% 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_711__5374834_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:32:25.018

% Could-be-implicit typings (5)
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $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 (31)
thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex, type,
    invers502456322omplex : complex > complex).
thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal, type,
    inverse_inverse_real : real > real).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    times_1246143675omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Osmult_001t__Complex__Ocomplex, type,
    smult_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Osmult_001t__Nat__Onat, type,
    smult_nat : nat > poly_nat > poly_nat).
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_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat, type,
    divide_divide_nat : nat > nat > nat).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_v_c____, type,
    c : complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_pa____, type,
    pa : poly_complex).
thf(sy_v_q____, type,
    q : poly_complex).
thf(sy_v_w____, type,
    w : complex).

% Relevant facts (176)
thf(fact_0_a00, axiom,
    ((~ (((poly_complex2 @ q @ zero_zero_complex) = zero_zero_complex))))). % a00
thf(fact_1_nc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ p)))))). % nc
thf(fact_2__092_060open_062poly_Aq_Aw_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_A_K_Apoly_Aq_A0_092_060close_062, axiom,
    (((poly_complex2 @ q @ w) = (times_times_complex @ (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ w) @ (poly_complex2 @ q @ zero_zero_complex))))). % \<open>poly q w = poly (smult (inverse (poly q 0)) q) w * poly q 0\<close>
thf(fact_3__092_060open_062_I_092_060And_062x_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((~ ((![X : complex, Y : complex]: ((poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ X) = (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ Y))))))). % \<open>(\<And>x y. poly (smult (inverse (poly q 0)) q) x = poly (smult (inverse (poly q 0)) q) y) \<Longrightarrow> False\<close>
thf(fact_4__092_060open_062poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_092_060close_062, axiom,
    (((poly_complex2 @ q @ zero_zero_complex) = (times_times_complex @ (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ zero_zero_complex) @ (poly_complex2 @ q @ zero_zero_complex))))). % \<open>poly q 0 = poly (smult (inverse (poly q 0)) q) 0 * poly q 0\<close>
thf(fact_5_qr, axiom,
    ((![Z : complex]: ((poly_complex2 @ q @ Z) = (times_times_complex @ (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ Z) @ (poly_complex2 @ q @ zero_zero_complex)))))). % qr
thf(fact_6__092_060open_062constant_A_Ipoly_Aq_J_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ q)))))). % \<open>constant (poly q) \<Longrightarrow> False\<close>
thf(fact_7_qnc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ q)))))). % qnc
thf(fact_8_rnc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q))))))). % rnc
thf(fact_9_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y2 : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y2 @ X2)))) = (ord_less_real @ Y2 @ S))))))))). % real_sup_exists
thf(fact_10_lgqr, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q))))). % lgqr
thf(fact_11_divide__less__0__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % divide_less_0_1_iff
thf(fact_12_divide__less__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B)))))). % divide_less_eq_1_neg
thf(fact_13_divide__less__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)))))). % divide_less_eq_1_pos
thf(fact_14_less__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)))))). % less_divide_eq_1_neg
thf(fact_15_less__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)))))). % less_divide_eq_1_pos
thf(fact_16_zero__less__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_divide_1_iff
thf(fact_17_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_18_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_19_zero__less__norm__iff, axiom,
    ((![X3 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X3)) = (~ ((X3 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_20_inverse__less__iff__less, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_real @ B @ A))))))). % inverse_less_iff_less
