% 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_946__5376856_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:34:34.410

% Could-be-implicit typings (5)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (32)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
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_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Polynomial_Odegree_001t__Complex__Ocomplex, type,
    degree_complex : poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Complex__Ocomplex, type,
    order_complex : complex > poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    order_poly_complex : poly_complex > poly_poly_complex > nat).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opseudo__mod_001t__Complex__Ocomplex, type,
    pseudo_mod_complex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex, type,
    power_power_complex : complex > nat > complex).
thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat, type,
    power_power_nat : nat > nat > nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    power_184595776omplex : poly_complex > nat > poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    power_power_poly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    power_432682568omplex : poly_poly_complex > nat > poly_poly_complex).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex, type,
    dvd_dvd_complex : complex > complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    dvd_dvd_poly_complex : poly_complex > poly_complex > $o).
thf(sy_v_a____, type,
    a : complex).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_na____, type,
    na : nat).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_pa____, type,
    pa : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).
thf(sy_v_qa____, type,
    qa : poly_complex).
thf(sy_v_s____, type,
    s : poly_complex).
thf(sy_v_x____, type,
    x : complex).

% Relevant facts (165)
thf(fact_0_that, axiom,
    (((poly_complex2 @ s @ x) = zero_zero_complex))). % that
thf(fact_1_assms_I3_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(3)
thf(fact_2_oa, axiom,
    ((~ (((order_complex @ a @ pa) = zero_zero_nat))))). % oa
thf(fact_3_a, axiom,
    (((poly_complex2 @ pa @ a) = zero_zero_complex))). % a
thf(fact_4_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X : complex]: (![Y : complex]: ((F @ X) = (F @ Y)))))))). % constant_def
thf(fact_5_n0, axiom,
    ((~ ((na = zero_zero_nat))))). % n0
thf(fact_6_assms_I2_J, axiom,
    (((degree_complex @ p) = n))). % assms(2)
thf(fact_7_True, axiom,
    ((?[A : complex]: ((poly_complex2 @ pa @ A) = zero_zero_complex)))). % True
thf(fact_8_False, axiom,
    ((~ (((degree_complex @ s) = zero_zero_nat))))). % False
thf(fact_9_dpn, axiom,
    (((degree_complex @ pa) = na))). % dpn
thf(fact_10_assms_I1_J, axiom,
    ((![X2 : complex]: (((poly_complex2 @ p @ X2) = zero_zero_complex) => ((poly_complex2 @ q @ X2) = zero_zero_complex))))). % assms(1)
thf(fact_11_pq0, axiom,
    ((![X2 : complex]: (((poly_complex2 @ pa @ X2) = zero_zero_complex) => ((poly_complex2 @ qa @ X2) = zero_zero_complex))))). % pq0
thf(fact_12__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062a_O_Apoly_Ap_Aa_A_061_A0_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![A : complex]: (~ (((poly_complex2 @ pa @ A) = zero_zero_complex)))))))). % \<open>\<And>thesis. (\<And>a. poly p a = 0 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_13_fundamental__theorem__of__algebra, axiom,
