% 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_432__5371786_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:05.930

% Could-be-implicit typings (3)
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Int__Oint, type,
    int : $tType).

% Explicit typings (26)
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint, type,
    one_one_int : int).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint, type,
    plus_plus_int : int > int > int).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_If_001t__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint, type,
    semiri2019852685at_int : nat > int).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal, type,
    semiri2110766477t_real : nat > real).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint, type,
    ord_less_eq_int : int > int > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Int__Oint_001t__Int__Oint, type,
    order_1320016787nt_int : (int > int) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Int__Oint_001t__Nat__Onat, type,
    order_682743095nt_nat : (int > nat) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Int__Oint_001t__Real__Oreal, type,
    order_335574163t_real : (int > real) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Int__Oint, type,
    order_1406747959at_int : (nat > int) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat, type,
    order_769474267at_nat : (nat > nat) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Real__Oreal, type,
    order_952716343t_real : (nat > real) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Int__Oint, type,
    order_934742803al_int : (real > int) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Nat__Onat, type,
    order_297469111al_nat : (real > nat) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Real__Oreal, type,
    order_1818878995l_real : (real > real) > $o).
thf(sy_v_N1____, type,
    n1 : nat).
thf(sy_v_N2____, type,
    n2 : nat).
thf(sy_v_f____, type,
    f : nat > nat).

% Relevant facts (248)
thf(fact_0__092_060open_062N1_A_L_AN2_A_092_060le_062_Af_A_IN1_A_L_AN2_J_092_060close_062, axiom,
    ((ord_less_eq_nat @ (plus_plus_nat @ n1 @ n2) @ (f @ (plus_plus_nat @ n1 @ n2))))). % \<open>N1 + N2 \<le> f (N1 + N2)\<close>
thf(fact_1_fz_I1_J, axiom,
    ((order_769474267at_nat @ f))). % fz(1)
thf(fact_2_of__nat__add, axiom,
    ((![M : nat, N : nat]: ((semiri1382578993at_nat @ (plus_plus_nat @ M @ N)) = (plus_plus_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)))))). % of_nat_add
thf(fact_3_of__nat__add, axiom,
    ((![M : nat, N : nat]: ((semiri2110766477t_real @ (plus_plus_nat @ M @ N)) = (plus_plus_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)))))). % of_nat_add
thf(fact_4_of__nat__add, axiom,
    ((![M : nat, N : nat]: ((semiri2019852685at_int @ (plus_plus_nat @ M @ N)) = (plus_plus_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N)))))). % of_nat_add
thf(fact_5_add__Suc__right, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ M @ (suc @ N)) = (suc @ (plus_plus_nat @ M @ N)))))). % add_Suc_right
thf(fact_6_of__nat__le__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)) = (ord_less_eq_nat @ M @ N))))). % of_nat_le_iff
thf(fact_7_of__nat__le__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)) = (ord_less_eq_nat @ M @ N))))). % of_nat_le_iff
thf(fact_8_of__nat__le__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N)) = (ord_less_eq_nat @ M @ N))))). % of_nat_le_iff
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__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_left
thf(fact_11_add__le__cancel__left, axiom,
    ((![C : int, A : int, B : int]: ((ord_less_eq_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B)) = (ord_less_eq_int @ A @ B))))). % add_le_cancel_left
thf(fact_12_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_13_add__le__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_14_add__le__cancel__right, axiom,
    ((![A : int, C : int, B : int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C)) = (ord_less_eq_int @ A @ B))))). % add_le_cancel_right
thf(fact_15_of__nat__eq__iff, axiom,
    ((![M : nat, N : nat]: (((semiri1382578993at_nat @ M) = (semiri1382578993at_nat @ N)) = (M = N))))). % of_nat_eq_iff
thf(fact_16_of__nat__eq__iff, axiom,
    ((![M : nat, N : nat]: (((semiri2110766477t_real @ M) = (semiri2110766477t_real @ N)) = (M = N))))). % of_nat_eq_iff
thf(fact_17_of__nat__eq__iff, axiom,
    ((![M : nat, N : nat]: (((semiri2019852685at_int @ M) = (semiri2019852685at_int @ N)) = (M = N))))). % of_nat_eq_iff
thf(fact_18_nat_Oinject, axiom,
    ((![X2 : nat, Y2 : nat]: (((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))). % nat.inject
thf(fact_19_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_20_add__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_21_add__left__cancel, axiom,
    ((![A : int, B : int, C : int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_22_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_23_add__right__cancel, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_24_add__right__cancel, axiom,
