% 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_774__5375432_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:33:01.031

% 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 (18)
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_Obounded__linear__axioms_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    real_V479504201omplex : (complex > complex) > $o).
thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001t__Complex__Ocomplex_001t__Real__Oreal, type,
    real_V1956525511x_real : (complex > real) > $o).
thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001t__Real__Oreal_001t__Complex__Ocomplex, type,
    real_V1677925191omplex : (real > complex) > $o).
thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001t__Real__Oreal_001t__Real__Oreal, type,
    real_V2133591749l_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_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 (165)
thf(fact_0_t_I2_J, axiom,
    ((ord_less_real @ t @ one_one_real))). % t(2)
thf(fact_1_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_2_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_3_mult_Oleft__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ one_one_complex @ A) = A)))). % mult.left_neutral
thf(fact_4_mult_Oleft__neutral, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % mult.left_neutral
thf(fact_5_mult_Oright__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ A @ one_one_complex) = A)))). % mult.right_neutral
thf(fact_6_mult_Oright__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.right_neutral
thf(fact_7_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_8_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_9_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_10_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_11_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_12_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : complex]: ((times_times_complex @ one_one_complex @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_13_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_14_mult_Ocomm__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ A @ one_one_complex) = A)))). % mult.comm_neutral
thf(fact_15_mult_Ocomm__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.comm_neutral
thf(fact_16_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_17_w0, axiom,
    ((~ ((w = zero_zero_complex))))). % w0
thf(fact_18_bounded__linear__axioms__def, axiom,
    ((real_V479504201omplex = (^[F : complex > complex]: (?[K : real]: (![X2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (F @ X2)) @ (times_times_real @ (real_V638595069omplex @ X2) @ K)))))))). % bounded_linear_axioms_def
thf(fact_19_bounded__linear__axioms__def, axiom,
    ((real_V1677925191omplex = (^[F : real > complex]: (?[K : real]: (![X2 : real]: (ord_less_eq_real @ (real_V638595069omplex @ (F @ X2)) @ (times_times_real @ (real_V646646907m_real @ X2) @ K)))))))). % bounded_linear_axioms_def
thf(fact_20_bounded__linear__axioms__def, axiom,
    ((real_V1956525511x_real = (^[F : complex > real]: (?[K : real]: (![X2 : complex]: (ord_less_eq_real @ (real_V646646907m_real @ (F @ X2)) @ (times_times_real @ (real_V638595069omplex @ X2) @ K)))))))). % bounded_linear_axioms_def
thf(fact_21_bounded__linear__axioms__def, axiom,
    ((real_V2133591749l_real = (^[F : real > real]: (?[K : real]: (![X2 : real]: (ord_less_eq_real @ (real_V646646907m_real @ (F @ X2)) @ (times_times_real @ (real_V646646907m_real @ X2) @ K)))))))). % bounded_linear_axioms_def
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_t_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ t))). % t(1)
thf(fact_25_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_26_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_27_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_28_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_29_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_30_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_31_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_32_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_33_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_34_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_35_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_36_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_37_ord__eq__less__subst, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((A = (F2 @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_real @ A @ (F2 @ C)))))))). % ord_eq_less_subst
thf(fact_38_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_real @ A @ B) => (((F2 @ B) = C) => ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_real @ (F2 @ A) @ C))))))). % ord_less_eq_subst
thf(fact_39_order__less__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_real @ A @ (F2 @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_less_subst1
thf(fact_40_order__less__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F2 @ B) @ C) => ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_less_subst2
thf(fact_41_lt__ex, axiom,
    ((![X : real]: (?[Y2 : real]: (ord_less_real @ Y2 @ X))))). % lt_ex
thf(fact_42_gt__ex, axiom,
    ((![X : real]: (?[X_1 : real]: (ord_less_real @ X @ X_1))))). % gt_ex
thf(fact_43_neqE, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) => ((~ ((ord_less_real @ X @ Y))) => (ord_less_real @ Y @ X)))))). % neqE
thf(fact_44_neq__iff, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) = (((ord_less_real @ X @ Y)) | ((ord_less_real @ Y @ X))))))). % neq_iff
thf(fact_45_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_46_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_47_less__imp__neq, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_48_less__asym, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_asym
thf(fact_49_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_50_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_51_less__linear, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) | ((X = Y) | (ord_less_real @ Y @ X)))))). % less_linear
thf(fact_52_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_53_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_54_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_55_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_56_less__imp__not__eq, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_57_less__not__sym, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_not_sym
