% 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_352__5370960_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:28.953

% Could-be-implicit typings (3)
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (18)
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Oone__class_Oone_001tf__a, type,
    one_one_a : a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_Itf__a_J, type,
    times_times_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Otimes__class_Otimes_001tf__a, type,
    times_times_a : a > a > a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J, type,
    zero_zero_poly_a : poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
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__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_c_Rings_Odivide__class_Odivide_001tf__a, type,
    divide_divide_a : a > a > a).
thf(sy_v_c____, type,
    c : a).
thf(sy_v_cs____, type,
    cs : poly_a).
thf(sy_v_d____, type,
    d : real).
thf(sy_v_da____, type,
    da : real).
thf(sy_v_e, type,
    e : real).
thf(sy_v_m____, type,
    m : real).

% Relevant facts (174)
thf(fact_0_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_1_ep, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % ep
thf(fact_2_H_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ da))). % H(1)
thf(fact_3_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_4_H_I3_J, axiom,
    ((ord_less_real @ da @ (divide_divide_real @ e @ m)))). % H(3)
thf(fact_5_H_I2_J, axiom,
    ((ord_less_real @ da @ one_one_real))). % H(2)
thf(fact_6_d_I3_J, axiom,
    ((ord_less_real @ d @ (divide_divide_real @ e @ m)))). % d(3)
thf(fact_7_em0, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ e @ m)))). % em0
thf(fact_8_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_9_dm_I2_J, axiom,
    ((ord_less_real @ (times_times_real @ d @ m) @ e))). % dm(2)
thf(fact_10_dm_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ (times_times_real @ d @ m)))). % dm(1)
thf(fact_11__092_060open_062_092_060exists_062ea_0620_O_Aea_A_060_A1_A_092_060and_062_Aea_A_060_Ae_A_P_Am_092_060close_062, axiom,
    ((?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ one_one_real) & (ord_less_real @ E @ (divide_divide_real @ e @ m))))))). % \<open>\<exists>ea>0. ea < 1 \<and> ea < e / m\<close>
thf(fact_12__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_A_092_060lbrakk_0620_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![D : real]: ((ord_less_real @ zero_zero_real @ D) => ((ord_less_real @ D @ one_one_real) => (~ ((ord_less_real @ D @ (divide_divide_real @ e @ m))))))))))). % \<open>\<And>thesis. (\<And>d. \<lbrakk>0 < d; d < 1; d < e / m\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_13_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_14_d1_I2_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ da))). % d1(2)
thf(fact_15_mult__less__iff1, axiom,
    ((![Z2 : real, X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ Z2) => ((ord_less_real @ (times_times_real @ X3 @ Z2) @ (times_times_real @ Y2 @ Z2)) = (ord_less_real @ X3 @ Y2)))))). % mult_less_iff1
thf(fact_16_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_17_not__square__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real)))))). % not_square_less_zero
thf(fact_18_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_19_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_20_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_21_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_22_d_I2_J, axiom,
    ((ord_less_real @ d @ one_one_real))). % d(2)
thf(fact_23_one0, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % one0
thf(fact_24_mult__cancel__right, axiom,
    ((![A : a, C : a, B : a]: (((times_times_a @ A @ C) = (times_times_a @ B @ C)) = (((C = zero_zero_a)) | ((A = B))))))). % mult_cancel_right
thf(fact_25_mult__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((times_times_real @ A @ C) = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % mult_cancel_right
thf(fact_26_mult__cancel__left, axiom,
    ((![C : a, A : a, B : a]: (((times_times_a @ C @ A) = (times_times_a @ C @ B)) = (((C = zero_zero_a)) | ((A = B))))))). % mult_cancel_left
thf(fact_27_mult__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((times_times_real @ C @ A) = (times_times_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % mult_cancel_left
thf(fact_28_mult__eq__0__iff, axiom,
    ((![A : a, B : a]: (((times_times_a @ A @ B) = zero_zero_a) = (((A = zero_zero_a)) | ((B = zero_zero_a))))))). % mult_eq_0_iff
thf(fact_29_mult__eq__0__iff, axiom,
    ((![A : poly_a, B : poly_a]: (((times_times_poly_a @ A @ B) = zero_zero_poly_a) = (((A = zero_zero_poly_a)) | ((B = zero_zero_poly_a))))))). % mult_eq_0_iff
thf(fact_30_mult__eq__0__iff, axiom,
    ((![A : real, B : real]: (((times_times_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % mult_eq_0_iff
thf(fact_31_mult__zero__right, axiom,
    ((![A : a]: ((times_times_a @ A @ zero_zero_a) = zero_zero_a)))). % mult_zero_right
thf(fact_32_mult__zero__right, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ A @ zero_zero_poly_a) = zero_zero_poly_a)))). % mult_zero_right
thf(fact_33_mult__zero__right, axiom,
    ((![A : real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real)))). % mult_zero_right
thf(fact_34_mult__zero__left, axiom,
    ((![A : a]: ((times_times_a @ zero_zero_a @ A) = zero_zero_a)))). % mult_zero_left
thf(fact_35_mult__zero__left, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ zero_zero_poly_a @ A) = zero_zero_poly_a)))). % mult_zero_left
thf(fact_36_mult__zero__left, axiom,
    ((![A : real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real)))). % mult_zero_left
