% 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/FFT/prob_118__3223822_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:16.015

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

% Explicit typings (16)
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal, type,
    neg_nu1973887165c_real : 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__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal, type,
    arcosh_real : real > real).
thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal, type,
    arsinh_real : real > real).
thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal, type,
    artanh_real : real > real).
thf(sy_c_Transcendental_Ocos_001t__Real__Oreal, type,
    cos_real : real > real).
thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal, type,
    ln_ln_real : real > real).
thf(sy_c_Transcendental_Osin_001t__Real__Oreal, type,
    sin_real : real > real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_x, type,
    x : real).

% Relevant facts (134)
thf(fact_0__C0_C, axiom,
    ((ord_less_real @ zero_zero_real @ x))). % "0"
thf(fact_1_cos__zero, axiom,
    (((cos_real @ zero_zero_real) = one_one_real))). % cos_zero
thf(fact_2_sin__zero, axiom,
    (((sin_real @ zero_zero_real) = zero_zero_real))). % sin_zero
thf(fact_3_cos__one__sin__zero, axiom,
    ((![X : real]: (((cos_real @ X) = one_one_real) => ((sin_real @ X) = zero_zero_real))))). % cos_one_sin_zero
thf(fact_4_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_5_arcosh__1, axiom,
    (((arcosh_real @ one_one_real) = zero_zero_real))). % arcosh_1
thf(fact_6_ln__one, axiom,
    (((ln_ln_real @ one_one_real) = zero_zero_real))). % ln_one
thf(fact_7_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_8_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_9_sin__zero__abs__cos__one, axiom,
    ((![X : real]: (((sin_real @ X) = zero_zero_real) => ((abs_abs_real @ (cos_real @ X)) = one_one_real))))). % sin_zero_abs_cos_one
thf(fact_10_sin__zero__norm__cos__one, axiom,
    ((![X : real]: (((sin_real @ X) = zero_zero_real) => ((real_V646646907m_real @ (cos_real @ X)) = one_one_real))))). % sin_zero_norm_cos_one
thf(fact_11_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_12_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_13_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_14_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_15_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_16_abs__0, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_0
thf(fact_17_ln__inj__iff, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ zero_zero_real @ Y) => (((ln_ln_real @ X) = (ln_ln_real @ Y)) = (X = Y))))))). % ln_inj_iff
thf(fact_18_ln__less__cancel__iff, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ zero_zero_real @ Y) => ((ord_less_real @ (ln_ln_real @ X) @ (ln_ln_real @ Y)) = (ord_less_real @ X @ Y))))))). % ln_less_cancel_iff
thf(fact_19_abs__1, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_1
thf(fact_20_zero__less__abs__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ A)) = (~ ((A = zero_zero_real))))))). % zero_less_abs_iff
thf(fact_21_ln__less__zero__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ (ln_ln_real @ X) @ zero_zero_real) = (ord_less_real @ X @ one_one_real)))))). % ln_less_zero_iff
thf(fact_22_ln__gt__zero__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ zero_zero_real @ (ln_ln_real @ X)) = (ord_less_real @ one_one_real @ X)))))). % ln_gt_zero_iff
thf(fact_23_ln__eq__zero__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => (((ln_ln_real @ X) = zero_zero_real) = (X = one_one_real)))))). % ln_eq_zero_iff
thf(fact_24_ln__less__self, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => (ord_less_real @ (ln_ln_real @ X) @ X))))). % ln_less_self
thf(fact_25_abs__of__pos, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_pos
thf(fact_26_abs__not__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (abs_abs_real @ A) @ zero_zero_real)))))). % abs_not_less_zero
thf(fact_27_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_28_abs__eq__0__iff, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0_iff
thf(fact_29_abs__one, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_one
thf(fact_30_ln__gt__zero__imp__gt__one, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ (ln_ln_real @ X)) => ((ord_less_real @ zero_zero_real @ X) => (ord_less_real @ one_one_real @ X)))))). % ln_gt_zero_imp_gt_one
thf(fact_31_ln__less__zero, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ one_one_real) => (ord_less_real @ (ln_ln_real @ X) @ zero_zero_real)))))). % ln_less_zero