    ((![B : int, A : int, C : int]: (((plus_plus_int @ B @ A) = (plus_plus_int @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_25_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_26_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_27_order__refl, axiom,
    ((![X : nat]: (ord_less_eq_nat @ X @ X)))). % order_refl
thf(fact_28_order__refl, axiom,
    ((![X : int]: (ord_less_eq_int @ X @ X)))). % order_refl
thf(fact_29_Suc__le__mono, axiom,
    ((![N : nat, M : nat]: ((ord_less_eq_nat @ (suc @ N) @ (suc @ M)) = (ord_less_eq_nat @ N @ M))))). % Suc_le_mono
thf(fact_30_nat__add__left__cancel__le, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ K @ M) @ (plus_plus_nat @ K @ N)) = (ord_less_eq_nat @ M @ N))))). % nat_add_left_cancel_le
thf(fact_31_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_32_le__trans, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ J @ K) => (ord_less_eq_nat @ I @ K)))))). % le_trans
thf(fact_33_eq__imp__le, axiom,
    ((![M : nat, N : nat]: ((M = N) => (ord_less_eq_nat @ M @ N))))). % eq_imp_le
thf(fact_34_le__antisym, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => ((ord_less_eq_nat @ N @ M) => (M = N)))))). % le_antisym
thf(fact_35_nat__le__linear, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) | (ord_less_eq_nat @ N @ M))))). % nat_le_linear
thf(fact_36_Nat_Oex__has__greatest__nat, axiom,
    ((![P : nat > $o, K : nat, B : nat]: ((P @ K) => ((![Y : nat]: ((P @ Y) => (ord_less_eq_nat @ Y @ B))) => (?[X3 : nat]: ((P @ X3) & (![Y3 : nat]: ((P @ Y3) => (ord_less_eq_nat @ Y3 @ X3)))))))))). % Nat.ex_has_greatest_nat
thf(fact_37_strict__mono__imp__increasing, axiom,
    ((![F : nat > nat, N : nat]: ((order_769474267at_nat @ F) => (ord_less_eq_nat @ N @ (F @ N)))))). % strict_mono_imp_increasing
thf(fact_38_strict__mono__eq, axiom,
    ((![F : nat > nat, X : nat, Y4 : nat]: ((order_769474267at_nat @ F) => (((F @ X) = (F @ Y4)) = (X = Y4)))))). % strict_mono_eq
thf(fact_39_strict__mono__less__eq, axiom,
    ((![F : real > real, X : real, Y4 : real]: ((order_1818878995l_real @ F) => ((ord_less_eq_real @ (F @ X) @ (F @ Y4)) = (ord_less_eq_real @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_40_strict__mono__less__eq, axiom,
    ((![F : nat > real, X : nat, Y4 : nat]: ((order_952716343t_real @ F) => ((ord_less_eq_real @ (F @ X) @ (F @ Y4)) = (ord_less_eq_nat @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_41_strict__mono__less__eq, axiom,
    ((![F : int > real, X : int, Y4 : int]: ((order_335574163t_real @ F) => ((ord_less_eq_real @ (F @ X) @ (F @ Y4)) = (ord_less_eq_int @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_42_strict__mono__less__eq, axiom,
    ((![F : real > nat, X : real, Y4 : real]: ((order_297469111al_nat @ F) => ((ord_less_eq_nat @ (F @ X) @ (F @ Y4)) = (ord_less_eq_real @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_43_strict__mono__less__eq, axiom,
    ((![F : int > nat, X : int, Y4 : int]: ((order_682743095nt_nat @ F) => ((ord_less_eq_nat @ (F @ X) @ (F @ Y4)) = (ord_less_eq_int @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_44_strict__mono__less__eq, axiom,
    ((![F : real > int, X : real, Y4 : real]: ((order_934742803al_int @ F) => ((ord_less_eq_int @ (F @ X) @ (F @ Y4)) = (ord_less_eq_real @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_45_strict__mono__less__eq, axiom,
    ((![F : nat > int, X : nat, Y4 : nat]: ((order_1406747959at_int @ F) => ((ord_less_eq_int @ (F @ X) @ (F @ Y4)) = (ord_less_eq_nat @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_46_strict__mono__less__eq, axiom,
    ((![F : int > int, X : int, Y4 : int]: ((order_1320016787nt_int @ F) => ((ord_less_eq_int @ (F @ X) @ (F @ Y4)) = (ord_less_eq_int @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_47_strict__mono__less__eq, axiom,
    ((![F : nat > nat, X : nat, Y4 : nat]: ((order_769474267at_nat @ F) => ((ord_less_eq_nat @ (F @ X) @ (F @ Y4)) = (ord_less_eq_nat @ X @ Y4)))))). % strict_mono_less_eq
thf(fact_48_transitive__stepwise__le, axiom,
    ((![M : nat, N : nat, R : nat > nat > $o]: ((ord_less_eq_nat @ M @ N) => ((![X3 : nat]: (R @ X3 @ X3)) => ((![X3 : nat, Y : nat, Z : nat]: ((R @ X3 @ Y) => ((R @ Y @ Z) => (R @ X3 @ Z)))) => ((![N2 : nat]: (R @ N2 @ (suc @ N2))) => (R @ M @ N)))))))). % transitive_stepwise_le
thf(fact_49_nat__induct__at__least, axiom,
    ((![M : nat, N : nat, P : nat > $o]: ((ord_less_eq_nat @ M @ N) => ((P @ M) => ((![N2 : nat]: ((ord_less_eq_nat @ M @ N2) => ((P @ N2) => (P @ (suc @ N2))))) => (P @ N))))))). % nat_induct_at_least
thf(fact_50_full__nat__induct, axiom,
    ((![P : nat > $o, N : nat]: ((![N2 : nat]: ((![M2 : nat]: ((ord_less_eq_nat @ (suc @ M2) @ N2) => (P @ M2))) => (P @ N2))) => (P @ N))))). % full_nat_induct
thf(fact_51_not__less__eq__eq, axiom,
    ((![M : nat, N : nat]: ((~ ((ord_less_eq_nat @ M @ N))) = (ord_less_eq_nat @ (suc @ N) @ M))))). % not_less_eq_eq
thf(fact_52_Suc__n__not__le__n, axiom,
    ((![N : nat]: (~ ((ord_less_eq_nat @ (suc @ N) @ N)))))). % Suc_n_not_le_n
