% 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_209__5369616_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:15.527

% Could-be-implicit typings (3)
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 (28)
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_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__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
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__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_Power_Opower__class_Opower_001t__Complex__Ocomplex, type,
    power_power_complex : complex > nat > complex).
thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat, type,
    power_power_nat : nat > nat > nat).
thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal, type,
    power_power_real : real > nat > 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_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex, type,
    real_V306493662omplex : real > complex).
thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal, type,
    real_V1205483228l_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_b, type,
    b : complex).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (241)
thf(fact_0__092_060open_062_092_060exists_062v_O_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_L_Av_A_094_An_J_A_060_A1_092_060close_062, axiom,
    ((?[V : complex]: (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ (power_power_complex @ V @ na))) @ one_one_real)))). % \<open>\<exists>v. cmod (complex_of_real (cmod b) / b + v ^ n) < 1\<close>
thf(fact_1_b, axiom,
    ((~ ((b = zero_zero_complex))))). % b
thf(fact_2_n, axiom,
    ((~ ((na = zero_zero_nat))))). % n
thf(fact_3_th0, axiom,
    (((real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) = one_one_real))). % th0
thf(fact_4_assms_I2_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(2)
thf(fact_5_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]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_6_of__real__1, axiom,
    (((real_V1205483228l_real @ one_one_real) = one_one_real))). % of_real_1
thf(fact_7_of__real__1, axiom,
    (((real_V306493662omplex @ one_one_real) = one_one_complex))). % of_real_1
thf(fact_8_of__real__eq__1__iff, axiom,
    ((![X3 : real]: (((real_V1205483228l_real @ X3) = one_one_real) = (X3 = one_one_real))))). % of_real_eq_1_iff
thf(fact_9_of__real__eq__1__iff, axiom,
    ((![X3 : real]: (((real_V306493662omplex @ X3) = one_one_complex) = (X3 = one_one_real))))). % of_real_eq_1_iff
thf(fact_10_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_11_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_12_power__inject__exp, axiom,
    ((![A : real, M : nat, N : nat]: ((ord_less_real @ one_one_real @ A) => (((power_power_real @ A @ M) = (power_power_real @ A @ N)) = (M = N)))))). % power_inject_exp
thf(fact_13_power__inject__exp, axiom,
    ((![A : nat, M : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => (((power_power_nat @ A @ M) = (power_power_nat @ A @ N)) = (M = N)))))). % power_inject_exp
thf(fact_14_power__strict__increasing__iff, axiom,
    ((![B : real, X3 : nat, Y2 : nat]: ((ord_less_real @ one_one_real @ B) => ((ord_less_real @ (power_power_real @ B @ X3) @ (power_power_real @ B @ Y2)) = (ord_less_nat @ X3 @ Y2)))))). % power_strict_increasing_iff
thf(fact_15_power__strict__increasing__iff, axiom,
    ((![B : nat, X3 : nat, Y2 : nat]: ((ord_less_nat @ one_one_nat @ B) => ((ord_less_nat @ (power_power_nat @ B @ X3) @ (power_power_nat @ B @ Y2)) = (ord_less_nat @ X3 @ Y2)))))). % power_strict_increasing_iff
thf(fact_16_of__real__power, axiom,
    ((![X3 : real, N : nat]: ((real_V306493662omplex @ (power_power_real @ X3 @ N)) = (power_power_complex @ (real_V306493662omplex @ X3) @ N))))). % of_real_power
thf(fact_17_of__real__power, axiom,
    ((![X3 : real, N : nat]: ((real_V1205483228l_real @ (power_power_real @ X3 @ N)) = (power_power_real @ (real_V1205483228l_real @ X3) @ N))))). % of_real_power
thf(fact_18_of__real__divide, axiom,
    ((![X3 : real, Y2 : real]: ((real_V306493662omplex @ (divide_divide_real @ X3 @ Y2)) = (divide1210191872omplex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2)))))). % of_real_divide
thf(fact_19_of__real__divide, axiom,
    ((![X3 : real, Y2 : real]: ((real_V1205483228l_real @ (divide_divide_real @ X3 @ Y2)) = (divide_divide_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2)))))). % of_real_divide
