% 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_221__5369668_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:21.283

% 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 (29)
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_NthRoot_Oroot, type,
    root : nat > 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_v____, type,
    v : complex).

% Relevant facts (234)
thf(fact_0_b, axiom,
    ((~ ((b = zero_zero_complex))))). % b
thf(fact_1_n, axiom,
    ((~ ((na = zero_zero_nat))))). % n
thf(fact_2_th2, axiom,
    (((real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) = one_one_real))). % th2
thf(fact_3_v, axiom,
    ((ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b) @ (power_power_complex @ v @ na))) @ one_one_real))). % v
thf(fact_4__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_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_L_Av_A_094_An_J_A_060_A1_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_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>\<And>thesis. (\<And>v. cmod (complex_of_real (cmod b) / b + v ^ n) < 1 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_6_assms_I2_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(2)
thf(fact_7_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_8_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_9_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_10_of__real__1, axiom,
    (((real_V1205483228l_real @ one_one_real) = one_one_real))). % of_real_1
thf(fact_11_of__real__1, axiom,
    (((real_V306493662omplex @ one_one_real) = one_one_complex))). % of_real_1
thf(fact_12_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_13_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_14_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_15_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_16_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_17_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_18_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_19_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_20_th1, axiom,
    (((power_power_complex @ (divide1210191872omplex @ v @ (real_V306493662omplex @ (root @ na @ (real_V638595069omplex @ b)))) @ na) = (divide1210191872omplex @ (power_power_complex @ v @ na) @ (real_V306493662omplex @ (real_V638595069omplex @ b)))))). % th1
thf(fact_21_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_22_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_23_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_24_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_25_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_26_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_27_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_28_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_29_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_30_power__one, axiom,
    ((![N : nat]: ((power_power_real @ one_one_real @ N) = one_one_real)))). % power_one
thf(fact_31_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_32_power__one__right, axiom,
    ((![A : complex]: ((power_power_complex @ 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_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_35_of__real__eq__iff, axiom,
    ((![X3 : real, Y2 : real]: (((real_V306493662omplex @ X3) = (real_V306493662omplex @ Y2)) = (X3 = Y2))))). % of_real_eq_iff
thf(fact_36_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_37_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_38__092_060open_062root_An_A_Icmod_Ab_J_A_094_An_A_061_Acmod_Ab_092_060close_062, axiom,
    (((power_power_real @ (root @ na @ (real_V638595069omplex @ b)) @ na) = (real_V638595069omplex @ b)))). % \<open>root n (cmod b) ^ n = cmod b\<close>
thf(fact_39_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_40_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_41_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_42_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_43_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_44_of__real__0, axiom,
    (((real_V306493662omplex @ zero_zero_real) = zero_zero_complex))). % of_real_0
thf(fact_45_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_46_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_47_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_48_sum__squares__eq__zero__iff, axiom,
    ((![X3 : real, Y2 : real]: (((plus_plus_real @ (times_times_real @ X3 @ X3) @ (times_times_real @ Y2 @ Y2)) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y2 = zero_zero_real))))))). % sum_squares_eq_zero_iff
thf(fact_49_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_50_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_51_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_52_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_53_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_54_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_55_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_56_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_57_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_58_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_59_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_60_power__mult, axiom,