thf(fact_53_le__Suc__eq, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ (suc @ N)) = (((ord_less_eq_nat @ M @ N)) | ((M = (suc @ N)))))))). % le_Suc_eq
thf(fact_54_Suc__le__D, axiom,
    ((![N : nat, M3 : nat]: ((ord_less_eq_nat @ (suc @ N) @ M3) => (?[M4 : nat]: (M3 = (suc @ M4))))))). % Suc_le_D
thf(fact_55_le__SucI, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ M @ (suc @ N)))))). % le_SucI
thf(fact_56_le__SucE, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ (suc @ N)) => ((~ ((ord_less_eq_nat @ M @ N))) => (M = (suc @ N))))))). % le_SucE
thf(fact_57_Suc__leD, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ (suc @ M) @ N) => (ord_less_eq_nat @ M @ N))))). % Suc_leD
thf(fact_58_nat__le__iff__add, axiom,
    ((ord_less_eq_nat = (^[M5 : nat]: (^[N3 : nat]: (?[K2 : nat]: (N3 = (plus_plus_nat @ M5 @ K2)))))))). % nat_le_iff_add
thf(fact_59_trans__le__add2, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ M @ J)))))). % trans_le_add2
thf(fact_60_trans__le__add1, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ J @ M)))))). % trans_le_add1
thf(fact_61_add__le__mono1, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ K)))))). % add_le_mono1
thf(fact_62_add__le__mono, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ K @ L) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L))))))). % add_le_mono
thf(fact_63_le__Suc__ex, axiom,
    ((![K : nat, L : nat]: ((ord_less_eq_nat @ K @ L) => (?[N2 : nat]: (L = (plus_plus_nat @ K @ N2))))))). % le_Suc_ex
thf(fact_64_add__leD2, axiom,
    ((![M : nat, K : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N) => (ord_less_eq_nat @ K @ N))))). % add_leD2
thf(fact_65_add__leD1, axiom,
    ((![M : nat, K : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N) => (ord_less_eq_nat @ M @ N))))). % add_leD1
thf(fact_66_le__add2, axiom,
    ((![N : nat, M : nat]: (ord_less_eq_nat @ N @ (plus_plus_nat @ M @ N))))). % le_add2
thf(fact_67_le__add1, axiom,
    ((![N : nat, M : nat]: (ord_less_eq_nat @ N @ (plus_plus_nat @ N @ M))))). % le_add1
thf(fact_68_add__leE, axiom,
    ((![M : nat, K : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N) => (~ (((ord_less_eq_nat @ M @ N) => (~ ((ord_less_eq_nat @ K @ N)))))))))). % add_leE
thf(fact_69_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_70_dual__order_Oantisym, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_71_dual__order_Oantisym, axiom,
    ((![B : int, A : int]: ((ord_less_eq_int @ B @ A) => ((ord_less_eq_int @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_72_dual__order_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z2 : real]: (Y5 = Z2))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A2)) & ((ord_less_eq_real @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_73_dual__order_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z2 : nat]: (Y5 = Z2))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A2)) & ((ord_less_eq_nat @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_74_dual__order_Oeq__iff, axiom,
    (((^[Y5 : int]: (^[Z2 : int]: (Y5 = Z2))) = (^[A2 : int]: (^[B2 : int]: (((ord_less_eq_int @ B2 @ A2)) & ((ord_less_eq_int @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_75_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_76_dual__order_Otrans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))))). % dual_order.trans
thf(fact_77_dual__order_Otrans, axiom,
    ((![B : int, A : int, C : int]: ((ord_less_eq_int @ B @ A) => ((ord_less_eq_int @ C @ B) => (ord_less_eq_int @ C @ A)))))). % dual_order.trans
thf(fact_78_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A3 : real, B3 : real]: ((ord_less_eq_real @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : real, B3 : real]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_79_linorder__wlog, axiom,
    ((![P : nat > nat > $o, A : nat, B : nat]: ((![A3 : nat, B3 : nat]: ((ord_less_eq_nat @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : nat, B3 : nat]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_80_linorder__wlog, axiom,
    ((![P : int > int > $o, A : int, B : int]: ((![A3 : int, B3 : int]: ((ord_less_eq_int @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : int, B3 : int]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_81_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_82_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_83_dual__order_Orefl, axiom,
    ((![A : int]: (ord_less_eq_int @ A @ A)))). % dual_order.refl
thf(fact_84_order__trans, axiom,
    ((![X : real, Y4 : real, Z3 : real]: ((ord_less_eq_real @ X @ Y4) => ((ord_less_eq_real @ Y4 @ Z3) => (ord_less_eq_real @ X @ Z3)))))). % order_trans
thf(fact_85_order__trans, axiom,
    ((![X : nat, Y4 : nat, Z3 : nat]: ((ord_less_eq_nat @ X @ Y4) => ((ord_less_eq_nat @ Y4 @ Z3) => (ord_less_eq_nat @ X @ Z3)))))). % order_trans
thf(fact_86_order__trans, axiom,
    ((![X : int, Y4 : int, Z3 : int]: ((ord_less_eq_int @ X @ Y4) => ((ord_less_eq_int @ Y4 @ Z3) => (ord_less_eq_int @ X @ Z3)))))). % order_trans