thf(fact_20_of__real__add, axiom,
    ((![X3 : real, Y2 : real]: ((real_V306493662omplex @ (plus_plus_real @ X3 @ Y2)) = (plus_plus_complex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2)))))). % of_real_add
thf(fact_21_of__real__add, axiom,
    ((![X3 : real, Y2 : real]: ((real_V1205483228l_real @ (plus_plus_real @ X3 @ Y2)) = (plus_plus_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2)))))). % of_real_add
thf(fact_22_norm__less__p1, axiom,
    ((![X3 : complex]: (ord_less_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ (plus_plus_complex @ (real_V306493662omplex @ (real_V638595069omplex @ X3)) @ one_one_complex)))))). % norm_less_p1
thf(fact_23_norm__less__p1, axiom,
    ((![X3 : real]: (ord_less_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ (plus_plus_real @ (real_V1205483228l_real @ (real_V646646907m_real @ X3)) @ one_one_real)))))). % norm_less_p1
thf(fact_24_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_25_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_26_power__one, axiom,
    ((![N : nat]: ((power_power_real @ one_one_real @ N) = one_one_real)))). % power_one
thf(fact_27_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_28_div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % div_by_1
thf(fact_29_div__by__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ one_one_complex) = A)))). % div_by_1
thf(fact_30_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_31_power__one__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_32_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_33_power__one__right, axiom,
    ((![A : real]: ((power_power_real @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_34_of__real__eq__iff, axiom,
    ((![X3 : real, Y2 : real]: (((real_V306493662omplex @ X3) = (real_V306493662omplex @ Y2)) = (X3 = Y2))))). % of_real_eq_iff
thf(fact_35_of__real__eq__iff, axiom,
    ((![X3 : real, Y2 : real]: (((real_V1205483228l_real @ X3) = (real_V1205483228l_real @ Y2)) = (X3 = Y2))))). % of_real_eq_iff
thf(fact_36_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_37_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_38_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_39_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_40_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_41_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_42_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_43_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_44_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_45_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_46_nat__zero__less__power__iff, axiom,
    ((![X3 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ X3 @ N)) = (((ord_less_nat @ zero_zero_nat @ X3)) | ((N = zero_zero_nat))))))). % nat_zero_less_power_iff
thf(fact_47_of__real__0, axiom,
    (((real_V306493662omplex @ zero_zero_real) = zero_zero_complex))). % of_real_0
thf(fact_48_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_49_of__real__eq__0__iff, axiom,
    ((![X3 : real]: (((real_V306493662omplex @ X3) = zero_zero_complex) = (X3 = zero_zero_real))))). % of_real_eq_0_iff
thf(fact_50_of__real__eq__0__iff, axiom,
    ((![X3 : real]: (((real_V1205483228l_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % of_real_eq_0_iff
thf(fact_51_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_52_div__self, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ A @ A) = one_one_nat))))). % div_self
thf(fact_53_div__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % div_self
thf(fact_54_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_55_zero__less__norm__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X3)) = (~ ((X3 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_56_power__eq__0__iff, axiom,
    ((![A : complex, N : nat]: (((power_power_complex @ A @ N) = zero_zero_complex) = (((A = zero_zero_complex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_57_power__eq__0__iff, axiom,
    ((![A : nat, N : nat]: (((power_power_nat @ A @ N) = zero_zero_nat) = (((A = zero_zero_nat)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_58_power__eq__0__iff, axiom,
    ((![A : real, N : nat]: (((power_power_real @ A @ N) = zero_zero_real) = (((A = zero_zero_real)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_59_power__strict__decreasing__iff, axiom,