thf(fact_21_inverse__less__iff__less__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_real @ B @ A))))))). % inverse_less_iff_less_neg
thf(fact_22_inverse__negative__iff__negative, axiom,
    ((![A : real]: ((ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % inverse_negative_iff_negative
thf(fact_23_inverse__inverse__eq, axiom,
    ((![A : complex]: ((invers502456322omplex @ (invers502456322omplex @ A)) = A)))). % inverse_inverse_eq
thf(fact_24_inverse__eq__iff__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) = (A = B))))). % inverse_eq_iff_eq
thf(fact_25_psize__eq__0__iff, axiom,
    ((![P2 : poly_complex]: (((fundam1709708056omplex @ P2) = zero_zero_nat) = (P2 = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_26_r01, axiom,
    (((poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ zero_zero_complex) = one_one_complex))). % r01
thf(fact_27_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_28_divide__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_right
thf(fact_29_divide__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((divide1210191872omplex @ C @ A) = (divide1210191872omplex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_left
thf(fact_30_divide__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % divide_eq_0_iff
thf(fact_31_times__divide__eq__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ A @ (divide1210191872omplex @ B @ C)) = (divide1210191872omplex @ (times_times_complex @ A @ B) @ C))))). % times_divide_eq_right
thf(fact_32_divide__divide__eq__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ A @ (divide1210191872omplex @ B @ C)) = (divide1210191872omplex @ (times_times_complex @ A @ C) @ B))))). % divide_divide_eq_right
thf(fact_33_divide__divide__eq__left, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ A @ B) @ C) = (divide1210191872omplex @ A @ (times_times_complex @ B @ C)))))). % divide_divide_eq_left
thf(fact_34_times__divide__eq__left, axiom,
    ((![B : complex, C : complex, A : complex]: ((times_times_complex @ (divide1210191872omplex @ B @ C) @ A) = (divide1210191872omplex @ (times_times_complex @ B @ A) @ C))))). % times_divide_eq_left
thf(fact_35_inverse__nonzero__iff__nonzero, axiom,
    ((![A : complex]: (((invers502456322omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % inverse_nonzero_iff_nonzero
thf(fact_36_inverse__zero, axiom,
    (((invers502456322omplex @ zero_zero_complex) = zero_zero_complex))). % inverse_zero
thf(fact_37_inverse__mult__distrib, axiom,
    ((![A : complex, B : complex]: ((invers502456322omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers502456322omplex @ A) @ (invers502456322omplex @ B)))))). % inverse_mult_distrib
thf(fact_38_inverse__1, axiom,
    (((inverse_inverse_real @ one_one_real) = one_one_real))). % inverse_1
thf(fact_39_inverse__1, axiom,
    (((invers502456322omplex @ one_one_complex) = one_one_complex))). % inverse_1
thf(fact_40_inverse__eq__1__iff, axiom,
    ((![X3 : real]: (((inverse_inverse_real @ X3) = one_one_real) = (X3 = one_one_real))))). % inverse_eq_1_iff
thf(fact_41_inverse__eq__1__iff, axiom,
    ((![X3 : complex]: (((invers502456322omplex @ X3) = one_one_complex) = (X3 = one_one_complex))))). % inverse_eq_1_iff
thf(fact_42_inverse__divide, axiom,
    ((![A : complex, B : complex]: ((invers502456322omplex @ (divide1210191872omplex @ A @ B)) = (divide1210191872omplex @ B @ A))))). % inverse_divide
thf(fact_43_less_Oprems, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ pa)))))). % less.prems
thf(fact_44_q_I1_J, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ pa)))). % q(1)
thf(fact_45_nonzero__mult__divide__mult__cancel__right2, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right2
thf(fact_46_nonzero__mult__divide__mult__cancel__right, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right
thf(fact_47_nonzero__mult__divide__mult__cancel__left2, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ B @ C)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left2
thf(fact_48_nonzero__mult__divide__mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left
thf(fact_49_mult__divide__mult__cancel__left__if, axiom,
    ((![C : complex, A : complex, B : complex]: (((C = zero_zero_complex) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = zero_zero_complex)) & ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B))))))). % mult_divide_mult_cancel_left_if
