% 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_671__5374556_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:32:02.329

% Could-be-implicit typings (6)
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__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (36)
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_Oconstant_001t__Real__Oreal_001t__Real__Oreal, type,
    fundam988576550l_real : (real > real) > $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__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
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__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_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex, type,
    numera632737353omplex : num > complex).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > 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__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_v_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 (233)
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_that, axiom,
    ((fundam1158420650omplex @ (poly_complex2 @ q)))). % that
thf(fact_3_q_I1_J, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ pa)))). % q(1)
thf(fact_4_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X : complex]: (![Y : complex]: ((F @ X) = (F @ Y)))))))). % constant_def
thf(fact_5__092_060open_062_092_060And_062y_Ax_O_Apoly_Ap_Ax_A_061_Apoly_Ap_Ay_092_060close_062, axiom,
    ((![X2 : complex, Y2 : complex]: ((poly_complex2 @ pa @ X2) = (poly_complex2 @ pa @ Y2))))). % \<open>\<And>y x. poly p x = poly p y\<close>
thf(fact_6_q_I2_J, axiom,
    ((![X3 : complex]: ((poly_complex2 @ q @ X3) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X3)))))). % q(2)
thf(fact_7_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_8_th, axiom,
    ((![X3 : complex]: ((poly_complex2 @ q @ (minus_minus_complex @ X3 @ c)) = (poly_complex2 @ pa @ X3))))). % th
thf(fact_9_less_Ohyps, axiom,
    ((![P : poly_complex]: ((ord_less_nat @ (fundam1709708056omplex @ P) @ (fundam1709708056omplex @ pa)) => ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex))))))). % less.hyps
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,
    ((?[Q : poly_complex]: (((fundam1709708056omplex @ Q) = (fundam1709708056omplex @ pa)) & (![X3 : complex]: ((poly_complex2 @ Q @ X3) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X3)))))))). % \<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,
    ((~ ((![Q : poly_complex]: (((fundam1709708056omplex @ Q) = (fundam1709708056omplex @ pa)) => (~ ((![X3 : complex]: ((poly_complex2 @ Q @ X3) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X3)))))))))))). % \<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_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q2 : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q2)) = (P = Q2))))). % poly_eq_poly_eq_iff
thf(fact_13_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_real, Q2 : poly_real]: (((poly_real2 @ P) = (poly_real2 @ Q2)) = (P = Q2))))). % poly_eq_poly_eq_iff
thf(fact_14_poly__offset, axiom,
    ((![P : poly_real, A : real]: (?[Q : poly_real]: (((fundam1947011094e_real @ Q) = (fundam1947011094e_real @ P)) & (![X3 : real]: ((poly_real2 @ Q @ X3) = (poly_real2 @ P @ (plus_plus_real @ A @ X3))))))))). % poly_offset
thf(fact_15_poly__offset, axiom,
    ((![P : poly_complex, A : complex]: (?[Q : poly_complex]: (((fundam1709708056omplex @ Q) = (fundam1709708056omplex @ P)) & (![X3 : complex]: ((poly_complex2 @ Q @ X3) = (poly_complex2 @ P @ (plus_plus_complex @ A @ X3))))))))). % poly_offset
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_c, axiom,
    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ c)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % c
thf(fact_18_n2, axiom,
    ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (fundam1709708056omplex @ pa)))). % n2
thf(fact_19_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_20_poly__0, axiom,
    ((![X2 : real]: ((poly_real2 @ zero_zero_poly_real @ X2) = zero_zero_real)))). % poly_0
thf(fact_21_poly__add, axiom,
    ((![P : poly_complex, Q2 : poly_complex, X2 : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P @ Q2) @ X2) = (plus_plus_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q2 @ X2)))))). % poly_add
thf(fact_22_poly__add, axiom,
    ((![P : poly_real, Q2 : poly_real, X2 : real]: ((poly_real2 @ (plus_plus_poly_real @ P @ Q2) @ X2) = (plus_plus_real @ (poly_real2 @ P @ X2) @ (poly_real2 @ Q2 @ X2)))))). % poly_add
thf(fact_23_poly__diff, axiom,
    ((![P : poly_real, Q2 : poly_real, X2 : real]: ((poly_real2 @ (minus_240770701y_real @ P @ Q2) @ X2) = (minus_minus_real @ (poly_real2 @ P @ X2) @ (poly_real2 @ Q2 @ X2)))))). % poly_diff
thf(fact_24_poly__diff, axiom,
    ((![P : poly_complex, Q2 : poly_complex, X2 : complex]: ((poly_complex2 @ (minus_174331535omplex @ P @ Q2) @ X2) = (minus_minus_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q2 @ X2)))))). % poly_diff
thf(fact_25_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X : complex]: ((poly_complex2 @ P @ X) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_26_poly__all__0__iff__0, axiom,
    ((![P : poly_real]: ((![X : real]: ((poly_real2 @ P @ X) = zero_zero_real)) = (P = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_27_complex__mod__triangle__sub, axiom,
    ((![W2 : complex, Z2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W2) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W2 @ Z2)) @ (real_V638595069omplex @ Z2)))))). % complex_mod_triangle_sub
thf(fact_28_poly__minimum__modulus__disc, axiom,
    ((![R : real, P : poly_complex]: (?[Z : complex]: (![W : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ W) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W))))))))). % poly_minimum_modulus_disc
thf(fact_29_poly__minimum__modulus, axiom,