    ((![B : real, M : nat, N : nat]: ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ B @ one_one_real) => ((ord_less_real @ (power_power_real @ B @ M) @ (power_power_real @ B @ N)) = (ord_less_nat @ N @ M))))))). % power_strict_decreasing_iff
thf(fact_60_power__strict__decreasing__iff, axiom,
    ((![B : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ B @ one_one_nat) => ((ord_less_nat @ (power_power_nat @ B @ M) @ (power_power_nat @ B @ N)) = (ord_less_nat @ N @ M))))))). % power_strict_decreasing_iff
thf(fact_61_IH, axiom,
    ((![M2 : nat]: ((ord_less_nat @ M2 @ na) => ((~ ((M2 = zero_zero_nat))) => (?[Z2 : complex]: (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ one_one_complex @ (times_times_complex @ b @ (power_power_complex @ Z2 @ M2)))) @ one_one_real))))))). % IH
thf(fact_62_nat__power__less__imp__less, axiom,
    ((![I : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ I) => ((ord_less_nat @ (power_power_nat @ I @ M) @ (power_power_nat @ I @ N)) => (ord_less_nat @ M @ N)))))). % nat_power_less_imp_less
thf(fact_63_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex))))). % zero_power
thf(fact_64_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat))))). % zero_power
thf(fact_65_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_real @ zero_zero_real @ N) = zero_zero_real))))). % zero_power
thf(fact_66_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_67_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_68_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_69_power__not__zero, axiom,
    ((![A : complex, N : nat]: ((~ ((A = zero_zero_complex))) => (~ (((power_power_complex @ A @ N) = zero_zero_complex))))))). % power_not_zero
thf(fact_70_power__not__zero, axiom,
    ((![A : nat, N : nat]: ((~ ((A = zero_zero_nat))) => (~ (((power_power_nat @ A @ N) = zero_zero_nat))))))). % power_not_zero
thf(fact_71_power__not__zero, axiom,
    ((![A : real, N : nat]: ((~ ((A = zero_zero_real))) => (~ (((power_power_real @ A @ N) = zero_zero_real))))))). % power_not_zero
thf(fact_72_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_complex @ zero_zero_complex @ N) = one_one_complex)) & ((~ ((N = zero_zero_nat))) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex)))))). % power_0_left
thf(fact_73_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ N) = one_one_nat)) & ((~ ((N = zero_zero_nat))) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat)))))). % power_0_left
thf(fact_74_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_real @ zero_zero_real @ N) = one_one_real)) & ((~ ((N = zero_zero_nat))) => ((power_power_real @ zero_zero_real @ N) = zero_zero_real)))))). % power_0_left
thf(fact_75_power__eq__imp__eq__norm, axiom,
    ((![W : complex, N : nat, Z3 : complex]: (((power_power_complex @ W @ N) = (power_power_complex @ Z3 @ N)) => ((ord_less_nat @ zero_zero_nat @ N) => ((real_V638595069omplex @ W) = (real_V638595069omplex @ Z3))))))). % power_eq_imp_eq_norm
thf(fact_76_power__eq__imp__eq__norm, axiom,
    ((![W : real, N : nat, Z3 : real]: (((power_power_real @ W @ N) = (power_power_real @ Z3 @ N)) => ((ord_less_nat @ zero_zero_nat @ N) => ((real_V646646907m_real @ W) = (real_V646646907m_real @ Z3))))))). % power_eq_imp_eq_norm
thf(fact_77_add__less__zeroD, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ (plus_plus_real @ X3 @ Y2) @ zero_zero_real) => ((ord_less_real @ X3 @ zero_zero_real) | (ord_less_real @ Y2 @ zero_zero_real)))))). % add_less_zeroD
thf(fact_78_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_79_not__one__less__zero, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ zero_zero_nat))))). % not_one_less_zero
thf(fact_80_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_81_zero__less__one, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % zero_less_one
thf(fact_82_zero__less__power, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (power_power_real @ A @ N)))))). % zero_less_power
thf(fact_83_zero__less__power, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ N)))))). % zero_less_power
thf(fact_84_power__0, axiom,
    ((![A : complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex)))). % power_0
thf(fact_85_power__0, axiom,
    ((![A : nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat)))). % power_0
thf(fact_86_power__0, axiom,
