% 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_450__5372370_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:14.601

% 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 (12)
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_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_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_a____, type,
    a : real).
thf(sy_v_b____, type,
    b : real).
thf(sy_v_c____, type,
    c : real).
thf(sy_v_m____, type,
    m : real).

% Relevant facts (131)
thf(fact_0_le__add__diff__inverse, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A))))). % le_add_diff_inverse
thf(fact_1_le__add__diff__inverse2, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))))). % le_add_diff_inverse2
thf(fact_2_abs__add__abs, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_add_abs
thf(fact_3_add__diff__cancel, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_4_diff__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_5_add__diff__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_left
thf(fact_6_add__diff__cancel__left_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_7_add__diff__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_right
thf(fact_8_add__diff__cancel__right_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_9_add__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_left
thf(fact_10_add__le__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_right
thf(fact_11_sin__bound__lemma, axiom,
    ((![X : real, Y : real, U : real, V : real]: ((X = Y) => ((ord_less_eq_real @ (abs_abs_real @ U) @ V) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ X @ U) @ Y)) @ V)))))). % sin_bound_lemma
thf(fact_12_add__right__cancel, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_13_add__left__cancel, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_14_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_15_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_16_add__right__imp__eq, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_17_add__left__imp__eq, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_18_add_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((plus_plus_real @ B @ (plus_plus_real @ A @ C)) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % add.left_commute
thf(fact_19_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_20_add_Oright__cancel, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_21_add_Oleft__cancel, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_22_add_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % add.assoc
thf(fact_23_group__cancel_Oadd2, axiom,
    ((![B3 : real, K : real, B : real, A : real]: ((B3 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B3) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_24_group__cancel_Oadd1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A3 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_25_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (K = L)) => ((plus_plus_real @ I @ K) = (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_26_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_27_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (minus_minus_real @ A @ C) @ B) = (minus_minus_real @ (minus_minus_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_28_diff__eq__diff__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_29_add__le__imp__le__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_right
thf(fact_30_add__le__imp__le__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_left
thf(fact_31_add__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_right_mono
thf(fact_32_add__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_left_mono
thf(fact_33_add__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_mono
thf(fact_34_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_35_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_36_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (K = L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_37_diff__eq__diff__less__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_38_diff__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_right_mono
thf(fact_39_diff__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_left_mono
thf(fact_40_diff__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ D @ C) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_mono
thf(fact_41_add__implies__diff, axiom,
    ((![C : real, B : real, A : real]: (((plus_plus_real @ C @ B) = A) => (C = (minus_minus_real @ A @ B)))))). % add_implies_diff
thf(fact_42_diff__diff__add, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C)))))). % diff_diff_add
thf(fact_43_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_44_Collect__mem__eq, axiom,
    ((![A3 : set_real]: ((collect_real @ (^[X2 : real]: (member_real @ X2 @ A3))) = A3)))). % Collect_mem_eq
thf(fact_45_diff__add__eq__diff__diff__swap, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_46_diff__add__eq, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B))))). % diff_add_eq
thf(fact_47_diff__diff__eq2, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_48_add__diff__eq, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C))))). % add_diff_eq
thf(fact_49_eq__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((A = (minus_minus_real @ C @ B)) = ((plus_plus_real @ A @ B) = C))))). % eq_diff_eq
thf(fact_50_diff__eq__eq, axiom,
    ((![A : real, B : real, C : real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B)))))). % diff_eq_eq
