% 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_779__5375466_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:33:03.788

% Could-be-implicit typings (2)
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).

% Explicit typings (16)
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__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__Real__Oreal, type,
    zero_zero_real : real).
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_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_v_a____, type,
    a : complex).
thf(sy_v_m____, type,
    m : real).
thf(sy_v_t____, type,
    t : real).
thf(sy_v_w____, type,
    w : complex).

% Relevant facts (179)
thf(fact_0_t_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ t))). % t(1)
thf(fact_1_t_I2_J, axiom,
    ((ord_less_real @ t @ one_one_real))). % t(2)
thf(fact_2__092_060open_062t_A_K_Acmod_Aw_A_092_060le_062_A1_A_K_Acmod_Aw_092_060close_062, axiom,
    ((ord_less_eq_real @ (times_times_real @ t @ (real_V638595069omplex @ w)) @ (times_times_real @ one_one_real @ (real_V638595069omplex @ w))))). % \<open>t * cmod w \<le> 1 * cmod w\<close>
thf(fact_3_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_4_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_5_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_6_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_7_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_8_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_9_of__real__eq__iff, axiom,
    ((![X : real, Y : real]: (((real_V306493662omplex @ X) = (real_V306493662omplex @ Y)) = (X = Y))))). % of_real_eq_iff
thf(fact_10_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_11_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_12_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_13_w0, axiom,
    ((~ ((w = zero_zero_complex))))). % w0
thf(fact_14_norm__ge__zero, axiom,
    ((![X : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X))))). % norm_ge_zero
thf(fact_15_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_16_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_17_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_18_mult__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D) => ((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 @ D))))))))). % mult_mono
thf(fact_19_mult__mono_H, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D) => ((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 @ D))))))))). % mult_mono'
thf(fact_20_zero__le__square, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A))))). % zero_le_square
thf(fact_21_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_22__092_060open_062_092_060And_062d2_O_A_I0_058_058_063_Ha_J_A_060_Ad2_A_092_060Longrightarrow_062_A_092_060exists_062e_0620_058_058_063_Ha_O_Ae_A_060_A_I1_058_058_063_Ha_J_A_092_060and_062_Ae_A_060_Ad2_092_060close_062, axiom,
    ((![D2 : real]: ((ord_less_real @ zero_zero_real @ D2) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ one_one_real) & (ord_less_real @ E @ D2)))))))). % \<open>\<And>d2. (0::?'a) < d2 \<Longrightarrow> \<exists>e>0::?'a. e < (1::?'a) \<and> e < d2\<close>
thf(fact_23_kas_I1_J, axiom,
    ((~ ((a = zero_zero_complex))))). % kas(1)
thf(fact_24_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_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 : 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_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 : 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_29_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_30_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_31_mult__zero__right, axiom,
    ((![A : real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real)))). % mult_zero_right
thf(fact_32_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_33_mult__zero__left, axiom,
    ((![A : real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real)))). % mult_zero_left
thf(fact_34_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_35_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_36_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_37_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_38_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_39_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_40_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_41_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_42_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_43_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_44_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_45_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_46_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_47_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_48_of__real__0, axiom,
    (((real_V306493662omplex @ zero_zero_real) = zero_zero_complex))). % of_real_0
thf(fact_49_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_50_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_51_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_52_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_53_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_54_of__real__1, axiom,
    (((real_V306493662omplex @ one_one_real) = one_one_complex))). % of_real_1
thf(fact_55_of__real__1, axiom,
    (((real_V1205483228l_real @ one_one_real) = one_one_real))). % of_real_1
thf(fact_56_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_57_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_58_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_59_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_60_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X2 : real, Y2 : real]: ((ord_less_real @ X2 @ Y2) => (ord_less_real @ (F @ X2) @ (F @ Y2)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_61_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X2 : real, Y2 : real]: ((ord_less_real @ X2 @ Y2) => (ord_less_real @ (F @ X2) @ (F @ Y2)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_62_order__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X2 : real, Y2 : real]: ((ord_less_real @ X2 @ Y2) => (ord_less_real @ (F @ X2) @ (F @ Y2)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_63_order__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X2 : real, Y2 : real]: ((ord_less_real @ X2 @ Y2) => (ord_less_real @ (F @ X2) @ (F @ Y2)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_64_lt__ex, axiom,