    ((![A : real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real)))). % power_0
thf(fact_87_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_88_nonzero__norm__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B))))))). % nonzero_norm_divide
thf(fact_89_zero__less__two, axiom,
    ((ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ one_one_real)))). % zero_less_two
thf(fact_90_zero__less__two, axiom,
    ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))). % zero_less_two
thf(fact_91_power__strict__decreasing, axiom,
    ((![N : nat, N2 : nat, A : real]: ((ord_less_nat @ N @ N2) => ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => (ord_less_real @ (power_power_real @ A @ N2) @ (power_power_real @ A @ N)))))))). % power_strict_decreasing
thf(fact_92_power__strict__decreasing, axiom,
    ((![N : nat, N2 : nat, A : nat]: ((ord_less_nat @ N @ N2) => ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (power_power_nat @ A @ N2) @ (power_power_nat @ A @ N)))))))). % power_strict_decreasing
thf(fact_93_one__less__power, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_real @ one_one_real @ (power_power_real @ A @ N))))))). % one_less_power
thf(fact_94_one__less__power, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ one_one_nat @ (power_power_nat @ A @ N))))))). % one_less_power
thf(fact_95_power__eq__1__iff, axiom,
    ((![W : complex, N : nat]: (((power_power_complex @ W @ N) = one_one_complex) => (((real_V638595069omplex @ W) = one_one_real) | (N = zero_zero_nat)))))). % power_eq_1_iff
thf(fact_96_power__eq__1__iff, axiom,
    ((![W : real, N : nat]: (((power_power_real @ W @ N) = one_one_real) => (((real_V646646907m_real @ W) = one_one_real) | (N = zero_zero_nat)))))). % power_eq_1_iff
thf(fact_97_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) => ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_real @ Y2 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_98_power__divide, axiom,
    ((![A : real, B : real, N : nat]: ((power_power_real @ (divide_divide_real @ A @ B) @ N) = (divide_divide_real @ (power_power_real @ A @ N) @ (power_power_real @ B @ N)))))). % power_divide
thf(fact_99_power__divide, axiom,
    ((![A : complex, B : complex, N : nat]: ((power_power_complex @ (divide1210191872omplex @ A @ B) @ N) = (divide1210191872omplex @ (power_power_complex @ A @ N) @ (power_power_complex @ B @ N)))))). % power_divide
thf(fact_100_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_101_norm__divide, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_divide
thf(fact_102_norm__power, axiom,
    ((![X3 : complex, N : nat]: ((real_V638595069omplex @ (power_power_complex @ X3 @ N)) = (power_power_real @ (real_V638595069omplex @ X3) @ N))))). % norm_power
thf(fact_103_norm__power, axiom,
    ((![X3 : real, N : nat]: ((real_V646646907m_real @ (power_power_real @ X3 @ N)) = (power_power_real @ (real_V646646907m_real @ X3) @ N))))). % norm_power
thf(fact_104_add__mono1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ one_one_real) @ (plus_plus_real @ B @ one_one_real)))))). % add_mono1
thf(fact_105_add__mono1, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ one_one_nat) @ (plus_plus_nat @ B @ one_one_nat)))))). % add_mono1
thf(fact_106_less__add__one, axiom,
    ((![A : real]: (ord_less_real @ A @ (plus_plus_real @ A @ one_one_real))))). % less_add_one
thf(fact_107_less__add__one, axiom,
    ((![A : nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat))))). % less_add_one
thf(fact_108_power__strict__increasing, axiom,
    ((![N : nat, N2 : nat, A : real]: ((ord_less_nat @ N @ N2) => ((ord_less_real @ one_one_real @ A) => (ord_less_real @ (power_power_real @ A @ N) @ (power_power_real @ A @ N2))))))). % power_strict_increasing
thf(fact_109_power__strict__increasing, axiom,
    ((![N : nat, N2 : nat, A : nat]: ((ord_less_nat @ N @ N2) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ A @ N2))))))). % power_strict_increasing
thf(fact_110_power__less__imp__less__exp, axiom,
    ((![A : real, M : nat, N : nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ (power_power_real @ A @ M) @ (power_power_real @ A @ N)) => (ord_less_nat @ M @ N)))))). % power_less_imp_less_exp
thf(fact_111_power__less__imp__less__exp, axiom,
    ((![A : nat, M : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ M) @ (power_power_nat @ A @ N)) => (ord_less_nat @ M @ N)))))). % power_less_imp_less_exp
