% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Fundamental_Theorem_Algebra/prob_339__5370854_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:21.931

% Could-be-implicit typings (4)
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (24)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001tf__a, type,
    fundam247907092size_a : poly_a > nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Oone__class_Oone_001tf__a, type,
    one_one_a : a).
thf(sy_c_Groups_Osgn__class_Osgn_001t__Real__Oreal, type,
    sgn_sgn_real : real > real).
thf(sy_c_Groups_Osgn__class_Osgn_001tf__a, type,
    sgn_sgn_a : a > a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J, type,
    zero_zero_poly_a : poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal, type,
    neg_nu533782273c_real : real > real).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal, type,
    neg_nu1973887165c_real : real > real).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001tf__a, type,
    neg_nu976519853_inc_a : a > a).
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_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_c_Rings_Odivide__class_Odivide_001tf__a, type,
    divide_divide_a : a > a > a).
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_Oln__class_Oln_001t__Real__Oreal, type,
    ln_ln_real : real > real).
thf(sy_v_c____, type,
    c : a).
thf(sy_v_cs____, type,
    cs : poly_a).
thf(sy_v_e, type,
    e : real).
thf(sy_v_m____, type,
    m : real).

% Relevant facts (146)
thf(fact_0_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_1_ep, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % ep
thf(fact_2_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_3_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_4_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_5_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_6_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_7_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_8_zero__neq__one, axiom,
    ((~ ((zero_zero_a = one_one_a))))). % zero_neq_one
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_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_12_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_13_zero__reorient, axiom,
    ((![X3 : a]: ((zero_zero_a = X3) = (X3 = zero_zero_a))))). % zero_reorient
thf(fact_14_zero__reorient, axiom,
    ((![X3 : poly_a]: ((zero_zero_poly_a = X3) = (X3 = zero_zero_poly_a))))). % zero_reorient
thf(fact_15_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) => ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_real @ Y2 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_16_one__reorient, axiom,
    ((![X3 : real]: ((one_one_real = X3) = (X3 = one_one_real))))). % one_reorient
thf(fact_17_em0, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ e @ m)))). % em0
thf(fact_18_dbl__inc__simps_I2_J, axiom,
    (((neg_nu1973887165c_real @ zero_zero_real) = one_one_real))). % dbl_inc_simps(2)
thf(fact_19_dbl__inc__simps_I2_J, axiom,
    (((neg_nu976519853_inc_a @ zero_zero_a) = one_one_a))). % dbl_inc_simps(2)
thf(fact_20_arcosh__1, axiom,
    (((arcosh_real @ one_one_real) = zero_zero_real))). % arcosh_1
thf(fact_21_dbl__dec__simps_I3_J, axiom,
    (((neg_nu533782273c_real @ one_one_real) = one_one_real))). % dbl_dec_simps(3)
thf(fact_22_sgn__pos, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => ((sgn_sgn_real @ A) = one_one_real))))). % sgn_pos
thf(fact_23_ln__one, axiom,
    (((ln_ln_real @ one_one_real) = zero_zero_real))). % ln_one
thf(fact_24_ex__gt__or__lt, axiom,
    ((![A : real]: (?[B : real]: ((ord_less_real @ A @ B) | (ord_less_real @ B @ A)))))). % ex_gt_or_lt
thf(fact_25_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ B2 @ A) => (~ ((A = B2))))))). % dual_order.strict_implies_not_eq
thf(fact_26_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % linordered_field_no_ub
