% 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_120__3223858_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:17.250

% 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 (15)
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_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_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal, type,
    real_V1205483228l_real : real > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_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_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_x, type,
    x : real).

% Relevant facts (122)
thf(fact_0__092_060open_062x_A_060_Api_092_060close_062, axiom,
    ((ord_less_real @ x @ pi))). % \<open>x < pi\<close>
thf(fact_1__C0_C, axiom,
    ((ord_less_real @ zero_zero_real @ x))). % "0"
thf(fact_2_sin__zero, axiom,
    (((sin_real @ zero_zero_real) = zero_zero_real))). % sin_zero
thf(fact_3_sin__pi, axiom,
    (((sin_real @ pi) = zero_zero_real))). % sin_pi
thf(fact_4_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_5_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_6_arsinh__0, axiom,
    (((arsinh_real @ zero_zero_real) = zero_zero_real))). % arsinh_0
thf(fact_7_artanh__0, axiom,
    (((artanh_real @ zero_zero_real) = zero_zero_real))). % artanh_0
thf(fact_8_pi__neq__zero, axiom,
    ((~ ((pi = zero_zero_real))))). % pi_neq_zero
thf(fact_9_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_10_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_11_pi__not__less__zero, axiom,
    ((~ ((ord_less_real @ pi @ zero_zero_real))))). % pi_not_less_zero
thf(fact_12_pi__gt__zero, axiom,
    ((ord_less_real @ zero_zero_real @ pi))). % pi_gt_zero
thf(fact_13_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_14_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_15_cot__pi, axiom,
    (((cot_real @ pi) = zero_zero_real))). % cot_pi
thf(fact_16_sin__of__real__pi, axiom,
    (((sin_real @ (real_V1205483228l_real @ pi)) = zero_zero_real))). % sin_of_real_pi
thf(fact_17_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_18_minf_I7_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z) => (~ ((ord_less_real @ T @ X2))))))))). % minf(7)
thf(fact_19_minf_I5_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z) => (ord_less_real @ X2 @ T))))))). % minf(5)
thf(fact_20_minf_I4_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z) => (~ ((X2 = T))))))))). % minf(4)
thf(fact_21_minf_I3_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z) => (~ ((X2 = T))))))))). % minf(3)
thf(fact_22_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_23_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_24_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_25_arsinh__minus__real, axiom,
    ((![X : real]: ((arsinh_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (arsinh_real @ X)))))). % arsinh_minus_real
thf(fact_26_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_27_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_28_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_29_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_30_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_31_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_32_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_33_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_34_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_35_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_36_abs__minus__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus_cancel
thf(fact_37_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_38_Collect__mem__eq, axiom,
    ((![A2 : set_real]: ((collect_real @ (^[X3 : real]: (member_real @ X3 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_39_sin__minus, axiom,
    ((![X : real]: ((sin_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (sin_real @ X)))))). % sin_minus
thf(fact_40_cot__zero, axiom,
    (((cot_real @ zero_zero_real) = zero_zero_real))). % cot_zero
thf(fact_41_cot__minus, axiom,
    ((![X : real]: ((cot_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (cot_real @ X)))))). % cot_minus
thf(fact_42_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_43_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_44_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_45_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_46_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_47_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_48_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_49_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_50_abs__of__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_nonneg
thf(fact_51_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_52_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_53_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_54_abs__of__nonpos, axiom,