thf(fact_112_power__one__over, axiom,
    ((![A : real, N : nat]: ((power_power_real @ (divide_divide_real @ one_one_real @ A) @ N) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ N)))))). % power_one_over
thf(fact_113_power__one__over, axiom,
    ((![A : complex, N : nat]: ((power_power_complex @ (divide1210191872omplex @ one_one_complex @ A) @ N) = (divide1210191872omplex @ one_one_complex @ (power_power_complex @ A @ N)))))). % power_one_over
thf(fact_114_norm__triangle__lt, axiom,
    ((![X3 : complex, Y2 : complex, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_115_norm__triangle__lt, axiom,
    ((![X3 : real, Y2 : real, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_116_norm__add__less, axiom,
    ((![X3 : complex, R : real, Y2 : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X3) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y2) @ S2) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ (plus_plus_real @ R @ S2))))))). % norm_add_less
thf(fact_117_norm__add__less, axiom,
    ((![X3 : real, R : real, Y2 : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X3) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S2) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ (plus_plus_real @ R @ S2))))))). % norm_add_less
thf(fact_118_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_119_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_120_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_121_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_122_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_123_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_124_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_125_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_126_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_127_mult__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_right
thf(fact_128_mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_right
thf(fact_129_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
thf(fact_130_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_131_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_132_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_133_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_134_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_135_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_136_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_137_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_138_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_139_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_140_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_141_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_142_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_143_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_144_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_145_of__real__mult, axiom,
    ((![X3 : real, Y2 : real]: ((real_V306493662omplex @ (times_times_real @ X3 @ Y2)) = (times_times_complex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2)))))). % of_real_mult
thf(fact_146_of__real__mult, axiom,
    ((![X3 : real, Y2 : real]: ((real_V1205483228l_real @ (times_times_real @ X3 @ Y2)) = (times_times_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2)))))). % of_real_mult
thf(fact_147_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_148_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_149_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_150_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_151_mult__cancel__left2, axiom,
    ((![C : real, A : real]: (((times_times_real @ C @ A) = C) = (((C = zero_zero_real)) | ((A = one_one_real))))))). % mult_cancel_left2
thf(fact_152_mult__cancel__left2, axiom,
    ((![C : complex, A : complex]: (((times_times_complex @ C @ A) = C) = (((C = zero_zero_complex)) | ((A = one_one_complex))))))). % mult_cancel_left2
thf(fact_153_mult__cancel__left1, axiom,
    ((![C : real, B : real]: ((C = (times_times_real @ C @ B)) = (((C = zero_zero_real)) | ((B = one_one_real))))))). % mult_cancel_left1
thf(fact_154_mult__cancel__left1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_left1
