% 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_692__5374682_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:32:13.587

% 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_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (32)
thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex, type,
    invers502456322omplex : complex > complex).
thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal, type,
    inverse_inverse_real : real > real).
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_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > 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__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_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    times_1246143675omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_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__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__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_Polynomial_Osmult_001t__Complex__Ocomplex, type,
    smult_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Osmult_001t__Real__Oreal, type,
    smult_real : real > poly_real > poly_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_q____, type,
    q : poly_complex).
thf(sy_v_x____, type,
    x : complex).
thf(sy_v_y____, type,
    y : complex).

% Relevant facts (172)
thf(fact_0_nc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ p)))))). % nc
thf(fact_1__092_060open_062constant_A_Ipoly_Aq_J_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ q)))))). % \<open>constant (poly q) \<Longrightarrow> False\<close>
thf(fact_2_qnc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ q)))))). % qnc
thf(fact_3_a00, axiom,
    ((~ (((poly_complex2 @ q @ zero_zero_complex) = zero_zero_complex))))). % a00
thf(fact_4_less_Oprems, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ pa)))))). % less.prems
thf(fact_5_q_I1_J, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ pa)))). % q(1)
thf(fact_6_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_7_q_I2_J, axiom,
    ((![X : complex]: ((poly_complex2 @ q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))). % q(2)
thf(fact_8_pqc0, axiom,
    (((poly_complex2 @ pa @ c) = (poly_complex2 @ q @ zero_zero_complex)))). % pqc0
thf(fact_9_that, axiom,
    ((![X2 : complex, Y : complex]: ((poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ X2) = (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ Y))))). % that
thf(fact_10_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_11_lgqr, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q))))). % lgqr
thf(fact_12_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y2 : complex]: ((F @ X3) = (F @ Y2)))))))). % constant_def
thf(fact_13_cq0, axiom,
    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % cq0
thf(fact_14_qr, axiom,
    ((![Z : complex]: ((poly_complex2 @ q @ Z) = (times_times_complex @ (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ Z) @ (poly_complex2 @ q @ zero_zero_complex)))))). % qr
thf(fact_15_c, axiom,
    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ c)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % c
thf(fact_16__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,
    ((~ ((![C : complex]: (~ ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ C)) @ (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_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062q_O_A_092_060lbrakk_062psize_Aq_A_061_Apsize_Ap_059_A_092_060forall_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ pa)) => (~ ((![X : complex]: ((poly_complex2 @ Q2 @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))))))))). % \<open>\<And>thesis. (\<And>q. \<lbrakk>psize q = psize p; \<forall>x. poly q x = poly p (c + x)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_18__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,
    ((?[Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ pa)) & (![X : complex]: ((poly_complex2 @ Q2 @ 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_19_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_20_smult__0__left, axiom,
    ((![P : poly_complex]: ((smult_complex @ zero_zero_complex @ P) = zero_z1746442943omplex)))). % smult_0_left
thf(fact_21_smult__eq__0__iff, axiom,
    ((![A : complex, P : poly_complex]: (((smult_complex @ A @ P) = zero_z1746442943omplex) = (((A = zero_zero_complex)) | ((P = zero_z1746442943omplex))))))). % smult_eq_0_iff
thf(fact_22_poly__mult, axiom,
    ((![P : poly_complex, Q : poly_complex, X2 : complex]: ((poly_complex2 @ (times_1246143675omplex @ P @ Q) @ X2) = (times_times_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q @ X2)))))). % poly_mult
thf(fact_23_poly__add, axiom,
    ((![P : poly_complex, Q : poly_complex, X2 : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P @ Q) @ X2) = (plus_plus_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q @ X2)))))). % poly_add
thf(fact_24_poly__add, axiom,