    ((![A : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((abs_abs_real @ A) = (uminus_uminus_real @ A)))))). % abs_of_nonpos
thf(fact_55_complete__real, axiom,
    ((![S : set_real]: ((?[X2 : real]: (member_real @ X2 @ S)) => ((?[Z2 : real]: (![X4 : real]: ((member_real @ X4 @ S) => (ord_less_eq_real @ X4 @ Z2)))) => (?[Y : real]: ((![X2 : real]: ((member_real @ X2 @ S) => (ord_less_eq_real @ X2 @ Y))) & (![Z2 : real]: ((![X4 : real]: ((member_real @ X4 @ S) => (ord_less_eq_real @ X4 @ Z2))) => (ord_less_eq_real @ Y @ Z2)))))))))). % complete_real
thf(fact_56_cot__of__real, axiom,
    ((![X : real]: ((real_V1205483228l_real @ (cot_real @ X)) = (cot_real @ (real_V1205483228l_real @ X)))))). % cot_of_real
thf(fact_57_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_58_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_59_abs__leI, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) => (ord_less_eq_real @ (abs_abs_real @ A) @ B)))))). % abs_leI
thf(fact_60_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_61_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_62_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_63_abs__le__D2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ (uminus_uminus_real @ A) @ B))))). % abs_le_D2
thf(fact_64_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_65_abs__le__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) = (((ord_less_eq_real @ A @ B)) & ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B))))))). % abs_le_iff
thf(fact_66_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
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_abs__ge__minus__self, axiom,
    ((![A : real]: (ord_less_eq_real @ (uminus_uminus_real @ A) @ (abs_abs_real @ A))))). % abs_ge_minus_self
thf(fact_69_abs__minus__le__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ (uminus_uminus_real @ (abs_abs_real @ A)) @ zero_zero_real)))). % abs_minus_le_zero
thf(fact_70_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_71_pinf_I6_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ Z @ X2) => (~ ((ord_less_eq_real @ X2 @ T))))))))). % pinf(6)
thf(fact_72_pinf_I8_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ Z @ X2) => (ord_less_eq_real @ T @ X2))))))). % pinf(8)
thf(fact_73_minf_I6_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z) => (ord_less_eq_real @ X2 @ T))))))). % minf(6)
thf(fact_74_minf_I8_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z) => (~ ((ord_less_eq_real @ T @ X2))))))))). % minf(8)
thf(fact_75_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_76_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_77_abs__real__def, axiom,
    ((abs_abs_real = (^[A3 : real]: (if_real @ (ord_less_real @ A3 @ zero_zero_real) @ (uminus_uminus_real @ A3) @ A3))))). % abs_real_def
thf(fact_78_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_79_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_80_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_81_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_82_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X3 : real]: (^[Y2 : real]: (((ord_less_real @ X3 @ Y2)) | ((X3 = Y2)))))))). % less_eq_real_def
thf(fact_83_abs__of__pos, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_pos
thf(fact_84_abs__not__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (abs_abs_real @ A) @ zero_zero_real)))))). % abs_not_less_zero
thf(fact_85_sin__of__real, axiom,
    ((![X : real]: ((sin_real @ (real_V1205483228l_real @ X)) = (real_V1205483228l_real @ (sin_real @ X)))))). % sin_of_real
thf(fact_86_pi__ge__zero, axiom,
    ((ord_less_eq_real @ zero_zero_real @ pi))). % pi_ge_zero
thf(fact_87_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_88_pinf_I1_J, axiom,
    ((![P : real > $o, P2 : real > $o, Q : real > $o, Q2 : real > $o]: ((?[Z2 : real]: (![X4 : real]: ((ord_less_real @ Z2 @ X4) => ((P @ X4) = (P2 @ X4))))) => ((?[Z2 : real]: (![X4 : real]: ((ord_less_real @ Z2 @ X4) => ((Q @ X4) = (Q2 @ X4))))) => (?[Z : real]: (![X2 : real]: ((ord_less_real @ Z @ X2) => ((((P @ X2)) & ((Q @ X2))) = (((P2 @ X2)) & ((Q2 @ X2)))))))))))). % pinf(1)
thf(fact_89_pinf_I2_J, axiom,
    ((![P : real > $o, P2 : real > $o, Q : real > $o, Q2 : real > $o]: ((?[Z2 : real]: (![X4 : real]: ((ord_less_real @ Z2 @ X4) => ((P @ X4) = (P2 @ X4))))) => ((?[Z2 : real]: (![X4 : real]: ((ord_less_real @ Z2 @ X4) => ((Q @ X4) = (Q2 @ X4))))) => (?[Z : real]: (![X2 : real]: ((ord_less_real @ Z @ X2) => ((((P @ X2)) | ((Q @ X2))) = (((P2 @ X2)) | ((Q2 @ X2)))))))))))). % pinf(2)
thf(fact_90_pinf_I3_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ Z @ X2) => (~ ((X2 = T))))))))). % pinf(3)
thf(fact_91_pinf_I4_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ Z @ X2) => (~ ((X2 = T))))))))). % pinf(4)
thf(fact_92_pinf_I5_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ Z @ X2) => (~ ((ord_less_real @ X2 @ T))))))))). % pinf(5)