thf(fact_27_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y3 : real]: (ord_less_real @ Y3 @ X4))))). % linordered_field_no_lb
thf(fact_28_sgn__sgn, axiom,
    ((![A : real]: ((sgn_sgn_real @ (sgn_sgn_real @ A)) = (sgn_sgn_real @ A))))). % sgn_sgn
thf(fact_29_divide__eq__0__iff, axiom,
    ((![A : real, B2 : real]: (((divide_divide_real @ A @ B2) = zero_zero_real) = (((A = zero_zero_real)) | ((B2 = zero_zero_real))))))). % divide_eq_0_iff
thf(fact_30_divide__cancel__left, axiom,
    ((![C : real, A : real, B2 : real]: (((divide_divide_real @ C @ A) = (divide_divide_real @ C @ B2)) = (((C = zero_zero_real)) | ((A = B2))))))). % divide_cancel_left
thf(fact_31_divide__cancel__right, axiom,
    ((![A : real, C : real, B2 : real]: (((divide_divide_real @ A @ C) = (divide_divide_real @ B2 @ C)) = (((C = zero_zero_real)) | ((A = B2))))))). % divide_cancel_right
thf(fact_32_division__ring__divide__zero, axiom,
    ((![A : a]: ((divide_divide_a @ A @ zero_zero_a) = zero_zero_a)))). % division_ring_divide_zero
thf(fact_33_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_34_div__0, axiom,
    ((![A : real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real)))). % div_0
thf(fact_35_div__by__0, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % div_by_0
thf(fact_36_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_37_ln__inj__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y2) => (((ln_ln_real @ X3) = (ln_ln_real @ Y2)) = (X3 = Y2))))))). % ln_inj_iff
thf(fact_38_ln__less__cancel__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y2) => ((ord_less_real @ (ln_ln_real @ X3) @ (ln_ln_real @ Y2)) = (ord_less_real @ X3 @ Y2))))))). % ln_less_cancel_iff
thf(fact_39_sgn__0, axiom,
    (((sgn_sgn_real @ zero_zero_real) = zero_zero_real))). % sgn_0
thf(fact_40_sgn__1, axiom,
    (((sgn_sgn_real @ one_one_real) = one_one_real))). % sgn_1
thf(fact_41_sgn__divide, axiom,
    ((![A : real, B2 : real]: ((sgn_sgn_real @ (divide_divide_real @ A @ B2)) = (divide_divide_real @ (sgn_sgn_real @ A) @ (sgn_sgn_real @ B2)))))). % sgn_divide
thf(fact_42_divide__eq__1__iff, axiom,
    ((![A : real, B2 : real]: (((divide_divide_real @ A @ B2) = one_one_real) = (((~ ((B2 = zero_zero_real)))) & ((A = B2))))))). % divide_eq_1_iff
thf(fact_43_one__eq__divide__iff, axiom,
    ((![A : real, B2 : real]: ((one_one_real = (divide_divide_real @ A @ B2)) = (((~ ((B2 = zero_zero_real)))) & ((A = B2))))))). % one_eq_divide_iff
thf(fact_44_divide__self, axiom,
    ((![A : a]: ((~ ((A = zero_zero_a))) => ((divide_divide_a @ A @ A) = one_one_a))))). % divide_self
thf(fact_45_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_46_divide__self__if, axiom,
    ((![A : a]: (((A = zero_zero_a) => ((divide_divide_a @ A @ A) = zero_zero_a)) & ((~ ((A = zero_zero_a))) => ((divide_divide_a @ A @ A) = one_one_a)))))). % divide_self_if
thf(fact_47_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_48_divide__eq__eq__1, axiom,
    ((![B2 : real, A : real]: (((divide_divide_real @ B2 @ A) = one_one_real) = (((~ ((A = zero_zero_real)))) & ((A = B2))))))). % divide_eq_eq_1
thf(fact_49_eq__divide__eq__1, axiom,
    ((![B2 : real, A : real]: ((one_one_real = (divide_divide_real @ B2 @ A)) = (((~ ((A = zero_zero_real)))) & ((A = B2))))))). % eq_divide_eq_1
thf(fact_50_one__divide__eq__0__iff, axiom,
    ((![A : real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % one_divide_eq_0_iff
thf(fact_51_zero__eq__1__divide__iff, axiom,
    ((![A : real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real))))). % zero_eq_1_divide_iff
thf(fact_52_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_53_sgn__less, axiom,
    ((![A : real]: ((ord_less_real @ (sgn_sgn_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % sgn_less
thf(fact_54_sgn__greater, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (sgn_sgn_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % sgn_greater