thf(fact_58_antisym__conv3, axiom,
    ((![Y : real, X : real]: ((~ ((ord_less_real @ Y @ X))) => ((~ ((ord_less_real @ X @ Y))) = (X = Y)))))). % antisym_conv3
thf(fact_59_less__imp__not__eq2, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_60_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_61_linorder__cases, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => ((~ ((X = Y))) => (ord_less_real @ Y @ X)))))). % linorder_cases
thf(fact_62_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_63_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_64_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_65_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_66_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_67_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_68_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_69_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_70_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_12 : real]: (P @ X_12)) => ((?[Z3 : real]: (![X3 : real]: ((P @ X3) => (ord_less_real @ X3 @ Z3)))) => (?[S : real]: (![Y3 : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y3 @ X2)))) = (ord_less_real @ Y3 @ S))))))))). % real_sup_exists
thf(fact_71_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_72_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_73_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_74_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_75_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_76_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_77_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_78_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_79_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_80_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_81_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_82_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_83_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_84_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_85_less__le__not__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X2 @ Y4)) & ((~ ((ord_less_eq_real @ Y4 @ X2)))))))))). % less_le_not_le
thf(fact_86_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_87_le__less__linear, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) | (ord_less_real @ Y @ X))))). % le_less_linear
thf(fact_88_dense__le, axiom,
    ((![Y : real, Z2 : real]: ((![X3 : real]: ((ord_less_real @ X3 @ Y) => (ord_less_eq_real @ X3 @ Z2))) => (ord_less_eq_real @ Y @ Z2))))). % dense_le
thf(fact_89_dense__ge, axiom,
    ((![Z2 : real, Y : real]: ((![X3 : real]: ((ord_less_real @ Z2 @ X3) => (ord_less_eq_real @ Y @ X3))) => (ord_less_eq_real @ Y @ Z2))))). % dense_ge
thf(fact_90_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_91_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_92_less__imp__le, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (ord_less_eq_real @ X @ Y))))). % less_imp_le
thf(fact_93_antisym__conv2, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) => ((~ ((ord_less_real @ X @ Y))) = (X = Y)))))). % antisym_conv2
thf(fact_94_antisym__conv1, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => ((ord_less_eq_real @ X @ Y) = (X = Y)))))). % antisym_conv1
thf(fact_95_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_96_not__less, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) = (ord_less_eq_real @ Y @ X))))). % not_less
thf(fact_97_not__le, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_eq_real @ X @ Y))) = (ord_less_real @ Y @ X))))). % not_le
thf(fact_98_order__less__le__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F2 @ B) @ C) => ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_less_le_subst2
thf(fact_99_order__less__le__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_real @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => (ord_less_eq_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_less_le_subst1
thf(fact_100_order__le__less__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F2 @ B) @ C) => ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => (ord_less_eq_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_real @ (F2 @ A) @ C))))))). % order_le_less_subst2
thf(fact_101_order__le__less__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F2 @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_real @ A @ (F2 @ C)))))))). % order_le_less_subst1
thf(fact_102_less__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X2 @ Y4)) & ((~ ((X2 = Y4)))))))))). % less_le
thf(fact_103_le__less, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y4 : real]: (((ord_less_real @ X2 @ Y4)) | ((X2 = Y4)))))))). % le_less
thf(fact_104_leI, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => (ord_less_eq_real @ Y @ X))))). % leI
thf(fact_105_leD, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ Y @ X) => (~ ((ord_less_real @ X @ Y))))))). % leD
thf(fact_106_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_107_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_108_norm__mult__less, axiom,
    ((![X : complex, R : real, Y : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y) @ S2) => (ord_less_real @ (real_V638595069omplex @ (times_times_complex @ X @ Y)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_109_norm__mult__less, axiom,
    ((![X : real, R : real, Y : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y) @ S2) => (ord_less_real @ (real_V646646907m_real @ (times_times_real @ X @ Y)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_110_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_111_dual__order_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z4 : real]: (Y5 = Z4))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((ord_less_eq_real @ A3 @ B3)))))))). % dual_order.eq_iff
thf(fact_112_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_113_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A2 : real, B2 : real]: ((ord_less_eq_real @ A2 @ B2) => (P @ A2 @ B2))) => ((![A2 : real, B2 : real]: ((P @ B2 @ A2) => (P @ A2 @ B2))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_114_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_115_order__trans, axiom,
    ((![X : real, Y : real, Z2 : real]: ((ord_less_eq_real @ X @ Y) => ((ord_less_eq_real @ Y @ Z2) => (ord_less_eq_real @ X @ Z2)))))). % order_trans
