% 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_215__5369648_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:18.427

% 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_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_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Parity_Osemiring__bit__shifts__class_Otake__bit_001t__Nat__Onat, type,
    semiri967765622it_nat : nat > nat > nat).
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__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_c_Transcendental_Oarcosh_001t__Real__Oreal, type,
    arcosh_real : real > real).
thf(sy_v_b, type,
    b : complex).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).

% Relevant facts (222)
thf(fact_0_b, axiom,
    ((~ ((b = zero_zero_complex))))). % b
thf(fact_1_th0, axiom,
    (((real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) = one_one_real))). % th0
thf(fact_2_assms_I2_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(2)
thf(fact_3_of__real__1, axiom,
    (((real_V1205483228l_real @ one_one_real) = one_one_real))). % of_real_1
thf(fact_4_of__real__1, axiom,
    (((real_V306493662omplex @ one_one_real) = one_one_complex))). % of_real_1
thf(fact_5_of__real__eq__1__iff, axiom,
    ((![X : real]: (((real_V1205483228l_real @ X) = one_one_real) = (X = one_one_real))))). % of_real_eq_1_iff
thf(fact_6_of__real__eq__1__iff, axiom,
    ((![X : real]: (((real_V306493662omplex @ X) = one_one_complex) = (X = one_one_real))))). % of_real_eq_1_iff
thf(fact_7_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_8_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_9_of__real__divide, axiom,
    ((![X : real, Y : real]: ((real_V1205483228l_real @ (divide_divide_real @ X @ Y)) = (divide_divide_real @ (real_V1205483228l_real @ X) @ (real_V1205483228l_real @ Y)))))). % of_real_divide
thf(fact_10_of__real__divide, axiom,
    ((![X : real, Y : real]: ((real_V306493662omplex @ (divide_divide_real @ X @ Y)) = (divide1210191872omplex @ (real_V306493662omplex @ X) @ (real_V306493662omplex @ Y)))))). % of_real_divide
thf(fact_11_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_12_div__by__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ one_one_complex) = A)))). % div_by_1
thf(fact_13_of__real__eq__iff, axiom,
    ((![X : real, Y : real]: (((real_V1205483228l_real @ X) = (real_V1205483228l_real @ Y)) = (X = Y))))). % of_real_eq_iff
thf(fact_14_of__real__eq__iff, axiom,
    ((![X : real, Y : real]: (((real_V306493662omplex @ X) = (real_V306493662omplex @ Y)) = (X = Y))))). % of_real_eq_iff
thf(fact_15_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_16_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_17_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_18_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_19_div__self, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ A @ A) = one_one_nat))))). % div_self
thf(fact_20_div__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % div_self
thf(fact_21_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_22_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_23_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_24_n, axiom,
    ((~ ((na = zero_zero_nat))))). % n
thf(fact_25_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_26_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_27_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_28_divide__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_right
thf(fact_29_divide__cancel__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_30_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_31_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_32_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_33_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_34_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_35_div__by__0, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % div_by_0
thf(fact_36_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_37_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_38_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_39_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_40_div__0, axiom,
    ((![A : real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real)))). % div_0
thf(fact_41_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_42_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_43_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_44_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_45_of__real__eq__0__iff, axiom,
    ((![X : real]: (((real_V306493662omplex @ X) = zero_zero_complex) = (X = zero_zero_real))))). % of_real_eq_0_iff
thf(fact_46_of__real__eq__0__iff, axiom,
    ((![X : real]: (((real_V1205483228l_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % of_real_eq_0_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_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_50_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_51_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_52_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_53_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_54_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_55_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_56_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_57_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_58_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_59_nonzero__of__real__divide, axiom,
    ((![Y : real, X : real]: ((~ ((Y = zero_zero_real))) => ((real_V306493662omplex @ (divide_divide_real @ X @ Y)) = (divide1210191872omplex @ (real_V306493662omplex @ X) @ (real_V306493662omplex @ Y))))))). % nonzero_of_real_divide
thf(fact_60_nonzero__of__real__divide, axiom,
    ((![Y : real, X : real]: ((~ ((Y = zero_zero_real))) => ((real_V1205483228l_real @ (divide_divide_real @ X @ Y)) = (divide_divide_real @ (real_V1205483228l_real @ X) @ (real_V1205483228l_real @ Y))))))). % nonzero_of_real_divide
thf(fact_61_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_62_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_63_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_64_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_65_one__reorient, axiom,