thf(fact_37_div__0, axiom,
    ((![A : real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real)))). % div_0
thf(fact_38_div__by__0, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % div_by_0
thf(fact_39_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_40_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_41_mult__cancel__right2, axiom,
    ((![A : a, C : a]: (((times_times_a @ A @ C) = C) = (((C = zero_zero_a)) | ((A = one_one_a))))))). % mult_cancel_right2
thf(fact_42_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_43_mult__cancel__right1, axiom,
    ((![C : a, B : a]: ((C = (times_times_a @ B @ C)) = (((C = zero_zero_a)) | ((B = one_one_a))))))). % mult_cancel_right1
thf(fact_44_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_45_mult__cancel__left2, axiom,
    ((![C : a, A : a]: (((times_times_a @ C @ A) = C) = (((C = zero_zero_a)) | ((A = one_one_a))))))). % mult_cancel_left2
thf(fact_46_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_47_mult__cancel__left1, axiom,
    ((![C : a, B : a]: ((C = (times_times_a @ C @ B)) = (((C = zero_zero_a)) | ((B = one_one_a))))))). % mult_cancel_left1
thf(fact_48_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_49_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_50_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_51_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_52_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_53_zero__neq__one, axiom,
    ((~ ((zero_zero_a = one_one_a))))). % zero_neq_one
thf(fact_54_mult__left__le__one__le, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y2) => ((ord_less_eq_real @ Y2 @ one_one_real) => (ord_less_eq_real @ (times_times_real @ Y2 @ X3) @ X3))))))). % mult_left_le_one_le
thf(fact_55_mult__right__le__one__le, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y2) => ((ord_less_eq_real @ Y2 @ one_one_real) => (ord_less_eq_real @ (times_times_real @ X3 @ Y2) @ X3))))))). % mult_right_le_one_le
thf(fact_56_mult__le__one, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ one_one_real))))))). % mult_le_one
thf(fact_57_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_58_mult__left__le, axiom,
    ((![C : real, A : real]: ((ord_less_eq_real @ C @ one_one_real) => ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (times_times_real @ A @ C) @ A)))))). % mult_left_le
thf(fact_59_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_60_ordered__comm__semiring__class_Ocomm__mult__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % ordered_comm_semiring_class.comm_mult_left_mono
thf(fact_61_zero__le__mult__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ zero_zero_real))))))))). % zero_le_mult_iff
thf(fact_62_mult__nonneg__nonpos2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real)))))). % mult_nonneg_nonpos2
thf(fact_63_mult__nonpos__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)))))). % mult_nonpos_nonneg
thf(fact_64_mult__nonneg__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)))))). % mult_nonneg_nonpos
thf(fact_65_mult__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B))))))). % mult_nonneg_nonneg
thf(fact_66_split__mult__neg__le, axiom,
    ((![A : real, B : real]: ((((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ B @ zero_zero_real)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B))) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real))))). % split_mult_neg_le
thf(fact_67_mult__le__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ zero_zero_real)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B))))))))). % mult_le_0_iff
thf(fact_68_mult__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_right_mono
thf(fact_69_mult__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_right_mono_neg
thf(fact_70_mult__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_left_mono
thf(fact_71_mult__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B))))))). % mult_nonpos_nonpos
thf(fact_72_mult__left__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_left_mono_neg
thf(fact_73_split__mult__pos__le, axiom,
    ((![A : real, B : real]: ((((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ zero_zero_real @ B)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real))) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)))))). % split_mult_pos_le
thf(fact_74_zero__le__square, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A))))). % zero_le_square
thf(fact_75_mult__mono_H, axiom,
    ((![A : real, B : real, C : real, D2 : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D2) => ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D2))))))))). % mult_mono'
thf(fact_76_mult__mono, axiom,
    ((![A : real, B : real, C : real, D2 : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D2) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D2))))))))). % mult_mono
thf(fact_77_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_78_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_79_mult__less__cancel__right2, axiom,
    ((![A : real, C : real]: ((ord_less_real @ (times_times_real @ A @ C) @ C) = (((((ord_less_eq_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ one_one_real)))) & ((((ord_less_eq_real @ C @ zero_zero_real)) => ((ord_less_real @ one_one_real @ A))))))))). % mult_less_cancel_right2
thf(fact_80_mult__less__cancel__right1, axiom,
    ((![C : real, B : real]: ((ord_less_real @ C @ (times_times_real @ B @ C)) = (((((ord_less_eq_real @ zero_zero_real @ C)) => ((ord_less_real @ one_one_real @ B)))) & ((((ord_less_eq_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ one_one_real))))))))). % mult_less_cancel_right1