thf(fact_32_ln__gt__zero, axiom,
    ((![X : real]: ((ord_less_real @ one_one_real @ X) => (ord_less_real @ zero_zero_real @ (ln_ln_real @ X)))))). % ln_gt_zero
thf(fact_33_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_34_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_35_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_36_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_37_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_38_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_39_Collect__mem__eq, axiom,
    ((![A2 : set_real]: ((collect_real @ (^[X2 : real]: (member_real @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_40_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_41_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_42_artanh__0, axiom,
    (((artanh_real @ zero_zero_real) = zero_zero_real))). % artanh_0
thf(fact_43_arsinh__0, axiom,
    (((arsinh_real @ zero_zero_real) = zero_zero_real))). % arsinh_0
thf(fact_44_norm__not__less__zero, axiom,
    ((![X : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_45_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_46_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_47_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_48_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_49_field__lbound__gt__zero, axiom,
    ((![D1 : real, D2 : real]: ((ord_less_real @ zero_zero_real @ D1) => ((ord_less_real @ zero_zero_real @ D2) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ D1) & (ord_less_real @ E @ D2))))))))). % field_lbound_gt_zero
thf(fact_50_dbl__inc__simps_I2_J, axiom,
    (((neg_nu1973887165c_real @ zero_zero_real) = one_one_real))). % dbl_inc_simps(2)
thf(fact_51_ln__ge__zero__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ X)) = (ord_less_eq_real @ one_one_real @ X)))))). % ln_ge_zero_iff
thf(fact_52_ln__le__zero__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_eq_real @ (ln_ln_real @ X) @ zero_zero_real) = (ord_less_eq_real @ X @ one_one_real)))))). % ln_le_zero_iff
thf(fact_53_ln__ge__zero__imp__ge__one, axiom,
    ((![X : real]: ((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ X)) => ((ord_less_real @ zero_zero_real @ X) => (ord_less_eq_real @ one_one_real @ X)))))). % ln_ge_zero_imp_ge_one
thf(fact_54_abs__of__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_nonneg
thf(fact_55_abs__le__self__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % abs_le_self_iff
thf(fact_56_abs__le__zero__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real))))). % abs_le_zero_iff
thf(fact_57_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_58_ln__le__cancel__iff, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ zero_zero_real @ Y) => ((ord_less_eq_real @ (ln_ln_real @ X) @ (ln_ln_real @ Y)) = (ord_less_eq_real @ X @ Y))))))). % ln_le_cancel_iff
thf(fact_59_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y2 : real]: (((ord_less_real @ X2 @ Y2)) | ((X2 = Y2)))))))). % less_eq_real_def
thf(fact_60_complete__real, axiom,
    ((![S : set_real]: ((?[X3 : real]: (member_real @ X3 @ S)) => ((?[Z : real]: (![X4 : real]: ((member_real @ X4 @ S) => (ord_less_eq_real @ X4 @ Z)))) => (?[Y3 : real]: ((![X3 : real]: ((member_real @ X3 @ S) => (ord_less_eq_real @ X3 @ Y3))) & (![Z : real]: ((![X4 : real]: ((member_real @ X4 @ S) => (ord_less_eq_real @ X4 @ Z))) => (ord_less_eq_real @ Y3 @ Z)))))))))). % complete_real
thf(fact_61_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_62_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_63_abs__le__D1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B))))). % abs_le_D1
thf(fact_64_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_65_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_66_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_67_abs__ge__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A))))). % abs_ge_zero
thf(fact_68_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_69_sin__x__le__x, axiom,
    ((![X : real]: ((ord_less_eq_real @ zero_zero_real @ X) => (ord_less_eq_real @ (sin_real @ X) @ X))))). % sin_x_le_x
thf(fact_70_cos__le__one, axiom,
    ((![X : real]: (ord_less_eq_real @ (cos_real @ X) @ one_one_real)))). % cos_le_one
thf(fact_71_sin__le__one, axiom,
    ((![X : real]: (ord_less_eq_real @ (sin_real @ X) @ one_one_real)))). % sin_le_one
thf(fact_72_abs__sin__x__le__abs__x, axiom,
    ((![X : real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ X)) @ (abs_abs_real @ X))))). % abs_sin_x_le_abs_x