    ((![P : poly_real, Q : poly_real, X2 : real]: ((poly_real2 @ (plus_plus_poly_real @ P @ Q) @ X2) = (plus_plus_real @ (poly_real2 @ P @ X2) @ (poly_real2 @ Q @ X2)))))). % poly_add
thf(fact_25_smult__smult, axiom,
    ((![A : complex, B : complex, P : poly_complex]: ((smult_complex @ A @ (smult_complex @ B @ P)) = (smult_complex @ (times_times_complex @ A @ B) @ P))))). % smult_smult
thf(fact_26_poly__smult, axiom,
    ((![A : complex, P : poly_complex, X2 : complex]: ((poly_complex2 @ (smult_complex @ A @ P) @ X2) = (times_times_complex @ A @ (poly_complex2 @ P @ X2)))))). % poly_smult
thf(fact_27_smult__add__left, axiom,
    ((![A : complex, B : complex, P : poly_complex]: ((smult_complex @ (plus_plus_complex @ A @ B) @ P) = (plus_p1547158847omplex @ (smult_complex @ A @ P) @ (smult_complex @ B @ P)))))). % smult_add_left
thf(fact_28_smult__add__left, axiom,
    ((![A : real, B : real, P : poly_real]: ((smult_real @ (plus_plus_real @ A @ B) @ P) = (plus_plus_poly_real @ (smult_real @ A @ P) @ (smult_real @ B @ P)))))). % smult_add_left
thf(fact_29_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_30_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_31_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_32_poly__offset, axiom,
    ((![P : poly_real, A : real]: (?[Q2 : poly_real]: (((fundam1947011094e_real @ Q2) = (fundam1947011094e_real @ P)) & (![X : real]: ((poly_real2 @ Q2 @ X) = (poly_real2 @ P @ (plus_plus_real @ A @ X))))))))). % poly_offset
thf(fact_33_poly__offset, axiom,
    ((![P : poly_complex, A : complex]: (?[Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ P)) & (![X : complex]: ((poly_complex2 @ Q2 @ X) = (poly_complex2 @ P @ (plus_plus_complex @ A @ X))))))))). % poly_offset
thf(fact_34_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_35_inverse__nonnegative__iff__nonnegative, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (inverse_inverse_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % inverse_nonnegative_iff_nonnegative
thf(fact_36_inverse__nonpositive__iff__nonpositive, axiom,
    ((![A : real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % inverse_nonpositive_iff_nonpositive
thf(fact_37_sum__squares__eq__zero__iff, axiom,
    ((![X2 : real, Y : real]: (((plus_plus_real @ (times_times_real @ X2 @ X2) @ (times_times_real @ Y @ Y)) = zero_zero_real) = (((X2 = zero_zero_real)) & ((Y = zero_zero_real))))))). % sum_squares_eq_zero_iff
thf(fact_38_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_39_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_40_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_41_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_42_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_43_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_44_add__right__cancel, axiom,
    ((![B : complex, A : complex, C2 : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C2 @ A)) = (B = C2))))). % add_right_cancel
thf(fact_45_add__right__cancel, axiom,
    ((![B : real, A : real, C2 : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C2 @ A)) = (B = C2))))). % add_right_cancel
thf(fact_46_add__left__cancel, axiom,
    ((![A : complex, B : complex, C2 : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C2)) = (B = C2))))). % add_left_cancel
thf(fact_47_add__left__cancel, axiom,
    ((![A : real, B : real, C2 : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C2)) = (B = C2))))). % add_left_cancel
thf(fact_48_inverse__inverse__eq, axiom,
    ((![A : complex]: ((invers502456322omplex @ (invers502456322omplex @ A)) = A)))). % inverse_inverse_eq
thf(fact_49_inverse__eq__iff__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) = (A = B))))). % inverse_eq_iff_eq
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 : complex, B : complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex))))). % add_cancel_right_right
thf(fact_52_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_53_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_54_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_55_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_56_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_57_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_58_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_59_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_60_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_61_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_62_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_63_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_64_add__le__cancel__right, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_right
thf(fact_65_add__le__cancel__left, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_left
thf(fact_66_inverse__nonzero__iff__nonzero, axiom,
    ((![A : complex]: (((invers502456322omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % inverse_nonzero_iff_nonzero
thf(fact_67_inverse__zero, axiom,
    (((invers502456322omplex @ zero_zero_complex) = zero_zero_complex))). % inverse_zero