thf(fact_51_group__cancel_Osub1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((minus_minus_real @ A3 @ B) = (plus_plus_real @ K @ (minus_minus_real @ A @ B))))))). % group_cancel.sub1
thf(fact_52_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_53_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_54_abs__minus__commute, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A)))))). % abs_minus_commute
thf(fact_55_eq__diff__eq_H, axiom,
    ((![X : real, Y : real, Z : real]: ((X = (minus_minus_real @ Y @ Z)) = (Y = (plus_plus_real @ X @ Z)))))). % eq_diff_eq'
thf(fact_56_add__le__add__imp__diff__le, axiom,
    ((![I : real, K : real, N : real, J : real]: ((ord_less_eq_real @ (plus_plus_real @ I @ K) @ N) => ((ord_less_eq_real @ N @ (plus_plus_real @ J @ K)) => ((ord_less_eq_real @ (plus_plus_real @ I @ K) @ N) => ((ord_less_eq_real @ N @ (plus_plus_real @ J @ K)) => (ord_less_eq_real @ (minus_minus_real @ N @ K) @ J)))))))). % add_le_add_imp_diff_le
thf(fact_57_add__le__imp__le__diff, axiom,
    ((![I : real, K : real, N : real]: ((ord_less_eq_real @ (plus_plus_real @ I @ K) @ N) => (ord_less_eq_real @ I @ (minus_minus_real @ N @ K)))))). % add_le_imp_le_diff
thf(fact_58_le__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) = (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))))). % le_diff_eq
thf(fact_59_diff__le__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B)))))). % diff_le_eq
thf(fact_60_abs__triangle__ineq, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_triangle_ineq
thf(fact_61_abs__triangle__ineq2__sym, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A)))))). % abs_triangle_ineq2_sym
thf(fact_62_abs__triangle__ineq3, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B)))))). % abs_triangle_ineq3
thf(fact_63_abs__triangle__ineq2, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B)))))). % abs_triangle_ineq2
thf(fact_64_abs__diff__triangle__ineq, axiom,
    ((![A : real, B : real, C : real, D : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ C)) @ (abs_abs_real @ (minus_minus_real @ B @ D))))))). % abs_diff_triangle_ineq
thf(fact_65_abs__triangle__ineq4, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_triangle_ineq4
thf(fact_66_abs__diff__le__iff, axiom,
    ((![X : real, A : real, R : real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ X @ A)) @ R) = (((ord_less_eq_real @ (minus_minus_real @ A @ R) @ X)) & ((ord_less_eq_real @ X @ (plus_plus_real @ A @ R)))))))). % abs_diff_le_iff
thf(fact_67_ath, axiom,
    ((![M : real, X : real, E : real]: ((ord_less_eq_real @ M @ X) => ((ord_less_real @ X @ (plus_plus_real @ M @ E)) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ X @ M)) @ E)))))). % ath
thf(fact_68_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_69_add__diff__add, axiom,
    ((![A : real, C : real, B : real, D : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) = (plus_plus_real @ (minus_minus_real @ A @ B) @ (minus_minus_real @ C @ D)))))). % add_diff_add
thf(fact_70_th000_I2_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % th000(2)
thf(fact_71_complete__real, axiom,
    ((![S : set_real]: ((?[X3 : real]: (member_real @ X3 @ S)) => ((?[Z2 : real]: (![X4 : real]: ((member_real @ X4 @ S) => (ord_less_eq_real @ X4 @ Z2)))) => (?[Y2 : real]: ((![X3 : real]: ((member_real @ X3 @ S) => (ord_less_eq_real @ X3 @ Y2))) & (![Z2 : real]: ((![X4 : real]: ((member_real @ X4 @ S) => (ord_less_eq_real @ X4 @ Z2))) => (ord_less_eq_real @ Y2 @ Z2)))))))))). % complete_real
thf(fact_72_is__num__normalize_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % is_num_normalize(1)
thf(fact_73_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_74_dual__order_Oeq__iff, axiom,
    (((^[Y3 : real]: (^[Z3 : real]: (Y3 = Z3))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A2)) & ((ord_less_eq_real @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_75_add__less__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_real @ A @ B))))). % add_less_cancel_left
thf(fact_76_add__less__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_real @ A @ B))))). % add_less_cancel_right
thf(fact_77_abs__1, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_1
thf(fact_78_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_79_less__add__one, axiom,
    ((![A : real]: (ord_less_real @ A @ (plus_plus_real @ A @ one_one_real))))). % less_add_one
thf(fact_80_add__mono1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ one_one_real) @ (plus_plus_real @ B @ one_one_real)))))). % add_mono1
thf(fact_81_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_82_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z2 : real]: (![X4 : real]: ((P @ X4) => (ord_less_real @ X4 @ Z2)))) => (?[S2 : real]: (![Y4 : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y4 @ X2)))) = (ord_less_real @ Y4 @ S2))))))))). % real_sup_exists
thf(fact_83_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_84_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_85_not__less__iff__gr__or__eq, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) = (((ord_less_real @ Y @ X)) | ((X = Y))))))). % not_less_iff_gr_or_eq
thf(fact_86_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_87_linorder__less__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B4 : real]: ((ord_less_real @ A4 @ B4) => (P @ A4 @ B4))) => ((![A4 : real]: (P @ A4 @ A4)) => ((![A4 : real, B4 : real]: ((P @ B4 @ A4) => (P @ A4 @ B4))) => (P @ A @ B))))))). % linorder_less_wlog