thf(fact_87_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_88_order__class_Oorder_Oantisym, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_89_order__class_Oorder_Oantisym, axiom,
    ((![A : int, B : int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_90_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_91_ord__le__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C)))))). % ord_le_eq_trans
thf(fact_92_ord__le__eq__trans, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_eq_int @ A @ B) => ((B = C) => (ord_less_eq_int @ A @ C)))))). % ord_le_eq_trans
thf(fact_93_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_94_ord__eq__le__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % ord_eq_le_trans
thf(fact_95_ord__eq__le__trans, axiom,
    ((![A : int, B : int, C : int]: ((A = B) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C)))))). % ord_eq_le_trans
thf(fact_96_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z2 : real]: (Y5 = Z2))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ A2 @ B2)) & ((ord_less_eq_real @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_97_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z2 : nat]: (Y5 = Z2))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A2 @ B2)) & ((ord_less_eq_nat @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_98_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : int]: (^[Z2 : int]: (Y5 = Z2))) = (^[A2 : int]: (^[B2 : int]: (((ord_less_eq_int @ A2 @ B2)) & ((ord_less_eq_int @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_99_antisym__conv, axiom,
    ((![Y4 : real, X : real]: ((ord_less_eq_real @ Y4 @ X) => ((ord_less_eq_real @ X @ Y4) = (X = Y4)))))). % antisym_conv
thf(fact_100_antisym__conv, axiom,
    ((![Y4 : nat, X : nat]: ((ord_less_eq_nat @ Y4 @ X) => ((ord_less_eq_nat @ X @ Y4) = (X = Y4)))))). % antisym_conv
thf(fact_101_antisym__conv, axiom,
    ((![Y4 : int, X : int]: ((ord_less_eq_int @ Y4 @ X) => ((ord_less_eq_int @ X @ Y4) = (X = Y4)))))). % antisym_conv
thf(fact_102_le__cases3, axiom,
    ((![X : real, Y4 : real, Z3 : real]: (((ord_less_eq_real @ X @ Y4) => (~ ((ord_less_eq_real @ Y4 @ Z3)))) => (((ord_less_eq_real @ Y4 @ X) => (~ ((ord_less_eq_real @ X @ Z3)))) => (((ord_less_eq_real @ X @ Z3) => (~ ((ord_less_eq_real @ Z3 @ Y4)))) => (((ord_less_eq_real @ Z3 @ Y4) => (~ ((ord_less_eq_real @ Y4 @ X)))) => (((ord_less_eq_real @ Y4 @ Z3) => (~ ((ord_less_eq_real @ Z3 @ X)))) => (~ (((ord_less_eq_real @ Z3 @ X) => (~ ((ord_less_eq_real @ X @ Y4)))))))))))))). % le_cases3
thf(fact_103_le__cases3, axiom,
    ((![X : nat, Y4 : nat, Z3 : nat]: (((ord_less_eq_nat @ X @ Y4) => (~ ((ord_less_eq_nat @ Y4 @ Z3)))) => (((ord_less_eq_nat @ Y4 @ X) => (~ ((ord_less_eq_nat @ X @ Z3)))) => (((ord_less_eq_nat @ X @ Z3) => (~ ((ord_less_eq_nat @ Z3 @ Y4)))) => (((ord_less_eq_nat @ Z3 @ Y4) => (~ ((ord_less_eq_nat @ Y4 @ X)))) => (((ord_less_eq_nat @ Y4 @ Z3) => (~ ((ord_less_eq_nat @ Z3 @ X)))) => (~ (((ord_less_eq_nat @ Z3 @ X) => (~ ((ord_less_eq_nat @ X @ Y4)))))))))))))). % le_cases3
thf(fact_104_le__cases3, axiom,
    ((![X : int, Y4 : int, Z3 : int]: (((ord_less_eq_int @ X @ Y4) => (~ ((ord_less_eq_int @ Y4 @ Z3)))) => (((ord_less_eq_int @ Y4 @ X) => (~ ((ord_less_eq_int @ X @ Z3)))) => (((ord_less_eq_int @ X @ Z3) => (~ ((ord_less_eq_int @ Z3 @ Y4)))) => (((ord_less_eq_int @ Z3 @ Y4) => (~ ((ord_less_eq_int @ Y4 @ X)))) => (((ord_less_eq_int @ Y4 @ Z3) => (~ ((ord_less_eq_int @ Z3 @ X)))) => (~ (((ord_less_eq_int @ Z3 @ X) => (~ ((ord_less_eq_int @ X @ Y4)))))))))))))). % le_cases3
thf(fact_105_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_106_order_Otrans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % order.trans
thf(fact_107_order_Otrans, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C)))))). % order.trans
thf(fact_108_le__cases, axiom,
    ((![X : real, Y4 : real]: ((~ ((ord_less_eq_real @ X @ Y4))) => (ord_less_eq_real @ Y4 @ X))))). % le_cases
thf(fact_109_le__cases, axiom,
    ((![X : nat, Y4 : nat]: ((~ ((ord_less_eq_nat @ X @ Y4))) => (ord_less_eq_nat @ Y4 @ X))))). % le_cases
thf(fact_110_le__cases, axiom,
    ((![X : int, Y4 : int]: ((~ ((ord_less_eq_int @ X @ Y4))) => (ord_less_eq_int @ Y4 @ X))))). % le_cases
thf(fact_111_eq__refl, axiom,
    ((![X : real, Y4 : real]: ((X = Y4) => (ord_less_eq_real @ X @ Y4))))). % eq_refl
thf(fact_112_eq__refl, axiom,
    ((![X : nat, Y4 : nat]: ((X = Y4) => (ord_less_eq_nat @ X @ Y4))))). % eq_refl
thf(fact_113_eq__refl, axiom,
    ((![X : int, Y4 : int]: ((X = Y4) => (ord_less_eq_int @ X @ Y4))))). % eq_refl
thf(fact_114_linear, axiom,
    ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) | (ord_less_eq_real @ Y4 @ X))))). % linear
thf(fact_115_linear, axiom,
    ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) | (ord_less_eq_nat @ Y4 @ X))))). % linear
thf(fact_116_linear, axiom,
    ((![X : int, Y4 : int]: ((ord_less_eq_int @ X @ Y4) | (ord_less_eq_int @ Y4 @ X))))). % linear
thf(fact_117_antisym, axiom,
    ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => ((ord_less_eq_real @ Y4 @ X) => (X = Y4)))))). % antisym