thf(fact_55_ln__eq__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ X3) => (((ln_ln_real @ X3) = zero_zero_real) = (X3 = one_one_real)))))). % ln_eq_zero_iff
thf(fact_56_ln__gt__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ (ln_ln_real @ X3)) = (ord_less_real @ one_one_real @ X3)))))). % ln_gt_zero_iff
thf(fact_57_ln__less__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ (ln_ln_real @ X3) @ zero_zero_real) = (ord_less_real @ X3 @ one_one_real)))))). % ln_less_zero_iff
thf(fact_58_divide__less__0__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % divide_less_0_1_iff
thf(fact_59_divide__less__eq__1__neg, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B2 @ A) @ one_one_real) = (ord_less_real @ A @ B2)))))). % divide_less_eq_1_neg
thf(fact_60_divide__less__eq__1__pos, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B2 @ A) @ one_one_real) = (ord_less_real @ B2 @ A)))))). % divide_less_eq_1_pos
thf(fact_61_less__divide__eq__1__neg, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B2 @ A)) = (ord_less_real @ B2 @ A)))))). % less_divide_eq_1_neg
thf(fact_62_less__divide__eq__1__pos, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B2 @ A)) = (ord_less_real @ A @ B2)))))). % less_divide_eq_1_pos
thf(fact_63_zero__less__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_divide_1_iff
thf(fact_64_sgn__0__0, axiom,
    ((![A : real]: (((sgn_sgn_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % sgn_0_0
thf(fact_65_sgn__eq__0__iff, axiom,
    ((![A : real]: (((sgn_sgn_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % sgn_eq_0_iff
thf(fact_66_ln__less__self, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ X3) => (ord_less_real @ (ln_ln_real @ X3) @ X3))))). % ln_less_self
thf(fact_67_divide__neg__neg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ Y2 @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_neg_neg
thf(fact_68_divide__neg__pos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y2) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_69_divide__pos__neg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ Y2 @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_70_divide__pos__pos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y2) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_pos_pos
thf(fact_71_divide__less__0__iff, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ (divide_divide_real @ A @ B2) @ zero_zero_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B2 @ zero_zero_real)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B2))))))))). % divide_less_0_iff
thf(fact_72_divide__less__cancel, axiom,
    ((![A : real, C : real, B2 : real]: ((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B2 @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B2)))) & ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B2 @ A)))) & ((~ ((C = zero_zero_real))))))))))). % divide_less_cancel
thf(fact_73_zero__less__divide__iff, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B2)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ zero_zero_real @ B2)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B2 @ zero_zero_real))))))))). % zero_less_divide_iff
thf(fact_74_divide__strict__right__mono, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_real @ A @ B2) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B2 @ C))))))). % divide_strict_right_mono
thf(fact_75_divide__strict__right__mono__neg, axiom,
    ((![B2 : real, A : real, C : real]: ((ord_less_real @ B2 @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B2 @ C))))))). % divide_strict_right_mono_neg
thf(fact_76_right__inverse__eq, axiom,
    ((![B2 : a, A : a]: ((~ ((B2 = zero_zero_a))) => (((divide_divide_a @ A @ B2) = one_one_a) = (A = B2)))))). % right_inverse_eq
thf(fact_77_right__inverse__eq, axiom,