    ((![P : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra
thf(fact_14_dsn, axiom,
    ((ord_less_nat @ (degree_complex @ s) @ na))). % dsn
thf(fact_15_poly__0, axiom,
    ((![X3 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))). % poly_0
thf(fact_16_poly__0, axiom,
    ((![X3 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))). % poly_0
thf(fact_17_poly__0, axiom,
    ((![X3 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))). % poly_0
thf(fact_18_oop, axiom,
    ((![A2 : complex]: (ord_less_eq_nat @ (order_complex @ A2 @ pa) @ na)))). % oop
thf(fact_19_order__0I, axiom,
    ((![P : poly_complex, A2 : complex]: ((~ (((poly_complex2 @ P @ A2) = zero_zero_complex))) => ((order_complex @ A2 @ P) = zero_zero_nat))))). % order_0I
thf(fact_20_order__0I, axiom,
    ((![P : poly_poly_complex, A2 : poly_complex]: ((~ (((poly_poly_complex2 @ P @ A2) = zero_z1746442943omplex))) => ((order_poly_complex @ A2 @ P) = zero_zero_nat))))). % order_0I
thf(fact_21_order__root, axiom,
    ((![P : poly_complex, A2 : complex]: (((poly_complex2 @ P @ A2) = zero_zero_complex) = (((P = zero_z1746442943omplex)) | ((~ (((order_complex @ A2 @ P) = zero_zero_nat))))))))). % order_root
thf(fact_22_order__root, axiom,
    ((![P : poly_poly_complex, A2 : poly_complex]: (((poly_poly_complex2 @ P @ A2) = zero_z1746442943omplex) = (((P = zero_z1040703943omplex)) | ((~ (((order_poly_complex @ A2 @ P) = zero_zero_nat))))))))). % order_root
thf(fact_23_sne, axiom,
    ((~ ((s = zero_z1746442943omplex))))). % sne
thf(fact_24_pne, axiom,
    ((~ ((pa = zero_z1746442943omplex))))). % pne
thf(fact_25_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X : complex]: ((poly_complex2 @ P @ X) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_26_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X : poly_complex]: ((poly_poly_complex2 @ P @ X) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_27_IH, axiom,
    ((![M : nat]: ((ord_less_nat @ M @ na) => (![P2 : poly_complex, Q : poly_complex]: ((![X4 : complex]: (((poly_complex2 @ P2 @ X4) = zero_zero_complex) => ((poly_complex2 @ Q @ X4) = zero_zero_complex))) => (((degree_complex @ P2) = M) => ((~ ((M = zero_zero_nat))) => (dvd_dvd_poly_complex @ P2 @ (power_184595776omplex @ Q @ M)))))))))). % IH
thf(fact_28_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q2 : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q2)) = (P = Q2))))). % poly_eq_poly_eq_iff
thf(fact_29_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_30_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_31_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_32_poly__power, axiom,
    ((![P : poly_poly_complex, N : nat, X3 : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P @ N) @ X3) = (power_184595776omplex @ (poly_poly_complex2 @ P @ X3) @ N))))). % poly_power
thf(fact_33_poly__power, axiom,
    ((![P : poly_nat, N : nat, X3 : nat]: ((poly_nat2 @ (power_power_poly_nat @ P @ N) @ X3) = (power_power_nat @ (poly_nat2 @ P @ X3) @ N))))). % poly_power
thf(fact_34_poly__power, axiom,
    ((![P : poly_complex, N : nat, X3 : complex]: ((poly_complex2 @ (power_184595776omplex @ P @ N) @ X3) = (power_power_complex @ (poly_complex2 @ P @ X3) @ N))))). % poly_power
thf(fact_35_divides__degree, axiom,
    ((![P : poly_complex, Q2 : poly_complex]: ((dvd_dvd_poly_complex @ P @ Q2) => ((ord_less_eq_nat @ (degree_complex @ P) @ (degree_complex @ Q2)) | (Q2 = zero_z1746442943omplex)))))). % divides_degree