thf(fact_118_antisym, axiom,
    ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => ((ord_less_eq_nat @ Y4 @ X) => (X = Y4)))))). % antisym
thf(fact_119_antisym, axiom,
    ((![X : int, Y4 : int]: ((ord_less_eq_int @ X @ Y4) => ((ord_less_eq_int @ Y4 @ X) => (X = Y4)))))). % antisym
thf(fact_120_eq__iff, axiom,
    (((^[Y5 : real]: (^[Z2 : real]: (Y5 = Z2))) = (^[X4 : real]: (^[Y6 : real]: (((ord_less_eq_real @ X4 @ Y6)) & ((ord_less_eq_real @ Y6 @ X4)))))))). % eq_iff
thf(fact_121_eq__iff, axiom,
    (((^[Y5 : nat]: (^[Z2 : nat]: (Y5 = Z2))) = (^[X4 : nat]: (^[Y6 : nat]: (((ord_less_eq_nat @ X4 @ Y6)) & ((ord_less_eq_nat @ Y6 @ X4)))))))). % eq_iff
thf(fact_122_eq__iff, axiom,
    (((^[Y5 : int]: (^[Z2 : int]: (Y5 = Z2))) = (^[X4 : int]: (^[Y6 : int]: (((ord_less_eq_int @ X4 @ Y6)) & ((ord_less_eq_int @ Y6 @ X4)))))))). % eq_iff
thf(fact_123_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_124_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_125_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > int, C : int]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_126_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > real, C : real]: ((ord_less_eq_nat @ A @ B) => (((F @ B) = C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_127_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (((F @ B) = C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_128_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > int, C : int]: ((ord_less_eq_nat @ A @ B) => (((F @ B) = C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_129_ord__le__eq__subst, axiom,
    ((![A : int, B : int, F : int > real, C : real]: ((ord_less_eq_int @ A @ B) => (((F @ B) = C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_130_ord__le__eq__subst, axiom,
    ((![A : int, B : int, F : int > nat, C : nat]: ((ord_less_eq_int @ A @ B) => (((F @ B) = C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_131_ord__le__eq__subst, axiom,
    ((![A : int, B : int, F : int > int, C : int]: ((ord_less_eq_int @ A @ B) => (((F @ B) = C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_132_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_133_ord__eq__le__subst, axiom,
    ((![A : nat, F : real > nat, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_134_ord__eq__le__subst, axiom,
    ((![A : int, F : real > int, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_135_ord__eq__le__subst, axiom,
    ((![A : real, F : nat > real, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_136_ord__eq__le__subst, axiom,
    ((![A : nat, F : nat > nat, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_137_ord__eq__le__subst, axiom,
    ((![A : int, F : nat > int, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_138_ord__eq__le__subst, axiom,
    ((![A : real, F : int > real, B : int, C : int]: ((A = (F @ B)) => ((ord_less_eq_int @ B @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_139_ord__eq__le__subst, axiom,
    ((![A : nat, F : int > nat, B : int, C : int]: ((A = (F @ B)) => ((ord_less_eq_int @ B @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_140_ord__eq__le__subst, axiom,
    ((![A : int, F : int > int, B : int, C : int]: ((A = (F @ B)) => ((ord_less_eq_int @ B @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_141_order__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_142_order__subst2, axiom,
    ((![A : real, B : real, F : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_nat @ (F @ B) @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % order_subst2
thf(fact_143_order__subst2, axiom,
    ((![A : real, B : real, F : real > int, C : int]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_int @ (F @ B) @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ (F @ A) @ C))))))). % order_subst2
thf(fact_144_order__subst2, axiom,
    ((![A : nat, B : nat, F : nat > real, C : real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_145_order__subst2, axiom,
    ((![A : nat, B : nat, F : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (F @ B) @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % order_subst2
thf(fact_146_order__subst2, axiom,
    ((![A : nat, B : nat, F : nat > int, C : int]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_int @ (F @ B) @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ (F @ A) @ C))))))). % order_subst2
thf(fact_147_order__subst2, axiom,
    ((![A : int, B : int, F : int > real, C : real]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_148_order__subst2, axiom,
    ((![A : int, B : int, F : int > nat, C : nat]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_nat @ (F @ B) @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % order_subst2
thf(fact_149_order__subst2, axiom,
    ((![A : int, B : int, F : int > int, C : int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (F @ B) @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ (F @ A) @ C))))))). % order_subst2
thf(fact_150_order__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_151_order__subst1, axiom,
