% 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_123__3223880_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:18.515

% Could-be-implicit typings (1)
thf(ty_n_t__Real__Oreal, type,
    real : $tType).

% Explicit typings (16)
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_real : 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__dec_001t__Real__Oreal, type,
    neg_nu533782273c_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_Real__Vector__Spaces_Oof__real_001t__Real__Oreal, type,
    real_V1205483228l_real : real > 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_Opi, type,
    pi : real).
thf(sy_c_Transcendental_Opowr_001t__Real__Oreal, type,
    powr_real : real > real > real).
thf(sy_c_Transcendental_Osin_001t__Real__Oreal, type,
    sin_real : real > real).
thf(sy_v_x, type,
    x : real).

% Relevant facts (135)
thf(fact_0__092_060open_062x_A_061_Api_092_060close_062, axiom,
    ((x = pi))). % \<open>x = pi\<close>
thf(fact_1__C0_C, axiom,
    ((ord_less_real @ zero_zero_real @ x))). % "0"
thf(fact_2_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_3_cos__zero, axiom,
    (((cos_real @ zero_zero_real) = one_one_real))). % cos_zero
thf(fact_4_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_5_cos__le__one, axiom,
    ((![X : real]: (ord_less_eq_real @ (cos_real @ X) @ one_one_real)))). % cos_le_one
thf(fact_6_of__real__1, axiom,
    (((real_V1205483228l_real @ one_one_real) = one_one_real))). % of_real_1
thf(fact_7_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_8_cos__of__real, axiom,
    ((![X : real]: ((cos_real @ (real_V1205483228l_real @ X)) = (real_V1205483228l_real @ (cos_real @ X)))))). % cos_of_real
thf(fact_9_cos__pi, axiom,
    (((cos_real @ pi) = (uminus_uminus_real @ one_one_real)))). % cos_pi
thf(fact_10_dbl__dec__simps_I3_J, axiom,
    (((neg_nu533782273c_real @ one_one_real) = one_one_real))). % dbl_dec_simps(3)
thf(fact_11_powr__one__eq__one, axiom,
    ((![A : real]: ((powr_real @ one_one_real @ A) = one_one_real)))). % powr_one_eq_one
thf(fact_12_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_13_neg__equal__iff__equal, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_14_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_15_neg__le__iff__le, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ B))))). % neg_le_iff_le
thf(fact_16_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_17_neg__0__equal__iff__equal, axiom,
    ((![A : real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A))))). % neg_0_equal_iff_equal
thf(fact_18_neg__equal__0__iff__equal, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % neg_equal_0_iff_equal
thf(fact_19_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_20_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_21_neg__less__iff__less, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ B))))). % neg_less_iff_less
thf(fact_22_powr__gt__zero, axiom,
    ((![X : real, A : real]: ((ord_less_real @ zero_zero_real @ (powr_real @ X @ A)) = (~ ((X = zero_zero_real))))))). % powr_gt_zero
thf(fact_23_powr__nonneg__iff, axiom,
    ((![A : real, X : real]: ((ord_less_eq_real @ (powr_real @ A @ X) @ zero_zero_real) = (A = zero_zero_real))))). % powr_nonneg_iff
thf(fact_24_powr__less__cancel__iff, axiom,
    ((![X : real, A : real, B : real]: ((ord_less_real @ one_one_real @ X) => ((ord_less_real @ (powr_real @ X @ A) @ (powr_real @ X @ B)) = (ord_less_real @ A @ B)))))). % powr_less_cancel_iff
thf(fact_25_norm__minus__cancel, axiom,
    ((![X : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X)) = (real_V646646907m_real @ X))))). % norm_minus_cancel
thf(fact_26_cos__minus, axiom,
    ((![X : real]: ((cos_real @ (uminus_uminus_real @ X)) = (cos_real @ X))))). % cos_minus
thf(fact_27_powr__0, axiom,
    ((![Z : real]: ((powr_real @ zero_zero_real @ Z) = zero_zero_real)))). % powr_0