thf(fact_73_dense__eq0__I, axiom,
    ((![X : real]: ((![E : real]: ((ord_less_real @ zero_zero_real @ E) => (ord_less_eq_real @ (abs_abs_real @ X) @ E))) => (X = zero_zero_real))))). % dense_eq0_I
thf(fact_74_ln__bound, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => (ord_less_eq_real @ (ln_ln_real @ X) @ X))))). % ln_bound
thf(fact_75_ln__ge__zero, axiom,
    ((![X : real]: ((ord_less_eq_real @ one_one_real @ X) => (ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ X)))))). % ln_ge_zero
thf(fact_76_abs__cos__le__one, axiom,
    ((![X : real]: (ord_less_eq_real @ (abs_abs_real @ (cos_real @ X)) @ one_one_real)))). % abs_cos_le_one
thf(fact_77_abs__sin__le__one, axiom,
    ((![X : real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ X)) @ one_one_real)))). % abs_sin_le_one
thf(fact_78_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_79_complete__interval, axiom,
    ((![A : real, B : real, P : real > $o]: ((ord_less_real @ A @ B) => ((P @ A) => ((~ ((P @ B))) => (?[C : real]: ((ord_less_eq_real @ A @ C) & ((ord_less_eq_real @ C @ B) & ((![X3 : real]: (((ord_less_eq_real @ A @ X3) & (ord_less_real @ X3 @ C)) => (P @ X3))) & (![D : real]: ((![X4 : real]: (((ord_less_eq_real @ A @ X4) & (ord_less_real @ X4 @ D)) => (P @ X4))) => (ord_less_eq_real @ D @ C))))))))))))). % complete_interval
thf(fact_80_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_81_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_82_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[B2 : real]: (^[A3 : real]: (((ord_less_eq_real @ B2 @ A3)) & ((~ ((A3 = B2)))))))))). % dual_order.strict_iff_order
thf(fact_83_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_84_dual__order_Oeq__iff, axiom,
    (((^[Y4 : real]: (^[Z2 : real]: (Y4 = Z2))) = (^[A3 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A3)) & ((ord_less_eq_real @ A3 @ B2)))))))). % dual_order.eq_iff
thf(fact_85_dual__order_Otrans, axiom,
    ((![B : real, A : real, C2 : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C2 @ B) => (ord_less_eq_real @ C2 @ A)))))). % dual_order.trans
thf(fact_86_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B3 : real]: ((ord_less_eq_real @ A4 @ B3) => (P @ A4 @ B3))) => ((![A4 : real, B3 : real]: ((P @ B3 @ A4) => (P @ A4 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_87_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_88_order__trans, axiom,
    ((![X : real, Y : real, Z3 : real]: ((ord_less_eq_real @ X @ Y) => ((ord_less_eq_real @ Y @ Z3) => (ord_less_eq_real @ X @ Z3)))))). % order_trans
thf(fact_89_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_90_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ A @ B) => ((B = C2) => (ord_less_eq_real @ A @ C2)))))). % ord_le_eq_trans
thf(fact_91_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C2 : real]: ((A = B) => ((ord_less_eq_real @ B @ C2) => (ord_less_eq_real @ A @ C2)))))). % ord_eq_le_trans
thf(fact_92_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y4 : real]: (^[Z2 : real]: (Y4 = Z2))) = (^[A3 : real]: (^[B2 : real]: (((ord_less_eq_real @ A3 @ B2)) & ((ord_less_eq_real @ B2 @ A3)))))))). % order_class.order.eq_iff
thf(fact_93_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_94_le__cases3, axiom,
    ((![X : real, Y : real, Z3 : real]: (((ord_less_eq_real @ X @ Y) => (~ ((ord_less_eq_real @ Y @ Z3)))) => (((ord_less_eq_real @ Y @ X) => (~ ((ord_less_eq_real @ X @ Z3)))) => (((ord_less_eq_real @ X @ Z3) => (~ ((ord_less_eq_real @ Z3 @ Y)))) => (((ord_less_eq_real @ Z3 @ Y) => (~ ((ord_less_eq_real @ Y @ X)))) => (((ord_less_eq_real @ Y @ Z3) => (~ ((ord_less_eq_real @ Z3 @ X)))) => (~ (((ord_less_eq_real @ Z3 @ X) => (~ ((ord_less_eq_real @ X @ Y)))))))))))))). % le_cases3
thf(fact_95_order_Otrans, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C2) => (ord_less_eq_real @ A @ C2)))))). % order.trans
thf(fact_96_le__cases, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_eq_real @ X @ Y))) => (ord_less_eq_real @ Y @ X))))). % le_cases
thf(fact_97_eq__refl, axiom,
    ((![X : real, Y : real]: ((X = Y) => (ord_less_eq_real @ X @ Y))))). % eq_refl
thf(fact_98_linear, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) | (ord_less_eq_real @ Y @ X))))). % linear
thf(fact_99_antisym, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) => ((ord_less_eq_real @ Y @ X) => (X = Y)))))). % antisym
thf(fact_100_eq__iff, axiom,
    (((^[Y4 : real]: (^[Z2 : real]: (Y4 = Z2))) = (^[X2 : real]: (^[Y2 : real]: (((ord_less_eq_real @ X2 @ Y2)) & ((ord_less_eq_real @ Y2 @ X2)))))))). % eq_iff