    ((![A : real, F : nat > real, B : nat, C : nat]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_152_order__subst1, axiom,
    ((![A : real, F : int > real, B : int, C : int]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_int @ B @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_153_order__subst1, axiom,
    ((![A : nat, F : real > nat, B : real, C : real]: ((ord_less_eq_nat @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % order_subst1
thf(fact_154_order__subst1, axiom,
    ((![A : nat, F : nat > nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % order_subst1
thf(fact_155_order__subst1, axiom,
    ((![A : nat, F : int > nat, B : int, C : int]: ((ord_less_eq_nat @ A @ (F @ B)) => ((ord_less_eq_int @ B @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % order_subst1
thf(fact_156_order__subst1, axiom,
    ((![A : int, F : real > int, B : real, C : real]: ((ord_less_eq_int @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ A @ (F @ C)))))))). % order_subst1
thf(fact_157_order__subst1, axiom,
    ((![A : int, F : nat > int, B : nat, C : nat]: ((ord_less_eq_int @ A @ (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ A @ (F @ C)))))))). % order_subst1
thf(fact_158_order__subst1, axiom,
    ((![A : int, F : int > int, B : int, C : int]: ((ord_less_eq_int @ A @ (F @ B)) => ((ord_less_eq_int @ B @ C) => ((![X3 : int, Y : int]: ((ord_less_eq_int @ X3 @ Y) => (ord_less_eq_int @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_int @ A @ (F @ C)))))))). % order_subst1
thf(fact_159_add__right__imp__eq, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_160_add__right__imp__eq, axiom,
    ((![B : int, A : int, C : int]: (((plus_plus_int @ B @ A) = (plus_plus_int @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_161_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_162_add__left__imp__eq, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_163_add__left__imp__eq, axiom,
    ((![A : int, B : int, C : int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_164_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_165_add_Oleft__commute, axiom,
    ((![B : nat, A : nat, C : nat]: ((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.left_commute
thf(fact_166_add_Oleft__commute, axiom,
    ((![B : int, A : int, C : int]: ((plus_plus_int @ B @ (plus_plus_int @ A @ C)) = (plus_plus_int @ A @ (plus_plus_int @ B @ C)))))). % add.left_commute
thf(fact_167_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_168_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B2 : nat]: (plus_plus_nat @ B2 @ A2)))))). % add.commute
thf(fact_169_add_Ocommute, axiom,
    ((plus_plus_int = (^[A2 : int]: (^[B2 : int]: (plus_plus_int @ B2 @ A2)))))). % add.commute
thf(fact_170_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_171_add_Oright__cancel, axiom,
    ((![B : int, A : int, C : int]: (((plus_plus_int @ B @ A) = (plus_plus_int @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_172_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_173_add_Oleft__cancel, axiom,
    ((![A : int, B : int, C : int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_174_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_175_add_Oassoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.assoc
thf(fact_176_add_Oassoc, axiom,
    ((![A : int, B : int, C : int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C)))))). % add.assoc
thf(fact_177_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_178_group__cancel_Oadd2, axiom,
    ((![B4 : nat, K : nat, B : nat, A : nat]: ((B4 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B4) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_179_group__cancel_Oadd2, axiom,
    ((![B4 : int, K : int, B : int, A : int]: ((B4 = (plus_plus_int @ K @ B)) => ((plus_plus_int @ A @ B4) = (plus_plus_int @ K @ (plus_plus_int @ A @ B))))))). % group_cancel.add2
thf(fact_180_group__cancel_Oadd2, axiom,
    ((![B4 : real, K : real, B : real, A : real]: ((B4 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B4) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_181_group__cancel_Oadd1, axiom,
    ((![A4 : nat, K : nat, A : nat, B : nat]: ((A4 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A4 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_182_group__cancel_Oadd1, axiom,
    ((![A4 : int, K : int, A : int, B : int]: ((A4 = (plus_plus_int @ K @ A)) => ((plus_plus_int @ A4 @ B) = (plus_plus_int @ K @ (plus_plus_int @ A @ B))))))). % group_cancel.add1
thf(fact_183_group__cancel_Oadd1, axiom,
    ((![A4 : real, K : real, A : real, B : real]: ((A4 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A4 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_184_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (K = L)) => ((plus_plus_nat @ I @ K) = (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_185_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : int, J : int, K : int, L : int]: (((I = J) & (K = L)) => ((plus_plus_int @ I @ K) = (plus_plus_int @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_186_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_187_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_188_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : int, B : int, C : int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_189_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_190_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_191_Suc__inject, axiom,