thf(fact_155_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_156_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_157_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_158_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_159_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_160_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_161_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_162_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_163_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_164_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_165_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_166_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_167_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_168_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_169_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_170_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_171_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_172_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_173_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_174_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_175_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_176_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_177_norm__mult, axiom,
    ((![X3 : complex, Y2 : complex]: ((real_V638595069omplex @ (times_times_complex @ X3 @ Y2)) = (times_times_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)))))). % norm_mult
thf(fact_178_norm__mult, axiom,
    ((![X3 : real, Y2 : real]: ((real_V646646907m_real @ (times_times_real @ X3 @ Y2)) = (times_times_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)))))). % norm_mult
thf(fact_179_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_180_divide__divide__times__eq, axiom,
    ((![X3 : complex, Y2 : complex, Z3 : complex, W : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ X3 @ Y2) @ (divide1210191872omplex @ Z3 @ W)) = (divide1210191872omplex @ (times_times_complex @ X3 @ W) @ (times_times_complex @ Y2 @ Z3)))))). % divide_divide_times_eq
thf(fact_181_times__divide__times__eq, axiom,
    ((![X3 : complex, Y2 : complex, Z3 : complex, W : complex]: ((times_times_complex @ (divide1210191872omplex @ X3 @ Y2) @ (divide1210191872omplex @ Z3 @ W)) = (divide1210191872omplex @ (times_times_complex @ X3 @ Z3) @ (times_times_complex @ Y2 @ W)))))). % times_divide_times_eq
thf(fact_182_norm__mult__less, axiom,
    ((![X3 : complex, R : real, Y2 : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X3) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y2) @ S2) => (ord_less_real @ (real_V638595069omplex @ (times_times_complex @ X3 @ Y2)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_183_norm__mult__less, axiom,
    ((![X3 : real, R : real, Y2 : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X3) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S2) => (ord_less_real @ (real_V646646907m_real @ (times_times_real @ X3 @ Y2)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_184_mult__right__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_185_mult__right__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_186_mult__left__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_187_mult__left__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_188_no__zero__divisors, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((~ ((B = zero_zero_nat))) => (~ (((times_times_nat @ A @ B) = zero_zero_nat)))))))). % no_zero_divisors
thf(fact_189_no__zero__divisors, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (~ (((times_times_complex @ A @ B) = zero_zero_complex)))))))). % no_zero_divisors
thf(fact_190_divisors__zero, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((A = zero_zero_nat) | (B = zero_zero_nat)))))). % divisors_zero
thf(fact_191_divisors__zero, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) => ((A = zero_zero_complex) | (B = zero_zero_complex)))))). % divisors_zero
thf(fact_192_mult__not__zero, axiom,
    ((![A : nat, B : nat]: ((~ (((times_times_nat @ A @ B) = zero_zero_nat))) => ((~ ((A = zero_zero_nat))) & (~ ((B = zero_zero_nat)))))))). % mult_not_zero
thf(fact_193_mult__not__zero, axiom,
    ((![A : complex, B : complex]: ((~ (((times_times_complex @ A @ B) = zero_zero_complex))) => ((~ ((A = zero_zero_complex))) & (~ ((B = zero_zero_complex)))))))). % mult_not_zero
