% 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_659__5374472_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:31:55.729

% 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 (34)
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_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    minus_174331535omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    minus_1169194391omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    minus_181436949y_real : poly_poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    minus_240770701y_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
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_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__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_q____, type,
    q : poly_complex).

% Relevant facts (245)
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_q_I2_J, axiom,
    ((![X : complex]: ((poly_complex2 @ q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))). % q(2)
thf(fact_3_that, axiom,
    ((fundam1158420650omplex @ (poly_complex2 @ q)))). % that
thf(fact_4_q_I1_J, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ pa)))). % q(1)
thf(fact_5_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_6_poly__diff, axiom,
    ((![P : poly_poly_real, Q : poly_poly_real, X2 : poly_real]: ((poly_poly_real2 @ (minus_181436949y_real @ P @ Q) @ X2) = (minus_240770701y_real @ (poly_poly_real2 @ P @ X2) @ (poly_poly_real2 @ Q @ X2)))))). % poly_diff
thf(fact_7_poly__diff, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, X2 : poly_complex]: ((poly_poly_complex2 @ (minus_1169194391omplex @ P @ Q) @ X2) = (minus_174331535omplex @ (poly_poly_complex2 @ P @ X2) @ (poly_poly_complex2 @ Q @ X2)))))). % poly_diff
thf(fact_8_poly__diff, axiom,
    ((![P : poly_complex, Q : poly_complex, X2 : complex]: ((poly_complex2 @ (minus_174331535omplex @ P @ Q) @ X2) = (minus_minus_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q @ X2)))))). % poly_diff
thf(fact_9_poly__diff, axiom,
    ((![P : poly_real, Q : poly_real, X2 : real]: ((poly_real2 @ (minus_240770701y_real @ P @ Q) @ X2) = (minus_minus_real @ (poly_real2 @ P @ X2) @ (poly_real2 @ Q @ X2)))))). % poly_diff
thf(fact_10__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_11__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_12_c, axiom,
    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ c)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % c
thf(fact_13_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_14_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_real, Q : poly_real]: (((poly_real2 @ P) = (poly_real2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_15_diff__eq__diff__eq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: (((minus_minus_complex @ A @ B) = (minus_minus_complex @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_16_diff__eq__diff__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_17_diff__eq__diff__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_18_diff__eq__diff__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex, D : poly_complex]: (((minus_174331535omplex @ A @ B) = (minus_174331535omplex @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_19_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ C) @ B) = (minus_minus_complex @ (minus_minus_complex @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_20_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (minus_minus_real @ A @ C) @ B) = (minus_minus_real @ (minus_minus_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_21_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((minus_240770701y_real @ (minus_240770701y_real @ A @ C) @ B) = (minus_240770701y_real @ (minus_240770701y_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_22_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (minus_174331535omplex @ A @ C) @ B) = (minus_174331535omplex @ (minus_174331535omplex @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_23_add__diff__cancel, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_24_add__diff__cancel, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_25_add__diff__cancel, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_26_add__diff__cancel, axiom,
    ((![A : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_27_diff__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_28_diff__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_29_diff__add__cancel, axiom,
    ((![A : poly_real, B : poly_real]: ((plus_plus_poly_real @ (minus_240770701y_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_30_diff__add__cancel, axiom,
    ((![A : poly_complex, B : poly_complex]: ((plus_p1547158847omplex @ (minus_174331535omplex @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_31_add__diff__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ C @ A) @ (plus_plus_complex @ C @ B)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_left
thf(fact_32_add__diff__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_left
thf(fact_33_add__diff__cancel__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)) = (minus_240770701y_real @ A @ B))))). % add_diff_cancel_left
thf(fact_34_add__diff__cancel__left, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ C @ A) @ (plus_p1547158847omplex @ C @ B)) = (minus_174331535omplex @ A @ B))))). % add_diff_cancel_left