    ((![X : nat, Y4 : nat]: (((suc @ X) = (suc @ Y4)) => (X = Y4))))). % Suc_inject
thf(fact_192_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_193_add__le__imp__le__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_right
thf(fact_194_add__le__imp__le__right, axiom,
    ((![A : int, C : int, B : int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C)) => (ord_less_eq_int @ A @ B))))). % add_le_imp_le_right
thf(fact_195_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_196_add__le__imp__le__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_left
thf(fact_197_add__le__imp__le__left, axiom,
    ((![C : int, A : int, B : int]: ((ord_less_eq_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B)) => (ord_less_eq_int @ A @ B))))). % add_le_imp_le_left
thf(fact_198_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A2 : nat]: (^[B2 : nat]: (?[C2 : nat]: (B2 = (plus_plus_nat @ A2 @ C2)))))))). % le_iff_add
thf(fact_199_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_200_add__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)))))). % add_right_mono
thf(fact_201_add__right__mono, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C)))))). % add_right_mono
thf(fact_202_less__eqE, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => (~ ((![C3 : nat]: (~ ((B = (plus_plus_nat @ A @ C3))))))))))). % less_eqE
thf(fact_203_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_204_add__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)))))). % add_left_mono
thf(fact_205_add__left__mono, axiom,
    ((![A : int, B : int, C : int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B)))))). % add_left_mono
thf(fact_206_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_207_add__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_mono
thf(fact_208_add__mono, axiom,
    ((![A : int, B : int, C : int, D : int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))))). % add_mono
thf(fact_209_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_210_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_211_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : int, J : int, K : int, L : int]: (((ord_less_eq_int @ I @ J) & (ord_less_eq_int @ K @ L)) => (ord_less_eq_int @ (plus_plus_int @ I @ K) @ (plus_plus_int @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_212_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_213_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_214_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : int, J : int, K : int, L : int]: (((I = J) & (ord_less_eq_int @ K @ L)) => (ord_less_eq_int @ (plus_plus_int @ I @ K) @ (plus_plus_int @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_215_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_216_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (K = L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_217_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : int, J : int, K : int, L : int]: (((ord_less_eq_int @ I @ J) & (K = L)) => (ord_less_eq_int @ (plus_plus_int @ I @ K) @ (plus_plus_int @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_218_lift__Suc__antimono__le, axiom,
    ((![F : nat > real, N : nat, N4 : nat]: ((![N2 : nat]: (ord_less_eq_real @ (F @ (suc @ N2)) @ (F @ N2))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_real @ (F @ N4) @ (F @ N))))))). % lift_Suc_antimono_le
thf(fact_219_lift__Suc__antimono__le, axiom,
    ((![F : nat > nat, N : nat, N4 : nat]: ((![N2 : nat]: (ord_less_eq_nat @ (F @ (suc @ N2)) @ (F @ N2))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_nat @ (F @ N4) @ (F @ N))))))). % lift_Suc_antimono_le
thf(fact_220_lift__Suc__antimono__le, axiom,
    ((![F : nat > int, N : nat, N4 : nat]: ((![N2 : nat]: (ord_less_eq_int @ (F @ (suc @ N2)) @ (F @ N2))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_int @ (F @ N4) @ (F @ N))))))). % lift_Suc_antimono_le
thf(fact_221_lift__Suc__mono__le, axiom,
    ((![F : nat > int, N : nat, N4 : nat]: ((![N2 : nat]: (ord_less_eq_int @ (F @ N2) @ (F @ (suc @ N2)))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_int @ (F @ N) @ (F @ N4))))))). % lift_Suc_mono_le
thf(fact_222_add__Suc, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ (suc @ M) @ N) = (suc @ (plus_plus_nat @ M @ N)))))). % add_Suc
thf(fact_223_nat__arith_Osuc1, axiom,
    ((![A4 : nat, K : nat, A : nat]: ((A4 = (plus_plus_nat @ K @ A)) => ((suc @ A4) = (plus_plus_nat @ K @ (suc @ A))))))). % nat_arith.suc1
thf(fact_224_add__Suc__shift, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ (suc @ M) @ N) = (plus_plus_nat @ M @ (suc @ N)))))). % add_Suc_shift