thf(fact_194_ring__class_Oring__distribs_I2_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)))))). % ring_class.ring_distribs(2)
thf(fact_195_ring__class_Oring__distribs_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)))))). % ring_class.ring_distribs(1)
thf(fact_196_comm__semiring__class_Odistrib, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)))))). % comm_semiring_class.distrib
thf(fact_197_distrib__left, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)))))). % distrib_left
thf(fact_198_distrib__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)))))). % distrib_right
thf(fact_199_combine__common__factor, axiom,
    ((![A : complex, E : complex, B : complex, C : complex]: ((plus_plus_complex @ (times_times_complex @ A @ E) @ (plus_plus_complex @ (times_times_complex @ B @ E) @ C)) = (plus_plus_complex @ (times_times_complex @ (plus_plus_complex @ A @ B) @ E) @ C))))). % combine_common_factor
thf(fact_200_power__commutes, axiom,
    ((![A : nat, N : nat]: ((times_times_nat @ (power_power_nat @ A @ N) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ N)))))). % power_commutes
thf(fact_201_power__commutes, axiom,
    ((![A : real, N : nat]: ((times_times_real @ (power_power_real @ A @ N) @ A) = (times_times_real @ A @ (power_power_real @ A @ N)))))). % power_commutes
thf(fact_202_power__commutes, axiom,
    ((![A : complex, N : nat]: ((times_times_complex @ (power_power_complex @ A @ N) @ A) = (times_times_complex @ A @ (power_power_complex @ A @ N)))))). % power_commutes
thf(fact_203_power__mult__distrib, axiom,
    ((![A : nat, B : nat, N : nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ N) = (times_times_nat @ (power_power_nat @ A @ N) @ (power_power_nat @ B @ N)))))). % power_mult_distrib
thf(fact_204_power__mult__distrib, axiom,
    ((![A : real, B : real, N : nat]: ((power_power_real @ (times_times_real @ A @ B) @ N) = (times_times_real @ (power_power_real @ A @ N) @ (power_power_real @ B @ N)))))). % power_mult_distrib
thf(fact_205_power__mult__distrib, axiom,
    ((![A : complex, B : complex, N : nat]: ((power_power_complex @ (times_times_complex @ A @ B) @ N) = (times_times_complex @ (power_power_complex @ A @ N) @ (power_power_complex @ B @ N)))))). % power_mult_distrib
thf(fact_206_power__commuting__commutes, axiom,
    ((![X3 : nat, Y2 : nat, N : nat]: (((times_times_nat @ X3 @ Y2) = (times_times_nat @ Y2 @ X3)) => ((times_times_nat @ (power_power_nat @ X3 @ N) @ Y2) = (times_times_nat @ Y2 @ (power_power_nat @ X3 @ N))))))). % power_commuting_commutes
thf(fact_207_power__commuting__commutes, axiom,
    ((![X3 : real, Y2 : real, N : nat]: (((times_times_real @ X3 @ Y2) = (times_times_real @ Y2 @ X3)) => ((times_times_real @ (power_power_real @ X3 @ N) @ Y2) = (times_times_real @ Y2 @ (power_power_real @ X3 @ N))))))). % power_commuting_commutes
thf(fact_208_power__commuting__commutes, axiom,
    ((![X3 : complex, Y2 : complex, N : nat]: (((times_times_complex @ X3 @ Y2) = (times_times_complex @ Y2 @ X3)) => ((times_times_complex @ (power_power_complex @ X3 @ N) @ Y2) = (times_times_complex @ Y2 @ (power_power_complex @ X3 @ N))))))). % power_commuting_commutes
thf(fact_209_power__add, axiom,
    ((![A : nat, M : nat, N : nat]: ((power_power_nat @ A @ (plus_plus_nat @ M @ N)) = (times_times_nat @ (power_power_nat @ A @ M) @ (power_power_nat @ A @ N)))))). % power_add
thf(fact_210_power__add, axiom,
    ((![A : real, M : nat, N : nat]: ((power_power_real @ A @ (plus_plus_nat @ M @ N)) = (times_times_real @ (power_power_real @ A @ M) @ (power_power_real @ A @ N)))))). % power_add
thf(fact_211_power__add, axiom,
    ((![A : complex, M : nat, N : nat]: ((power_power_complex @ A @ (plus_plus_nat @ M @ N)) = (times_times_complex @ (power_power_complex @ A @ M) @ (power_power_complex @ A @ N)))))). % power_add
thf(fact_212_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_213_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_214_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_215_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_216_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_217_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_218_frac__eq__eq, axiom,
    ((![Y2 : complex, Z3 : complex, X3 : complex, W : complex]: ((~ ((Y2 = zero_zero_complex))) => ((~ ((Z3 = zero_zero_complex))) => (((divide1210191872omplex @ X3 @ Y2) = (divide1210191872omplex @ W @ Z3)) = ((times_times_complex @ X3 @ Z3) = (times_times_complex @ W @ Y2)))))))). % frac_eq_eq