    ((![X : complex]: ((one_one_complex = X) = (X = one_one_complex))))). % one_reorient
thf(fact_66_right__inverse__eq, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => (((divide1210191872omplex @ A @ B) = one_one_complex) = (A = B)))))). % right_inverse_eq
thf(fact_67_right__inverse__eq, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => (((divide_divide_real @ A @ B) = one_one_real) = (A = B)))))). % right_inverse_eq
thf(fact_68_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_69_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_70_arcosh__1, axiom,
    (((arcosh_real @ one_one_real) = zero_zero_real))). % arcosh_1
thf(fact_71_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_72_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_73_take__bit__of__1__eq__0__iff, axiom,
    ((![N : nat]: (((semiri967765622it_nat @ N @ one_one_nat) = zero_zero_nat) = (N = zero_zero_nat))))). % take_bit_of_1_eq_0_iff
thf(fact_74_zero__le__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_divide_1_iff
thf(fact_75_divide__le__0__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % divide_le_0_1_iff
thf(fact_76_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_77_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_78_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_79_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_80_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_81_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_82_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_83_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_84_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_85_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_86_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_87_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_88_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_89_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_90_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_91_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_92_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_93_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_94_mult_Oleft__neutral, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % mult.left_neutral
thf(fact_95_mult_Oleft__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ one_one_complex @ A) = A)))). % mult.left_neutral
thf(fact_96_mult_Oright__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.right_neutral
thf(fact_97_mult_Oright__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ A @ one_one_complex) = A)))). % mult.right_neutral
thf(fact_98_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_99_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_100_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_101_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_102_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_103_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_104_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_105_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_106_of__real__mult, axiom,
    ((![X : real, Y : real]: ((real_V306493662omplex @ (times_times_real @ X @ Y)) = (times_times_complex @ (real_V306493662omplex @ X) @ (real_V306493662omplex @ Y)))))). % of_real_mult
thf(fact_107_of__real__mult, axiom,
    ((![X : real, Y : real]: ((real_V1205483228l_real @ (times_times_real @ X @ Y)) = (times_times_real @ (real_V1205483228l_real @ X) @ (real_V1205483228l_real @ Y)))))). % of_real_mult
thf(fact_108_take__bit__of__0, axiom,
    ((![N : nat]: ((semiri967765622it_nat @ N @ zero_zero_nat) = zero_zero_nat)))). % take_bit_of_0
thf(fact_109_of__real__power, axiom,
    ((![X : real, N : nat]: ((real_V306493662omplex @ (power_power_real @ X @ N)) = (power_power_complex @ (real_V306493662omplex @ X) @ N))))). % of_real_power
thf(fact_110_of__real__power, axiom,
    ((![X : real, N : nat]: ((real_V1205483228l_real @ (power_power_real @ X @ N)) = (power_power_real @ (real_V1205483228l_real @ X) @ N))))). % of_real_power
thf(fact_111_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_112_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_113_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_114_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_115_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_116_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_117_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_118_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_119_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_120_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_121_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_122_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_123_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_124_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_125_nonzero__mult__div__cancel__left, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_126_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_127_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_128_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_129_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_130_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_131_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_132_nonzero__mult__div__cancel__right, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((divide_divide_real @ (times_times_real @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_133_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_134_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_135_zero__less__norm__iff, axiom,
    ((![X : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X)) = (~ ((X = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_136_zero__less__norm__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X)) = (~ ((X = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_137_norm__le__zero__iff, axiom,