thf(fact_50_zero__eq__1__divide__iff, axiom,
    ((![A : real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real))))). % zero_eq_1_divide_iff
thf(fact_51_one__divide__eq__0__iff, axiom,
    ((![A : real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % one_divide_eq_0_iff
thf(fact_52_eq__divide__eq__1, axiom,
    ((![B : real, A : real]: ((one_one_real = (divide_divide_real @ B @ A)) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % eq_divide_eq_1
thf(fact_53_divide__eq__eq__1, axiom,
    ((![B : real, A : real]: (((divide_divide_real @ B @ A) = one_one_real) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % divide_eq_eq_1
thf(fact_54_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_55_divide__self__if, axiom,
    ((![A : complex]: (((A = zero_zero_complex) => ((divide1210191872omplex @ A @ A) = zero_zero_complex)) & ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex)))))). % divide_self_if
thf(fact_56_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_57_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_58_one__eq__divide__iff, axiom,
    ((![A : real, B : real]: ((one_one_real = (divide_divide_real @ A @ B)) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_59_one__eq__divide__iff, axiom,
    ((![A : complex, B : complex]: ((one_one_complex = (divide1210191872omplex @ A @ B)) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_60_divide__eq__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = one_one_real) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_61_divide__eq__1__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = one_one_complex) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_62_inverse__positive__iff__positive, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % inverse_positive_iff_positive
thf(fact_63_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_64_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_65_nonzero__divide__mult__cancel__right, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((divide_divide_real @ B @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ A)))))). % nonzero_divide_mult_cancel_right
thf(fact_66_nonzero__divide__mult__cancel__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ B @ (times_times_complex @ A @ B)) = (divide1210191872omplex @ one_one_complex @ A)))))). % nonzero_divide_mult_cancel_right
thf(fact_67_nonzero__divide__mult__cancel__left, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ B)))))). % nonzero_divide_mult_cancel_left
thf(fact_68_nonzero__divide__mult__cancel__left, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ (times_times_complex @ A @ B)) = (divide1210191872omplex @ one_one_complex @ B)))))). % nonzero_divide_mult_cancel_left
thf(fact_69_right__inverse, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((times_times_real @ A @ (inverse_inverse_real @ A)) = one_one_real))))). % right_inverse
thf(fact_70_right__inverse, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((times_times_complex @ A @ (invers502456322omplex @ A)) = one_one_complex))))). % right_inverse
thf(fact_71_left__inverse, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((times_times_real @ (inverse_inverse_real @ A) @ A) = one_one_real))))). % left_inverse
thf(fact_72_left__inverse, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((times_times_complex @ (invers502456322omplex @ A) @ A) = one_one_complex))))). % left_inverse
thf(fact_73_norm__mult, axiom,
    ((![X3 : complex, Y3 : complex]: ((real_V638595069omplex @ (times_times_complex @ X3 @ Y3)) = (times_times_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y3)))))). % norm_mult
thf(fact_74_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X2 : complex]: (![Y4 : complex]: ((F @ X2) = (F @ Y4)))))))). % constant_def
thf(fact_75_norm__mult__less, axiom,
    ((![X3 : complex, R : real, Y3 : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X3) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y3) @ S2) => (ord_less_real @ (real_V638595069omplex @ (times_times_complex @ X3 @ Y3)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_76_norm__not__less__zero, axiom,
    ((![X3 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_77_divide__divide__eq__left_H, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ A @ B) @ C) = (divide1210191872omplex @ A @ (times_times_complex @ C @ B)))))). % divide_divide_eq_left'