thf(fact_93_pinf_I7_J, axiom,
    ((![T : real]: (?[Z : real]: (![X2 : real]: ((ord_less_real @ Z @ X2) => (ord_less_real @ T @ X2))))))). % pinf(7)
thf(fact_94_minf_I1_J, axiom,
    ((![P : real > $o, P2 : real > $o, Q : real > $o, Q2 : real > $o]: ((?[Z2 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z2) => ((P @ X4) = (P2 @ X4))))) => ((?[Z2 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z2) => ((Q @ X4) = (Q2 @ X4))))) => (?[Z : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z) => ((((P @ X2)) & ((Q @ X2))) = (((P2 @ X2)) & ((Q2 @ X2)))))))))))). % minf(1)
thf(fact_95_minf_I2_J, axiom,
    ((![P : real > $o, P2 : real > $o, Q : real > $o, Q2 : real > $o]: ((?[Z2 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z2) => ((P @ X4) = (P2 @ X4))))) => ((?[Z2 : real]: (![X4 : real]: ((ord_less_real @ X4 @ Z2) => ((Q @ X4) = (Q2 @ X4))))) => (?[Z : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z) => ((((P @ X2)) | ((Q @ X2))) = (((P2 @ X2)) | ((Q2 @ X2)))))))))))). % minf(2)
thf(fact_96_of__real__eq__minus__of__real__iff, axiom,
    ((![X : real, Y3 : real]: (((real_V1205483228l_real @ X) = (uminus_uminus_real @ (real_V1205483228l_real @ Y3))) = (X = (uminus_uminus_real @ Y3)))))). % of_real_eq_minus_of_real_iff
thf(fact_97_minus__of__real__eq__of__real__iff, axiom,
    ((![X : real, Y3 : real]: (((uminus_uminus_real @ (real_V1205483228l_real @ X)) = (real_V1205483228l_real @ Y3)) = ((uminus_uminus_real @ X) = Y3))))). % minus_of_real_eq_of_real_iff
thf(fact_98_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_99_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_100_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_101_abs__minus, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus
thf(fact_102_abs__0, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_0
thf(fact_103_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_104_linorder__neqE__linordered__idom, axiom,
    ((![X : real, Y3 : real]: ((~ ((X = Y3))) => ((~ ((ord_less_real @ X @ Y3))) => (ord_less_real @ Y3 @ X)))))). % linorder_neqE_linordered_idom
thf(fact_105_abs__eq__0__iff, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0_iff
thf(fact_106_abs__eq__iff, axiom,
    ((![X : real, Y3 : real]: (((abs_abs_real @ X) = (abs_abs_real @ Y3)) = (((X = Y3)) | ((X = (uminus_uminus_real @ Y3)))))))). % abs_eq_iff
thf(fact_107_abs__less__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (abs_abs_real @ A) @ B) = (((ord_less_real @ A @ B)) & ((ord_less_real @ (uminus_uminus_real @ A) @ B))))))). % abs_less_iff
thf(fact_108_eq__abs__iff_H, axiom,
    ((![A : real, B : real]: ((A = (abs_abs_real @ B)) = (((ord_less_eq_real @ zero_zero_real @ A)) & ((((B = A)) | ((B = (uminus_uminus_real @ A)))))))))). % eq_abs_iff'
thf(fact_109_abs__eq__iff_H, axiom,
    ((![A : real, B : real]: (((abs_abs_real @ A) = B) = (((ord_less_eq_real @ zero_zero_real @ B)) & ((((A = B)) | ((A = (uminus_uminus_real @ B)))))))))). % abs_eq_iff'
thf(fact_110_abs__if, axiom,
    ((abs_abs_real = (^[A3 : real]: (if_real @ (ord_less_real @ A3 @ zero_zero_real) @ (uminus_uminus_real @ A3) @ A3))))). % abs_if
thf(fact_111_abs__if__raw, axiom,
    ((abs_abs_real = (^[A3 : real]: (if_real @ (ord_less_real @ A3 @ zero_zero_real) @ (uminus_uminus_real @ A3) @ A3))))). % abs_if_raw
thf(fact_112_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_113_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_114_verit__comp__simplify1_I1_J, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_115_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_116_verit__comp__simplify1_I3_J, axiom,
    ((![B2 : real, A4 : real]: ((~ ((ord_less_eq_real @ B2 @ A4))) = (ord_less_real @ A4 @ B2))))). % verit_comp_simplify1(3)
thf(fact_117_verit__negate__coefficient_I2_J, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % verit_negate_coefficient(2)
thf(fact_118_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_119_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) & ((![X2 : real]: (((ord_less_eq_real @ A @ X2) & (ord_less_real @ X2 @ C)) => (P @ X2))) & (![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_120_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, Y : real]: ((ord_less_eq_real @ X4 @ Y) => (ord_less_eq_real @ (F @ X4) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C2)))))))). % order_subst1
thf(fact_121_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, Y : real]: ((ord_less_eq_real @ X4 @ Y) => (ord_less_eq_real @ (F @ X4) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C2))))))). % order_subst2

% 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, Y3 : real]: ((if_real @ $false @ X @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Real__Oreal_T, axiom,
    ((![X : real, Y3 : real]: ((if_real @ $true @ X @ Y3) = X)))).

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