thf(fact_28_powr__eq__0__iff, axiom,
    ((![W : real, Z : real]: (((powr_real @ W @ Z) = zero_zero_real) = (W = zero_zero_real))))). % powr_eq_0_iff
thf(fact_29_neg__0__le__iff__le, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real))))). % neg_0_le_iff_le
thf(fact_30_neg__le__0__iff__le, axiom,
    ((![A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_eq_real @ zero_zero_real @ A))))). % neg_le_0_iff_le
thf(fact_31_less__eq__neg__nonpos, axiom,
    ((![A : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real))))). % less_eq_neg_nonpos
thf(fact_32_neg__less__eq__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % neg_less_eq_nonneg
thf(fact_33_less__neg__neg, axiom,
    ((![A : real]: ((ord_less_real @ A @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real))))). % less_neg_neg
thf(fact_34_neg__less__pos, axiom,
    ((![A : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ A) = (ord_less_real @ zero_zero_real @ A))))). % neg_less_pos
thf(fact_35_neg__0__less__iff__less, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real))))). % neg_0_less_iff_less
thf(fact_36_neg__less__0__iff__less, axiom,
    ((![A : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_real @ zero_zero_real @ A))))). % neg_less_0_iff_less
thf(fact_37_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_38_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_39_powr__eq__one__iff, axiom,
    ((![A : real, X : real]: ((ord_less_real @ one_one_real @ A) => (((powr_real @ A @ X) = one_one_real) = (X = zero_zero_real)))))). % powr_eq_one_iff
thf(fact_40_powr__one, axiom,
    ((![X : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((powr_real @ X @ one_one_real) = X))))). % powr_one
thf(fact_41_powr__one__gt__zero__iff, axiom,
    ((![X : real]: (((powr_real @ X @ one_one_real) = X) = (ord_less_eq_real @ zero_zero_real @ X))))). % powr_one_gt_zero_iff
thf(fact_42_powr__le__cancel__iff, axiom,
    ((![X : real, A : real, B : real]: ((ord_less_real @ one_one_real @ X) => ((ord_less_eq_real @ (powr_real @ X @ A) @ (powr_real @ X @ B)) = (ord_less_eq_real @ A @ B)))))). % powr_le_cancel_iff
thf(fact_43_powr__zero__eq__one, axiom,
    ((![X : real]: (((X = zero_zero_real) => ((powr_real @ X @ zero_zero_real) = zero_zero_real)) & ((~ ((X = zero_zero_real))) => ((powr_real @ X @ zero_zero_real) = one_one_real)))))). % powr_zero_eq_one
thf(fact_44_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_45_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_46_of__real__minus, axiom,
    ((![X : real]: ((real_V1205483228l_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (real_V1205483228l_real @ X)))))). % of_real_minus
thf(fact_47_minus__of__real__eq__of__real__iff, axiom,
    ((![X : real, Y : real]: (((uminus_uminus_real @ (real_V1205483228l_real @ X)) = (real_V1205483228l_real @ Y)) = ((uminus_uminus_real @ X) = Y))))). % minus_of_real_eq_of_real_iff
thf(fact_48_of__real__eq__minus__of__real__iff, axiom,
    ((![X : real, Y : real]: (((real_V1205483228l_real @ X) = (uminus_uminus_real @ (real_V1205483228l_real @ Y))) = (X = (uminus_uminus_real @ Y)))))). % of_real_eq_minus_of_real_iff
thf(fact_49_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_50_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_51_dbl__dec__simps_I2_J, axiom,
    (((neg_nu533782273c_real @ zero_zero_real) = (uminus_uminus_real @ one_one_real)))). % dbl_dec_simps(2)
thf(fact_52_cos__of__real__pi, axiom,
    (((cos_real @ (real_V1205483228l_real @ pi)) = (uminus_uminus_real @ one_one_real)))). % cos_of_real_pi
thf(fact_53_le__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))))). % le_minus_one_simps(4)
thf(fact_54_le__minus__one__simps_I3_J, axiom,
    ((~ ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))))). % le_minus_one_simps(3)
thf(fact_55_le__minus__one__simps_I2_J, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ one_one_real))). % le_minus_one_simps(2)