thf(fact_36_dvd__imp__order__le, axiom,
    ((![Q2 : poly_complex, P : poly_complex, A2 : complex]: ((~ ((Q2 = zero_z1746442943omplex))) => ((dvd_dvd_poly_complex @ P @ Q2) => (ord_less_eq_nat @ (order_complex @ A2 @ P) @ (order_complex @ A2 @ Q2))))))). % dvd_imp_order_le
thf(fact_37_dvd__imp__degree__le, axiom,
    ((![P : poly_complex, Q2 : poly_complex]: ((dvd_dvd_poly_complex @ P @ Q2) => ((~ ((Q2 = zero_z1746442943omplex))) => (ord_less_eq_nat @ (degree_complex @ P) @ (degree_complex @ Q2))))))). % dvd_imp_degree_le
thf(fact_38_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_39_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_40_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_41_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_42_zero__le, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X3)))). % zero_le
thf(fact_43_order__degree, axiom,
    ((![P : poly_complex, A2 : complex]: ((~ ((P = zero_z1746442943omplex))) => (ord_less_eq_nat @ (order_complex @ A2 @ P) @ (degree_complex @ P)))))). % order_degree
thf(fact_44_zero__reorient, axiom,
    ((![X3 : complex]: ((zero_zero_complex = X3) = (X3 = zero_zero_complex))))). % zero_reorient
thf(fact_45_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_46_zero__reorient, axiom,
    ((![X3 : poly_complex]: ((zero_z1746442943omplex = X3) = (X3 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_47_power__mono__iff, axiom,
    ((![A2 : nat, B : nat, N : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A2) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_eq_nat @ (power_power_nat @ A2 @ N) @ (power_power_nat @ B @ N)) = (ord_less_eq_nat @ A2 @ B)))))))). % power_mono_iff
thf(fact_48_pow__divides__pow__iff, axiom,
    ((![N : nat, A2 : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((dvd_dvd_nat @ (power_power_nat @ A2 @ N) @ (power_power_nat @ B @ N)) = (dvd_dvd_nat @ A2 @ B)))))). % pow_divides_pow_iff
thf(fact_49_power__eq__0__iff, axiom,
    ((![A2 : complex, N : nat]: (((power_power_complex @ A2 @ N) = zero_zero_complex) = (((A2 = zero_zero_complex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_50_power__eq__0__iff, axiom,
    ((![A2 : poly_complex, N : nat]: (((power_184595776omplex @ A2 @ N) = zero_z1746442943omplex) = (((A2 = zero_z1746442943omplex)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_51_power__eq__0__iff, axiom,
    ((![A2 : nat, N : nat]: (((power_power_nat @ A2 @ N) = zero_zero_nat) = (((A2 = zero_zero_nat)) & ((ord_less_nat @ zero_zero_nat @ N))))))). % power_eq_0_iff
thf(fact_52_power__strict__mono, axiom,
    ((![A2 : nat, B : nat, N : nat]: ((ord_less_nat @ A2 @ B) => ((ord_less_eq_nat @ zero_zero_nat @ A2) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_nat @ (power_power_nat @ A2 @ N) @ (power_power_nat @ B @ N)))))))). % power_strict_mono
thf(fact_53_bot__nat__0_Oextremum, axiom,
    ((![A2 : nat]: (ord_less_eq_nat @ zero_zero_nat @ A2)))). % bot_nat_0.extremum
thf(fact_54_le0, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % le0
thf(fact_55_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A2 : nat]: ((~ ((A2 = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A2))))). % bot_nat_0.not_eq_extremum
thf(fact_56_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_57_nat__zero__less__power__iff, axiom,
    ((![X3 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ X3 @ N)) = (((ord_less_nat @ zero_zero_nat @ X3)) | ((N = zero_zero_nat))))))). % nat_zero_less_power_iff