thf(fact_78_divide__divide__times__eq, axiom,
    ((![X3 : complex, Y3 : complex, Z2 : complex, W : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ X3 @ Y3) @ (divide1210191872omplex @ Z2 @ W)) = (divide1210191872omplex @ (times_times_complex @ X3 @ W) @ (times_times_complex @ Y3 @ Z2)))))). % divide_divide_times_eq
thf(fact_79_times__divide__times__eq, axiom,
    ((![X3 : complex, Y3 : complex, Z2 : complex, W : complex]: ((times_times_complex @ (divide1210191872omplex @ X3 @ Y3) @ (divide1210191872omplex @ Z2 @ W)) = (divide1210191872omplex @ (times_times_complex @ X3 @ Z2) @ (times_times_complex @ Y3 @ W)))))). % times_divide_times_eq
thf(fact_80_mult__commute__imp__mult__inverse__commute, axiom,
    ((![Y3 : complex, X3 : complex]: (((times_times_complex @ Y3 @ X3) = (times_times_complex @ X3 @ Y3)) => ((times_times_complex @ (invers502456322omplex @ Y3) @ X3) = (times_times_complex @ X3 @ (invers502456322omplex @ Y3))))))). % mult_commute_imp_mult_inverse_commute
thf(fact_81_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % linordered_field_no_ub
thf(fact_82_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y : real]: (ord_less_real @ Y @ X4))))). % linordered_field_no_lb
thf(fact_83_nonzero__eq__divide__eq, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((A = (divide1210191872omplex @ B @ C)) = ((times_times_complex @ A @ C) = B)))))). % nonzero_eq_divide_eq
thf(fact_84_nonzero__divide__eq__eq, axiom,
    ((![C : complex, B : complex, A : complex]: ((~ ((C = zero_zero_complex))) => (((divide1210191872omplex @ B @ C) = A) = (B = (times_times_complex @ A @ C))))))). % nonzero_divide_eq_eq
thf(fact_85_eq__divide__imp, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A @ C) = B) => (A = (divide1210191872omplex @ B @ C))))))). % eq_divide_imp
thf(fact_86_divide__eq__imp, axiom,
    ((![C : complex, B : complex, A : complex]: ((~ ((C = zero_zero_complex))) => ((B = (times_times_complex @ A @ C)) => ((divide1210191872omplex @ B @ C) = A)))))). % divide_eq_imp
thf(fact_87_eq__divide__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((A = (divide1210191872omplex @ B @ C)) = (((((~ ((C = zero_zero_complex)))) => (((times_times_complex @ A @ C) = B)))) & ((((C = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % eq_divide_eq
thf(fact_88_divide__eq__eq, axiom,
    ((![B : complex, C : complex, A : complex]: (((divide1210191872omplex @ B @ C) = A) = (((((~ ((C = zero_zero_complex)))) => ((B = (times_times_complex @ A @ C))))) & ((((C = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % divide_eq_eq
thf(fact_89_frac__eq__eq, axiom,
    ((![Y3 : complex, Z2 : complex, X3 : complex, W : complex]: ((~ ((Y3 = zero_zero_complex))) => ((~ ((Z2 = zero_zero_complex))) => (((divide1210191872omplex @ X3 @ Y3) = (divide1210191872omplex @ W @ Z2)) = ((times_times_complex @ X3 @ Z2) = (times_times_complex @ W @ Y3)))))))). % frac_eq_eq
thf(fact_90_inverse__eq__imp__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) => (A = B))))). % inverse_eq_imp_eq
thf(fact_91_nonzero__inverse__mult__distrib, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => ((invers502456322omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers502456322omplex @ B) @ (invers502456322omplex @ A)))))))). % nonzero_inverse_mult_distrib
thf(fact_92_inverse__unique, axiom,
    ((![A : real, B : real]: (((times_times_real @ A @ B) = one_one_real) => ((inverse_inverse_real @ A) = B))))). % inverse_unique
thf(fact_93_inverse__unique, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = one_one_complex) => ((invers502456322omplex @ A) = B))))). % inverse_unique
thf(fact_94_divide__inverse__commute, axiom,
    ((divide1210191872omplex = (^[A2 : complex]: (^[B2 : complex]: (times_times_complex @ (invers502456322omplex @ B2) @ A2)))))). % divide_inverse_commute
thf(fact_95_divide__inverse, axiom,
    ((divide1210191872omplex = (^[A2 : complex]: (^[B2 : complex]: (times_times_complex @ A2 @ (invers502456322omplex @ B2))))))). % divide_inverse
thf(fact_96_field__class_Ofield__divide__inverse, axiom,
    ((divide1210191872omplex = (^[A2 : complex]: (^[B2 : complex]: (times_times_complex @ A2 @ (invers502456322omplex @ B2))))))). % field_class.field_divide_inverse
thf(fact_97_divide__strict__left__mono__neg, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => (ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B)))))))). % divide_strict_left_mono_neg