    ((![P : poly_complex]: (?[Z : complex]: (![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W)))))))). % poly_minimum_modulus
thf(fact_30_nonconstant__length, axiom,
    ((![P : poly_real]: ((~ ((fundam988576550l_real @ (poly_real2 @ P)))) => (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (fundam1947011094e_real @ P)))))). % nonconstant_length
thf(fact_31_nonconstant__length, axiom,
    ((![P : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (fundam1709708056omplex @ P)))))). % nonconstant_length
thf(fact_32_norm__le__zero__iff, axiom,
    ((![X2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X2) @ zero_zero_real) = (X2 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_33_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_34_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_35_le__add__diff__inverse2, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((plus_plus_nat @ (minus_minus_nat @ A @ B) @ B) = A))))). % le_add_diff_inverse2
thf(fact_36_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_37_le__add__diff__inverse, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A))))). % le_add_diff_inverse
thf(fact_38_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_39_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_40_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_41_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_42_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_43_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_44_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_45_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_46_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_47_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_48_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_49_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_50_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_51_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_52_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_53_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_54_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_55_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_56_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_57_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_58_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_59_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_60_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_61_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_62_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_63_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_64_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_65_add__le__cancel__left, axiom,
    ((![C2 : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_left
thf(fact_66_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_67_add__le__cancel__right, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_68_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_69_diff__self, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % diff_self
thf(fact_70_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_71_diff__0__right, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_0_right
thf(fact_72_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_73_diff__zero, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_zero
thf(fact_74_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_75_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_76_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_77_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_78_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_79_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_80_add__diff__cancel, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_81_add__diff__cancel, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_82_diff__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_83_diff__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_84_add__diff__cancel__left, axiom,
    ((![C2 : real, A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_left
thf(fact_85_add__diff__cancel__left, axiom,
    ((![C2 : complex, A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ C2 @ A) @ (plus_plus_complex @ C2 @ B)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_left
thf(fact_86_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_87_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_88_add__diff__cancel__right, axiom,
    ((![A : real, C2 : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_right
thf(fact_89_add__diff__cancel__right, axiom,
    ((![A : complex, C2 : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ C2) @ (plus_plus_complex @ B @ C2)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_right
thf(fact_90_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_91_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_92_norm__numeral, axiom,
    ((![W2 : num]: ((real_V638595069omplex @ (numera632737353omplex @ W2)) = (numeral_numeral_real @ W2))))). % norm_numeral
thf(fact_93_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_94_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_95_add__le__same__cancel1, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat))))). % add_le_same_cancel1
thf(fact_96_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_97_add__le__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat))))). % add_le_same_cancel2
thf(fact_98_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_99_le__add__same__cancel1, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_eq_nat @ zero_zero_nat @ B))))). % le_add_same_cancel1
thf(fact_100_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_101_le__add__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_eq_nat @ zero_zero_nat @ B))))). % le_add_same_cancel2