thf(fact_68_inverse__mult__distrib, axiom,
    ((![A : complex, B : complex]: ((invers502456322omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers502456322omplex @ A) @ (invers502456322omplex @ B)))))). % inverse_mult_distrib
thf(fact_69_smult__0__right, axiom,
    ((![A : complex]: ((smult_complex @ A @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % smult_0_right
thf(fact_70_mult__smult__right, axiom,
    ((![P : poly_complex, A : complex, Q : poly_complex]: ((times_1246143675omplex @ P @ (smult_complex @ A @ Q)) = (smult_complex @ A @ (times_1246143675omplex @ P @ Q)))))). % mult_smult_right
thf(fact_71_mult__smult__left, axiom,
    ((![A : complex, P : poly_complex, Q : poly_complex]: ((times_1246143675omplex @ (smult_complex @ A @ P) @ Q) = (smult_complex @ A @ (times_1246143675omplex @ P @ Q)))))). % mult_smult_left
thf(fact_72_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_73_norm__eq__zero, axiom,
    ((![X2 : complex]: (((real_V638595069omplex @ X2) = zero_zero_real) = (X2 = zero_zero_complex))))). % norm_eq_zero
thf(fact_74_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_75_smult__add__right, axiom,
    ((![A : complex, P : poly_complex, Q : poly_complex]: ((smult_complex @ A @ (plus_p1547158847omplex @ P @ Q)) = (plus_p1547158847omplex @ (smult_complex @ A @ P) @ (smult_complex @ A @ Q)))))). % smult_add_right
thf(fact_76_norm__ge__zero, axiom,
    ((![X2 : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X2))))). % norm_ge_zero
thf(fact_77_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_78_mult_Oleft__commute, axiom,
    ((![B : complex, A : complex, C2 : complex]: ((times_times_complex @ B @ (times_times_complex @ A @ C2)) = (times_times_complex @ A @ (times_times_complex @ B @ C2)))))). % mult.left_commute
thf(fact_79_mult_Ocommute, axiom,
    ((times_times_complex = (^[A2 : complex]: (^[B2 : complex]: (times_times_complex @ B2 @ A2)))))). % mult.commute
thf(fact_80_mult_Oassoc, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C2) = (times_times_complex @ A @ (times_times_complex @ B @ C2)))))). % mult.assoc
thf(fact_81_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C2) = (times_times_complex @ A @ (times_times_complex @ B @ C2)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_82_add__right__imp__eq, axiom,
    ((![B : complex, A : complex, C2 : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C2 @ A)) => (B = C2))))). % add_right_imp_eq
thf(fact_83_add__right__imp__eq, axiom,
    ((![B : real, A : real, C2 : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C2 @ A)) => (B = C2))))). % add_right_imp_eq
thf(fact_84_add__left__imp__eq, axiom,
    ((![A : complex, B : complex, C2 : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C2)) => (B = C2))))). % add_left_imp_eq
thf(fact_85_add__left__imp__eq, axiom,
    ((![A : real, B : real, C2 : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C2)) => (B = C2))))). % add_left_imp_eq
thf(fact_86_add_Oleft__commute, axiom,
    ((![B : complex, A : complex, C2 : complex]: ((plus_plus_complex @ B @ (plus_plus_complex @ A @ C2)) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C2)))))). % add.left_commute
thf(fact_87_add_Oleft__commute, axiom,
    ((![B : real, A : real, C2 : real]: ((plus_plus_real @ B @ (plus_plus_real @ A @ C2)) = (plus_plus_real @ A @ (plus_plus_real @ B @ C2)))))). % add.left_commute
thf(fact_88_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_89_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_90_add_Oright__cancel, axiom,
    ((![B : complex, A : complex, C2 : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C2 @ A)) = (B = C2))))). % add.right_cancel
thf(fact_91_add_Oright__cancel, axiom,
    ((![B : real, A : real, C2 : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C2 @ A)) = (B = C2))))). % add.right_cancel
thf(fact_92_add_Oleft__cancel, axiom,
    ((![A : complex, B : complex, C2 : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C2)) = (B = C2))))). % add.left_cancel
thf(fact_93_add_Oleft__cancel, axiom,
    ((![A : real, B : real, C2 : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C2)) = (B = C2))))). % add.left_cancel
thf(fact_94_add_Oassoc, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C2) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C2)))))). % add.assoc
thf(fact_95_add_Oassoc, axiom,
    ((![A : real, B : real, C2 : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C2) = (plus_plus_real @ A @ (plus_plus_real @ B @ C2)))))). % add.assoc
thf(fact_96_group__cancel_Oadd2, axiom,
    ((![B3 : complex, K : complex, B : complex, A : complex]: ((B3 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B3) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_97_group__cancel_Oadd2, axiom,
    ((![B3 : real, K : real, B : real, A : real]: ((B3 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B3) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_98_group__cancel_Oadd1, axiom,