thf(fact_81_mult__less__cancel__left2, axiom,
    ((![C : real, A : real]: ((ord_less_real @ (times_times_real @ C @ A) @ C) = (((((ord_less_eq_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ one_one_real)))) & ((((ord_less_eq_real @ C @ zero_zero_real)) => ((ord_less_real @ one_one_real @ A))))))))). % mult_less_cancel_left2
thf(fact_82_mult__less__cancel__left1, axiom,
    ((![C : real, B : real]: ((ord_less_real @ C @ (times_times_real @ C @ B)) = (((((ord_less_eq_real @ zero_zero_real @ C)) => ((ord_less_real @ one_one_real @ B)))) & ((((ord_less_eq_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ one_one_real))))))))). % mult_less_cancel_left1
thf(fact_83_mult__le__cancel__right2, axiom,
    ((![A : real, C : real]: ((ord_less_eq_real @ (times_times_real @ A @ C) @ C) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ one_one_real)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ one_one_real @ A))))))))). % mult_le_cancel_right2
thf(fact_84_mult__le__cancel__right1, axiom,
    ((![C : real, B : real]: ((ord_less_eq_real @ C @ (times_times_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ one_one_real @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ one_one_real))))))))). % mult_le_cancel_right1
thf(fact_85_mult__le__cancel__left2, axiom,
    ((![C : real, A : real]: ((ord_less_eq_real @ (times_times_real @ C @ A) @ C) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ one_one_real)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ one_one_real @ A))))))))). % mult_le_cancel_left2
thf(fact_86_mult__le__cancel__left1, axiom,
    ((![C : real, B : real]: ((ord_less_eq_real @ C @ (times_times_real @ C @ B)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ one_one_real @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ one_one_real))))))))). % mult_le_cancel_left1
thf(fact_87_mult__less__le__imp__less, axiom,
    ((![A : real, B : real, C : real, D2 : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D2) => ((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 @ D2))))))))). % mult_less_le_imp_less
thf(fact_88_mult__le__less__imp__less, axiom,
    ((![A : real, B : real, C : real, D2 : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ D2) => ((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 @ D2))))))))). % mult_le_less_imp_less
thf(fact_89_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_90_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_91_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_92_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_93_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_94_mult__strict__mono_H, axiom,
    ((![A : real, B : real, C : real, D2 : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D2) => ((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 @ D2))))))))). % mult_strict_mono'
thf(fact_95_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_96_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_97_mult__strict__mono, axiom,
    ((![A : real, B : real, C : real, D2 : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D2) => ((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 @ D2))))))))). % mult_strict_mono
thf(fact_98_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_99_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_100_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_101_mult__le__cancel__iff2, axiom,
    ((![Z2 : real, X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ Z2) => ((ord_less_eq_real @ (times_times_real @ Z2 @ X3) @ (times_times_real @ Z2 @ Y2)) = (ord_less_eq_real @ X3 @ Y2)))))). % mult_le_cancel_iff2
thf(fact_102_mult__le__cancel__iff1, axiom,
    ((![Z2 : real, X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ Z2) => ((ord_less_eq_real @ (times_times_real @ X3 @ Z2) @ (times_times_real @ Y2 @ Z2)) = (ord_less_eq_real @ X3 @ Y2)))))). % mult_le_cancel_iff1
thf(fact_103_less__1__mult, axiom,
    ((![M : real, N : real]: ((ord_less_real @ one_one_real @ M) => ((ord_less_real @ one_one_real @ N) => (ord_less_real @ one_one_real @ (times_times_real @ M @ N))))))). % less_1_mult
thf(fact_104_mult__right__cancel, axiom,
    ((![C : a, A : a, B : a]: ((~ ((C = zero_zero_a))) => (((times_times_a @ A @ C) = (times_times_a @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_105_mult__right__cancel, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => (((times_times_real @ A @ C) = (times_times_real @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_106_mult__left__cancel, axiom,
    ((![C : a, A : a, B : a]: ((~ ((C = zero_zero_a))) => (((times_times_a @ C @ A) = (times_times_a @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_107_mult__left__cancel, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => (((times_times_real @ C @ A) = (times_times_real @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_108_no__zero__divisors, axiom,
    ((![A : a, B : a]: ((~ ((A = zero_zero_a))) => ((~ ((B = zero_zero_a))) => (~ (((times_times_a @ A @ B) = zero_zero_a)))))))). % no_zero_divisors
thf(fact_109_no__zero__divisors, axiom,
    ((![A : poly_a, B : poly_a]: ((~ ((A = zero_zero_poly_a))) => ((~ ((B = zero_zero_poly_a))) => (~ (((times_times_poly_a @ A @ B) = zero_zero_poly_a)))))))). % no_zero_divisors
thf(fact_110_no__zero__divisors, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((~ ((B = zero_zero_real))) => (~ (((times_times_real @ A @ B) = zero_zero_real)))))))). % no_zero_divisors
thf(fact_111_divisors__zero, axiom,
    ((![A : a, B : a]: (((times_times_a @ A @ B) = zero_zero_a) => ((A = zero_zero_a) | (B = zero_zero_a)))))). % divisors_zero
thf(fact_112_divisors__zero, axiom,