thf(fact_219_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_220_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_221_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_222_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_223_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_224_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_225_mult__imp__div__pos__less, axiom,
    ((![Y2 : real, X3 : real, Z3 : real]: ((ord_less_real @ zero_zero_real @ Y2) => ((ord_less_real @ X3 @ (times_times_real @ Z3 @ Y2)) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ Z3)))))). % mult_imp_div_pos_less
thf(fact_226_mult__imp__less__div__pos, axiom,
    ((![Y2 : real, Z3 : real, X3 : real]: ((ord_less_real @ zero_zero_real @ Y2) => ((ord_less_real @ (times_times_real @ Z3 @ Y2) @ X3) => (ord_less_real @ Z3 @ (divide_divide_real @ X3 @ Y2))))))). % mult_imp_less_div_pos
thf(fact_227_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_228_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_229_add__divide__eq__if__simps_I2_J, axiom,
    ((![Z3 : complex, A : complex, B : complex]: (((Z3 = zero_zero_complex) => ((plus_plus_complex @ (divide1210191872omplex @ A @ Z3) @ B) = B)) & ((~ ((Z3 = zero_zero_complex))) => ((plus_plus_complex @ (divide1210191872omplex @ A @ Z3) @ B) = (divide1210191872omplex @ (plus_plus_complex @ A @ (times_times_complex @ B @ Z3)) @ Z3))))))). % add_divide_eq_if_simps(2)
thf(fact_230_add__divide__eq__if__simps_I1_J, axiom,
    ((![Z3 : complex, A : complex, B : complex]: (((Z3 = zero_zero_complex) => ((plus_plus_complex @ A @ (divide1210191872omplex @ B @ Z3)) = A)) & ((~ ((Z3 = zero_zero_complex))) => ((plus_plus_complex @ A @ (divide1210191872omplex @ B @ Z3)) = (divide1210191872omplex @ (plus_plus_complex @ (times_times_complex @ A @ Z3) @ B) @ Z3))))))). % add_divide_eq_if_simps(1)
thf(fact_231_add__frac__eq, axiom,
    ((![Y2 : complex, Z3 : complex, X3 : complex, W : complex]: ((~ ((Y2 = zero_zero_complex))) => ((~ ((Z3 = zero_zero_complex))) => ((plus_plus_complex @ (divide1210191872omplex @ X3 @ Y2) @ (divide1210191872omplex @ W @ Z3)) = (divide1210191872omplex @ (plus_plus_complex @ (times_times_complex @ X3 @ Z3) @ (times_times_complex @ W @ Y2)) @ (times_times_complex @ Y2 @ Z3)))))))). % add_frac_eq
thf(fact_232_add__frac__num, axiom,
    ((![Y2 : complex, X3 : complex, Z3 : complex]: ((~ ((Y2 = zero_zero_complex))) => ((plus_plus_complex @ (divide1210191872omplex @ X3 @ Y2) @ Z3) = (divide1210191872omplex @ (plus_plus_complex @ X3 @ (times_times_complex @ Z3 @ Y2)) @ Y2)))))). % add_frac_num
thf(fact_233_add__num__frac, axiom,
    ((![Y2 : complex, Z3 : complex, X3 : complex]: ((~ ((Y2 = zero_zero_complex))) => ((plus_plus_complex @ Z3 @ (divide1210191872omplex @ X3 @ Y2)) = (divide1210191872omplex @ (plus_plus_complex @ X3 @ (times_times_complex @ Z3 @ Y2)) @ Y2)))))). % add_num_frac
thf(fact_234_add__divide__eq__iff, axiom,
    ((![Z3 : complex, X3 : complex, Y2 : complex]: ((~ ((Z3 = zero_zero_complex))) => ((plus_plus_complex @ X3 @ (divide1210191872omplex @ Y2 @ Z3)) = (divide1210191872omplex @ (plus_plus_complex @ (times_times_complex @ X3 @ Z3) @ Y2) @ Z3)))))). % add_divide_eq_iff
thf(fact_235_divide__add__eq__iff, axiom,
    ((![Z3 : complex, X3 : complex, Y2 : complex]: ((~ ((Z3 = zero_zero_complex))) => ((plus_plus_complex @ (divide1210191872omplex @ X3 @ Z3) @ Y2) = (divide1210191872omplex @ (plus_plus_complex @ X3 @ (times_times_complex @ Y2 @ Z3)) @ Z3)))))). % divide_add_eq_iff
thf(fact_236_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_237_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_238_mult__less__cancel__right__disj, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_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))))))))). % mult_less_cancel_right_disj
thf(fact_239_mult__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 @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono
thf(fact_240_mult__strict__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))))). % mult_strict_right_mono

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![V2 : complex]: ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ (power_power_complex @ V2 @ na))) @ one_one_real) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