thf(fact_98_divide__strict__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => (ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B)))))))). % divide_strict_left_mono
thf(fact_99_mult__imp__less__div__pos, axiom,
    ((![Y3 : real, Z2 : real, X3 : real]: ((ord_less_real @ zero_zero_real @ Y3) => ((ord_less_real @ (times_times_real @ Z2 @ Y3) @ X3) => (ord_less_real @ Z2 @ (divide_divide_real @ X3 @ Y3))))))). % mult_imp_less_div_pos
thf(fact_100_mult__imp__div__pos__less, axiom,
    ((![Y3 : real, X3 : real, Z2 : real]: ((ord_less_real @ zero_zero_real @ Y3) => ((ord_less_real @ X3 @ (times_times_real @ Z2 @ Y3)) => (ord_less_real @ (divide_divide_real @ X3 @ Y3) @ Z2)))))). % mult_imp_div_pos_less
thf(fact_101_pos__less__divide__eq, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (ord_less_real @ (times_times_real @ A @ C) @ B)))))). % pos_less_divide_eq
thf(fact_102_pos__divide__less__eq, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (divide_divide_real @ B @ C) @ A) = (ord_less_real @ B @ (times_times_real @ A @ C))))))). % pos_divide_less_eq
thf(fact_103_neg__less__divide__eq, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (ord_less_real @ B @ (times_times_real @ A @ C))))))). % neg_less_divide_eq
thf(fact_104_neg__divide__less__eq, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ C) @ A) = (ord_less_real @ (times_times_real @ A @ C) @ B)))))). % neg_divide_less_eq
thf(fact_105_less__divide__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ (times_times_real @ A @ C) @ B)))) & ((((~ ((ord_less_real @ zero_zero_real @ C)))) => ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ (times_times_real @ A @ C))))) & ((((~ ((ord_less_real @ C @ zero_zero_real)))) => ((ord_less_real @ A @ zero_zero_real))))))))))))). % less_divide_eq
thf(fact_106_divide__less__eq, axiom,
    ((![B : real, C : real, A : real]: ((ord_less_real @ (divide_divide_real @ B @ C) @ A) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ B @ (times_times_real @ A @ C))))) & ((((~ ((ord_less_real @ zero_zero_real @ C)))) => ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ (times_times_real @ A @ C) @ B)))) & ((((~ ((ord_less_real @ C @ zero_zero_real)))) => ((ord_less_real @ zero_zero_real @ A))))))))))))). % divide_less_eq
thf(fact_107_field__class_Ofield__inverse, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((times_times_real @ (inverse_inverse_real @ A) @ A) = one_one_real))))). % field_class.field_inverse
thf(fact_108_field__class_Ofield__inverse, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((times_times_complex @ (invers502456322omplex @ A) @ A) = one_one_complex))))). % field_class.field_inverse
thf(fact_109_nonzero__imp__inverse__nonzero, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => (~ (((invers502456322omplex @ A) = zero_zero_complex))))))). % nonzero_imp_inverse_nonzero
thf(fact_110_nonzero__inverse__inverse__eq, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((invers502456322omplex @ (invers502456322omplex @ A)) = A))))). % nonzero_inverse_inverse_eq
thf(fact_111_nonzero__inverse__eq__imp__eq, axiom,
    ((![A : complex, B : complex]: (((invers502456322omplex @ A) = (invers502456322omplex @ B)) => ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (A = B))))))). % nonzero_inverse_eq_imp_eq
thf(fact_112_inverse__zero__imp__zero, axiom,
    ((![A : complex]: (((invers502456322omplex @ A) = zero_zero_complex) => (A = zero_zero_complex))))). % inverse_zero_imp_zero
thf(fact_113_field__class_Ofield__inverse__zero, axiom,
    (((invers502456322omplex @ zero_zero_complex) = zero_zero_complex))). % field_class.field_inverse_zero
thf(fact_114_norm__divide, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_divide
thf(fact_115_norm__inverse, axiom,
    ((![A : complex]: ((real_V638595069omplex @ (invers502456322omplex @ A)) = (inverse_inverse_real @ (real_V638595069omplex @ A)))))). % norm_inverse
thf(fact_116_divide__strict__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono_neg
thf(fact_117_divide__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono
thf(fact_118_zero__less__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ zero_zero_real @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real))))))))). % zero_less_divide_iff
thf(fact_119_divide__less__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A)))) & ((~ ((C = zero_zero_real))))))))))). % divide_less_cancel