    ((![A : complex, M : nat, N : nat]: ((power_power_complex @ A @ (times_times_nat @ M @ N)) = (power_power_complex @ (power_power_complex @ A @ M) @ N))))). % power_mult
thf(fact_61_power__mult, axiom,
    ((![A : real, M : nat, N : nat]: ((power_power_real @ A @ (times_times_nat @ M @ N)) = (power_power_real @ (power_power_real @ A @ M) @ N))))). % power_mult
thf(fact_62_power__mult, axiom,
    ((![A : nat, M : nat, N : nat]: ((power_power_nat @ A @ (times_times_nat @ M @ N)) = (power_power_nat @ (power_power_nat @ A @ M) @ N))))). % power_mult
thf(fact_63_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_64_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_65_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_66_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_67_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_68_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_69_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_70_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_71_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_72_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_73_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_74_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_75_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_76_power__0, axiom,
    ((![A : complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex)))). % power_0
thf(fact_77_power__0, axiom,
    ((![A : real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real)))). % power_0
thf(fact_78_power__0, axiom,
    ((![A : nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat)))). % power_0
thf(fact_79_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_80_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_81_sum__squares__gt__zero__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ X3 @ X3) @ (times_times_real @ Y2 @ Y2))) = (((~ ((X3 = zero_zero_real)))) | ((~ ((Y2 = zero_zero_real))))))))). % sum_squares_gt_zero_iff
thf(fact_82_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_83_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_84_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_85_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_86_power__Suc__less, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => (ord_less_real @ (times_times_real @ A @ (power_power_real @ A @ N)) @ (power_power_real @ A @ N))))))). % power_Suc_less
thf(fact_87_power__Suc__less, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (times_times_nat @ A @ (power_power_nat @ A @ N)) @ (power_power_nat @ A @ N))))))). % power_Suc_less
thf(fact_88_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_89_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_90_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_91_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_92_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_93_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_94_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_95_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_96_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_97_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_98_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_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_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_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__divide, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_divide
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_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_105_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_106_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_107_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_108_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_109_left__right__inverse__power, axiom,
    ((![X3 : real, Y2 : real, N : nat]: (((times_times_real @ X3 @ Y2) = one_one_real) => ((times_times_real @ (power_power_real @ X3 @ N) @ (power_power_real @ Y2 @ N)) = one_one_real))))). % left_right_inverse_power
thf(fact_110_left__right__inverse__power, axiom,
    ((![X3 : complex, Y2 : complex, N : nat]: (((times_times_complex @ X3 @ Y2) = one_one_complex) => ((times_times_complex @ (power_power_complex @ X3 @ N) @ (power_power_complex @ Y2 @ N)) = one_one_complex))))). % left_right_inverse_power
thf(fact_111_left__right__inverse__power, axiom,
    ((![X3 : nat, Y2 : nat, N : nat]: (((times_times_nat @ X3 @ Y2) = one_one_nat) => ((times_times_nat @ (power_power_nat @ X3 @ N) @ (power_power_nat @ Y2 @ N)) = one_one_nat))))). % left_right_inverse_power
thf(fact_112_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_113_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_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__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_116_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_117_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_118_power__less__power__Suc, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ one_one_real @ A) => (ord_less_real @ (power_power_real @ A @ N) @ (times_times_real @ A @ (power_power_real @ A @ N))))))). % power_less_power_Suc