    ((![X : real]: (?[Y2 : real]: (ord_less_real @ Y2 @ X))))). % lt_ex
thf(fact_65_gt__ex, axiom,
    ((![X : real]: (?[X_1 : real]: (ord_less_real @ X @ X_1))))). % gt_ex
thf(fact_66_neqE, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) => ((~ ((ord_less_real @ X @ Y))) => (ord_less_real @ Y @ X)))))). % neqE
thf(fact_67_neq__iff, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) = (((ord_less_real @ X @ Y)) | ((ord_less_real @ Y @ X))))))). % neq_iff
thf(fact_68_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_69_dense, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (?[Z : real]: ((ord_less_real @ X @ Z) & (ord_less_real @ Z @ Y))))))). % dense
thf(fact_70_less__imp__neq, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_71_less__asym, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_asym
thf(fact_72_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_73_less__trans, axiom,
    ((![X : real, Y : real, Z2 : real]: ((ord_less_real @ X @ Y) => ((ord_less_real @ Y @ Z2) => (ord_less_real @ X @ Z2)))))). % less_trans
thf(fact_74_less__linear, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) | ((X = Y) | (ord_less_real @ Y @ X)))))). % less_linear
thf(fact_75_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_76_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_77_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_78_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_79_less__imp__not__eq, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_80_less__not__sym, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_not_sym
thf(fact_81_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_82_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_83_antisym__conv3, axiom,
    ((![Y : real, X : real]: ((~ ((ord_less_real @ Y @ X))) => ((~ ((ord_less_real @ X @ Y))) = (X = Y)))))). % antisym_conv3
thf(fact_84_less__imp__not__eq2, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_85_less__imp__triv, axiom,
    ((![X : real, Y : real, P : $o]: ((ord_less_real @ X @ Y) => ((ord_less_real @ Y @ X) => P))))). % less_imp_triv
thf(fact_86_linorder__cases, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => ((~ ((X = Y))) => (ord_less_real @ Y @ X)))))). % linorder_cases
thf(fact_87_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_88_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_89_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_90_less__imp__not__less, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_imp_not_less
thf(fact_91_linorder__less__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A2 : real, B2 : real]: ((ord_less_real @ A2 @ B2) => (P @ A2 @ B2))) => ((![A2 : real]: (P @ A2 @ A2)) => ((![A2 : real, B2 : real]: ((P @ B2 @ A2) => (P @ A2 @ B2))) => (P @ A @ B))))))). % linorder_less_wlog
thf(fact_92_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_93_not__less__iff__gr__or__eq, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) = (((ord_less_real @ Y @ X)) | ((X = Y))))))). % not_less_iff_gr_or_eq
thf(fact_94_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_95_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_96_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_97_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_98_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_99_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_100_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_101_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_102_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_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_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_111_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_112_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_113_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_114_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_115_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_116_not__square__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real)))))). % not_square_less_zero
thf(fact_117_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_118_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_119_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_120_norm__not__less__zero, axiom,
    ((![X : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_121_norm__not__less__zero, axiom,
    ((![X : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_122_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_12 : real]: (P @ X_12)) => ((?[Z3 : real]: (![X2 : real]: ((P @ X2) => (ord_less_real @ X2 @ Z3)))) => (?[S2 : real]: (![Y3 : real]: ((?[X3 : real]: (((P @ X3)) & ((ord_less_real @ Y3 @ X3)))) = (ord_less_real @ Y3 @ S2))))))))). % real_sup_exists
thf(fact_123_order_Onot__eq__order__implies__strict, axiom,
    ((![A : real, B : real]: ((~ ((A = B))) => ((ord_less_eq_real @ A @ B) => (ord_less_real @ A @ B)))))). % order.not_eq_order_implies_strict
thf(fact_124_dual__order_Ostrict__implies__order, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (ord_less_eq_real @ B @ A))))). % dual_order.strict_implies_order
thf(fact_125_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[B3 : real]: (^[A3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((~ ((A3 = B3)))))))))). % dual_order.strict_iff_order
thf(fact_126_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[B3 : real]: (^[A3 : real]: (((ord_less_real @ B3 @ A3)) | ((A3 = B3)))))))). % dual_order.order_iff_strict
thf(fact_127_order_Ostrict__implies__order, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B))))). % order.strict_implies_order
thf(fact_128_dense__le__bounded, axiom,
    ((![X : real, Y : real, Z2 : real]: ((ord_less_real @ X @ Y) => ((![W : real]: ((ord_less_real @ X @ W) => ((ord_less_real @ W @ Y) => (ord_less_eq_real @ W @ Z2)))) => (ord_less_eq_real @ Y @ Z2)))))). % dense_le_bounded
thf(fact_129_dense__ge__bounded, axiom,
    ((![Z2 : real, X : real, Y : real]: ((ord_less_real @ Z2 @ X) => ((![W : real]: ((ord_less_real @ Z2 @ W) => ((ord_less_real @ W @ X) => (ord_less_eq_real @ Y @ W)))) => (ord_less_eq_real @ Y @ Z2)))))). % dense_ge_bounded