thf(fact_120_divide__less__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ zero_zero_real)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B))))))))). % divide_less_0_iff
thf(fact_121_divide__pos__pos, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y3))))))). % divide_pos_pos
thf(fact_122_divide__pos__neg, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X3 @ Y3) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_123_divide__neg__pos, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y3) => (ord_less_real @ (divide_divide_real @ X3 @ Y3) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_124_divide__neg__neg, axiom,
    ((![X3 : real, Y3 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ Y3 @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y3))))))). % divide_neg_neg
thf(fact_125_right__inverse__eq, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => (((divide_divide_real @ A @ B) = one_one_real) = (A = B)))))). % right_inverse_eq
thf(fact_126_right__inverse__eq, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => (((divide1210191872omplex @ A @ B) = one_one_complex) = (A = B)))))). % right_inverse_eq
thf(fact_127_positive__imp__inverse__positive, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)))))). % positive_imp_inverse_positive
thf(fact_128_negative__imp__inverse__negative, axiom,
    ((![A : real]: ((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real))))). % negative_imp_inverse_negative
thf(fact_129_inverse__positive__imp__positive, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)) => ((~ ((A = zero_zero_real))) => (ord_less_real @ zero_zero_real @ A)))))). % inverse_positive_imp_positive
thf(fact_130_inverse__negative__imp__negative, axiom,
    ((![A : real]: ((ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real) => ((~ ((A = zero_zero_real))) => (ord_less_real @ A @ zero_zero_real)))))). % inverse_negative_imp_negative
thf(fact_131_less__imp__inverse__less__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A))))))). % less_imp_inverse_less_neg
thf(fact_132_inverse__less__imp__less__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ B @ A)))))). % inverse_less_imp_less_neg
thf(fact_133_less__imp__inverse__less, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A))))))). % less_imp_inverse_less
thf(fact_134_inverse__less__imp__less, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ B @ A)))))). % inverse_less_imp_less
thf(fact_135_nonzero__norm__divide, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B))))))). % nonzero_norm_divide
thf(fact_136_inverse__eq__divide, axiom,
    ((inverse_inverse_real = (divide_divide_real @ one_one_real)))). % inverse_eq_divide
thf(fact_137_inverse__eq__divide, axiom,
    ((invers502456322omplex = (divide1210191872omplex @ one_one_complex)))). % inverse_eq_divide
thf(fact_138_nonzero__norm__inverse, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((real_V638595069omplex @ (invers502456322omplex @ A)) = (inverse_inverse_real @ (real_V638595069omplex @ A))))))). % nonzero_norm_inverse
thf(fact_139_less__divide__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ A @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ A))))))))). % less_divide_eq_1
thf(fact_140_divide__less__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ A)))) | ((((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ A @ B)))) | ((A = zero_zero_real))))))))). % divide_less_eq_1
thf(fact_141_one__less__inverse__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ one_one_real @ (inverse_inverse_real @ X3)) = (((ord_less_real @ zero_zero_real @ X3)) & ((ord_less_real @ X3 @ one_one_real))))))). % one_less_inverse_iff
thf(fact_142_one__less__inverse, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => (ord_less_real @ one_one_real @ (inverse_inverse_real @ A))))))). % one_less_inverse
thf(fact_143_nonzero__inverse__eq__divide, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((inverse_inverse_real @ A) = (divide_divide_real @ one_one_real @ A)))))). % nonzero_inverse_eq_divide
thf(fact_144_nonzero__inverse__eq__divide, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((invers502456322omplex @ A) = (divide1210191872omplex @ one_one_complex @ A)))))). % nonzero_inverse_eq_divide
thf(fact_145_poly__smult, axiom,