    ((![B2 : real, A : real]: ((~ ((B2 = zero_zero_real))) => (((divide_divide_real @ A @ B2) = one_one_real) = (A = B2)))))). % right_inverse_eq
thf(fact_78_ln__gt__zero, axiom,
    ((![X3 : real]: ((ord_less_real @ one_one_real @ X3) => (ord_less_real @ zero_zero_real @ (ln_ln_real @ X3)))))). % ln_gt_zero
thf(fact_79_ln__less__zero, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ X3 @ one_one_real) => (ord_less_real @ (ln_ln_real @ X3) @ zero_zero_real)))))). % ln_less_zero
thf(fact_80_ln__gt__zero__imp__gt__one, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (ln_ln_real @ X3)) => ((ord_less_real @ zero_zero_real @ X3) => (ord_less_real @ one_one_real @ X3)))))). % ln_gt_zero_imp_gt_one
thf(fact_81_divide__less__eq__1, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ (divide_divide_real @ B2 @ A) @ one_one_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B2 @ A)))) | ((((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ A @ B2)))) | ((A = zero_zero_real))))))))). % divide_less_eq_1
thf(fact_82_less__divide__eq__1, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ B2 @ A)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ A @ B2)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B2 @ A))))))))). % less_divide_eq_1
thf(fact_83_sgn__1__pos, axiom,
    ((![A : real]: (((sgn_sgn_real @ A) = one_one_real) = (ord_less_real @ zero_zero_real @ A))))). % sgn_1_pos
thf(fact_84_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B2 : real, C : real]: ((A = (F @ B2)) => ((ord_less_real @ B2 @ C) => ((![X : real, Y3 : real]: ((ord_less_real @ X @ Y3) => (ord_less_real @ (F @ X) @ (F @ Y3)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_85_ord__less__eq__subst, axiom,
    ((![A : real, B2 : real, F : real > real, C : real]: ((ord_less_real @ A @ B2) => (((F @ B2) = C) => ((![X : real, Y3 : real]: ((ord_less_real @ X @ Y3) => (ord_less_real @ (F @ X) @ (F @ Y3)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_86_order__less__subst1, axiom,
    ((![A : real, F : real > real, B2 : real, C : real]: ((ord_less_real @ A @ (F @ B2)) => ((ord_less_real @ B2 @ C) => ((![X : real, Y3 : real]: ((ord_less_real @ X @ Y3) => (ord_less_real @ (F @ X) @ (F @ Y3)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_87_order__less__subst2, axiom,
    ((![A : real, B2 : real, F : real > real, C : real]: ((ord_less_real @ A @ B2) => ((ord_less_real @ (F @ B2) @ C) => ((![X : real, Y3 : real]: ((ord_less_real @ X @ Y3) => (ord_less_real @ (F @ X) @ (F @ Y3)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_88_lt__ex, axiom,
    ((![X3 : real]: (?[Y3 : real]: (ord_less_real @ Y3 @ X3))))). % lt_ex
thf(fact_89_gt__ex, axiom,
    ((![X3 : real]: (?[X_12 : real]: (ord_less_real @ X3 @ X_12))))). % gt_ex
thf(fact_90_neqE, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) => ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_real @ Y2 @ X3)))))). % neqE
thf(fact_91_neq__iff, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) = (((ord_less_real @ X3 @ Y2)) | ((ord_less_real @ Y2 @ X3))))))). % neq_iff
thf(fact_92_order_Oasym, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (~ ((ord_less_real @ B2 @ A))))))). % order.asym
thf(fact_93_dense, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (?[Z2 : real]: ((ord_less_real @ X3 @ Z2) & (ord_less_real @ Z2 @ Y2))))))). % dense
thf(fact_94_less__imp__neq, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((X3 = Y2))))))). % less_imp_neq
thf(fact_95_less__asym, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((ord_less_real @ Y2 @ X3))))))). % less_asym
thf(fact_96_less__asym_H, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (~ ((ord_less_real @ B2 @ A))))))). % less_asym'
thf(fact_97_less__trans, axiom,
    ((![X3 : real, Y2 : real, Z3 : real]: ((ord_less_real @ X3 @ Y2) => ((ord_less_real @ Y2 @ Z3) => (ord_less_real @ X3 @ Z3)))))). % less_trans