thf(fact_58_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_59_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A2 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A2) => (A2 = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_60_gcd__nat_Onot__eq__extremum, axiom,
    ((![A2 : nat]: ((~ ((A2 = zero_zero_nat))) = (((dvd_dvd_nat @ A2 @ zero_zero_nat)) & ((~ ((A2 = zero_zero_nat))))))))). % gcd_nat.not_eq_extremum
thf(fact_61_gcd__nat_Oextremum__unique, axiom,
    ((![A2 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A2) = (A2 = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_62_gcd__nat_Oextremum__strict, axiom,
    ((![A2 : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A2) & (~ ((zero_zero_nat = A2))))))))). % gcd_nat.extremum_strict
thf(fact_63_gcd__nat_Oextremum, axiom,
    ((![A2 : nat]: (dvd_dvd_nat @ A2 @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_64_nat__power__less__imp__less, axiom,
    ((![I : nat, M2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ I) => ((ord_less_nat @ (power_power_nat @ I @ M2) @ (power_power_nat @ I @ N)) => (ord_less_nat @ M2 @ N)))))). % nat_power_less_imp_less
thf(fact_65_nat__dvd__not__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ M2) => ((ord_less_nat @ M2 @ N) => (~ ((dvd_dvd_nat @ N @ M2)))))))). % nat_dvd_not_less
thf(fact_66_dvd__pos__nat, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((dvd_dvd_nat @ M2 @ N) => (ord_less_nat @ zero_zero_nat @ M2)))))). % dvd_pos_nat
thf(fact_67_dvd__imp__le, axiom,
    ((![K : nat, N : nat]: ((dvd_dvd_nat @ K @ N) => ((ord_less_nat @ zero_zero_nat @ N) => (ord_less_eq_nat @ K @ N)))))). % dvd_imp_le
thf(fact_68_nat__neq__iff, axiom,
    ((![M2 : nat, N : nat]: ((~ ((M2 = N))) = (((ord_less_nat @ M2 @ N)) | ((ord_less_nat @ N @ M2))))))). % nat_neq_iff
thf(fact_69_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_70_less__not__refl2, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ N @ M2) => (~ ((M2 = N))))))). % less_not_refl2
thf(fact_71_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_72_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_73_nat__less__induct, axiom,
    ((![P3 : nat > $o, N : nat]: ((![N2 : nat]: ((![M : nat]: ((ord_less_nat @ M @ N2) => (P3 @ M))) => (P3 @ N2))) => (P3 @ N))))). % nat_less_induct
thf(fact_74_infinite__descent, axiom,
    ((![P3 : nat > $o, N : nat]: ((![N2 : nat]: ((~ ((P3 @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P3 @ M))))))) => (P3 @ N))))). % infinite_descent
thf(fact_75_linorder__neqE__nat, axiom,
    ((![X3 : nat, Y2 : nat]: ((~ ((X3 = Y2))) => ((~ ((ord_less_nat @ X3 @ Y2))) => (ord_less_nat @ Y2 @ X3)))))). % linorder_neqE_nat
thf(fact_76_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_77_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_78_eq__imp__le, axiom,
    ((![M2 : nat, N : nat]: ((M2 = N) => (ord_less_eq_nat @ M2 @ N))))). % eq_imp_le
thf(fact_79_le__antisym, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_eq_nat @ M2 @ N) => ((ord_less_eq_nat @ N @ M2) => (M2 = N)))))). % le_antisym
thf(fact_80_nat__le__linear, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_eq_nat @ M2 @ N) | (ord_less_eq_nat @ N @ M2))))). % nat_le_linear
thf(fact_81_Nat_Oex__has__greatest__nat, axiom,
    ((![P3 : nat > $o, K : nat, B : nat]: ((P3 @ K) => ((![Y3 : nat]: ((P3 @ Y3) => (ord_less_eq_nat @ Y3 @ B))) => (?[X4 : nat]: ((P3 @ X4) & (![Y4 : nat]: ((P3 @ Y4) => (ord_less_eq_nat @ Y4 @ X4)))))))))). % Nat.ex_has_greatest_nat
thf(fact_82_power__not__zero, axiom,