thf(fact_35_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_36_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_37_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_38_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_39__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_40_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_41_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_42_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_43_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_44_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_45_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_46_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_47_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_48_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_49_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_50_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_51_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_52_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_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__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_55_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_56_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_57_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_58_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ A) = zero_zero_poly_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_59_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_complex]: ((minus_174331535omplex @ A @ A) = zero_z1746442943omplex)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_60_diff__zero, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_zero
thf(fact_61_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_62_diff__zero, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ zero_zero_poly_real) = A)))). % diff_zero
thf(fact_63_diff__zero, axiom,
    ((![A : poly_complex]: ((minus_174331535omplex @ A @ zero_z1746442943omplex) = A)))). % diff_zero
thf(fact_64_diff__0__right, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_0_right
thf(fact_65_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_66_diff__0__right, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ zero_zero_poly_real) = A)))). % diff_0_right
thf(fact_67_diff__0__right, axiom,
    ((![A : poly_complex]: ((minus_174331535omplex @ A @ zero_z1746442943omplex) = A)))). % diff_0_right
thf(fact_68_diff__self, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % diff_self
thf(fact_69_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_70_diff__self, axiom,
    ((![A : poly_real]: ((minus_240770701y_real @ A @ A) = zero_zero_poly_real)))). % diff_self
thf(fact_71_diff__self, axiom,
    ((![A : poly_complex]: ((minus_174331535omplex @ A @ A) = zero_z1746442943omplex)))). % diff_self
thf(fact_72_add__diff__cancel__right_H, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_73_add__diff__cancel__right_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_74_add__diff__cancel__right_H, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_75_add__diff__cancel__right_H, axiom,
    ((![A : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_76_add__diff__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ C) @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_right
thf(fact_77_add__diff__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_right
thf(fact_78_add__diff__cancel__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)) = (minus_240770701y_real @ A @ B))))). % add_diff_cancel_right
thf(fact_79_add__diff__cancel__right, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ A @ C) @ (plus_p1547158847omplex @ B @ C)) = (minus_174331535omplex @ A @ B))))). % add_diff_cancel_right
thf(fact_80_add__diff__cancel__left_H, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_81_add__diff__cancel__left_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_82_add__diff__cancel__left_H, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_83_add__diff__cancel__left_H, axiom,
    ((![A : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_84_poly__0, axiom,
    ((![X2 : real]: ((poly_real2 @ zero_zero_poly_real @ X2) = zero_zero_real)))). % poly_0
thf(fact_85_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_86_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_87_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_88_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_89_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_90_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_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 : 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_93_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_94_diff__ge__0__iff__ge, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ (minus_240770701y_real @ A @ B)) = (ord_le1180086932y_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_95_diff__ge__0__iff__ge, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_96_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_97_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_98_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_99_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_100_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_101_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_102_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_103_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_104_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_105_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_106_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_107_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_108_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_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_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_112_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_113_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_114_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_115_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_116_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_117_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A3 : complex]: (^[B3 : complex]: (plus_plus_complex @ B3 @ A3)))))). % add.commute