thf(fact_98_less__linear, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) | ((X3 = Y2) | (ord_less_real @ Y2 @ X3)))))). % less_linear
thf(fact_99_less__irrefl, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ X3 @ X3)))))). % less_irrefl
thf(fact_100_ord__eq__less__trans, axiom,
    ((![A : real, B2 : real, C : real]: ((A = B2) => ((ord_less_real @ B2 @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_101_ord__less__eq__trans, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_real @ A @ B2) => ((B2 = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_102_dual__order_Oasym, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ B2 @ A) => (~ ((ord_less_real @ A @ B2))))))). % dual_order.asym
thf(fact_103_less__imp__not__eq, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((X3 = Y2))))))). % less_imp_not_eq
thf(fact_104_less__not__sym, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((ord_less_real @ Y2 @ X3))))))). % less_not_sym
thf(fact_105_antisym__conv3, axiom,
    ((![Y2 : real, X3 : real]: ((~ ((ord_less_real @ Y2 @ X3))) => ((~ ((ord_less_real @ X3 @ Y2))) = (X3 = Y2)))))). % antisym_conv3
thf(fact_106_less__imp__not__eq2, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((Y2 = X3))))))). % less_imp_not_eq2
thf(fact_107_less__imp__triv, axiom,
    ((![X3 : real, Y2 : real, P : $o]: ((ord_less_real @ X3 @ Y2) => ((ord_less_real @ Y2 @ X3) => P))))). % less_imp_triv
thf(fact_108_linorder__cases, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_real @ X3 @ Y2))) => ((~ ((X3 = Y2))) => (ord_less_real @ Y2 @ X3)))))). % linorder_cases
thf(fact_109_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_110_order_Ostrict__trans, axiom,
    ((![A : real, B2 : real, C : real]: ((ord_less_real @ A @ B2) => ((ord_less_real @ B2 @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_111_less__imp__not__less, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ Y2) => (~ ((ord_less_real @ Y2 @ X3))))))). % less_imp_not_less
thf(fact_112_linorder__less__wlog, axiom,
    ((![P : real > real > $o, A : real, B2 : real]: ((![A2 : real, B : real]: ((ord_less_real @ A2 @ B) => (P @ A2 @ B))) => ((![A2 : real]: (P @ A2 @ A2)) => ((![A2 : real, B : real]: ((P @ B @ A2) => (P @ A2 @ B))) => (P @ A @ B2))))))). % linorder_less_wlog
thf(fact_113_dual__order_Ostrict__trans, axiom,
    ((![B2 : real, A : real, C : real]: ((ord_less_real @ B2 @ A) => ((ord_less_real @ C @ B2) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_114_not__less__iff__gr__or__eq, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((ord_less_real @ X3 @ Y2))) = (((ord_less_real @ Y2 @ X3)) | ((X3 = Y2))))))). % not_less_iff_gr_or_eq
thf(fact_115_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (~ ((A = B2))))))). % order.strict_implies_not_eq
thf(fact_116_sgn__one, axiom,
    (((sgn_sgn_real @ one_one_real) = one_one_real))). % sgn_one
thf(fact_117_sgn__zero, axiom,
    (((sgn_sgn_real @ zero_zero_real) = zero_zero_real))). % sgn_zero
thf(fact_118_sgn__zero, axiom,
    (((sgn_sgn_a @ zero_zero_a) = zero_zero_a))). % sgn_zero
thf(fact_119_arsinh__0, axiom,
    (((arsinh_real @ zero_zero_real) = zero_zero_real))). % arsinh_0
thf(fact_120_artanh__0, axiom,
    (((artanh_real @ zero_zero_real) = zero_zero_real))). % artanh_0
thf(fact_121_sgn__zero__iff, axiom,
    ((![X3 : real]: (((sgn_sgn_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % sgn_zero_iff
thf(fact_122_sgn__zero__iff, axiom,
    ((![X3 : a]: (((sgn_sgn_a @ X3) = zero_zero_a) = (X3 = zero_zero_a))))). % sgn_zero_iff
thf(fact_123_psize__eq__0__iff, axiom,
    ((![P2 : poly_a]: (((fundam247907092size_a @ P2) = zero_zero_nat) = (P2 = zero_zero_poly_a))))). % psize_eq_0_iff
thf(fact_124_ln__le__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ (ln_ln_real @ X3) @ zero_zero_real) = (ord_less_eq_real @ X3 @ one_one_real)))))). % ln_le_zero_iff
thf(fact_125_order__refl, axiom,
    ((![X3 : real]: (ord_less_eq_real @ X3 @ X3)))). % order_refl