    ((![A2 : complex, N : nat]: ((~ ((A2 = zero_zero_complex))) => (~ (((power_power_complex @ A2 @ N) = zero_zero_complex))))))). % power_not_zero
thf(fact_83_power__not__zero, axiom,
    ((![A2 : poly_complex, N : nat]: ((~ ((A2 = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A2 @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_84_power__not__zero, axiom,
    ((![A2 : nat, N : nat]: ((~ ((A2 = zero_zero_nat))) => (~ (((power_power_nat @ A2 @ N) = zero_zero_nat))))))). % power_not_zero
thf(fact_85_dvd__power__same, axiom,
    ((![X3 : poly_complex, Y2 : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X3 @ Y2) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X3 @ N) @ (power_184595776omplex @ Y2 @ N)))))). % dvd_power_same
thf(fact_86_dvd__power__same, axiom,
    ((![X3 : nat, Y2 : nat, N : nat]: ((dvd_dvd_nat @ X3 @ Y2) => (dvd_dvd_nat @ (power_power_nat @ X3 @ N) @ (power_power_nat @ Y2 @ N)))))). % dvd_power_same
thf(fact_87_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_88_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_89_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_90_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_91_gr__implies__not0, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_92_infinite__descent0, axiom,
    ((![P3 : nat > $o, N : nat]: ((P3 @ zero_zero_nat) => ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((~ ((P3 @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P3 @ M)))))))) => (P3 @ N)))))). % infinite_descent0
thf(fact_93_bot__nat__0_Oextremum__strict, axiom,
    ((![A2 : nat]: (~ ((ord_less_nat @ A2 @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_94_less__eq__nat_Osimps_I1_J, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % less_eq_nat.simps(1)
thf(fact_95_le__0__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_0_eq
thf(fact_96_bot__nat__0_Oextremum__unique, axiom,
    ((![A2 : nat]: ((ord_less_eq_nat @ A2 @ zero_zero_nat) = (A2 = zero_zero_nat))))). % bot_nat_0.extremum_unique
thf(fact_97_bot__nat__0_Oextremum__uniqueI, axiom,
    ((![A2 : nat]: ((ord_less_eq_nat @ A2 @ zero_zero_nat) => (A2 = zero_zero_nat))))). % bot_nat_0.extremum_uniqueI
thf(fact_98_nat__less__le, axiom,
    ((ord_less_nat = (^[M3 : nat]: (^[N3 : nat]: (((ord_less_eq_nat @ M3 @ N3)) & ((~ ((M3 = N3)))))))))). % nat_less_le
thf(fact_99_less__imp__le__nat, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_eq_nat @ M2 @ N))))). % less_imp_le_nat
thf(fact_100_le__eq__less__or__eq, axiom,
    ((ord_less_eq_nat = (^[M3 : nat]: (^[N3 : nat]: (((ord_less_nat @ M3 @ N3)) | ((M3 = N3)))))))). % le_eq_less_or_eq
thf(fact_101_less__or__eq__imp__le, axiom,
    ((![M2 : nat, N : nat]: (((ord_less_nat @ M2 @ N) | (M2 = N)) => (ord_less_eq_nat @ M2 @ N))))). % less_or_eq_imp_le
thf(fact_102_le__neq__implies__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_eq_nat @ M2 @ N) => ((~ ((M2 = N))) => (ord_less_nat @ M2 @ N)))))). % le_neq_implies_less
thf(fact_103_less__mono__imp__le__mono, axiom,
    ((![F2 : nat > nat, I : nat, J : nat]: ((![I2 : nat, J2 : nat]: ((ord_less_nat @ I2 @ J2) => (ord_less_nat @ (F2 @ I2) @ (F2 @ J2)))) => ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (F2 @ I) @ (F2 @ J))))))). % less_mono_imp_le_mono
thf(fact_104_zero__le__power, axiom,
    ((![A2 : nat, N : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A2) => (ord_less_eq_nat @ zero_zero_nat @ (power_power_nat @ A2 @ N)))))). % zero_le_power
thf(fact_105_power__mono, axiom,