thf(fact_118_add_Ocommute, axiom,
    ((plus_plus_real = (^[A3 : real]: (^[B3 : real]: (plus_plus_real @ B3 @ A3)))))). % add.commute
thf(fact_119_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_120_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_121_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_122_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_123_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_124_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_125_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_126_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_127_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_128_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_129_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_130_le__iff__diff__le__0, axiom,
    ((ord_le1180086932y_real = (^[A3 : poly_real]: (^[B3 : poly_real]: (ord_le1180086932y_real @ (minus_240770701y_real @ A3 @ B3) @ zero_zero_poly_real)))))). % le_iff_diff_le_0
thf(fact_131_le__iff__diff__le__0, axiom,
    ((ord_less_eq_real = (^[A3 : real]: (^[B3 : real]: (ord_less_eq_real @ (minus_minus_real @ A3 @ B3) @ zero_zero_real)))))). % le_iff_diff_le_0
thf(fact_132_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_133_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_134_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_135_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_136_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_137_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_138_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_139_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_140_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_141_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_142_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_143_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_144_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_145_le__diff__eq, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (minus_240770701y_real @ C @ B)) = (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ C))))). % le_diff_eq
thf(fact_146_le__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) = (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))))). % le_diff_eq
thf(fact_147_diff__le__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ (minus_240770701y_real @ A @ B) @ C) = (ord_le1180086932y_real @ A @ (plus_plus_poly_real @ C @ B)))))). % diff_le_eq
thf(fact_148_diff__le__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B)))))). % diff_le_eq
thf(fact_149_diff__eq__diff__less__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((ord_le1180086932y_real @ A @ B) = (ord_le1180086932y_real @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_150_diff__eq__diff__less__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_151_diff__right__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ C)))))). % diff_right_mono
thf(fact_152_diff__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_right_mono
thf(fact_153_diff__left__mono, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: ((ord_le1180086932y_real @ B @ A) => (ord_le1180086932y_real @ (minus_240770701y_real @ C @ A) @ (minus_240770701y_real @ C @ B)))))). % diff_left_mono
thf(fact_154_diff__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_left_mono
thf(fact_155_diff__mono, axiom,
    ((![A : poly_real, B : poly_real, D : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => ((ord_le1180086932y_real @ D @ C) => (ord_le1180086932y_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ D))))))). % diff_mono
thf(fact_156_diff__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ D @ C) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_mono
thf(fact_157_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : complex]: (^[Z2 : complex]: (Y2 = Z2))) = (^[A3 : complex]: (^[B3 : complex]: ((minus_minus_complex @ A3 @ B3) = zero_zero_complex)))))). % eq_iff_diff_eq_0
thf(fact_158_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : real]: (^[Z2 : real]: (Y2 = Z2))) = (^[A3 : real]: (^[B3 : real]: ((minus_minus_real @ A3 @ B3) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_159_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_real]: (^[Z2 : poly_real]: (Y2 = Z2))) = (^[A3 : poly_real]: (^[B3 : poly_real]: ((minus_240770701y_real @ A3 @ B3) = zero_zero_poly_real)))))). % eq_iff_diff_eq_0
thf(fact_160_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_complex]: (^[Z2 : poly_complex]: (Y2 = Z2))) = (^[A3 : poly_complex]: (^[B3 : poly_complex]: ((minus_174331535omplex @ A3 @ B3) = zero_z1746442943omplex)))))). % eq_iff_diff_eq_0
thf(fact_161_poly__minimum__modulus__disc, axiom,
    ((![R : real, P : poly_complex]: (?[Z3 : complex]: (![W : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ W) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z3)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W))))))))). % poly_minimum_modulus_disc
thf(fact_162_poly__minimum__modulus, axiom,
    ((![P : poly_complex]: (?[Z3 : complex]: (![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z3)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W)))))))). % poly_minimum_modulus
thf(fact_163_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y3 : complex]: ((F @ X3) = (F @ Y3)))))))). % constant_def
thf(fact_164_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_165_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_166_add__implies__diff, axiom,