thf(fact_56_le__minus__one__simps_I1_J, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real))). % le_minus_one_simps(1)
thf(fact_57_less__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))))). % less_minus_one_simps(4)
thf(fact_58_less__minus__one__simps_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))))). % less_minus_one_simps(3)
thf(fact_59_less__minus__one__simps_I2_J, axiom,
    ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ one_one_real))). % less_minus_one_simps(2)
thf(fact_60_less__minus__one__simps_I1_J, axiom,
    ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real))). % less_minus_one_simps(1)
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_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_63_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_64_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_65_powr__inj, axiom,
    ((![A : real, X : real, Y : real]: ((ord_less_real @ zero_zero_real @ A) => ((~ ((A = one_one_real))) => (((powr_real @ A @ X) = (powr_real @ A @ Y)) = (X = Y))))))). % powr_inj
thf(fact_66_powr__le1, axiom,
    ((![A : real, X : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ X @ one_one_real) => (ord_less_eq_real @ (powr_real @ X @ A) @ one_one_real))))))). % powr_le1
thf(fact_67_powr__mono, axiom,
    ((![A : real, B : real, X : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ one_one_real @ X) => (ord_less_eq_real @ (powr_real @ X @ A) @ (powr_real @ X @ B))))))). % powr_mono
thf(fact_68_cos__inj__pi, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ X @ pi) => ((ord_less_eq_real @ zero_zero_real @ Y) => ((ord_less_eq_real @ Y @ pi) => (((cos_real @ X) = (cos_real @ Y)) => (X = Y))))))))). % cos_inj_pi
thf(fact_69_pi__ge__zero, axiom,
    ((ord_less_eq_real @ zero_zero_real @ pi))). % pi_ge_zero
thf(fact_70_pi__gt__zero, axiom,
    ((ord_less_real @ zero_zero_real @ pi))). % pi_gt_zero
thf(fact_71_powr__mono2, axiom,
    ((![A : real, X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ X @ Y) => (ord_less_eq_real @ (powr_real @ X @ A) @ (powr_real @ Y @ A)))))))). % powr_mono2
thf(fact_72_gr__one__powr, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ one_one_real @ X) => ((ord_less_real @ zero_zero_real @ Y) => (ord_less_real @ one_one_real @ (powr_real @ X @ Y))))))). % gr_one_powr
thf(fact_73_pi__neq__zero, axiom,
    ((~ ((pi = zero_zero_real))))). % pi_neq_zero
thf(fact_74_powr__mono2_H, axiom,
    ((![A : real, X : real, Y : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ X) => ((ord_less_eq_real @ X @ Y) => (ord_less_eq_real @ (powr_real @ Y @ A) @ (powr_real @ X @ A)))))))). % powr_mono2'
thf(fact_75_powr__non__neg, axiom,
    ((![A : real, X : real]: (~ ((ord_less_real @ (powr_real @ A @ X) @ zero_zero_real)))))). % powr_non_neg
thf(fact_76_powr__ge__pzero, axiom,
    ((![X : real, Y : real]: (ord_less_eq_real @ zero_zero_real @ (powr_real @ X @ Y))))). % powr_ge_pzero
thf(fact_77_cos__mono__le__eq, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ X @ pi) => ((ord_less_eq_real @ zero_zero_real @ Y) => ((ord_less_eq_real @ Y @ pi) => ((ord_less_eq_real @ (cos_real @ X) @ (cos_real @ Y)) = (ord_less_eq_real @ Y @ X))))))))). % cos_mono_le_eq
thf(fact_78_powr__less__mono, axiom,
    ((![A : real, B : real, X : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ one_one_real @ X) => (ord_less_real @ (powr_real @ X @ A) @ (powr_real @ X @ B))))))). % powr_less_mono
thf(fact_79_powr__mono__both, axiom,
    ((![A : real, B : real, X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ one_one_real @ X) => ((ord_less_eq_real @ X @ Y) => (ord_less_eq_real @ (powr_real @ X @ A) @ (powr_real @ Y @ B))))))))). % powr_mono_both
thf(fact_80_powr__less__mono2, axiom,
