A @ C)) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % add.left_commute
thf(fact_158_add_Oleft__commute, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: ((plus_plus_poly_real @ B @ (plus_plus_poly_real @ A @ C)) = (plus_plus_poly_real @ A @ (plus_plus_poly_real @ B @ C)))))). % add.left_commute
thf(fact_159_add_Oleft__commute, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ B @ (plus_p1547158847omplex @ A @ C)) = (plus_p1547158847omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % add.left_commute
thf(fact_160_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A3 : complex]: (^[B3 : complex]: (plus_plus_complex @ B3 @ A3)))))). % add.commute
thf(fact_161_add_Ocommute, axiom,
    ((plus_plus_real = (^[A3 : real]: (^[B3 : real]: (plus_plus_real @ B3 @ A3)))))). % add.commute
thf(fact_162_add_Ocommute, axiom,
    ((plus_plus_poly_real = (^[A3 : poly_real]: (^[B3 : poly_real]: (plus_plus_poly_real @ B3 @ A3)))))). % add.commute
thf(fact_163_add_Ocommute, axiom,
    ((plus_p1547158847omplex = (^[A3 : poly_complex]: (^[B3 : poly_complex]: (plus_p1547158847omplex @ B3 @ A3)))))). % add.commute
thf(fact_164_add_Oright__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_165_add_Oright__cancel, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_166_add_Oright__cancel, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: (((plus_plus_poly_real @ B @ A) = (plus_plus_poly_real @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_167_add_Oright__cancel, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ B @ A) = (plus_p1547158847omplex @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_168_add_Oleft__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_169_add_Oleft__cancel, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_170_add_Oleft__cancel, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: (((plus_plus_poly_real @ A @ B) = (plus_plus_poly_real @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_171_add_Oleft__cancel, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ A @ B) = (plus_p1547158847omplex @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_172_norm__le__zero__iff, axiom,
    ((![X2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X2) @ zero_zero_real) = (X2 = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_173_less_Ohyps, axiom,
    ((![P : poly_complex]: ((ord_less_nat @ (fundam1709708056omplex @ P) @ (fundam1709708056omplex @ pa)) => ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z2 : complex]: ((poly_complex2 @ P @ Z2) = zero_zero_complex))))))). % less.hyps
thf(fact_174_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_175_norm__eq__zero, axiom,
    ((![X2 : complex]: (((real_V638595069omplex @ X2) = zero_zero_real) = (X2 = zero_zero_complex))))). % norm_eq_zero
thf(fact_176_norm__add__leD, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ C) => (ord_less_eq_real @ (real_V646646907m_real @ B) @ (plus_plus_real @ (real_V646646907m_real @ A) @ C)))))). % norm_add_leD
thf(fact_177_norm__add__leD, axiom,
    ((![A : complex, B : complex, C : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ C) => (ord_less_eq_real @ (real_V638595069omplex @ B) @ (plus_plus_real @ (real_V638595069omplex @ A) @ C)))))). % norm_add_leD
thf(fact_178_norm__triangle__le, axiom,
    ((![X2 : real, Y : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X2) @ (real_V646646907m_real @ Y)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X2 @ Y)) @ E))))). % norm_triangle_le
thf(fact_179_norm__triangle__le, axiom,
    ((![X2 : complex, Y : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X2) @ (real_V638595069omplex @ Y)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X2 @ Y)) @ E))))). % norm_triangle_le
thf(fact_180_norm__triangle__ineq, axiom,
    ((![X2 : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X2 @ Y)) @ (plus_plus_real @ (real_V646646907m_real @ X2) @ (real_V646646907m_real @ Y)))))). % norm_triangle_ineq
thf(fact_181_norm__triangle__ineq, axiom,
    ((![X2 : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X2 @ Y)) @ (plus_plus_real @ (real_V638595069omplex @ X2) @ (real_V638595069omplex @ Y)))))). % norm_triangle_ineq
thf(fact_182_norm__triangle__mono, axiom,
    ((![A : real, R : real, B : real, S : real]: ((ord_less_eq_real @ (real_V646646907m_real @ A) @ R) => ((ord_less_eq_real @ (real_V646646907m_real @ B) @ S) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_183_norm__triangle__mono, axiom,
    ((![A : complex, R : real, B : complex, S : real]: ((ord_less_eq_real @ (real_V638595069omplex @ A) @ R) => ((ord_less_eq_real @ (real_V638595069omplex @ B) @ S) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_184_order__refl, axiom,
    ((![X2 : real]: (ord_less_eq_real @ X2 @ X2)))). % order_refl
