% 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_127__3223962_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:21.065

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

% Explicit typings (15)
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > 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_If_001t__Real__Oreal, type,
    if_real : $o > real > real > real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal, type,
    real_V1205483228l_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_Ocot_001t__Real__Oreal, type,
    cot_real : real > real).
thf(sy_c_Transcendental_Opi, type,
    pi : real).
thf(sy_c_Transcendental_Osin_001t__Real__Oreal, type,
    sin_real : real > real).
thf(sy_v_x, type,
    x : real).

% Relevant facts (128)
thf(fact_0_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_1__092_060open_062x_A_N_Api_A_060_Api_092_060close_062, axiom,
    ((ord_less_real @ (minus_minus_real @ x @ pi) @ pi))). % \<open>x - pi < pi\<close>
thf(fact_2__C0_C, axiom,
    ((ord_less_real @ zero_zero_real @ x))). % "0"
thf(fact_3_pi1, axiom,
    ((ord_less_real @ pi @ x))). % pi1
thf(fact_4__092_060open_0620_A_060_Ax_A_N_Api_092_060close_062, axiom,
    ((ord_less_real @ zero_zero_real @ (minus_minus_real @ x @ pi)))). % \<open>0 < x - pi\<close>
thf(fact_5_calculation_I1_J, axiom,
    (((ord_less_real @ zero_zero_real @ x) => ((ord_less_real @ x @ pi) => (~ (((sin_real @ x) = zero_zero_real))))))). % calculation(1)
thf(fact_6_sin__pi__minus, axiom,
    ((![X : real]: ((sin_real @ (minus_minus_real @ pi @ X)) = (sin_real @ X))))). % sin_pi_minus
thf(fact_7_sin__pi, axiom,
    (((sin_real @ pi) = zero_zero_real))). % sin_pi
thf(fact_8_sin__zero, axiom,
    (((sin_real @ zero_zero_real) = zero_zero_real))). % sin_zero
thf(fact_9_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_10_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_11_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_12_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_13_pi__neq__zero, axiom,
    ((~ ((pi = zero_zero_real))))). % pi_neq_zero
thf(fact_14_eq__iff__diff__eq__0, axiom,
    (((^[Y : real]: (^[Z : real]: (Y = Z))) = (^[A2 : real]: (^[B : real]: ((minus_minus_real @ A2 @ B) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_15_diff__gt__0__iff__gt, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B2)) = (ord_less_real @ B2 @ A))))). % diff_gt_0_iff_gt
thf(fact_16_diff__strict__right__mono, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_real @ A @ B2) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B2 @ C)))))). % diff_strict_right_mono
thf(fact_17_diff__strict__left__mono, axiom,
    ((![B2 : real, A : real, C : real]: ((ord_less_real @ B2 @ A) => (ord_less_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B2)))))). % diff_strict_left_mono
thf(fact_18_diff__eq__diff__less, axiom,
    ((![A : real, B2 : real, C : real, D : real]: (((minus_minus_real @ A @ B2) = (minus_minus_real @ C @ D)) => ((ord_less_real @ A @ B2) = (ord_less_real @ C @ D)))))). % diff_eq_diff_less
thf(fact_19_diff__strict__mono, axiom,
    ((![A : real, B2 : real, D : real, C : real]: ((ord_less_real @ A @ B2) => ((ord_less_real @ D @ C) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B2 @ D))))))). % diff_strict_mono
thf(fact_20_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_21_diff__right__commute, axiom,
    ((![A : real, C : real, B2 : real]: ((minus_minus_real @ (minus_minus_real @ A @ C) @ B2) = (minus_minus_real @ (minus_minus_real @ A @ B2) @ C))))). % diff_right_commute
thf(fact_22_diff__eq__diff__eq, axiom,