    ((![A : real, X : real, Y : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_real @ X @ Y) => (ord_less_real @ (powr_real @ X @ A) @ (powr_real @ Y @ A)))))))). % powr_less_mono2
thf(fact_81_cos__mono__less__eq, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ X @ pi) => ((ord_less_eq_real @ zero_zero_real @ Y) => ((ord_less_eq_real @ Y @ pi) => ((ord_less_real @ (cos_real @ X) @ (cos_real @ Y)) = (ord_less_real @ Y @ X))))))))). % cos_mono_less_eq
thf(fact_82_pi__not__less__zero, axiom,
    ((~ ((ord_less_real @ pi @ zero_zero_real))))). % pi_not_less_zero
thf(fact_83_powr__less__cancel, axiom,
    ((![X : real, A : real, B : real]: ((ord_less_real @ (powr_real @ X @ A) @ (powr_real @ X @ B)) => ((ord_less_real @ one_one_real @ X) => (ord_less_real @ A @ B)))))). % powr_less_cancel
thf(fact_84_cos__monotone__0__pi, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ zero_zero_real @ Y) => ((ord_less_real @ Y @ X) => ((ord_less_eq_real @ X @ pi) => (ord_less_real @ (cos_real @ X) @ (cos_real @ Y)))))))). % cos_monotone_0_pi
thf(fact_85_ge__one__powr__ge__zero, axiom,
    ((![X : real, A : real]: ((ord_less_eq_real @ one_one_real @ X) => ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ one_one_real @ (powr_real @ X @ A))))))). % ge_one_powr_ge_zero
thf(fact_86_powr__less__mono2__neg, axiom,
    ((![A : real, X : real, Y : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ Y) => (ord_less_real @ (powr_real @ Y @ A) @ (powr_real @ X @ A)))))))). % powr_less_mono2_neg
thf(fact_87_cos__monotone__0__pi__le, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ zero_zero_real @ Y) => ((ord_less_eq_real @ Y @ X) => ((ord_less_eq_real @ X @ pi) => (ord_less_eq_real @ (cos_real @ X) @ (cos_real @ Y)))))))). % cos_monotone_0_pi_le
thf(fact_88_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_real = (uminus_uminus_real @ one_one_real)))))). % zero_neq_neg_one
thf(fact_89_cos__monotone__minus__pi__0, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ (uminus_uminus_real @ pi) @ Y) => ((ord_less_real @ Y @ X) => ((ord_less_eq_real @ X @ zero_zero_real) => (ord_less_real @ (cos_real @ Y) @ (cos_real @ X)))))))). % cos_monotone_minus_pi_0
thf(fact_90_cos__monotone__minus__pi__0_H, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ (uminus_uminus_real @ pi) @ Y) => ((ord_less_eq_real @ Y @ X) => ((ord_less_eq_real @ X @ zero_zero_real) => (ord_less_eq_real @ (cos_real @ Y) @ (cos_real @ X)))))))). % cos_monotone_minus_pi_0'
thf(fact_91_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_92_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_93_le__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A)))))). % le_minus_iff
thf(fact_94_minus__le__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ A))))). % minus_le_iff
thf(fact_95_le__imp__neg__le, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % le_imp_neg_le
thf(fact_96_less__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ (uminus_uminus_real @ A)))))). % less_minus_iff
thf(fact_97_minus__less__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ B) = (ord_less_real @ (uminus_uminus_real @ B) @ A))))). % minus_less_iff
thf(fact_98_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_99_norm__not__less__zero, axiom,
    ((![X : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_100_cos__total, axiom,
    ((![Y : real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ Y) => ((ord_less_eq_real @ Y @ one_one_real) => (?[X2 : real]: (((ord_less_eq_real @ zero_zero_real @ X2) & ((ord_less_eq_real @ X2 @ pi) & ((cos_real @ X2) = Y))) & (![Y2 : real]: (((ord_less_eq_real @ zero_zero_real @ Y2) & ((ord_less_eq_real @ Y2 @ pi) & ((cos_real @ Y2) = Y))) => (Y2 = X2)))))))))). % cos_total
thf(fact_101_one__neq__neg__one, axiom,
    ((~ ((one_one_real = (uminus_uminus_real @ one_one_real)))))). % one_neq_neg_one
thf(fact_102_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_103_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_104_cos__ge__minus__one, axiom,