    ((![A3 : complex, K : complex, A : complex, B : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A3 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_99_group__cancel_Oadd1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A3 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_100_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_101_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C2) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C2)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_102_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : real, B : real, C2 : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C2) = (plus_plus_real @ A @ (plus_plus_real @ B @ C2)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_103_inverse__eq__imp__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) => (A = B))))). % inverse_eq_imp_eq
thf(fact_104_complex__mod__triangle__sub, axiom,
    ((![W2 : complex, Z3 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W2) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W2 @ Z3)) @ (real_V638595069omplex @ Z3)))))). % complex_mod_triangle_sub
thf(fact_105_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_106_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_107_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_108_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_109_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_110_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_111_add__le__imp__le__right, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_right
thf(fact_112_add__le__imp__le__left, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_left
thf(fact_113_add__right__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)))))). % add_right_mono
thf(fact_114_add__left__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)))))). % add_left_mono
thf(fact_115_add__mono, axiom,
    ((![A : real, B : real, C2 : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C2 @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ D))))))). % add_mono
thf(fact_116_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_117_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_118_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_119_nonzero__imp__inverse__nonzero, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => (~ (((invers502456322omplex @ A) = zero_zero_complex))))))). % nonzero_imp_inverse_nonzero
thf(fact_120_nonzero__inverse__inverse__eq, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((invers502456322omplex @ (invers502456322omplex @ A)) = A))))). % nonzero_inverse_inverse_eq
thf(fact_121_nonzero__inverse__eq__imp__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) => ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (A = B))))))). % nonzero_inverse_eq_imp_eq
thf(fact_122_inverse__zero__imp__zero, axiom,
    ((![A : complex]: (((invers502456322omplex @ A) = zero_zero_complex) => (A = zero_zero_complex))))). % inverse_zero_imp_zero
thf(fact_123_field__class_Ofield__inverse__zero, axiom,
    (((invers502456322omplex @ zero_zero_complex) = zero_zero_complex))). % field_class.field_inverse_zero
thf(fact_124_norm__mult, axiom,
    ((![X2 : complex, Y : complex]: ((real_V638595069omplex @ (times_times_complex @ X2 @ Y)) = (times_times_real @ (real_V638595069omplex @ X2) @ (real_V638595069omplex @ Y)))))). % norm_mult
thf(fact_125_mult__commute__imp__mult__inverse__commute, axiom,
    ((![Y : complex, X2 : complex]: (((times_times_complex @ Y @ X2) = (times_times_complex @ X2 @ Y)) => ((times_times_complex @ (invers502456322omplex @ Y) @ X2) = (times_times_complex @ X2 @ (invers502456322omplex @ Y))))))). % mult_commute_imp_mult_inverse_commute
thf(fact_126_norm__inverse, axiom,
    ((![A : complex]: ((real_V638595069omplex @ (invers502456322omplex @ A)) = (inverse_inverse_real @ (real_V638595069omplex @ A)))))). % norm_inverse
thf(fact_127_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_128_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_129_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_130_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_131_add__increasing2, axiom,
    ((![C2 : real, B : real, A : real]: ((ord_less_eq_real @ zero_zero_real @ C2) => ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C2))))))). % add_increasing2
thf(fact_132_add__decreasing2, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_eq_real @ C2 @ zero_zero_real) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ B)))))). % add_decreasing2
thf(fact_133_add__increasing, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C2) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C2))))))). % add_increasing
thf(fact_134_add__decreasing, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ C2 @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ B)))))). % add_decreasing
thf(fact_135_nonzero__inverse__mult__distrib, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => ((invers502456322omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers502456322omplex @ B) @ (invers502456322omplex @ A)))))))). % nonzero_inverse_mult_distrib