    ((![A2 : nat, B : nat, N : nat]: ((ord_less_eq_nat @ A2 @ B) => ((ord_less_eq_nat @ zero_zero_nat @ A2) => (ord_less_eq_nat @ (power_power_nat @ A2 @ N) @ (power_power_nat @ B @ N))))))). % power_mono
thf(fact_106_zero__less__power, axiom,
    ((![A2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ A2) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A2 @ N)))))). % zero_less_power
thf(fact_107_dvd__power__le, axiom,
    ((![X3 : poly_complex, Y2 : poly_complex, N : nat, M2 : nat]: ((dvd_dvd_poly_complex @ X3 @ Y2) => ((ord_less_eq_nat @ N @ M2) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X3 @ N) @ (power_184595776omplex @ Y2 @ M2))))))). % dvd_power_le
thf(fact_108_dvd__power__le, axiom,
    ((![X3 : nat, Y2 : nat, N : nat, M2 : nat]: ((dvd_dvd_nat @ X3 @ Y2) => ((ord_less_eq_nat @ N @ M2) => (dvd_dvd_nat @ (power_power_nat @ X3 @ N) @ (power_power_nat @ Y2 @ M2))))))). % dvd_power_le
thf(fact_109_power__le__dvd, axiom,
    ((![A2 : poly_complex, N : nat, B : poly_complex, M2 : nat]: ((dvd_dvd_poly_complex @ (power_184595776omplex @ A2 @ N) @ B) => ((ord_less_eq_nat @ M2 @ N) => (dvd_dvd_poly_complex @ (power_184595776omplex @ A2 @ M2) @ B)))))). % power_le_dvd
thf(fact_110_power__le__dvd, axiom,
    ((![A2 : nat, N : nat, B : nat, M2 : nat]: ((dvd_dvd_nat @ (power_power_nat @ A2 @ N) @ B) => ((ord_less_eq_nat @ M2 @ N) => (dvd_dvd_nat @ (power_power_nat @ A2 @ M2) @ B)))))). % power_le_dvd
thf(fact_111_le__imp__power__dvd, axiom,
    ((![M2 : nat, N : nat, A2 : poly_complex]: ((ord_less_eq_nat @ M2 @ N) => (dvd_dvd_poly_complex @ (power_184595776omplex @ A2 @ M2) @ (power_184595776omplex @ A2 @ N)))))). % le_imp_power_dvd
thf(fact_112_le__imp__power__dvd, axiom,
    ((![M2 : nat, N : nat, A2 : nat]: ((ord_less_eq_nat @ M2 @ N) => (dvd_dvd_nat @ (power_power_nat @ A2 @ M2) @ (power_power_nat @ A2 @ N)))))). % le_imp_power_dvd
thf(fact_113_ex__least__nat__le, axiom,
    ((![P3 : nat > $o, N : nat]: ((P3 @ N) => ((~ ((P3 @ zero_zero_nat))) => (?[K2 : nat]: ((ord_less_eq_nat @ K2 @ N) & ((![I3 : nat]: ((ord_less_nat @ I3 @ K2) => (~ ((P3 @ I3))))) & (P3 @ K2))))))))). % ex_least_nat_le
thf(fact_114_power__less__imp__less__base, axiom,
    ((![A2 : nat, N : nat, B : nat]: ((ord_less_nat @ (power_power_nat @ A2 @ N) @ (power_power_nat @ B @ N)) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ A2 @ B)))))). % power_less_imp_less_base
thf(fact_115_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex))))). % zero_power
thf(fact_116_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_184595776omplex @ zero_z1746442943omplex @ N) = zero_z1746442943omplex))))). % zero_power
thf(fact_117_zero__power, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat))))). % zero_power
thf(fact_118_power__eq__imp__eq__base, axiom,
    ((![A2 : nat, N : nat, B : nat]: (((power_power_nat @ A2 @ N) = (power_power_nat @ B @ N)) => ((ord_less_eq_nat @ zero_zero_nat @ A2) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ N) => (A2 = B)))))))). % power_eq_imp_eq_base
thf(fact_119_power__eq__iff__eq__base, axiom,
    ((![N : nat, A2 : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_eq_nat @ zero_zero_nat @ A2) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (((power_power_nat @ A2 @ N) = (power_power_nat @ B @ N)) = (A2 = B)))))))). % power_eq_iff_eq_base
thf(fact_120_dvd__0__right, axiom,
    ((![A2 : complex]: (dvd_dvd_complex @ A2 @ zero_zero_complex)))). % dvd_0_right
thf(fact_121_dvd__0__right, axiom,