thf(fact_88_less__imp__not__less, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_imp_not_less
thf(fact_89_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_90_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_91_linorder__cases, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => ((~ ((X = Y))) => (ord_less_real @ Y @ X)))))). % linorder_cases
thf(fact_92_less__imp__triv, axiom,
    ((![X : real, Y : real, P : $o]: ((ord_less_real @ X @ Y) => ((ord_less_real @ Y @ X) => P))))). % less_imp_triv
thf(fact_93_less__imp__not__eq2, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_94_antisym__conv3, axiom,
    ((![Y : real, X : real]: ((~ ((ord_less_real @ Y @ X))) => ((~ ((ord_less_real @ X @ Y))) = (X = Y)))))). % antisym_conv3
thf(fact_95_less__not__sym, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_not_sym
thf(fact_96_less__imp__not__eq, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_97_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_98_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_99_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_100_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_101_less__linear, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) | ((X = Y) | (ord_less_real @ Y @ X)))))). % less_linear
thf(fact_102_less__trans, axiom,
    ((![X : real, Y : real, Z : real]: ((ord_less_real @ X @ Y) => ((ord_less_real @ Y @ Z) => (ord_less_real @ X @ Z)))))). % less_trans
thf(fact_103_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_104_less__asym, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((ord_less_real @ Y @ X))))))). % less_asym
thf(fact_105_less__imp__neq, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_106_dense, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (?[Z4 : real]: ((ord_less_real @ X @ Z4) & (ord_less_real @ Z4 @ Y))))))). % dense
thf(fact_107_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_108_neq__iff, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) = (((ord_less_real @ X @ Y)) | ((ord_less_real @ Y @ X))))))). % neq_iff
thf(fact_109_neqE, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) => ((~ ((ord_less_real @ X @ Y))) => (ord_less_real @ Y @ X)))))). % neqE
thf(fact_110_gt__ex, axiom,
    ((![X : real]: (?[X_12 : real]: (ord_less_real @ X @ X_12))))). % gt_ex
thf(fact_111_lt__ex, axiom,
    ((![X : real]: (?[Y2 : real]: (ord_less_real @ Y2 @ X))))). % lt_ex
thf(fact_112_order__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (ord_less_real @ (F @ X4) @ (F @ Y2)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_113_order__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (ord_less_real @ (F @ X4) @ (F @ Y2)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_114_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (ord_less_real @ (F @ X4) @ (F @ Y2)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_115_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (ord_less_real @ (F @ X4) @ (F @ Y2)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_116_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_117_leD, axiom,
    ((![Y : real, X : real]: ((ord_less_eq_real @ Y @ X) => (~ ((ord_less_real @ X @ Y))))))). % leD
thf(fact_118_leI, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => (ord_less_eq_real @ Y @ X))))). % leI
thf(fact_119_le__less, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y5 : real]: (((ord_less_real @ X2 @ Y5)) | ((X2 = Y5)))))))). % le_less
thf(fact_120_less__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y5 : real]: (((ord_less_eq_real @ X2 @ Y5)) & ((~ ((X2 = Y5)))))))))). % less_le
thf(fact_121_order__le__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (ord_less_real @ (F @ X4) @ (F @ Y2)))) => (ord_less_real @ A @ (F @ C)))))))). % order_le_less_subst1
thf(fact_122_order__le__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_real @ (F @ X4) @ (F @ Y2)))) => (ord_less_real @ (F @ A) @ C))))))). % order_le_less_subst2
thf(fact_123_order__less__le__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_real @ (F @ X4) @ (F @ Y2)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_le_subst1
thf(fact_124_order__less__le__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X4 : real, Y2 : real]: ((ord_less_real @ X4 @ Y2) => (ord_less_real @ (F @ X4) @ (F @ Y2)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_le_subst2
thf(fact_125_not__le, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_eq_real @ X @ Y))) = (ord_less_real @ Y @ X))))). % not_le
thf(fact_126_not__less, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) = (ord_less_eq_real @ Y @ X))))). % not_less
thf(fact_127_le__neq__trans, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((~ ((A = B))) => (ord_less_real @ A @ B)))))). % le_neq_trans
thf(fact_128_antisym__conv1, axiom,
    ((![X : real, Y : real]: ((~ ((ord_less_real @ X @ Y))) => ((ord_less_eq_real @ X @ Y) = (X = Y)))))). % antisym_conv1
thf(fact_129_antisym__conv2, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ Y) => ((~ ((ord_less_real @ X @ Y))) = (X = Y)))))). % antisym_conv2
thf(fact_130_less__imp__le, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ Y) => (ord_less_eq_real @ X @ Y))))). % less_imp_le

% Conjectures (2)
thf(conj_0, hypothesis,
    ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ a @ b)) @ c))).
thf(conj_1, conjecture,
    ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ b @ m)) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ a @ m)) @ c)))).