    ((![C : complex, B : complex, A : complex]: (((plus_plus_complex @ C @ B) = A) => (C = (minus_minus_complex @ A @ B)))))). % add_implies_diff
thf(fact_167_add__implies__diff, axiom,
    ((![C : real, B : real, A : real]: (((plus_plus_real @ C @ B) = A) => (C = (minus_minus_real @ A @ B)))))). % add_implies_diff
thf(fact_168_add__implies__diff, axiom,
    ((![C : poly_real, B : poly_real, A : poly_real]: (((plus_plus_poly_real @ C @ B) = A) => (C = (minus_240770701y_real @ A @ B)))))). % add_implies_diff
thf(fact_169_add__implies__diff, axiom,
    ((![C : poly_complex, B : poly_complex, A : poly_complex]: (((plus_p1547158847omplex @ C @ B) = A) => (C = (minus_174331535omplex @ A @ B)))))). % add_implies_diff
thf(fact_170_diff__diff__add, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ A @ (plus_plus_complex @ B @ C)))))). % diff_diff_add
thf(fact_171_diff__diff__add, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C)))))). % diff_diff_add
thf(fact_172_diff__diff__add, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((minus_240770701y_real @ (minus_240770701y_real @ A @ B) @ C) = (minus_240770701y_real @ A @ (plus_plus_poly_real @ B @ C)))))). % diff_diff_add
thf(fact_173_diff__diff__add, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((minus_174331535omplex @ (minus_174331535omplex @ A @ B) @ C) = (minus_174331535omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % diff_diff_add
thf(fact_174_diff__add__eq__diff__diff__swap, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ A @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ (minus_minus_complex @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_175_diff__add__eq__diff__diff__swap, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_176_diff__add__eq__diff__diff__swap, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((minus_240770701y_real @ A @ (plus_plus_poly_real @ B @ C)) = (minus_240770701y_real @ (minus_240770701y_real @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_177_diff__add__eq__diff__diff__swap, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((minus_174331535omplex @ A @ (plus_p1547158847omplex @ B @ C)) = (minus_174331535omplex @ (minus_174331535omplex @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_178_diff__add__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B))))). % diff_add_eq
thf(fact_179_diff__add__eq, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B))))). % diff_add_eq
thf(fact_180_diff__add__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ (minus_240770701y_real @ A @ B) @ C) = (minus_240770701y_real @ (plus_plus_poly_real @ A @ C) @ B))))). % diff_add_eq
thf(fact_181_diff__add__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ (minus_174331535omplex @ A @ B) @ C) = (minus_174331535omplex @ (plus_p1547158847omplex @ A @ C) @ B))))). % diff_add_eq
thf(fact_182_diff__diff__eq2, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_183_diff__diff__eq2, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_184_diff__diff__eq2, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((minus_240770701y_real @ A @ (minus_240770701y_real @ B @ C)) = (minus_240770701y_real @ (plus_plus_poly_real @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_185_diff__diff__eq2, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((minus_174331535omplex @ A @ (minus_174331535omplex @ B @ C)) = (minus_174331535omplex @ (plus_p1547158847omplex @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_186_add__diff__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ B) @ C))))). % add_diff_eq
thf(fact_187_add__diff__eq, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C))))). % add_diff_eq
thf(fact_188_add__diff__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ A @ (minus_240770701y_real @ B @ C)) = (minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ C))))). % add_diff_eq
thf(fact_189_add__diff__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ A @ (minus_174331535omplex @ B @ C)) = (minus_174331535omplex @ (plus_p1547158847omplex @ A @ B) @ C))))). % add_diff_eq
thf(fact_190_eq__diff__eq, axiom,
    ((![A : complex, C : complex, B : complex]: ((A = (minus_minus_complex @ C @ B)) = ((plus_plus_complex @ A @ B) = C))))). % eq_diff_eq
thf(fact_191_eq__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((A = (minus_minus_real @ C @ B)) = ((plus_plus_real @ A @ B) = C))))). % eq_diff_eq
thf(fact_192_eq__diff__eq, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((A = (minus_240770701y_real @ C @ B)) = ((plus_plus_poly_real @ A @ B) = C))))). % eq_diff_eq
thf(fact_193_eq__diff__eq, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((A = (minus_174331535omplex @ C @ B)) = ((plus_p1547158847omplex @ A @ B) = C))))). % eq_diff_eq
thf(fact_194_diff__eq__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((minus_minus_complex @ A @ B) = C) = (A = (plus_plus_complex @ C @ B)))))). % diff_eq_eq
thf(fact_195_diff__eq__eq, axiom,
    ((![A : real, B : real, C : real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B)))))). % diff_eq_eq
thf(fact_196_diff__eq__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: (((minus_240770701y_real @ A @ B) = C) = (A = (plus_plus_poly_real @ C @ B)))))). % diff_eq_eq
thf(fact_197_diff__eq__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((minus_174331535omplex @ A @ B) = C) = (A = (plus_p1547158847omplex @ C @ B)))))). % diff_eq_eq
thf(fact_198_group__cancel_Osub1, axiom,
    ((![A2 : complex, K : complex, A : complex, B : complex]: ((A2 = (plus_plus_complex @ K @ A)) => ((minus_minus_complex @ A2 @ B) = (plus_plus_complex @ K @ (minus_minus_complex @ A @ B))))))). % group_cancel.sub1