    ((![A2 : nat]: (dvd_dvd_nat @ A2 @ zero_zero_nat)))). % dvd_0_right
thf(fact_122_dvd__0__right, axiom,
    ((![A2 : poly_complex]: (dvd_dvd_poly_complex @ A2 @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_123_dvd__0__left__iff, axiom,
    ((![A2 : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A2) = (A2 = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_124_dvd__0__left__iff, axiom,
    ((![A2 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A2) = (A2 = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_125_dvd__0__left__iff, axiom,
    ((![A2 : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A2) = (A2 = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_126_order__refl, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ X3 @ X3)))). % order_refl
thf(fact_127_pseudo__mod_I2_J, axiom,
    ((![G : poly_complex, F2 : poly_complex]: ((~ ((G = zero_z1746442943omplex))) => (((pseudo_mod_complex @ F2 @ G) = zero_z1746442943omplex) | (ord_less_nat @ (degree_complex @ (pseudo_mod_complex @ F2 @ G)) @ (degree_complex @ G))))))). % pseudo_mod(2)
thf(fact_128_nat__descend__induct, axiom,
    ((![N : nat, P3 : nat > $o, M2 : nat]: ((![K2 : nat]: ((ord_less_nat @ N @ K2) => (P3 @ K2))) => ((![K2 : nat]: ((ord_less_eq_nat @ K2 @ N) => ((![I3 : nat]: ((ord_less_nat @ K2 @ I3) => (P3 @ I3))) => (P3 @ K2)))) => (P3 @ M2)))))). % nat_descend_induct
thf(fact_129_gcd__nat_Onot__eq__order__implies__strict, axiom,
    ((![A2 : nat, B : nat]: ((~ ((A2 = B))) => ((dvd_dvd_nat @ A2 @ B) => ((dvd_dvd_nat @ A2 @ B) & (~ ((A2 = B))))))))). % gcd_nat.not_eq_order_implies_strict
thf(fact_130_gcd__nat_Ostrict__implies__not__eq, axiom,
    ((![A2 : nat, B : nat]: (((dvd_dvd_nat @ A2 @ B) & (~ ((A2 = B)))) => (~ ((A2 = B))))))). % gcd_nat.strict_implies_not_eq
thf(fact_131_gcd__nat_Ostrict__implies__order, axiom,
    ((![A2 : nat, B : nat]: (((dvd_dvd_nat @ A2 @ B) & (~ ((A2 = B)))) => (dvd_dvd_nat @ A2 @ B))))). % gcd_nat.strict_implies_order
thf(fact_132_gcd__nat_Ostrict__iff__order, axiom,
    ((![A2 : nat, B : nat]: ((((dvd_dvd_nat @ A2 @ B)) & ((~ ((A2 = B))))) = (((dvd_dvd_nat @ A2 @ B)) & ((~ ((A2 = B))))))))). % gcd_nat.strict_iff_order
thf(fact_133_gcd__nat_Oorder__iff__strict, axiom,
    ((dvd_dvd_nat = (^[A3 : nat]: (^[B2 : nat]: (((((dvd_dvd_nat @ A3 @ B2)) & ((~ ((A3 = B2)))))) | ((A3 = B2)))))))). % gcd_nat.order_iff_strict
thf(fact_134_gcd__nat_Ostrict__trans2, axiom,
    ((![A2 : nat, B : nat, C : nat]: (((dvd_dvd_nat @ A2 @ B) & (~ ((A2 = B)))) => ((dvd_dvd_nat @ B @ C) => ((dvd_dvd_nat @ A2 @ C) & (~ ((A2 = C))))))))). % gcd_nat.strict_trans2
thf(fact_135_gcd__nat_Ostrict__trans1, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A2 @ B) => (((dvd_dvd_nat @ B @ C) & (~ ((B = C)))) => ((dvd_dvd_nat @ A2 @ C) & (~ ((A2 = C))))))))). % gcd_nat.strict_trans1
thf(fact_136_gcd__nat_Ostrict__trans, axiom,
    ((![A2 : nat, B : nat, C : nat]: (((dvd_dvd_nat @ A2 @ B) & (~ ((A2 = B)))) => (((dvd_dvd_nat @ B @ C) & (~ ((B = C)))) => ((dvd_dvd_nat @ A2 @ C) & (~ ((A2 = C))))))))). % gcd_nat.strict_trans
thf(fact_137_gcd__nat_Oantisym, axiom,
    ((![A2 : nat, B : nat]: ((dvd_dvd_nat @ A2 @ B) => ((dvd_dvd_nat @ B @ A2) => (A2 = B)))))). % gcd_nat.antisym
thf(fact_138_gcd__nat_Oirrefl, axiom,
    ((![A2 : nat]: (~ (((dvd_dvd_nat @ A2 @ A2) & (~ ((A2 = A2))))))))). % gcd_nat.irrefl
thf(fact_139_gcd__nat_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z2 : nat]: (Y5 = Z2))) = (^[A3 : nat]: (^[B2 : nat]: (((dvd_dvd_nat @ A3 @ B2)) & ((dvd_dvd_nat @ B2 @ A3)))))))). % gcd_nat.eq_iff