thf(fact_126_sgn__le__0__iff, axiom,
    ((![X3 : real]: ((ord_less_eq_real @ (sgn_sgn_real @ X3) @ zero_zero_real) = (ord_less_eq_real @ X3 @ zero_zero_real))))). % sgn_le_0_iff
thf(fact_127_zero__le__sgn__iff, axiom,
    ((![X3 : real]: ((ord_less_eq_real @ zero_zero_real @ (sgn_sgn_real @ X3)) = (ord_less_eq_real @ zero_zero_real @ X3))))). % zero_le_sgn_iff
thf(fact_128_divide__le__0__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % divide_le_0_1_iff
thf(fact_129_zero__le__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_divide_1_iff
thf(fact_130_ln__le__cancel__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y2) => ((ord_less_eq_real @ (ln_ln_real @ X3) @ (ln_ln_real @ Y2)) = (ord_less_eq_real @ X3 @ Y2))))))). % ln_le_cancel_iff
thf(fact_131_divide__le__eq__1__neg, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B2 @ A) @ one_one_real) = (ord_less_eq_real @ A @ B2)))))). % divide_le_eq_1_neg
thf(fact_132_divide__le__eq__1__pos, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B2 @ A) @ one_one_real) = (ord_less_eq_real @ B2 @ A)))))). % divide_le_eq_1_pos
thf(fact_133_le__divide__eq__1__neg, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B2 @ A)) = (ord_less_eq_real @ B2 @ A)))))). % le_divide_eq_1_neg
thf(fact_134_le__divide__eq__1__pos, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B2 @ A)) = (ord_less_eq_real @ A @ B2)))))). % le_divide_eq_1_pos
thf(fact_135_ln__ge__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ X3)) = (ord_less_eq_real @ one_one_real @ X3)))))). % ln_ge_zero_iff
thf(fact_136_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_137_complete__interval, axiom,
    ((![A : real, B2 : real, P : real > $o]: ((ord_less_real @ A @ B2) => ((P @ A) => ((~ ((P @ B2))) => (?[C2 : real]: ((ord_less_eq_real @ A @ C2) & ((ord_less_eq_real @ C2 @ B2) & ((![X4 : real]: (((ord_less_eq_real @ A @ X4) & (ord_less_real @ X4 @ C2)) => (P @ X4))) & (![D : real]: ((![X : real]: (((ord_less_eq_real @ A @ X) & (ord_less_real @ X @ D)) => (P @ X))) => (ord_less_eq_real @ D @ C2))))))))))))). % complete_interval
thf(fact_138_order_Onot__eq__order__implies__strict, axiom,
    ((![A : real, B2 : real]: ((~ ((A = B2))) => ((ord_less_eq_real @ A @ B2) => (ord_less_real @ A @ B2)))))). % order.not_eq_order_implies_strict
thf(fact_139_dual__order_Ostrict__implies__order, axiom,
    ((![B2 : real, A : real]: ((ord_less_real @ B2 @ A) => (ord_less_eq_real @ B2 @ A))))). % dual_order.strict_implies_order
thf(fact_140_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[B3 : real]: (^[A3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((~ ((A3 = B3)))))))))). % dual_order.strict_iff_order
thf(fact_141_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[B3 : real]: (^[A3 : real]: (((ord_less_real @ B3 @ A3)) | ((A3 = B3)))))))). % dual_order.order_iff_strict
thf(fact_142_order_Ostrict__implies__order, axiom,
    ((![A : real, B2 : real]: ((ord_less_real @ A @ B2) => (ord_less_eq_real @ A @ B2))))). % order.strict_implies_order
thf(fact_143_dense__le__bounded, axiom,
    ((![X3 : real, Y2 : real, Z3 : real]: ((ord_less_real @ X3 @ Y2) => ((![W : real]: ((ord_less_real @ X3 @ W) => ((ord_less_real @ W @ Y2) => (ord_less_eq_real @ W @ Z3)))) => (ord_less_eq_real @ Y2 @ Z3)))))). % dense_le_bounded
thf(fact_144_dense__ge__bounded, axiom,
    ((![Z3 : real, X3 : real, Y2 : real]: ((ord_less_real @ Z3 @ X3) => ((![W : real]: ((ord_less_real @ Z3 @ W) => ((ord_less_real @ W @ X3) => (ord_less_eq_real @ Y2 @ W)))) => (ord_less_eq_real @ Y2 @ Z3)))))). % dense_ge_bounded
thf(fact_145_dual__order_Ostrict__trans2, axiom,
    ((![B2 : real, A : real, C : real]: ((ord_less_real @ B2 @ A) => ((ord_less_eq_real @ C @ B2) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans2

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_real @ zero_zero_real @ one_one_real))).