thf(fact_185_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_186_add__less__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_real @ A @ B))))). % add_less_cancel_left
thf(fact_187_add__less__cancel__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)) = (ord_less_poly_real @ A @ B))))). % add_less_cancel_left
thf(fact_188_add__less__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ B))))). % add_less_cancel_left
thf(fact_189_add__less__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_real @ A @ B))))). % add_less_cancel_right
thf(fact_190_add__less__cancel__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)) = (ord_less_poly_real @ A @ B))))). % add_less_cancel_right
thf(fact_191_add__less__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_nat @ A @ B))))). % add_less_cancel_right
thf(fact_192_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_193_psize__eq__0__iff, axiom,
    ((![P : poly_real]: (((fundam1947011094e_real @ P) = zero_zero_nat) = (P = zero_zero_poly_real))))). % psize_eq_0_iff
thf(fact_194_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_195_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ A)) = (ord_less_poly_real @ zero_zero_poly_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_196_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_197_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ A) @ zero_zero_poly_real) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_198_less__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel2
thf(fact_199_less__add__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (plus_plus_poly_real @ B @ A)) = (ord_less_poly_real @ zero_zero_poly_real @ B))))). % less_add_same_cancel2
thf(fact_200_less__add__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B))))). % less_add_same_cancel2
thf(fact_201_less__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel1
thf(fact_202_less__add__same__cancel1, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (plus_plus_poly_real @ A @ B)) = (ord_less_poly_real @ zero_zero_poly_real @ B))))). % less_add_same_cancel1
thf(fact_203_less__add__same__cancel1, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B))))). % less_add_same_cancel1
thf(fact_204_add__less__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel2
thf(fact_205_add__less__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ B) @ B) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % add_less_same_cancel2
thf(fact_206_add__less__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat))))). % add_less_same_cancel2
thf(fact_207_add__less__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel1
thf(fact_208_add__less__same__cancel1, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ B @ A) @ B) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % add_less_same_cancel1
thf(fact_209_add__less__same__cancel1, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ B) = (ord_less_nat @ A @ zero_zero_nat))))). % add_less_same_cancel1
thf(fact_210_leD, axiom,
    ((![Y : nat, X2 : nat]: ((ord_less_eq_nat @ Y @ X2) => (~ ((ord_less_nat @ X2 @ Y))))))). % leD
thf(fact_211_leD, axiom,
    ((![Y : real, X2 : real]: ((ord_less_eq_real @ Y @ X2) => (~ ((ord_less_real @ X2 @ Y))))))). % leD
thf(fact_212_leI, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_nat @ X2 @ Y))) => (ord_less_eq_nat @ Y @ X2))))). % leI
thf(fact_213_leI, axiom,
    ((![X2 : real, Y : real]: ((~ ((ord_less_real @ X2 @ Y))) => (ord_less_eq_real @ Y @ X2))))). % leI
thf(fact_214_le__less, axiom,
    ((ord_less_eq_nat = (^[X3 : nat]: (^[Y2 : nat]: (((ord_less_nat @ X3 @ Y2)) | ((X3 = Y2)))))))). % le_less
thf(fact_215_le__less, axiom,
    ((ord_less_eq_real = (^[X3 : real]: (^[Y2 : real]: (((ord_less_real @ X3 @ Y2)) | ((X3 = Y2)))))))). % le_less
thf(fact_216_less__le, axiom,
    ((ord_less_nat = (^[X3 : nat]: (^[Y2 : nat]: (((ord_less_eq_nat @ X3 @ Y2)) & ((~ ((X3 = Y2)))))))))). % less_le
thf(fact_217_less__le, axiom,
    ((ord_less_real = (^[X3 : real]: (^[Y2 : real]: (((ord_less_eq_real @ X3 @ Y2)) & ((~ ((X3 = Y2)))))))))). % less_le
thf(fact_218_order__le__less__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_nat @ B @ C) => ((![X4 : nat, Y3 : nat]: ((ord_less_nat @ X4 @ Y3) => (ord_less_nat @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % order_le_less_subst1
thf(fact_219_order__le__less__subst1, axiom,
    ((![A : real, F2 : nat > real, B : nat, C : nat]: ((ord_less_eq_real @ A @ (F2 @ B)) => ((ord_less_nat @ B @ C) => ((![X4 : nat, Y3 : nat]: ((ord_less_nat @ X4 @ Y3) => (ord_less_real @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_le_less_subst1
thf(fact_220_order__le__less__subst2, axiom,
    ((![A : real, B : real, F2 : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_nat @ (F2 @ B) @ C) => ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ Y3) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % order_le_less_subst2