thf(fact_199_group__cancel_Osub1, axiom,
    ((![A2 : real, K : real, A : real, B : real]: ((A2 = (plus_plus_real @ K @ A)) => ((minus_minus_real @ A2 @ B) = (plus_plus_real @ K @ (minus_minus_real @ A @ B))))))). % group_cancel.sub1
thf(fact_200_group__cancel_Osub1, axiom,
    ((![A2 : poly_real, K : poly_real, A : poly_real, B : poly_real]: ((A2 = (plus_plus_poly_real @ K @ A)) => ((minus_240770701y_real @ A2 @ B) = (plus_plus_poly_real @ K @ (minus_240770701y_real @ A @ B))))))). % group_cancel.sub1
thf(fact_201_group__cancel_Osub1, axiom,
    ((![A2 : poly_complex, K : poly_complex, A : poly_complex, B : poly_complex]: ((A2 = (plus_p1547158847omplex @ K @ A)) => ((minus_174331535omplex @ A2 @ B) = (plus_p1547158847omplex @ K @ (minus_174331535omplex @ A @ B))))))). % group_cancel.sub1
thf(fact_202_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_203_le__add__diff__inverse2, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ B @ A) => ((plus_plus_poly_real @ (minus_240770701y_real @ A @ B) @ B) = A))))). % le_add_diff_inverse2
thf(fact_204_le__add__diff__inverse2, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))))). % le_add_diff_inverse2
thf(fact_205_le__add__diff__inverse, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ B @ A) => ((plus_plus_poly_real @ B @ (minus_240770701y_real @ A @ B)) = A))))). % le_add_diff_inverse
thf(fact_206_le__add__diff__inverse, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A))))). % le_add_diff_inverse
thf(fact_207_less_Ohyps, axiom,
    ((![P : poly_complex]: ((ord_less_nat @ (fundam1709708056omplex @ P) @ (fundam1709708056omplex @ pa)) => ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z3 : complex]: ((poly_complex2 @ P @ Z3) = zero_zero_complex))))))). % less.hyps
thf(fact_208_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_209_norm__eq__zero, axiom,
    ((![X2 : complex]: (((real_V638595069omplex @ X2) = zero_zero_real) = (X2 = zero_zero_complex))))). % norm_eq_zero
thf(fact_210_norm__diff__triangle__ineq, axiom,
    ((![A : real, B : real, C : real, D : real]: (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (real_V646646907m_real @ (minus_minus_real @ A @ C)) @ (real_V646646907m_real @ (minus_minus_real @ B @ D))))))). % norm_diff_triangle_ineq
thf(fact_211_norm__diff__triangle__ineq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ D))) @ (plus_plus_real @ (real_V638595069omplex @ (minus_minus_complex @ A @ C)) @ (real_V638595069omplex @ (minus_minus_complex @ B @ D))))))). % norm_diff_triangle_ineq
thf(fact_212_complex__mod__triangle__ineq2, axiom,
    ((![B : complex, A : complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V638595069omplex @ (plus_plus_complex @ B @ A)) @ (real_V638595069omplex @ B)) @ (real_V638595069omplex @ A))))). % complex_mod_triangle_ineq2
thf(fact_213_norm__triangle__sub, axiom,
    ((![X2 : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ X2) @ (plus_plus_real @ (real_V646646907m_real @ Y) @ (real_V646646907m_real @ (minus_minus_real @ X2 @ Y))))))). % norm_triangle_sub
thf(fact_214_norm__triangle__sub, axiom,
    ((![X2 : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ X2) @ (plus_plus_real @ (real_V638595069omplex @ Y) @ (real_V638595069omplex @ (minus_minus_complex @ X2 @ Y))))))). % norm_triangle_sub
thf(fact_215_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_216_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_217_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_218_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_219_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_220_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_221_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_222_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_223_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_224_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_225_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_226_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_227_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_228_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_229_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_230_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_231_diff__gt__0__iff__gt, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_232_diff__gt__0__iff__gt, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (minus_240770701y_real @ A @ B)) = (ord_less_poly_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_233_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_234_gr__implies__not__zero, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_235_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_236_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_237_add__less__imp__less__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_imp_less_right
thf(fact_238_add__less__imp__less__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_imp_less_right
thf(fact_239_add__less__imp__less__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_imp_less_left
thf(fact_240_add__less__imp__less__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_imp_less_left
thf(fact_241_add__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_strict_right_mono
thf(fact_242_add__strict__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)))))). % add_strict_right_mono
thf(fact_243_add__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_strict_left_mono
thf(fact_244_add__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)))))). % add_strict_left_mono

% Conjectures (1)
thf(conj_0, conjecture,
    ((![X4 : complex]: ((poly_complex2 @ q @ (minus_minus_complex @ X4 @ c)) = (poly_complex2 @ pa @ X4))))).