    ((![A : real, B2 : real, C : real, D : real]: (((minus_minus_real @ A @ B2) = (minus_minus_real @ C @ D)) => ((A = B2) = (C = D)))))). % diff_eq_diff_eq
thf(fact_23_less__iff__diff__less__0, axiom,
    ((ord_less_real = (^[A2 : real]: (^[B : real]: (ord_less_real @ (minus_minus_real @ A2 @ B) @ zero_zero_real)))))). % less_iff_diff_less_0
thf(fact_24_pi__not__less__zero, axiom,
    ((~ ((ord_less_real @ pi @ zero_zero_real))))). % pi_not_less_zero
thf(fact_25_pi__gt__zero, axiom,
    ((ord_less_real @ zero_zero_real @ pi))). % pi_gt_zero
thf(fact_26_artanh__0, axiom,
    (((artanh_real @ zero_zero_real) = zero_zero_real))). % artanh_0
thf(fact_27_arsinh__0, axiom,
    (((arsinh_real @ zero_zero_real) = zero_zero_real))). % arsinh_0
thf(fact_28_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_29_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_30_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_31_sin__periodic__pi__diff, axiom,
    ((![X : real]: ((sin_real @ (minus_minus_real @ X @ pi)) = (uminus_uminus_real @ (sin_real @ X)))))). % sin_periodic_pi_diff
thf(fact_32_sin__zero__pi__iff, axiom,
    ((![X : real]: ((ord_less_real @ (abs_abs_real @ X) @ pi) => (((sin_real @ X) = zero_zero_real) = (X = zero_zero_real)))))). % sin_zero_pi_iff
thf(fact_33_cot__pi, axiom,
    (((cot_real @ pi) = zero_zero_real))). % cot_pi
thf(fact_34_sin__of__real__pi, axiom,
    (((sin_real @ (real_V1205483228l_real @ pi)) = zero_zero_real))). % sin_of_real_pi
thf(fact_35_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_36_neg__equal__iff__equal, axiom,
    ((![A : real, B2 : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B2)) = (A = B2))))). % neg_equal_iff_equal
thf(fact_37_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_38_arsinh__minus__real, axiom,
    ((![X : real]: ((arsinh_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (arsinh_real @ X)))))). % arsinh_minus_real
thf(fact_39_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_40_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_41_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_42_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_43_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_44_neg__less__iff__less, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ (uminus_uminus_real @ B2) @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ B2))))). % neg_less_iff_less
thf(fact_45_minus__diff__eq, axiom,
    ((![A : real, B2 : real]: ((uminus_uminus_real @ (minus_minus_real @ A @ B2)) = (minus_minus_real @ B2 @ A))))). % minus_diff_eq
thf(fact_46_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_47_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_48_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_49_abs__minus__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus_cancel
thf(fact_50_sin__minus, axiom,
    ((![X : real]: ((sin_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (sin_real @ X)))))). % sin_minus
thf(fact_51_cot__zero, axiom,
    (((cot_real @ zero_zero_real) = zero_zero_real))). % cot_zero
thf(fact_52_cot__minus, axiom,
    ((![X : real]: ((cot_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (cot_real @ X)))))). % cot_minus
thf(fact_53_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_54_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_55_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_56_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_57_diff__0, axiom,
    ((![A : real]: ((minus_minus_real @ zero_zero_real @ A) = (uminus_uminus_real @ A))))). % diff_0
thf(fact_58_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_59_cot__of__real, axiom,
    ((![X : real]: ((real_V1205483228l_real @ (cot_real @ X)) = (cot_real @ (real_V1205483228l_real @ X)))))). % cot_of_real