thf(fact_119_power__less__power__Suc, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ N) @ (times_times_nat @ A @ (power_power_nat @ A @ N))))))). % power_less_power_Suc
thf(fact_120_power__gt1__lemma, axiom,
    ((![A : real, N : nat]: ((ord_less_real @ one_one_real @ A) => (ord_less_real @ one_one_real @ (times_times_real @ A @ (power_power_real @ A @ N))))))). % power_gt1_lemma
thf(fact_121_power__gt1__lemma, axiom,
    ((![A : nat, N : nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ N))))))). % power_gt1_lemma
thf(fact_122_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_123_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_124_real__root__lt__1__iff, axiom,
    ((![N : nat, X3 : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ (root @ N @ X3) @ one_one_real) = (ord_less_real @ X3 @ one_one_real)))))). % real_root_lt_1_iff
thf(fact_125_real__root__gt__1__iff, axiom,
    ((![N : nat, Y2 : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ one_one_real @ (root @ N @ Y2)) = (ord_less_real @ one_one_real @ Y2)))))). % real_root_gt_1_iff
thf(fact_126_real__root__one, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((root @ N @ one_one_real) = one_one_real))))). % real_root_one
thf(fact_127_real__root__eq__1__iff, axiom,
    ((![N : nat, X3 : real]: ((ord_less_nat @ zero_zero_nat @ N) => (((root @ N @ X3) = one_one_real) = (X3 = one_one_real)))))). % real_root_eq_1_iff
thf(fact_128_real__root__less__iff, axiom,
    ((![N : nat, X3 : real, Y2 : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ (root @ N @ X3) @ (root @ N @ Y2)) = (ord_less_real @ X3 @ Y2)))))). % real_root_less_iff
thf(fact_129_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_130_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_131_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_132_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_133_div__mult__self4, axiom,
    ((![B : nat, C : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ A) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self4
thf(fact_134_div__mult__self3, axiom,
    ((![B : nat, C : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ C @ B) @ A) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self3
thf(fact_135_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_136_divide__eq__0__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % divide_eq_0_iff
thf(fact_137_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_138_divide__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((divide_divide_real @ C @ A) = (divide_divide_real @ C @ B)) = (((C = zero_zero_real)) | ((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_divide__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((divide_divide_real @ A @ C) = (divide_divide_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_right
thf(fact_141_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_142_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_143_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_144_times__divide__eq__left, axiom,
    ((![B : real, C : real, A : real]: ((times_times_real @ (divide_divide_real @ B @ C) @ A) = (divide_divide_real @ (times_times_real @ B @ A) @ C))))). % times_divide_eq_left
thf(fact_145_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_146_divide__divide__eq__left, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ B @ C)))))). % divide_divide_eq_left
thf(fact_147_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_148_divide__divide__eq__right, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ C) @ B))))). % divide_divide_eq_right
thf(fact_149_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_150_times__divide__eq__right, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ B) @ C))))). % times_divide_eq_right
thf(fact_151_div__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => ((divide_divide_nat @ M @ N) = zero_zero_nat))))). % div_less
thf(fact_152_real__divide__square__eq, axiom,
    ((![R : real, A : real]: ((divide_divide_real @ (times_times_real @ R @ A) @ (times_times_real @ R @ R)) = (divide_divide_real @ A @ R))))). % real_divide_square_eq
thf(fact_153_real__root__zero, axiom,
    ((![N : nat]: ((root @ N @ zero_zero_real) = zero_zero_real)))). % real_root_zero
thf(fact_154_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_155_mult__divide__mult__cancel__left__if, axiom,
    ((![C : real, A : real, B : real]: (((C = zero_zero_real) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = zero_zero_real)) & ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B))))))). % mult_divide_mult_cancel_left_if
thf(fact_156_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_157_nonzero__mult__divide__mult__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left
thf(fact_158_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_159_nonzero__mult__divide__mult__cancel__left2, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ C @ A) @ (times_times_real @ B @ C)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left2
thf(fact_160_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_161_nonzero__mult__divide__mult__cancel__right, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right