    ((![X : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X) @ zero_zero_real) = (X = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_138_norm__le__zero__iff, axiom,
    ((![X : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X) @ zero_zero_real) = (X = zero_zero_real))))). % norm_le_zero_iff
thf(fact_139_take__bit__0, axiom,
    ((![A : nat]: ((semiri967765622it_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % take_bit_0
thf(fact_140_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_141_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_142_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_143_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_144_divide__le__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B)))))). % divide_le_eq_1_neg
thf(fact_145_divide__le__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A)))))). % divide_le_eq_1_pos
thf(fact_146_le__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ B @ A)))))). % le_divide_eq_1_neg
thf(fact_147_le__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B)))))). % le_divide_eq_1_pos
thf(fact_148_IH, axiom,
    ((![M : nat]: ((ord_less_nat @ M @ na) => ((~ ((M = zero_zero_nat))) => (?[Z : complex]: (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ one_one_complex @ (times_times_complex @ b @ (power_power_complex @ Z @ M)))) @ one_one_real))))))). % IH
thf(fact_149_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_150_norm__power, axiom,
    ((![X : complex, N : nat]: ((real_V638595069omplex @ (power_power_complex @ X @ N)) = (power_power_real @ (real_V638595069omplex @ X) @ N))))). % norm_power
thf(fact_151_norm__power, axiom,
    ((![X : real, N : nat]: ((real_V646646907m_real @ (power_power_real @ X @ N)) = (power_power_real @ (real_V646646907m_real @ X) @ N))))). % norm_power
thf(fact_152_norm__mult__less, axiom,
    ((![X : complex, R : real, Y : complex, S : real]: ((ord_less_real @ (real_V638595069omplex @ X) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y) @ S) => (ord_less_real @ (real_V638595069omplex @ (times_times_complex @ X @ Y)) @ (times_times_real @ R @ S))))))). % norm_mult_less
thf(fact_153_norm__mult__less, axiom,
    ((![X : real, R : real, Y : real, S : real]: ((ord_less_real @ (real_V646646907m_real @ X) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y) @ S) => (ord_less_real @ (real_V646646907m_real @ (times_times_real @ X @ Y)) @ (times_times_real @ R @ S))))))). % norm_mult_less
thf(fact_154_norm__power__ineq, axiom,
    ((![X : complex, N : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (power_power_complex @ X @ N)) @ (power_power_real @ (real_V638595069omplex @ X) @ N))))). % norm_power_ineq
thf(fact_155_norm__power__ineq, axiom,
    ((![X : real, N : nat]: (ord_less_eq_real @ (real_V646646907m_real @ (power_power_real @ X @ N)) @ (power_power_real @ (real_V646646907m_real @ X) @ N))))). % norm_power_ineq
thf(fact_156_mult_Oassoc, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C)))))). % mult.assoc
thf(fact_157_mult__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))))). % mult_mono
thf(fact_158_mult__mono_H, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))))). % mult_mono'
thf(fact_159_less__1__mult, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ one_one_nat @ M2) => ((ord_less_nat @ one_one_nat @ N) => (ord_less_nat @ one_one_nat @ (times_times_nat @ M2 @ N))))))). % less_1_mult
thf(fact_160_less__1__mult, axiom,
    ((![M2 : real, N : real]: ((ord_less_real @ one_one_real @ M2) => ((ord_less_real @ one_one_real @ N) => (ord_less_real @ one_one_real @ (times_times_real @ M2 @ N))))))). % less_1_mult
thf(fact_161_mult_Ocommute, axiom,
    ((times_times_complex = (^[A2 : complex]: (^[B2 : complex]: (times_times_complex @ B2 @ A2)))))). % mult.commute
thf(fact_162_mult__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % mult_left_mono
thf(fact_163_mult__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))))). % mult_right_mono
thf(fact_164_mult__neg__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))))). % mult_neg_neg
thf(fact_165_mult_Oleft__commute, axiom,
    ((![B : complex, A : complex, C : complex]: ((times_times_complex @ B @ (times_times_complex @ A @ C)) = (times_times_complex @ A @ (times_times_complex @ B @ C)))))). % mult.left_commute
thf(fact_166_not__square__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real)))))). % not_square_less_zero
thf(fact_167_split__mult__neg__le, axiom,
    ((![A : nat, B : nat]: ((((ord_less_eq_nat @ zero_zero_nat @ A) & (ord_less_eq_nat @ B @ zero_zero_nat)) | ((ord_less_eq_nat @ A @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ B))) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))). % split_mult_neg_le
thf(fact_168_mult__nonneg__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))))). % mult_nonneg_nonneg
thf(fact_169_mult__nonneg__nonpos, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))))). % mult_nonneg_nonpos
thf(fact_170_mult__nonpos__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))))). % mult_nonpos_nonneg
thf(fact_171_mult__less__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (times_times_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))))))))). % mult_less_0_iff
thf(fact_172_mult__nonneg__nonpos2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)))))). % mult_nonneg_nonpos2
thf(fact_173_mult__neg__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))))). % mult_neg_pos
thf(fact_174_mult__neg__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real)))))). % mult_neg_pos
thf(fact_175_mult__pos__neg, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))))). % mult_pos_neg
thf(fact_176_mult__pos__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real)))))). % mult_pos_neg
thf(fact_177_mult__pos__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))))). % mult_pos_pos
thf(fact_178_mult__pos__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))))). % mult_pos_pos
thf(fact_179_linordered__field__no__lb, axiom,
    ((![X2 : real]: (?[Y2 : real]: (ord_less_real @ Y2 @ X2))))). % linordered_field_no_lb
thf(fact_180_linordered__field__no__ub, axiom,