thf(fact_60_equation__minus__iff, axiom,
    ((![A : real, B2 : real]: ((A = (uminus_uminus_real @ B2)) = (B2 = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_61_minus__equation__iff, axiom,
    ((![A : real, B2 : real]: (((uminus_uminus_real @ A) = B2) = ((uminus_uminus_real @ B2) = A))))). % minus_equation_iff
thf(fact_62_minus__diff__minus, axiom,
    ((![A : real, B2 : real]: ((minus_minus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B2)) = (uminus_uminus_real @ (minus_minus_real @ A @ B2)))))). % minus_diff_minus
thf(fact_63_abs__real__def, axiom,
    ((abs_abs_real = (^[A2 : real]: (if_real @ (ord_less_real @ A2 @ zero_zero_real) @ (uminus_uminus_real @ A2) @ A2))))). % abs_real_def
thf(fact_64_abs__of__neg, axiom,
    ((![A : real]: ((ord_less_real @ A @ zero_zero_real) => ((abs_abs_real @ A) = (uminus_uminus_real @ A)))))). % abs_of_neg
thf(fact_65_abs__minus__commute, axiom,
    ((![A : real, B2 : real]: ((abs_abs_real @ (minus_minus_real @ A @ B2)) = (abs_abs_real @ (minus_minus_real @ B2 @ A)))))). % abs_minus_commute
thf(fact_66_minus__less__iff, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ B2) = (ord_less_real @ (uminus_uminus_real @ B2) @ A))))). % minus_less_iff
thf(fact_67_less__minus__iff, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ (uminus_uminus_real @ B2)) = (ord_less_real @ B2 @ (uminus_uminus_real @ A)))))). % less_minus_iff
thf(fact_68_minus__diff__commute, axiom,
    ((![B2 : real, A : real]: ((minus_minus_real @ (uminus_uminus_real @ B2) @ A) = (minus_minus_real @ (uminus_uminus_real @ A) @ B2))))). % minus_diff_commute
thf(fact_69_abs__of__pos, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_pos
thf(fact_70_abs__not__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (abs_abs_real @ A) @ zero_zero_real)))))). % abs_not_less_zero
thf(fact_71_sin__of__real, axiom,
    ((![X : real]: ((sin_real @ (real_V1205483228l_real @ X)) = (real_V1205483228l_real @ (sin_real @ X)))))). % sin_of_real
thf(fact_72_of__real__diff, axiom,
    ((![X : real, Y2 : real]: ((real_V1205483228l_real @ (minus_minus_real @ X @ Y2)) = (minus_minus_real @ (real_V1205483228l_real @ X) @ (real_V1205483228l_real @ Y2)))))). % of_real_diff
thf(fact_73_of__real__eq__minus__of__real__iff, axiom,
    ((![X : real, Y2 : real]: (((real_V1205483228l_real @ X) = (uminus_uminus_real @ (real_V1205483228l_real @ Y2))) = (X = (uminus_uminus_real @ Y2)))))). % of_real_eq_minus_of_real_iff
thf(fact_74_minus__of__real__eq__of__real__iff, axiom,
    ((![X : real, Y2 : real]: (((uminus_uminus_real @ (real_V1205483228l_real @ X)) = (real_V1205483228l_real @ Y2)) = ((uminus_uminus_real @ X) = Y2))))). % minus_of_real_eq_of_real_iff
thf(fact_75_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_76_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_77_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_78_verit__minus__simplify_I3_J, axiom,
    ((![B2 : real]: ((minus_minus_real @ zero_zero_real @ B2) = (uminus_uminus_real @ B2))))). % verit_minus_simplify(3)
thf(fact_79_abs__minus, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus
thf(fact_80_abs__0, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_0
thf(fact_81_verit__minus__simplify_I4_J, axiom,
    ((![B2 : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B2)) = B2)))). % verit_minus_simplify(4)
thf(fact_82_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_83_linorder__neqE__linordered__idom, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) => ((~ ((ord_less_real @ X @ Y2))) => (ord_less_real @ Y2 @ X)))))). % linorder_neqE_linordered_idom