    ((![A : poly_a, B : poly_a]: (((times_times_poly_a @ A @ B) = zero_zero_poly_a) => ((A = zero_zero_poly_a) | (B = zero_zero_poly_a)))))). % divisors_zero
thf(fact_113_divisors__zero, axiom,
    ((![A : real, B : real]: (((times_times_real @ A @ B) = zero_zero_real) => ((A = zero_zero_real) | (B = zero_zero_real)))))). % divisors_zero
thf(fact_114_mult__not__zero, axiom,
    ((![A : a, B : a]: ((~ (((times_times_a @ A @ B) = zero_zero_a))) => ((~ ((A = zero_zero_a))) & (~ ((B = zero_zero_a)))))))). % mult_not_zero
thf(fact_115_mult__not__zero, axiom,
    ((![A : poly_a, B : poly_a]: ((~ (((times_times_poly_a @ A @ B) = zero_zero_poly_a))) => ((~ ((A = zero_zero_poly_a))) & (~ ((B = zero_zero_poly_a)))))))). % mult_not_zero
thf(fact_116_mult__not__zero, axiom,
    ((![A : real, B : real]: ((~ (((times_times_real @ A @ B) = zero_zero_real))) => ((~ ((A = zero_zero_real))) & (~ ((B = zero_zero_real)))))))). % mult_not_zero
thf(fact_117_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) => ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_real @ Y2 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_118_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_119_mult__less__cancel__right__disj, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ A @ B)))) | ((((ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ B @ A))))))))). % mult_less_cancel_right_disj
thf(fact_120_mult__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono
thf(fact_121_mult__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 @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono_neg
thf(fact_122_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
thf(fact_123_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_124_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_125_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_126_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_127_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_128_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_129_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_130_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_131_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_132_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_133_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_134_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_135_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_136_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_137_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_138_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_139_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_140_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_141_division__ring__divide__zero, axiom,
    ((![A : a]: ((divide_divide_a @ A @ zero_zero_a) = zero_zero_a)))). % 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_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_144_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_145_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_146_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_147_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_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 : 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_150_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_151_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_152_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_153_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_154_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_155_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_156_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_157_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_158_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_159_divide__self__if, axiom,
    ((![A : a]: (((A = zero_zero_a) => ((divide_divide_a @ A @ A) = zero_zero_a)) & ((~ ((A = zero_zero_a))) => ((divide_divide_a @ A @ A) = one_one_a)))))). % divide_self_if
thf(fact_160_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_161_divide__self, axiom,
    ((![A : a]: ((~ ((A = zero_zero_a))) => ((divide_divide_a @ A @ A) = one_one_a))))). % divide_self
thf(fact_162_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_163_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_164_divide__eq__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = one_one_real) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_165_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_166_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_167_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_168_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_169_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_170_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y3 : real]: (ord_less_real @ Y3 @ X4))))). % linordered_field_no_lb
thf(fact_171_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % linordered_field_no_ub
thf(fact_172_times__divide__times__eq, axiom,
    ((![X3 : real, Y2 : real, Z2 : real, W : real]: ((times_times_real @ (divide_divide_real @ X3 @ Y2) @ (divide_divide_real @ Z2 @ W)) = (divide_divide_real @ (times_times_real @ X3 @ Z2) @ (times_times_real @ Y2 @ W)))))). % times_divide_times_eq
thf(fact_173_divide__divide__times__eq, axiom,
    ((![X3 : real, Y2 : real, Z2 : real, W : real]: ((divide_divide_real @ (divide_divide_real @ X3 @ Y2) @ (divide_divide_real @ Z2 @ W)) = (divide_divide_real @ (times_times_real @ X3 @ W) @ (times_times_real @ Y2 @ Z2)))))). % divide_divide_times_eq

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_real @ (times_times_real @ da @ m) @ e))).