    ((![X2 : real]: (?[X_1 : real]: (ord_less_real @ X2 @ X_1))))). % linordered_field_no_ub
thf(fact_181_mult__pos__neg2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)))))). % mult_pos_neg2
thf(fact_182_mult__pos__neg2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ A) @ zero_zero_real)))))). % mult_pos_neg2
thf(fact_183_zero__less__mult__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (times_times_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_mult_iff
thf(fact_184_ordered__comm__semiring__class_Ocomm__mult__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % ordered_comm_semiring_class.comm_mult_left_mono
thf(fact_185_mult__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ A))))))))). % mult_le_cancel_left
thf(fact_186_mult__le__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ A))))))))). % mult_le_cancel_right
thf(fact_187_mult__left__less__imp__less, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ A @ B)))))). % mult_left_less_imp_less
thf(fact_188_mult__left__less__imp__less, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ A @ B)))))). % mult_left_less_imp_less
thf(fact_189_mult__strict__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))))). % mult_strict_mono
thf(fact_190_mult__strict__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_strict_mono
thf(fact_191_mult__less__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (((((ord_less_eq_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((ord_less_eq_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A))))))))). % mult_less_cancel_left
thf(fact_192_mult__right__less__imp__less, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ A @ B)))))). % mult_right_less_imp_less
thf(fact_193_mult__right__less__imp__less, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ A @ B)))))). % mult_right_less_imp_less
thf(fact_194_mult__strict__mono_H, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))))). % mult_strict_mono'
thf(fact_195_mult__strict__mono_H, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_strict_mono'
thf(fact_196_linorder__neqE__linordered__idom, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) => ((~ ((ord_less_real @ X @ Y))) => (ord_less_real @ Y @ X)))))). % linorder_neqE_linordered_idom
thf(fact_197_mult__less__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (((((ord_less_eq_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((ord_less_eq_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A))))))))). % mult_less_cancel_right
thf(fact_198_zero__less__mult__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ B)))))). % zero_less_mult_pos
thf(fact_199_zero__less__mult__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B)))))). % zero_less_mult_pos
thf(fact_200_norm__mult, axiom,
    ((![X : complex, Y : complex]: ((real_V638595069omplex @ (times_times_complex @ X @ Y)) = (times_times_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)))))). % norm_mult
thf(fact_201_norm__mult, axiom,
    ((![X : real, Y : real]: ((real_V646646907m_real @ (times_times_real @ X @ Y)) = (times_times_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_mult
thf(fact_202_mult__le__cancel__left__neg, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_eq_real @ B @ A)))))). % mult_le_cancel_left_neg
thf(fact_203_mult__le__cancel__left__pos, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_eq_real @ A @ B)))))). % mult_le_cancel_left_pos
thf(fact_204_mult__left__le__imp__le, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ A @ B)))))). % mult_left_le_imp_le
thf(fact_205_mult__left__le__imp__le, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ B)))))). % mult_left_le_imp_le
thf(fact_206_zero__less__mult__pos2, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ B @ A)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ B)))))). % zero_less_mult_pos2
thf(fact_207_zero__less__mult__pos2, axiom,
    ((![B : real, A : real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B)))))). % zero_less_mult_pos2
thf(fact_208_norm__mult__ineq, axiom,
    ((![X : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (times_times_complex @ X @ Y)) @ (times_times_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)))))). % norm_mult_ineq
thf(fact_209_norm__mult__ineq, axiom,
    ((![X : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ (times_times_real @ X @ Y)) @ (times_times_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_mult_ineq
thf(fact_210_mult__right__le__imp__le, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ A @ B)))))). % mult_right_le_imp_le
thf(fact_211_mult__right__le__imp__le, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ B)))))). % mult_right_le_imp_le
thf(fact_212_mult__less__cancel__left__neg, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ B @ A)))))). % mult_less_cancel_left_neg
thf(fact_213_mult__less__cancel__left__pos, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ A @ B)))))). % mult_less_cancel_left_pos
thf(fact_214_mult__strict__left__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_strict_left_mono_neg
thf(fact_215_mult__le__less__imp__less, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))))). % mult_le_less_imp_less
thf(fact_216_mult__le__less__imp__less, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ D) => ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_le_less_imp_less
thf(fact_217_mult__less__le__imp__less, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))))). % mult_less_le_imp_less
thf(fact_218_mult__less__le__imp__less, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_less_le_imp_less
thf(fact_219_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))))))). % mult_strict_left_mono
thf(fact_220_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))))))). % mult_strict_left_mono
thf(fact_221_mult__less__cancel__left__disj, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (((((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_left_disj

% Conjectures (1)
thf(conj_0, conjecture,
    (((real_V638595069omplex @ (divide1210191872omplex @ (real_V306493662omplex @ (real_V638595069omplex @ b)) @ b)) = one_one_real))).