thf(fact_84_verit__comp__simplify1_I1_J, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_85_verit__negate__coefficient_I3_J, axiom,
    ((![A : real, B2 : real]: ((A = B2) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B2)))))). % verit_negate_coefficient(3)
thf(fact_86_verit__negate__coefficient_I2_J, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (ord_less_real @ (uminus_uminus_real @ B2) @ (uminus_uminus_real @ A)))))). % verit_negate_coefficient(2)
thf(fact_87_abs__eq__0__iff, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0_iff
thf(fact_88_abs__eq__iff, axiom,
    ((![X : real, Y2 : real]: (((abs_abs_real @ X) = (abs_abs_real @ Y2)) = (((X = Y2)) | ((X = (uminus_uminus_real @ Y2)))))))). % abs_eq_iff
thf(fact_89_abs__less__iff, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ (abs_abs_real @ A) @ B2) = (((ord_less_real @ A @ B2)) & ((ord_less_real @ (uminus_uminus_real @ A) @ B2))))))). % abs_less_iff
thf(fact_90_abs__if, axiom,
    ((abs_abs_real = (^[A2 : real]: (if_real @ (ord_less_real @ A2 @ zero_zero_real) @ (uminus_uminus_real @ A2) @ A2))))). % abs_if
thf(fact_91_abs__if__raw, axiom,
    ((abs_abs_real = (^[A2 : real]: (if_real @ (ord_less_real @ A2 @ zero_zero_real) @ (uminus_uminus_real @ A2) @ A2))))). % abs_if_raw
thf(fact_92_lemma__interval__lt, axiom,
    ((![A : real, X : real, B2 : real]: ((ord_less_real @ A @ X) => ((ord_less_real @ X @ B2) => (?[D3 : real]: ((ord_less_real @ zero_zero_real @ D3) & (![Y3 : real]: ((ord_less_real @ (abs_abs_real @ (minus_minus_real @ X @ Y3)) @ D3) => ((ord_less_real @ A @ Y3) & (ord_less_real @ Y3 @ B2))))))))))). % lemma_interval_lt
thf(fact_93_artanh__minus__real, axiom,
    ((![X : real]: ((ord_less_real @ (abs_abs_real @ X) @ one_one_real) => ((artanh_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (artanh_real @ X))))))). % artanh_minus_real
thf(fact_94_sin__periodic__pi, axiom,
    ((![X : real]: ((sin_real @ (plus_plus_real @ X @ pi)) = (uminus_uminus_real @ (sin_real @ X)))))). % sin_periodic_pi
thf(fact_95_add__right__cancel, axiom,
    ((![B2 : real, A : real, C : real]: (((plus_plus_real @ B2 @ A) = (plus_plus_real @ C @ A)) = (B2 = C))))). % add_right_cancel
thf(fact_96_add__left__cancel, axiom,
    ((![A : real, B2 : real, C : real]: (((plus_plus_real @ A @ B2) = (plus_plus_real @ A @ C)) = (B2 = C))))). % add_left_cancel
thf(fact_97_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_98_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_99_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_100_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_101_add__cancel__left__left, axiom,
    ((![B2 : real, A : real]: (((plus_plus_real @ B2 @ A) = A) = (B2 = zero_zero_real))))). % add_cancel_left_left
thf(fact_102_add__cancel__left__right, axiom,
    ((![A : real, B2 : real]: (((plus_plus_real @ A @ B2) = A) = (B2 = zero_zero_real))))). % add_cancel_left_right
thf(fact_103_add__cancel__right__left, axiom,
    ((![A : real, B2 : real]: ((A = (plus_plus_real @ B2 @ A)) = (B2 = zero_zero_real))))). % add_cancel_right_left
thf(fact_104_add__cancel__right__right, axiom,
    ((![A : real, B2 : real]: ((A = (plus_plus_real @ A @ B2)) = (B2 = zero_zero_real))))). % add_cancel_right_right
thf(fact_105_add__less__cancel__right, axiom,
    ((![A : real, C : real, B2 : real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B2 @ C)) = (ord_less_real @ A @ B2))))). % add_less_cancel_right
thf(fact_106_add__less__cancel__left, axiom,
    ((![C : real, A : real, B2 : real]: ((ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B2)) = (ord_less_real @ A @ B2))))). % add_less_cancel_left
thf(fact_107_add__diff__cancel, axiom,