thf(fact_102_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_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_zero__less__norm__iff, axiom,
    ((![X2 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X2)) = (~ ((X2 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_111_zero__less__norm__iff, axiom,
    ((![X2 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X2)) = (~ ((X2 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_112_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_113_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_114_norm__eq__zero, axiom,
    ((![X2 : real]: (((real_V646646907m_real @ X2) = zero_zero_real) = (X2 = zero_zero_real))))). % norm_eq_zero
thf(fact_115_norm__eq__zero, axiom,
    ((![X2 : complex]: (((real_V638595069omplex @ X2) = zero_zero_real) = (X2 = zero_zero_complex))))). % norm_eq_zero
thf(fact_116_poly__IVT__neg, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ A)) => ((ord_less_real @ (poly_real2 @ P @ B) @ zero_zero_real) => (?[X4 : real]: ((ord_less_real @ A @ X4) & ((ord_less_real @ X4 @ B) & ((poly_real2 @ P @ X4) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_117_poly__IVT__pos, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ B)) => (?[X4 : real]: ((ord_less_real @ A @ X4) & ((ord_less_real @ X4 @ B) & ((poly_real2 @ P @ X4) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_118_norm__not__less__zero, axiom,
    ((![X2 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X2) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_119_norm__add__less, axiom,
    ((![X2 : real, R : real, Y2 : real, S : real]: ((ord_less_real @ (real_V646646907m_real @ X2) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X2 @ Y2)) @ (plus_plus_real @ R @ S))))))). % norm_add_less
thf(fact_120_norm__add__less, axiom,
    ((![X2 : complex, R : real, Y2 : complex, S : real]: ((ord_less_real @ (real_V638595069omplex @ X2) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y2) @ S) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X2 @ Y2)) @ (plus_plus_real @ R @ S))))))). % norm_add_less
thf(fact_121_norm__triangle__lt, axiom,
    ((![X2 : real, Y2 : real, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V646646907m_real @ X2) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X2 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_122_norm__triangle__lt, axiom,
    ((![X2 : complex, Y2 : complex, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V638595069omplex @ X2) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X2 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_123_norm__diff__triangle__less, axiom,
    ((![X2 : complex, Y2 : complex, E1 : real, Z2 : complex, E2 : real]: ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X2 @ Y2)) @ E1) => ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Y2 @ Z2)) @ E2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X2 @ Z2)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_124_norm__ge__zero, axiom,
    ((![X2 : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X2))))). % norm_ge_zero
thf(fact_125_poly__cont, axiom,
    ((![E : real, Z2 : real, P : poly_real]: ((ord_less_real @ zero_zero_real @ E) => (?[D : real]: ((ord_less_real @ zero_zero_real @ D) & (![W : real]: (((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ (minus_minus_real @ W @ Z2))) & (ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ W @ Z2)) @ D)) => (ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ (poly_real2 @ P @ W) @ (poly_real2 @ P @ Z2))) @ E))))))))). % poly_cont
thf(fact_126_poly__cont, axiom,
    ((![E : real, Z2 : complex, P : poly_complex]: ((ord_less_real @ zero_zero_real @ E) => (?[D : real]: ((ord_less_real @ zero_zero_real @ D) & (![W : complex]: (((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ (minus_minus_complex @ W @ Z2))) & (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W @ Z2)) @ D)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ P @ W) @ (poly_complex2 @ P @ Z2))) @ E))))))))). % poly_cont
thf(fact_127_poly__bound__exists, axiom,
    ((![R : real, P : poly_real]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z3) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P @ Z3)) @ M)))))))). % poly_bound_exists
thf(fact_128_poly__bound__exists, axiom,
    ((![R : real, P : poly_complex]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z3)) @ M)))))))). % poly_bound_exists
thf(fact_129_norm__diff__ineq, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)) @ (real_V646646907m_real @ (plus_plus_real @ A @ B)))))). % norm_diff_ineq
thf(fact_130_norm__diff__ineq, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)) @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)))))). % norm_diff_ineq
thf(fact_131_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_132_zero__reorient, axiom,
    ((![X2 : real]: ((zero_zero_real = X2) = (X2 = zero_zero_real))))). % zero_reorient
thf(fact_133_linorder__neqE__linordered__idom, axiom,
    ((![X2 : real, Y2 : real]: ((~ ((X2 = Y2))) => ((~ ((ord_less_real @ X2 @ Y2))) => (ord_less_real @ Y2 @ X2)))))). % linorder_neqE_linordered_idom
thf(fact_134_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_135_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_136_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_137_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_138_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_139_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_140_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_141_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_142_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_143_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_144_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_145_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_146_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_147_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A3 : complex]: (^[B3 : complex]: (plus_plus_complex @ B3 @ A3)))))). % add.commute