    ((![A : complex, P2 : poly_complex, X3 : complex]: ((poly_complex2 @ (smult_complex @ A @ P2) @ X3) = (times_times_complex @ A @ (poly_complex2 @ P2 @ X3)))))). % poly_smult
thf(fact_146_poly__smult, axiom,
    ((![A : nat, P2 : poly_nat, X3 : nat]: ((poly_nat2 @ (smult_nat @ A @ P2) @ X3) = (times_times_nat @ A @ (poly_nat2 @ P2 @ X3)))))). % poly_smult
thf(fact_147_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_148_div__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % div_self
thf(fact_149_div__self, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ A @ A) = one_one_nat))))). % div_self
thf(fact_150_div__mult__mult1__if, axiom,
    ((![C : nat, A : nat, B : nat]: (((C = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = zero_zero_nat)) & ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (divide_divide_nat @ A @ B))))))). % div_mult_mult1_if
thf(fact_151_div__mult__mult2, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) = (divide_divide_nat @ A @ B)))))). % div_mult_mult2
thf(fact_152_div__mult__mult1, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (divide_divide_nat @ A @ B)))))). % div_mult_mult1
thf(fact_153_nonzero__mult__div__cancel__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_154_nonzero__mult__div__cancel__right, axiom,
    ((![B : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_155_nonzero__mult__div__cancel__left, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_156_nonzero__mult__div__cancel__left, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_157_mult__cancel__right2, axiom,
    ((![A : real, C : real]: (((times_times_real @ A @ C) = C) = (((C = zero_zero_real)) | ((A = one_one_real))))))). % mult_cancel_right2
thf(fact_158_mult__cancel__right2, axiom,
    ((![A : complex, C : complex]: (((times_times_complex @ A @ C) = C) = (((C = zero_zero_complex)) | ((A = one_one_complex))))))). % mult_cancel_right2
thf(fact_159_mult__cancel__right1, axiom,
    ((![C : real, B : real]: ((C = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((B = one_one_real))))))). % mult_cancel_right1
thf(fact_160_mult__cancel__right1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_right1
thf(fact_161_div__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => ((divide_divide_nat @ M @ N) = zero_zero_nat))))). % div_less
thf(fact_162_div__mult__self__is__m, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((divide_divide_nat @ (times_times_nat @ M @ N) @ N) = M))))). % div_mult_self_is_m
thf(fact_163_div__mult__self1__is__m, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((divide_divide_nat @ (times_times_nat @ N @ M) @ N) = M))))). % div_mult_self1_is_m
thf(fact_164_mult__smult__left, axiom,
    ((![A : complex, P2 : poly_complex, Q : poly_complex]: ((times_1246143675omplex @ (smult_complex @ A @ P2) @ Q) = (smult_complex @ A @ (times_1246143675omplex @ P2 @ Q)))))). % mult_smult_left
thf(fact_165_mult__smult__right, axiom,
    ((![P2 : poly_complex, A : complex, Q : poly_complex]: ((times_1246143675omplex @ P2 @ (smult_complex @ A @ Q)) = (smult_complex @ A @ (times_1246143675omplex @ P2 @ Q)))))). % mult_smult_right
thf(fact_166_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_167_less_Ohyps, axiom,
    ((![P2 : poly_complex]: ((ord_less_nat @ (fundam1709708056omplex @ P2) @ (fundam1709708056omplex @ pa)) => ((~ ((fundam1158420650omplex @ (poly_complex2 @ P2)))) => (?[Z3 : complex]: ((poly_complex2 @ P2 @ Z3) = zero_zero_complex))))))). % less.hyps
thf(fact_168_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_169_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_170_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_171_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_172_mult__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_173_mult__eq__0__iff, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = (((A = zero_zero_nat)) | ((B = zero_zero_nat))))))). % mult_eq_0_iff
thf(fact_174_mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_left
thf(fact_175_mult__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_left

% Conjectures (1)
thf(conj_0, conjecture,
    (((ord_less_real @ (real_V638595069omplex @ (poly_complex2 @ (smult_complex @ (invers502456322omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ q) @ w)) @ one_one_real) = (ord_less_real @ (real_V638595069omplex @ (divide1210191872omplex @ (poly_complex2 @ q @ w) @ (poly_complex2 @ q @ zero_zero_complex))) @ one_one_real)))).