thf(fact_116_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_117_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_118_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_119_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z4 : real]: (Y5 = Z4))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ A3 @ B3)) & ((ord_less_eq_real @ B3 @ A3)))))))). % order_class.order.eq_iff
thf(fact_120_antisym__conv, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ Y @ X) => ((ord_less_eq_real @ X @ Y) = (X = Y)))))). % antisym_conv
thf(fact_121_le__cases3, axiom,
    ((![X : real, Y : real, Z2 : real]: (((ord_less_eq_real @ X @ Y) => (~ ((ord_less_eq_real @ Y @ Z2)))) => (((ord_less_eq_real @ Y @ X) => (~ ((ord_less_eq_real @ X @ Z2)))) => (((ord_less_eq_real @ X @ Z2) => (~ ((ord_less_eq_real @ Z2 @ Y)))) => (((ord_less_eq_real @ Z2 @ Y) => (~ ((ord_less_eq_real @ Y @ X)))) => (((ord_less_eq_real @ Y @ Z2) => (~ ((ord_less_eq_real @ Z2 @ X)))) => (~ (((ord_less_eq_real @ Z2 @ X) => (~ ((ord_less_eq_real @ X @ Y)))))))))))))). % le_cases3
thf(fact_122_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_123_le__cases, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_eq_real @ X @ Y))) => (ord_less_eq_real @ Y @ X))))). % le_cases
thf(fact_124_eq__refl, axiom,
    ((![X : real, Y : real]: ((X = Y) => (ord_less_eq_real @ X @ Y))))). % eq_refl
thf(fact_125_linear, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) | (ord_less_eq_real @ Y @ X))))). % linear
thf(fact_126_antisym, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) => ((ord_less_eq_real @ Y @ X) => (X = Y)))))). % antisym
thf(fact_127_eq__iff, axiom,
    (((^[Y5 : real]: (^[Z4 : real]: (Y5 = Z4))) = (^[X2 : real]: (^[Y4 : real]: (((ord_less_eq_real @ X2 @ Y4)) & ((ord_less_eq_real @ Y4 @ X2)))))))). % eq_iff
thf(fact_128_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F2 @ B) = C) => ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => (ord_less_eq_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_129_ord__eq__le__subst, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((A = (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => (ord_less_eq_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_130_order__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F2 @ B) @ C) => ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => (ord_less_eq_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_131_order__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ Y2) => (ord_less_eq_real @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_132_mult_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((times_times_real @ B @ (times_times_real @ A @ C)) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.left_commute
thf(fact_133_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_134_mult_Ocommute, axiom,
    ((times_times_real = (^[A3 : real]: (^[B3 : real]: (times_times_real @ B3 @ A3)))))). % mult.commute
thf(fact_135_mult_Ocommute, axiom,
    ((times_times_complex = (^[A3 : complex]: (^[B3 : complex]: (times_times_complex @ B3 @ A3)))))). % mult.commute
thf(fact_136_mult_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.assoc
thf(fact_137_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_138_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_139_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_140_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_141_one__reorient, axiom,
    ((![X : complex]: ((one_one_complex = X) = (X = one_one_complex))))). % one_reorient
thf(fact_142_bounded__linear__axioms_Ointro, axiom,
    ((![F2 : complex > complex]: ((?[K2 : real]: (![X3 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (F2 @ X3)) @ (times_times_real @ (real_V638595069omplex @ X3) @ K2)))) => (real_V479504201omplex @ F2))))). % bounded_linear_axioms.intro
thf(fact_143_bounded__linear__axioms_Ointro, axiom,
    ((![F2 : real > complex]: ((?[K2 : real]: (![X3 : real]: (ord_less_eq_real @ (real_V638595069omplex @ (F2 @ X3)) @ (times_times_real @ (real_V646646907m_real @ X3) @ K2)))) => (real_V1677925191omplex @ F2))))). % bounded_linear_axioms.intro
thf(fact_144_bounded__linear__axioms_Ointro, axiom,
    ((![F2 : complex > real]: ((?[K2 : real]: (![X3 : complex]: (ord_less_eq_real @ (real_V646646907m_real @ (F2 @ X3)) @ (times_times_real @ (real_V638595069omplex @ X3) @ K2)))) => (real_V1956525511x_real @ F2))))). % bounded_linear_axioms.intro
thf(fact_145_bounded__linear__axioms_Ointro, axiom,
    ((![F2 : real > real]: ((?[K2 : real]: (![X3 : real]: (ord_less_eq_real @ (real_V646646907m_real @ (F2 @ X3)) @ (times_times_real @ (real_V646646907m_real @ X3) @ K2)))) => (real_V2133591749l_real @ F2))))). % bounded_linear_axioms.intro
thf(fact_146_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_147_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_148_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_149_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_150_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_151_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_152_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_153_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_154_field__le__mult__one__interval, axiom,
    ((![X : real, Y : real]: ((![Z : real]: ((ord_less_real @ zero_zero_real @ Z) => ((ord_less_real @ Z @ one_one_real) => (ord_less_eq_real @ (times_times_real @ Z @ X) @ Y)))) => (ord_less_eq_real @ X @ Y))))). % field_le_mult_one_interval
thf(fact_155_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_156_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_157_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_158_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_159_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_160_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_161_mult__zero__left, axiom,
    ((![A : real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real)))). % mult_zero_left
thf(fact_162_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_163_mult__zero__right, axiom,
    ((![A : real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real)))). % mult_zero_right
thf(fact_164_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (times_times_real @ t @ (real_V638595069omplex @ w)) @ (times_times_real @ one_one_real @ (real_V638595069omplex @ w))))).