thf(fact_221_order__le__less__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F2 @ B) @ C) => ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ Y3) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_le_less_subst2
thf(fact_222_order__less__le__subst1, axiom,
    ((![A : nat, F2 : real > nat, B : real, C : real]: ((ord_less_nat @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ Y3) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_nat @ A @ (F2 @ C)))))))). % order_less_le_subst1
thf(fact_223_order__less__le__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_real @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ Y3) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_less_le_subst1
thf(fact_224_order__less__le__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X4 : nat, Y3 : nat]: ((ord_less_nat @ X4 @ Y3) => (ord_less_nat @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_nat @ (F2 @ A) @ C))))))). % order_less_le_subst2
thf(fact_225_order__less__le__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > real, C : real]: ((ord_less_nat @ A @ B) => ((ord_less_eq_real @ (F2 @ B) @ C) => ((![X4 : nat, Y3 : nat]: ((ord_less_nat @ X4 @ Y3) => (ord_less_real @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_less_le_subst2
thf(fact_226_not__le, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_eq_nat @ X2 @ Y))) = (ord_less_nat @ Y @ X2))))). % not_le
thf(fact_227_not__le, axiom,
    ((![X2 : real, Y : real]: ((~ ((ord_less_eq_real @ X2 @ Y))) = (ord_less_real @ Y @ X2))))). % not_le
thf(fact_228_not__less, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_nat @ X2 @ Y))) = (ord_less_eq_nat @ Y @ X2))))). % not_less
thf(fact_229_not__less, axiom,
    ((![X2 : real, Y : real]: ((~ ((ord_less_real @ X2 @ Y))) = (ord_less_eq_real @ Y @ X2))))). % not_less
thf(fact_230_le__neq__trans, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((~ ((A = B))) => (ord_less_nat @ A @ B)))))). % le_neq_trans
thf(fact_231_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_232_antisym__conv1, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_nat @ X2 @ Y))) => ((ord_less_eq_nat @ X2 @ Y) = (X2 = Y)))))). % antisym_conv1
thf(fact_233_antisym__conv1, axiom,
    ((![X2 : real, Y : real]: ((~ ((ord_less_real @ X2 @ Y))) => ((ord_less_eq_real @ X2 @ Y) = (X2 = Y)))))). % antisym_conv1
thf(fact_234_antisym__conv2, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) => ((~ ((ord_less_nat @ X2 @ Y))) = (X2 = Y)))))). % antisym_conv2
thf(fact_235_antisym__conv2, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) => ((~ ((ord_less_real @ X2 @ Y))) = (X2 = Y)))))). % antisym_conv2
thf(fact_236_less__imp__le, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (ord_less_eq_nat @ X2 @ Y))))). % less_imp_le
thf(fact_237_less__imp__le, axiom,
    ((![X2 : real, Y : real]: ((ord_less_real @ X2 @ Y) => (ord_less_eq_real @ X2 @ Y))))). % less_imp_le
thf(fact_238_le__less__trans, axiom,
    ((![X2 : nat, Y : nat, Z : nat]: ((ord_less_eq_nat @ X2 @ Y) => ((ord_less_nat @ Y @ Z) => (ord_less_nat @ X2 @ Z)))))). % le_less_trans
thf(fact_239_le__less__trans, axiom,
    ((![X2 : real, Y : real, Z : real]: ((ord_less_eq_real @ X2 @ Y) => ((ord_less_real @ Y @ Z) => (ord_less_real @ X2 @ Z)))))). % le_less_trans
thf(fact_240_less__le__trans, axiom,
    ((![X2 : nat, Y : nat, Z : nat]: ((ord_less_nat @ X2 @ Y) => ((ord_less_eq_nat @ Y @ Z) => (ord_less_nat @ X2 @ Z)))))). % less_le_trans
thf(fact_241_less__le__trans, axiom,
    ((![X2 : real, Y : real, Z : real]: ((ord_less_real @ X2 @ Y) => ((ord_less_eq_real @ Y @ Z) => (ord_less_real @ X2 @ Z)))))). % less_le_trans
thf(fact_242_dense__ge, axiom,
    ((![Z : real, Y : real]: ((![X4 : real]: ((ord_less_real @ Z @ X4) => (ord_less_eq_real @ Y @ X4))) => (ord_less_eq_real @ Y @ Z))))). % dense_ge
thf(fact_243_dense__le, axiom,
    ((![Y : real, Z : real]: ((![X4 : real]: ((ord_less_real @ X4 @ Y) => (ord_less_eq_real @ X4 @ Z))) => (ord_less_eq_real @ Y @ Z))))). % dense_le
thf(fact_244_le__less__linear, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) | (ord_less_nat @ Y @ X2))))). % le_less_linear
thf(fact_245_le__less__linear, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) | (ord_less_real @ Y @ X2))))). % le_less_linear
thf(fact_246_le__imp__less__or__eq, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) => ((ord_less_nat @ X2 @ Y) | (X2 = Y)))))). % le_imp_less_or_eq
thf(fact_247_le__imp__less__or__eq, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) => ((ord_less_real @ X2 @ Y) | (X2 = Y)))))). % le_imp_less_or_eq

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![Q3 : poly_complex]: (((fundam1709708056omplex @ Q3) = (fundam1709708056omplex @ pa)) => ((![X4 : complex]: ((poly_complex2 @ Q3 @ X4) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X4)))) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