thf(fact_148_add_Ocommute, axiom,
    ((plus_plus_real = (^[A3 : real]: (^[B3 : real]: (plus_plus_real @ B3 @ A3)))))). % add.commute
thf(fact_149_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_150_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_151_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_152_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_153_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_154_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_155_diff__eq__diff__eq, axiom,
    ((![A : complex, B : complex, C2 : complex, D2 : complex]: (((minus_minus_complex @ A @ B) = (minus_minus_complex @ C2 @ D2)) => ((A = B) = (C2 = D2)))))). % diff_eq_diff_eq
thf(fact_156_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : complex, C2 : complex, B : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ C2) @ B) = (minus_minus_complex @ (minus_minus_complex @ A @ B) @ C2))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_157_zero__le, axiom,
    ((![X2 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X2)))). % zero_le
thf(fact_158_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_159_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_160_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_161_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_162_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_163_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_164_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_165_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_166_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_167_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_168_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_169_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (K = L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_170_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_171_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_172_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_173_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_174_add__mono, axiom,
    ((![A : real, B : real, C2 : real, D2 : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C2 @ D2) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ D2))))))). % add_mono
thf(fact_175_add__mono, axiom,
    ((![A : nat, B : nat, C2 : nat, D2 : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C2 @ D2) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ D2))))))). % add_mono
thf(fact_176_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_177_add__left__mono, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)))))). % add_left_mono
thf(fact_178_less__eqE, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => (~ ((![C : nat]: (~ ((B = (plus_plus_nat @ A @ C))))))))))). % less_eqE
thf(fact_179_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_180_add__right__mono, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)))))). % add_right_mono
thf(fact_181_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A3 : nat]: (^[B3 : nat]: (?[C3 : nat]: (B3 = (plus_plus_nat @ A3 @ C3)))))))). % le_iff_add
thf(fact_182_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_183_add__le__imp__le__left, axiom,
    ((![C2 : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_left
thf(fact_184_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_185_add__le__imp__le__right, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_right
thf(fact_186_eq__iff__diff__eq__0, axiom,
    (((^[Y3 : real]: (^[Z4 : real]: (Y3 = Z4))) = (^[A3 : real]: (^[B3 : real]: ((minus_minus_real @ A3 @ B3) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_187_eq__iff__diff__eq__0, axiom,
    (((^[Y3 : complex]: (^[Z4 : complex]: (Y3 = Z4))) = (^[A3 : complex]: (^[B3 : complex]: ((minus_minus_complex @ A3 @ B3) = zero_zero_complex)))))). % eq_iff_diff_eq_0
thf(fact_188_add__mono__thms__linordered__field_I5_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_nat @ I @ J) & (ord_less_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(5)
thf(fact_189_add__mono__thms__linordered__field_I5_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(5)
thf(fact_190_add__mono__thms__linordered__field_I2_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (ord_less_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(2)
thf(fact_191_add__mono__thms__linordered__field_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(2)
thf(fact_192_add__mono__thms__linordered__field_I1_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_nat @ I @ J) & (K = L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(1)
thf(fact_193_add__mono__thms__linordered__field_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (K = L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(1)
thf(fact_194_add__strict__mono, axiom,
    ((![A : nat, B : nat, C2 : nat, D2 : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C2 @ D2) => (ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ D2))))))). % add_strict_mono
thf(fact_195_add__strict__mono, axiom,
    ((![A : real, B : real, C2 : real, D2 : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C2 @ D2) => (ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ D2))))))). % add_strict_mono
thf(fact_196_add__strict__left__mono, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)))))). % add_strict_left_mono
thf(fact_197_add__strict__left__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)))))). % add_strict_left_mono
thf(fact_198_add__strict__right__mono, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)))))). % add_strict_right_mono
thf(fact_199_add__strict__right__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)))))). % add_strict_right_mono