thf(fact_162_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_163_nonzero__mult__divide__mult__cancel__right2, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ A @ C) @ (times_times_real @ C @ B)) = (divide_divide_real @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right2
thf(fact_164_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_165_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_166_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_167_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_168_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_169_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_170_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_171_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_172_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_173_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_174_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_175_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_176_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_177_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_178_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_179_not__real__square__gt__zero, axiom,
    ((![X3 : real]: ((~ ((ord_less_real @ zero_zero_real @ (times_times_real @ X3 @ X3)))) = (X3 = zero_zero_real))))). % not_real_square_gt_zero
thf(fact_180_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_181_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_182_root__0, axiom,
    ((![X3 : real]: ((root @ zero_zero_nat @ X3) = zero_zero_real)))). % root_0
thf(fact_183_real__root__eq__iff, axiom,
    ((![N : nat, X3 : real, Y2 : real]: ((ord_less_nat @ zero_zero_nat @ N) => (((root @ N @ X3) = (root @ N @ Y2)) = (X3 = Y2)))))). % real_root_eq_iff
thf(fact_184_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_185_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_186_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_187_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_188_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_189_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_190_div__mult__self1, axiom,
    ((![B : nat, A : nat, C : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ A @ (times_times_nat @ C @ B)) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self1
thf(fact_191_div__mult__self2, axiom,
    ((![B : nat, A : nat, C : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (plus_plus_nat @ A @ (times_times_nat @ B @ C)) @ B) = (plus_plus_nat @ C @ (divide_divide_nat @ A @ B))))))). % div_mult_self2
thf(fact_192_real__root__eq__0__iff, axiom,
    ((![N : nat, X3 : real]: ((ord_less_nat @ zero_zero_nat @ N) => (((root @ N @ X3) = zero_zero_real) = (X3 = zero_zero_real)))))). % real_root_eq_0_iff
thf(fact_193_real__root__lt__0__iff, axiom,
    ((![N : nat, X3 : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ (root @ N @ X3) @ zero_zero_real) = (ord_less_real @ X3 @ zero_zero_real)))))). % real_root_lt_0_iff
thf(fact_194_real__root__gt__0__iff, axiom,
    ((![N : nat, Y2 : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ zero_zero_real @ (root @ N @ Y2)) = (ord_less_real @ zero_zero_real @ Y2)))))). % real_root_gt_0_iff
thf(fact_195_div__mult2__eq, axiom,
    ((![M : nat, N : nat, Q : nat]: ((divide_divide_nat @ M @ (times_times_nat @ N @ Q)) = (divide_divide_nat @ (divide_divide_nat @ M @ N) @ Q))))). % div_mult2_eq
thf(fact_196_norm__not__less__zero, axiom,
    ((![X3 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_197_realpow__pos__nth__unique, axiom,
    ((![N : nat, A : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ zero_zero_real @ A) => (?[X : real]: (((ord_less_real @ zero_zero_real @ X) & ((power_power_real @ X @ N) = A)) & (![Y : real]: (((ord_less_real @ zero_zero_real @ Y) & ((power_power_real @ Y @ N) = A)) => (Y = X)))))))))). % realpow_pos_nth_unique
thf(fact_198_realpow__pos__nth, axiom,
    ((![N : nat, A : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ zero_zero_real @ A) => (?[R2 : real]: ((ord_less_real @ zero_zero_real @ R2) & ((power_power_real @ R2 @ N) = A)))))))). % realpow_pos_nth
thf(fact_199_real__root__gt__zero, axiom,
    ((![N : nat, X3 : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ zero_zero_real @ X3) => (ord_less_real @ zero_zero_real @ (root @ N @ X3))))))). % real_root_gt_zero
thf(fact_200_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y3 : real]: (ord_less_real @ Y3 @ X4))))). % linordered_field_no_lb
thf(fact_201_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % linordered_field_no_ub
thf(fact_202_less__mult__imp__div__less, axiom,
    ((![M : nat, I : nat, N : nat]: ((ord_less_nat @ M @ (times_times_nat @ I @ N)) => (ord_less_nat @ (divide_divide_nat @ M @ N) @ I))))). % less_mult_imp_div_less
thf(fact_203_nonzero__of__real__divide, axiom,
    ((![Y2 : real, X3 : real]: ((~ ((Y2 = zero_zero_real))) => ((real_V306493662omplex @ (divide_divide_real @ X3 @ Y2)) = (divide1210191872omplex @ (real_V306493662omplex @ X3) @ (real_V306493662omplex @ Y2))))))). % nonzero_of_real_divide
thf(fact_204_nonzero__of__real__divide, axiom,
    ((![Y2 : real, X3 : real]: ((~ ((Y2 = zero_zero_real))) => ((real_V1205483228l_real @ (divide_divide_real @ X3 @ Y2)) = (divide_divide_real @ (real_V1205483228l_real @ X3) @ (real_V1205483228l_real @ Y2))))))). % nonzero_of_real_divide