    ((![A : real, B2 : real]: ((minus_minus_real @ (plus_plus_real @ A @ B2) @ B2) = A)))). % add_diff_cancel
thf(fact_108_diff__add__cancel, axiom,
    ((![A : real, B2 : real]: ((plus_plus_real @ (minus_minus_real @ A @ B2) @ B2) = A)))). % diff_add_cancel
thf(fact_109_add__diff__cancel__left, axiom,
    ((![C : real, A : real, B2 : real]: ((minus_minus_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B2)) = (minus_minus_real @ A @ B2))))). % add_diff_cancel_left
thf(fact_110_add__diff__cancel__left_H, axiom,
    ((![A : real, B2 : real]: ((minus_minus_real @ (plus_plus_real @ A @ B2) @ A) = B2)))). % add_diff_cancel_left'
thf(fact_111_add__diff__cancel__right, axiom,
    ((![A : real, C : real, B2 : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B2 @ C)) = (minus_minus_real @ A @ B2))))). % add_diff_cancel_right
thf(fact_112_add__diff__cancel__right_H, axiom,
    ((![A : real, B2 : real]: ((minus_minus_real @ (plus_plus_real @ A @ B2) @ B2) = A)))). % add_diff_cancel_right'
thf(fact_113_add__minus__cancel, axiom,
    ((![A : real, B2 : real]: ((plus_plus_real @ A @ (plus_plus_real @ (uminus_uminus_real @ A) @ B2)) = B2)))). % add_minus_cancel
thf(fact_114_minus__add__cancel, axiom,
    ((![A : real, B2 : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ (plus_plus_real @ A @ B2)) = B2)))). % minus_add_cancel
thf(fact_115_minus__add__distrib, axiom,
    ((![A : real, B2 : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B2)) = (plus_plus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B2)))))). % minus_add_distrib
thf(fact_116_abs__add__abs, axiom,
    ((![A : real, B2 : real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B2))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B2)))))). % abs_add_abs
thf(fact_117_abs__1, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_1
thf(fact_118_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_119_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_120_less__add__same__cancel2, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ (plus_plus_real @ B2 @ A)) = (ord_less_real @ zero_zero_real @ B2))))). % less_add_same_cancel2
thf(fact_121_less__add__same__cancel1, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B2)) = (ord_less_real @ zero_zero_real @ B2))))). % less_add_same_cancel1
thf(fact_122_add__less__same__cancel2, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ (plus_plus_real @ A @ B2) @ B2) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel2
thf(fact_123_add__less__same__cancel1, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ (plus_plus_real @ B2 @ A) @ B2) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel1
thf(fact_124_diff__numeral__special_I9_J, axiom,
    (((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real))). % diff_numeral_special(9)
thf(fact_125_add_Oright__inverse, axiom,
    ((![A : real]: ((plus_plus_real @ A @ (uminus_uminus_real @ A)) = zero_zero_real)))). % add.right_inverse
thf(fact_126_add_Oleft__inverse, axiom,
    ((![A : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real)))). % add.left_inverse
thf(fact_127_uminus__add__conv__diff, axiom,
    ((![A : real, B2 : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ B2) = (minus_minus_real @ B2 @ A))))). % uminus_add_conv_diff

% Helper facts (3)
thf(help_If_3_1_If_001t__Real__Oreal_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Real__Oreal_T, axiom,
    ((![X : real, Y2 : real]: ((if_real @ $false @ X @ Y2) = Y2)))).
thf(help_If_1_1_If_001t__Real__Oreal_T, axiom,
    ((![X : real, Y2 : real]: ((if_real @ $true @ X @ Y2) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((~ (((sin_real @ (minus_minus_real @ x @ pi)) = zero_zero_real))))).