thf(fact_200_add__less__imp__less__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_imp_less_left
thf(fact_201_add__less__imp__less__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_imp_less_left
thf(fact_202_add__less__imp__less__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_imp_less_right
thf(fact_203_add__less__imp__less__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_imp_less_right
thf(fact_204_diff__mono, axiom,
    ((![A : real, B : real, D2 : real, C2 : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ D2 @ C2) => (ord_less_eq_real @ (minus_minus_real @ A @ C2) @ (minus_minus_real @ B @ D2))))))). % diff_mono
thf(fact_205_diff__left__mono, axiom,
    ((![B : real, A : real, C2 : real]: ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ (minus_minus_real @ C2 @ A) @ (minus_minus_real @ C2 @ B)))))). % diff_left_mono
thf(fact_206_diff__right__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C2) @ (minus_minus_real @ B @ C2)))))). % diff_right_mono
thf(fact_207_diff__eq__diff__less__eq, axiom,
    ((![A : real, B : real, C2 : real, D2 : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C2 @ D2)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C2 @ D2)))))). % diff_eq_diff_less_eq
thf(fact_208_diff__strict__mono, axiom,
    ((![A : real, B : real, D2 : real, C2 : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ D2 @ C2) => (ord_less_real @ (minus_minus_real @ A @ C2) @ (minus_minus_real @ B @ D2))))))). % diff_strict_mono
thf(fact_209_diff__eq__diff__less, axiom,
    ((![A : real, B : real, C2 : real, D2 : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C2 @ D2)) => ((ord_less_real @ A @ B) = (ord_less_real @ C2 @ D2)))))). % diff_eq_diff_less
thf(fact_210_diff__strict__left__mono, axiom,
    ((![B : real, A : real, C2 : real]: ((ord_less_real @ B @ A) => (ord_less_real @ (minus_minus_real @ C2 @ A) @ (minus_minus_real @ C2 @ B)))))). % diff_strict_left_mono
thf(fact_211_diff__strict__right__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ A @ C2) @ (minus_minus_real @ B @ C2)))))). % diff_strict_right_mono
thf(fact_212_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_213_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_214_diff__eq__eq, axiom,
    ((![A : real, B : real, C2 : real]: (((minus_minus_real @ A @ B) = C2) = (A = (plus_plus_real @ C2 @ B)))))). % diff_eq_eq
thf(fact_215_diff__eq__eq, axiom,
    ((![A : complex, B : complex, C2 : complex]: (((minus_minus_complex @ A @ B) = C2) = (A = (plus_plus_complex @ C2 @ B)))))). % diff_eq_eq
thf(fact_216_eq__diff__eq, axiom,
    ((![A : real, C2 : real, B : real]: ((A = (minus_minus_real @ C2 @ B)) = ((plus_plus_real @ A @ B) = C2))))). % eq_diff_eq
thf(fact_217_eq__diff__eq, axiom,
    ((![A : complex, C2 : complex, B : complex]: ((A = (minus_minus_complex @ C2 @ B)) = ((plus_plus_complex @ A @ B) = C2))))). % eq_diff_eq
thf(fact_218_add__diff__eq, axiom,
    ((![A : real, B : real, C2 : real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C2)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C2))))). % add_diff_eq
thf(fact_219_add__diff__eq, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((plus_plus_complex @ A @ (minus_minus_complex @ B @ C2)) = (minus_minus_complex @ (plus_plus_complex @ A @ B) @ C2))))). % add_diff_eq
thf(fact_220_diff__diff__eq2, axiom,
    ((![A : real, B : real, C2 : real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C2)) = (minus_minus_real @ (plus_plus_real @ A @ C2) @ B))))). % diff_diff_eq2
thf(fact_221_diff__diff__eq2, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((minus_minus_complex @ A @ (minus_minus_complex @ B @ C2)) = (minus_minus_complex @ (plus_plus_complex @ A @ C2) @ B))))). % diff_diff_eq2
thf(fact_222_diff__add__eq, axiom,
    ((![A : real, B : real, C2 : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C2) = (minus_minus_real @ (plus_plus_real @ A @ C2) @ B))))). % diff_add_eq
thf(fact_223_diff__add__eq, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ C2) = (minus_minus_complex @ (plus_plus_complex @ A @ C2) @ B))))). % diff_add_eq
thf(fact_224_diff__add__eq__diff__diff__swap, axiom,
    ((![A : real, B : real, C2 : real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C2)) = (minus_minus_real @ (minus_minus_real @ A @ C2) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_225_diff__add__eq__diff__diff__swap, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((minus_minus_complex @ A @ (plus_plus_complex @ B @ C2)) = (minus_minus_complex @ (minus_minus_complex @ A @ C2) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_226_diff__diff__add, axiom,
    ((![A : real, B : real, C2 : real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C2) = (minus_minus_real @ A @ (plus_plus_real @ B @ C2)))))). % diff_diff_add
thf(fact_227_diff__diff__add, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ B) @ C2) = (minus_minus_complex @ A @ (plus_plus_complex @ B @ C2)))))). % diff_diff_add
thf(fact_228_add__implies__diff, axiom,
    ((![C2 : real, B : real, A : real]: (((plus_plus_real @ C2 @ B) = A) => (C2 = (minus_minus_real @ A @ B)))))). % add_implies_diff
thf(fact_229_add__implies__diff, axiom,
    ((![C2 : complex, B : complex, A : complex]: (((plus_plus_complex @ C2 @ B) = A) => (C2 = (minus_minus_complex @ A @ B)))))). % add_implies_diff
thf(fact_230_norm__minus__commute, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (minus_minus_complex @ A @ B)) = (real_V638595069omplex @ (minus_minus_complex @ B @ A)))))). % norm_minus_commute
thf(fact_231_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_232_add__decreasing, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ C2 @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ B)))))). % add_decreasing

% Conjectures (1)
thf(conj_0, conjecture,
    ($false)).