thf(fact_130_dual__order_Ostrict__trans2, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans2
thf(fact_131_dual__order_Ostrict__trans1, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans1
thf(fact_132_order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ A3 @ B3)) & ((~ ((A3 = B3)))))))))). % order.strict_iff_order
thf(fact_133_order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[A3 : real]: (^[B3 : real]: (((ord_less_real @ A3 @ B3)) | ((A3 = B3)))))))). % order.order_iff_strict
thf(fact_134_order_Ostrict__trans2, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans2
thf(fact_135_order_Ostrict__trans1, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans1
thf(fact_136_not__le__imp__less, axiom,
    ((![Y : real, X : real]: ((~ ((ord_less_eq_real @ Y @ X))) => (ord_less_real @ X @ Y))))). % not_le_imp_less
thf(fact_137_less__le__not__le, axiom,
    ((ord_less_real = (^[X3 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X3 @ Y4)) & ((~ ((ord_less_eq_real @ Y4 @ X3)))))))))). % less_le_not_le
thf(fact_138_le__imp__less__or__eq, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) => ((ord_less_real @ X @ Y) | (X = Y)))))). % le_imp_less_or_eq
thf(fact_139_le__less__linear, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) | (ord_less_real @ Y @ X))))). % le_less_linear
thf(fact_140_dense__le, axiom,
    ((![Y : real, Z2 : real]: ((![X2 : real]: ((ord_less_real @ X2 @ Y) => (ord_less_eq_real @ X2 @ Z2))) => (ord_less_eq_real @ Y @ Z2))))). % dense_le
thf(fact_141_dense__ge, axiom,
    ((![Z2 : real, Y : real]: ((![X2 : real]: ((ord_less_real @ Z2 @ X2) => (ord_less_eq_real @ Y @ X2))) => (ord_less_eq_real @ Y @ Z2))))). % dense_ge
thf(fact_142_less__le__trans, axiom,
    ((![X : real, Y : real, Z2 : real]: ((ord_less_real @ X @ Y) => ((ord_less_eq_real @ Y @ Z2) => (ord_less_real @ X @ Z2)))))). % less_le_trans
thf(fact_143_le__less__trans, axiom,
    ((![X : real, Y : real, Z2 : real]: ((ord_less_eq_real @ X @ Y) => ((ord_less_real @ Y @ Z2) => (ord_less_real @ X @ Z2)))))). % le_less_trans
thf(fact_144_less__imp__le, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (ord_less_eq_real @ X @ Y))))). % less_imp_le
thf(fact_145_antisym__conv2, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) => ((~ ((ord_less_real @ X @ Y))) = (X = Y)))))). % antisym_conv2
thf(fact_146_antisym__conv1, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => ((ord_less_eq_real @ X @ Y) = (X = Y)))))). % antisym_conv1
thf(fact_147_le__neq__trans, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((~ ((A = B))) => (ord_less_real @ A @ B)))))). % le_neq_trans
thf(fact_148_not__less, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) = (ord_less_eq_real @ Y @ X))))). % not_less
thf(fact_149_not__le, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_eq_real @ X @ Y))) = (ord_less_real @ Y @ X))))). % not_le
thf(fact_150_order__less__le__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X2 : real, Y2 : real]: ((ord_less_real @ X2 @ Y2) => (ord_less_real @ (F @ X2) @ (F @ Y2)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_le_subst2
thf(fact_151_order__less__le__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X2 : real, Y2 : real]: ((ord_less_eq_real @ X2 @ Y2) => (ord_less_eq_real @ (F @ X2) @ (F @ Y2)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_le_subst1
thf(fact_152_order__le__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X2 : real, Y2 : real]: ((ord_less_eq_real @ X2 @ Y2) => (ord_less_eq_real @ (F @ X2) @ (F @ Y2)))) => (ord_less_real @ (F @ A) @ C))))))). % order_le_less_subst2
thf(fact_153_order__le__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X2 : real, Y2 : real]: ((ord_less_real @ X2 @ Y2) => (ord_less_real @ (F @ X2) @ (F @ Y2)))) => (ord_less_real @ A @ (F @ C)))))))). % order_le_less_subst1
thf(fact_154_less__le, axiom,
    ((ord_less_real = (^[X3 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X3 @ Y4)) & ((~ ((X3 = Y4)))))))))). % less_le
thf(fact_155_le__less, axiom,
    ((ord_less_eq_real = (^[X3 : real]: (^[Y4 : real]: (((ord_less_real @ X3 @ Y4)) | ((X3 = Y4)))))))). % le_less
thf(fact_156_leI, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => (ord_less_eq_real @ Y @ X))))). % leI
thf(fact_157_leD, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ Y @ X) => (~ ((ord_less_real @ X @ Y))))))). % leD
thf(fact_158_mult__right__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_159_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_160_mult__left__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_161_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_162_no__zero__divisors, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (~ (((times_times_complex @ A @ B) = zero_zero_complex)))))))). % no_zero_divisors
thf(fact_163_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_164_divisors__zero, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) => ((A = zero_zero_complex) | (B = zero_zero_complex)))))). % divisors_zero
thf(fact_165_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_166_mult__not__zero, axiom,
    ((![A : complex, B : complex]: ((~ (((times_times_complex @ A @ B) = zero_zero_complex))) => ((~ ((A = zero_zero_complex))) & (~ ((B = zero_zero_complex)))))))). % mult_not_zero
thf(fact_167_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_168_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_169_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_170_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_171_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_172_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_173_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_174_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_175_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_176_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_177_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_178_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

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (real_V638595069omplex @ (times_times_complex @ (real_V306493662omplex @ t) @ w)) @ (real_V638595069omplex @ w)))).