thf(fact_101_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C2 : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C2) => ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ Y3) => (ord_less_eq_real @ (F @ X4) @ (F @ Y3)))) => (ord_less_eq_real @ (F @ A) @ C2))))))). % ord_le_eq_subst
thf(fact_102_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C2 : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C2) => ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ Y3) => (ord_less_eq_real @ (F @ X4) @ (F @ Y3)))) => (ord_less_eq_real @ A @ (F @ C2)))))))). % ord_eq_le_subst
thf(fact_103_order__subst2, axiom,
    ((![A : real, B : real, F : real > real, C2 : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C2) => ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ Y3) => (ord_less_eq_real @ (F @ X4) @ (F @ Y3)))) => (ord_less_eq_real @ (F @ A) @ C2))))))). % order_subst2
thf(fact_104_order__subst1, axiom,
    ((![A : real, F : real > real, B : real, C2 : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C2) => ((![X4 : real, Y3 : real]: ((ord_less_eq_real @ X4 @ Y3) => (ord_less_eq_real @ (F @ X4) @ (F @ Y3)))) => (ord_less_eq_real @ A @ (F @ C2)))))))). % order_subst1
thf(fact_105_ex__gt__or__lt, axiom,
    ((![A : real]: (?[B3 : real]: ((ord_less_real @ A @ B3) | (ord_less_real @ B3 @ A)))))). % ex_gt_or_lt
thf(fact_106_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_107_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_108_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_109_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C2 : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C2 @ B) => (ord_less_real @ C2 @ A)))))). % dual_order.strict_trans
thf(fact_110_linorder__less__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B3 : real]: ((ord_less_real @ A4 @ B3) => (P @ A4 @ B3))) => ((![A4 : real]: (P @ A4 @ A4)) => ((![A4 : real, B3 : real]: ((P @ B3 @ A4) => (P @ A4 @ B3))) => (P @ A @ B))))))). % linorder_less_wlog
thf(fact_111_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_112_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C2) => (ord_less_real @ A @ C2)))))). % order.strict_trans
thf(fact_113_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_114_linorder__cases, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => ((~ ((X = Y))) => (ord_less_real @ Y @ X)))))). % linorder_cases
thf(fact_115_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_116_less__imp__not__eq2, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_117_antisym__conv3, axiom,
    ((![Y : real, X : real]: ((~ ((ord_less_real @ Y @ X))) => ((~ ((ord_less_real @ X @ Y))) = (X = Y)))))). % antisym_conv3
thf(fact_118_less__not__sym, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_not_sym
thf(fact_119_less__imp__not__eq, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_120_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_121_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ A @ B) => ((B = C2) => (ord_less_real @ A @ C2)))))). % ord_less_eq_trans
thf(fact_122_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C2 : real]: ((A = B) => ((ord_less_real @ B @ C2) => (ord_less_real @ A @ C2)))))). % ord_eq_less_trans
thf(fact_123_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_124_less__linear, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) | ((X = Y) | (ord_less_real @ Y @ X)))))). % less_linear
thf(fact_125_less__trans, axiom,
    ((![X : real, Y : real, Z3 : real]: ((ord_less_real @ X @ Y) => ((ord_less_real @ Y @ Z3) => (ord_less_real @ X @ Z3)))))). % less_trans
thf(fact_126_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_127_less__asym, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_asym
thf(fact_128_less__imp__neq, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_129_dense, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (?[Z4 : real]: ((ord_less_real @ X @ Z4) & (ord_less_real @ Z4 @ Y))))))). % dense
thf(fact_130_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_131_neq__iff, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) = (((ord_less_real @ X @ Y)) | ((ord_less_real @ Y @ X))))))). % neq_iff
thf(fact_132_neqE, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) => ((~ ((ord_less_real @ X @ Y))) => (ord_less_real @ Y @ X)))))). % neqE
thf(fact_133_gt__ex, axiom,
    ((![X : real]: (?[X_1 : real]: (ord_less_real @ X @ X_1))))). % gt_ex

% Conjectures (1)
thf(conj_0, conjecture,
    (((~ (((sin_real @ x) = zero_zero_real))) | (~ (((cos_real @ x) = one_one_real)))))).