thf(fact_205_real__root__mult__exp, axiom,
    ((![M : nat, N : nat, X3 : real]: ((root @ (times_times_nat @ M @ N) @ X3) = (root @ M @ (root @ N @ X3)))))). % real_root_mult_exp
thf(fact_206_real__root__commute, axiom,
    ((![M : nat, N : nat, X3 : real]: ((root @ M @ (root @ N @ X3)) = (root @ N @ (root @ M @ X3)))))). % real_root_commute
thf(fact_207_real__root__strict__increasing, axiom,
    ((![N : nat, N2 : nat, X3 : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_nat @ N @ N2) => ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ X3 @ one_one_real) => (ord_less_real @ (root @ N @ X3) @ (root @ N2 @ X3))))))))). % real_root_strict_increasing
thf(fact_208_real__root__pow__pos, axiom,
    ((![N : nat, X3 : real]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_real @ zero_zero_real @ X3) => ((power_power_real @ (root @ N @ X3) @ N) = X3)))))). % real_root_pow_pos
thf(fact_209_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_210_times__divide__times__eq, axiom,
    ((![X3 : real, Y2 : real, Z3 : real, W : real]: ((times_times_real @ (divide_divide_real @ X3 @ Y2) @ (divide_divide_real @ Z3 @ W)) = (divide_divide_real @ (times_times_real @ X3 @ Z3) @ (times_times_real @ Y2 @ W)))))). % times_divide_times_eq
thf(fact_211_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_212_divide__divide__times__eq, axiom,
    ((![X3 : real, Y2 : real, Z3 : real, W : real]: ((divide_divide_real @ (divide_divide_real @ X3 @ Y2) @ (divide_divide_real @ Z3 @ W)) = (divide_divide_real @ (times_times_real @ X3 @ W) @ (times_times_real @ Y2 @ Z3)))))). % divide_divide_times_eq
thf(fact_213_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_214_divide__divide__eq__left_H, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ C @ B)))))). % divide_divide_eq_left'
thf(fact_215_add__divide__distrib, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (divide1210191872omplex @ A @ C) @ (divide1210191872omplex @ B @ C)))))). % add_divide_distrib
thf(fact_216_add__divide__distrib, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)))))). % add_divide_distrib
thf(fact_217_dividend__less__times__div, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ M @ (plus_plus_nat @ N @ (times_times_nat @ N @ (divide_divide_nat @ M @ N)))))))). % dividend_less_times_div
thf(fact_218_dividend__less__div__times, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ M @ (plus_plus_nat @ N @ (times_times_nat @ (divide_divide_nat @ M @ N) @ N))))))). % dividend_less_div_times
thf(fact_219_div__eq__dividend__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ M) => (((divide_divide_nat @ M @ N) = M) = (N = one_one_nat)))))). % div_eq_dividend_iff
thf(fact_220_div__less__dividend, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ one_one_nat @ N) => ((ord_less_nat @ zero_zero_nat @ M) => (ord_less_nat @ (divide_divide_nat @ M @ N) @ M)))))). % div_less_dividend
thf(fact_221_Euclidean__Division_Odiv__eq__0__iff, axiom,
    ((![M : nat, N : nat]: (((divide_divide_nat @ M @ N) = zero_zero_nat) = (((ord_less_nat @ M @ N)) | ((N = zero_zero_nat))))))). % Euclidean_Division.div_eq_0_iff
thf(fact_222_split__div, axiom,
    ((![P : nat > $o, M : nat, N : nat]: ((P @ (divide_divide_nat @ M @ N)) = (((((N = zero_zero_nat)) => ((P @ zero_zero_nat)))) & ((((~ ((N = zero_zero_nat)))) => ((![I2 : nat]: (![J : nat]: (((ord_less_nat @ J @ N)) => ((((M = (plus_plus_nat @ (times_times_nat @ N @ I2) @ J))) => ((P @ I2))))))))))))))). % split_div
thf(fact_223_real__root__divide, axiom,
    ((![N : nat, X3 : real, Y2 : real]: ((root @ N @ (divide_divide_real @ X3 @ Y2)) = (divide_divide_real @ (root @ N @ X3) @ (root @ N @ Y2)))))). % real_root_divide
thf(fact_224_real__root__mult, axiom,
    ((![N : nat, X3 : real, Y2 : real]: ((root @ N @ (times_times_real @ X3 @ Y2)) = (times_times_real @ (root @ N @ X3) @ (root @ N @ Y2)))))). % real_root_mult
thf(fact_225_divide__neg__neg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ Y2 @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_neg_neg
thf(fact_226_divide__neg__pos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y2) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_227_divide__pos__neg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ Y2 @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_228_divide__pos__pos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y2) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_pos_pos
thf(fact_229_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_230_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_231_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_232_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_233_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

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_real @ (times_times_real @ (real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) @ (real_V638595069omplex @ (plus_plus_complex @ one_one_complex @ (times_times_complex @ b @ (divide1210191872omplex @ (power_power_complex @ v @ na) @ (real_V306493662omplex @ (real_V638595069omplex @ b))))))) @ (times_times_real @ (real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) @ one_one_real)))).