thf(fact_225_diff__Suc__diff__eq2, axiom,
    ((![K : nat, J : nat, I : nat]: ((ord_less_eq_nat @ K @ J) => ((minus_minus_nat @ (suc @ (minus_minus_nat @ J @ K)) @ I) = (minus_minus_nat @ (suc @ J) @ (plus_plus_nat @ K @ I))))))). % diff_Suc_diff_eq2
thf(fact_226_diff__Suc__diff__eq1, axiom,
    ((![K : nat, J : nat, I : nat]: ((ord_less_eq_nat @ K @ J) => ((minus_minus_nat @ I @ (suc @ (minus_minus_nat @ J @ K))) = (minus_minus_nat @ (plus_plus_nat @ I @ K) @ (suc @ J))))))). % diff_Suc_diff_eq1
thf(fact_227_int__ops_I5_J, axiom,
    ((![A : nat, B : nat]: ((semiri2019852685at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ (semiri2019852685at_int @ B)))))). % int_ops(5)
thf(fact_228_int__plus, axiom,
    ((![N : nat, M : nat]: ((semiri2019852685at_int @ (plus_plus_nat @ N @ M)) = (plus_plus_int @ (semiri2019852685at_int @ N) @ (semiri2019852685at_int @ M)))))). % int_plus
thf(fact_229_zadd__int__left, axiom,
    ((![M : nat, N : nat, Z3 : int]: ((plus_plus_int @ (semiri2019852685at_int @ M) @ (plus_plus_int @ (semiri2019852685at_int @ N) @ Z3)) = (plus_plus_int @ (semiri2019852685at_int @ (plus_plus_nat @ M @ N)) @ Z3))))). % zadd_int_left
thf(fact_230_diff__Suc__1, axiom,
    ((![N : nat]: ((minus_minus_nat @ (suc @ N) @ one_one_nat) = N)))). % diff_Suc_1
thf(fact_231_diff__Suc__Suc, axiom,
    ((![M : nat, N : nat]: ((minus_minus_nat @ (suc @ M) @ (suc @ N)) = (minus_minus_nat @ M @ N))))). % diff_Suc_Suc
thf(fact_232_Suc__diff__diff, axiom,
    ((![M : nat, N : nat, K : nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ M) @ N) @ (suc @ K)) = (minus_minus_nat @ (minus_minus_nat @ M @ N) @ K))))). % Suc_diff_diff
thf(fact_233_diff__diff__cancel, axiom,
    ((![I : nat, N : nat]: ((ord_less_eq_nat @ I @ N) => ((minus_minus_nat @ N @ (minus_minus_nat @ N @ I)) = I))))). % diff_diff_cancel
thf(fact_234_diff__diff__left, axiom,
    ((![I : nat, J : nat, K : nat]: ((minus_minus_nat @ (minus_minus_nat @ I @ J) @ K) = (minus_minus_nat @ I @ (plus_plus_nat @ J @ K)))))). % diff_diff_left
thf(fact_235_Nat_Oadd__diff__assoc, axiom,
    ((![K : nat, J : nat, I : nat]: ((ord_less_eq_nat @ K @ J) => ((plus_plus_nat @ I @ (minus_minus_nat @ J @ K)) = (minus_minus_nat @ (plus_plus_nat @ I @ J) @ K)))))). % Nat.add_diff_assoc
thf(fact_236_Nat_Oadd__diff__assoc2, axiom,
    ((![K : nat, J : nat, I : nat]: ((ord_less_eq_nat @ K @ J) => ((plus_plus_nat @ (minus_minus_nat @ J @ K) @ I) = (minus_minus_nat @ (plus_plus_nat @ J @ I) @ K)))))). % Nat.add_diff_assoc2
thf(fact_237_Nat_Odiff__diff__right, axiom,
    ((![K : nat, J : nat, I : nat]: ((ord_less_eq_nat @ K @ J) => ((minus_minus_nat @ I @ (minus_minus_nat @ J @ K)) = (minus_minus_nat @ (plus_plus_nat @ I @ K) @ J)))))). % Nat.diff_diff_right
thf(fact_238_int__ops_I2_J, axiom,
    (((semiri2019852685at_int @ one_one_nat) = one_one_int))). % int_ops(2)
thf(fact_239_nat__int__comparison_I1_J, axiom,
    (((^[Y5 : nat]: (^[Z2 : nat]: (Y5 = Z2))) = (^[A2 : nat]: (^[B2 : nat]: ((semiri2019852685at_int @ A2) = (semiri2019852685at_int @ B2))))))). % nat_int_comparison(1)
thf(fact_240_int__if, axiom,
    ((![P : $o, A : nat, B : nat]: ((P => ((semiri2019852685at_int @ (if_nat @ P @ A @ B)) = (semiri2019852685at_int @ A))) & ((~ (P)) => ((semiri2019852685at_int @ (if_nat @ P @ A @ B)) = (semiri2019852685at_int @ B))))))). % int_if
thf(fact_241_int__int__eq, axiom,
    ((![M : nat, N : nat]: (((semiri2019852685at_int @ M) = (semiri2019852685at_int @ N)) = (M = N))))). % int_int_eq
thf(fact_242_zle__iff__zadd, axiom,
    ((ord_less_eq_int = (^[W : int]: (^[Z4 : int]: (?[N3 : nat]: (Z4 = (plus_plus_int @ W @ (semiri2019852685at_int @ N3))))))))). % zle_iff_zadd
thf(fact_243_diff__commute, axiom,
    ((![I : nat, J : nat, K : nat]: ((minus_minus_nat @ (minus_minus_nat @ I @ J) @ K) = (minus_minus_nat @ (minus_minus_nat @ I @ K) @ J))))). % diff_commute
thf(fact_244_int__ge__induct, axiom,
    ((![K : int, I : int, P : int > $o]: ((ord_less_eq_int @ K @ I) => ((P @ K) => ((![I2 : int]: ((ord_less_eq_int @ K @ I2) => ((P @ I2) => (P @ (plus_plus_int @ I2 @ one_one_int))))) => (P @ I))))))). % int_ge_induct
thf(fact_245_diff__Suc__eq__diff__pred, axiom,
    ((![M : nat, N : nat]: ((minus_minus_nat @ M @ (suc @ N)) = (minus_minus_nat @ (minus_minus_nat @ M @ one_one_nat) @ N))))). % diff_Suc_eq_diff_pred
thf(fact_246_int__Suc, axiom,
    ((![N : nat]: ((semiri2019852685at_int @ (suc @ N)) = (plus_plus_int @ (semiri2019852685at_int @ N) @ one_one_int))))). % int_Suc
thf(fact_247_int__ops_I4_J, axiom,
    ((![A : nat]: ((semiri2019852685at_int @ (suc @ A)) = (plus_plus_int @ (semiri2019852685at_int @ A) @ one_one_int))))). % int_ops(4)

% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X : nat, Y4 : nat]: ((if_nat @ $false @ X @ Y4) = Y4)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X : nat, Y4 : nat]: ((if_nat @ $true @ X @ Y4) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (semiri2110766477t_real @ (suc @ (plus_plus_nat @ n1 @ n2))) @ (semiri2110766477t_real @ (suc @ (f @ (plus_plus_nat @ n1 @ n2))))))).