thf(fact_136_norm__mult__ineq, axiom,
    ((![X2 : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (times_times_complex @ X2 @ Y)) @ (times_times_real @ (real_V638595069omplex @ X2) @ (real_V638595069omplex @ Y)))))). % norm_mult_ineq
thf(fact_137_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_138_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_139_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_140_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_141_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_142_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_143_norm__add__leD, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ C2) => (ord_less_eq_real @ (real_V646646907m_real @ B) @ (plus_plus_real @ (real_V646646907m_real @ A) @ C2)))))). % norm_add_leD
thf(fact_144_norm__add__leD, axiom,
    ((![A : complex, B : complex, C2 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ C2) => (ord_less_eq_real @ (real_V638595069omplex @ B) @ (plus_plus_real @ (real_V638595069omplex @ A) @ C2)))))). % norm_add_leD
thf(fact_145_nonzero__norm__inverse, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((real_V638595069omplex @ (invers502456322omplex @ A)) = (inverse_inverse_real @ (real_V638595069omplex @ A))))))). % nonzero_norm_inverse
thf(fact_146_sum__squares__le__zero__iff, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ X2 @ X2) @ (times_times_real @ Y @ Y)) @ zero_zero_real) = (((X2 = zero_zero_real)) & ((Y = zero_zero_real))))))). % sum_squares_le_zero_iff
thf(fact_147_division__ring__inverse__add, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((~ ((B = zero_zero_real))) => ((plus_plus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (times_times_real @ (times_times_real @ (inverse_inverse_real @ A) @ (plus_plus_real @ A @ B)) @ (inverse_inverse_real @ B)))))))). % division_ring_inverse_add
thf(fact_148_division__ring__inverse__add, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => ((plus_plus_complex @ (invers502456322omplex @ A) @ (invers502456322omplex @ B)) = (times_times_complex @ (times_times_complex @ (invers502456322omplex @ A) @ (plus_plus_complex @ A @ B)) @ (invers502456322omplex @ B)))))))). % division_ring_inverse_add
thf(fact_149_inverse__add, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((~ ((B = zero_zero_real))) => ((plus_plus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (times_times_real @ (times_times_real @ (plus_plus_real @ A @ B) @ (inverse_inverse_real @ A)) @ (inverse_inverse_real @ B)))))))). % inverse_add
thf(fact_150_inverse__add, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => ((plus_plus_complex @ (invers502456322omplex @ A) @ (invers502456322omplex @ B)) = (times_times_complex @ (times_times_complex @ (plus_plus_complex @ A @ B) @ (invers502456322omplex @ A)) @ (invers502456322omplex @ B)))))))). % inverse_add
thf(fact_151_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_152_mult__cancel__right, axiom,
    ((![A : complex, C2 : complex, B : complex]: (((times_times_complex @ A @ C2) = (times_times_complex @ B @ C2)) = (((C2 = zero_zero_complex)) | ((A = B))))))). % mult_cancel_right
thf(fact_153_mult__cancel__left, axiom,
    ((![C2 : complex, A : complex, B : complex]: (((times_times_complex @ C2 @ A) = (times_times_complex @ C2 @ B)) = (((C2 = zero_zero_complex)) | ((A = B))))))). % mult_cancel_left
thf(fact_154_mult__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_155_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_156_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_157_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_158_add__less__cancel__left, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)) = (ord_less_real @ A @ B))))). % add_less_cancel_left
thf(fact_159_add__less__cancel__left, axiom,
    ((![C2 : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)) = (ord_less_nat @ A @ B))))). % add_less_cancel_left
thf(fact_160_add__less__cancel__right, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)) = (ord_less_real @ A @ B))))). % add_less_cancel_right
thf(fact_161_add__less__cancel__right, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)) = (ord_less_nat @ A @ B))))). % add_less_cancel_right
thf(fact_162_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_163_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_164_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_165_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_166_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_167_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_168_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_169_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_170_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_171_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

% Conjectures (1)
thf(conj_0, conjecture,
    (((poly_complex2 @ q @ x) = (poly_complex2 @ q @ y)))).