    ((![X : real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (cos_real @ X))))). % cos_ge_minus_one
thf(fact_105_arcosh__1, axiom,
    (((arcosh_real @ one_one_real) = zero_zero_real))). % arcosh_1
thf(fact_106_arsinh__0, axiom,
    (((arsinh_real @ zero_zero_real) = zero_zero_real))). % arsinh_0
thf(fact_107_artanh__0, axiom,
    (((artanh_real @ zero_zero_real) = zero_zero_real))). % artanh_0
thf(fact_108_calculation, axiom,
    (((ord_less_real @ zero_zero_real @ x) => ((ord_less_real @ x @ pi) => (~ (((sin_real @ x) = zero_zero_real))))))). % calculation
thf(fact_109_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_110_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_111_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_112_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_113_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_114_arsinh__minus__real, axiom,
    ((![X : real]: ((arsinh_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (arsinh_real @ X)))))). % arsinh_minus_real
thf(fact_115_sin__zero, axiom,
    (((sin_real @ zero_zero_real) = zero_zero_real))). % sin_zero
thf(fact_116_sin__minus, axiom,
    ((![X : real]: ((sin_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (sin_real @ X)))))). % sin_minus
thf(fact_117_sin__pi, axiom,
    (((sin_real @ pi) = zero_zero_real))). % sin_pi
thf(fact_118_sin__of__real__pi, axiom,
    (((sin_real @ (real_V1205483228l_real @ pi)) = zero_zero_real))). % sin_of_real_pi
thf(fact_119_sin__of__real, axiom,
    ((![X : real]: ((sin_real @ (real_V1205483228l_real @ X)) = (real_V1205483228l_real @ (sin_real @ X)))))). % sin_of_real
thf(fact_120_powr__powr__swap, axiom,
    ((![X : real, A : real, B : real]: ((powr_real @ (powr_real @ X @ A) @ B) = (powr_real @ (powr_real @ X @ B) @ A))))). % powr_powr_swap
thf(fact_121_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_122_sin__le__one, axiom,
    ((![X : real]: (ord_less_eq_real @ (sin_real @ X) @ one_one_real)))). % sin_le_one
thf(fact_123_sin__gt__zero, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ pi) => (ord_less_real @ zero_zero_real @ (sin_real @ X))))))). % sin_gt_zero
thf(fact_124_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_125_sin__x__ge__neg__x, axiom,
    ((![X : real]: ((ord_less_eq_real @ zero_zero_real @ X) => (ord_less_eq_real @ (uminus_uminus_real @ X) @ (sin_real @ X)))))). % sin_x_ge_neg_x
thf(fact_126_sin__ge__zero, axiom,
    ((![X : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ X @ pi) => (ord_less_eq_real @ zero_zero_real @ (sin_real @ X))))))). % sin_ge_zero
thf(fact_127_sin__ge__minus__one, axiom,
    ((![X : real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (sin_real @ X))))). % sin_ge_minus_one
thf(fact_128_verit__la__disequality, axiom,
    ((![A : real, B : real]: ((A = B) | ((~ ((ord_less_eq_real @ A @ B))) | (~ ((ord_less_eq_real @ B @ A)))))))). % verit_la_disequality
thf(fact_129_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_130_verit__comp__simplify1_I1_J, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_131_verit__negate__coefficient_I3_J, axiom,
    ((![A : real, B : real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B)))))). % verit_negate_coefficient(3)
thf(fact_132_sin__eq__0__pi, axiom,
    ((![X : real]: ((ord_less_real @ (uminus_uminus_real @ pi) @ X) => ((ord_less_real @ X @ pi) => (((sin_real @ X) = zero_zero_real) => (X = zero_zero_real))))))). % sin_eq_0_pi
thf(fact_133_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_134_sincos__principal__value, axiom,
    ((![X : real]: (?[Y3 : real]: (((ord_less_real @ (uminus_uminus_real @ pi) @ Y3) & (ord_less_eq_real @ Y3 @ pi)) & (((sin_real @ Y3) = (sin_real @ X)) & ((cos_real @ Y3) = (cos_real @ X)))))))). % sincos_principal_value

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