thf(fact_140_gcd__nat_Otrans, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A2 @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A2 @ C)))))). % gcd_nat.trans
thf(fact_141_gcd__nat_Orefl, axiom,
    ((![A2 : nat]: (dvd_dvd_nat @ A2 @ A2)))). % gcd_nat.refl
thf(fact_142_gcd__nat_Oasym, axiom,
    ((![A2 : nat, B : nat]: (((dvd_dvd_nat @ A2 @ B) & (~ ((A2 = B)))) => (~ (((dvd_dvd_nat @ B @ A2) & (~ ((B = A2)))))))))). % gcd_nat.asym
thf(fact_143_dvd__antisym, axiom,
    ((![M2 : nat, N : nat]: ((dvd_dvd_nat @ M2 @ N) => ((dvd_dvd_nat @ N @ M2) => (M2 = N)))))). % dvd_antisym
thf(fact_144_dual__order_Oantisym, axiom,
    ((![B : nat, A2 : nat]: ((ord_less_eq_nat @ B @ A2) => ((ord_less_eq_nat @ A2 @ B) => (A2 = B)))))). % dual_order.antisym
thf(fact_145_dual__order_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z2 : nat]: (Y5 = Z2))) = (^[A3 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A3)) & ((ord_less_eq_nat @ A3 @ B2)))))))). % dual_order.eq_iff
thf(fact_146_dual__order_Otrans, axiom,
    ((![B : nat, A2 : nat, C : nat]: ((ord_less_eq_nat @ B @ A2) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ C @ A2)))))). % dual_order.trans
thf(fact_147_linorder__wlog, axiom,
    ((![P3 : nat > nat > $o, A2 : nat, B : nat]: ((![A : nat, B3 : nat]: ((ord_less_eq_nat @ A @ B3) => (P3 @ A @ B3))) => ((![A : nat, B3 : nat]: ((P3 @ B3 @ A) => (P3 @ A @ B3))) => (P3 @ A2 @ B)))))). % linorder_wlog
thf(fact_148_dual__order_Orefl, axiom,
    ((![A2 : nat]: (ord_less_eq_nat @ A2 @ A2)))). % dual_order.refl
thf(fact_149_order__trans, axiom,
    ((![X3 : nat, Y2 : nat, Z3 : nat]: ((ord_less_eq_nat @ X3 @ Y2) => ((ord_less_eq_nat @ Y2 @ Z3) => (ord_less_eq_nat @ X3 @ Z3)))))). % order_trans
thf(fact_150_order__class_Oorder_Oantisym, axiom,
    ((![A2 : nat, B : nat]: ((ord_less_eq_nat @ A2 @ B) => ((ord_less_eq_nat @ B @ A2) => (A2 = B)))))). % order_class.order.antisym
thf(fact_151_ord__le__eq__trans, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A2 @ B) => ((B = C) => (ord_less_eq_nat @ A2 @ C)))))). % ord_le_eq_trans
thf(fact_152_ord__eq__le__trans, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((A2 = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A2 @ C)))))). % ord_eq_le_trans
thf(fact_153_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z2 : nat]: (Y5 = Z2))) = (^[A3 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A3 @ B2)) & ((ord_less_eq_nat @ B2 @ A3)))))))). % order_class.order.eq_iff
thf(fact_154_antisym__conv, axiom,
    ((![Y2 : nat, X3 : nat]: ((ord_less_eq_nat @ Y2 @ X3) => ((ord_less_eq_nat @ X3 @ Y2) = (X3 = Y2)))))). % antisym_conv
thf(fact_155_le__cases3, axiom,
    ((![X3 : nat, Y2 : nat, Z3 : nat]: (((ord_less_eq_nat @ X3 @ Y2) => (~ ((ord_less_eq_nat @ Y2 @ Z3)))) => (((ord_less_eq_nat @ Y2 @ X3) => (~ ((ord_less_eq_nat @ X3 @ Z3)))) => (((ord_less_eq_nat @ X3 @ Z3) => (~ ((ord_less_eq_nat @ Z3 @ Y2)))) => (((ord_less_eq_nat @ Z3 @ Y2) => (~ ((ord_less_eq_nat @ Y2 @ X3)))) => (((ord_less_eq_nat @ Y2 @ Z3) => (~ ((ord_less_eq_nat @ Z3 @ X3)))) => (~ (((ord_less_eq_nat @ Z3 @ X3) => (~ ((ord_less_eq_nat @ X3 @ Y2)))))))))))))). % le_cases3
thf(fact_156_order_Otrans, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A2 @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A2 @ C)))))). % order.trans
thf(fact_157_le__cases, axiom,
    ((![X3 : nat, Y2 : nat]: ((~ ((ord_less_eq_nat @ X3 @ Y2))) => (ord_less_eq_nat @ Y2 @ X3))))). % le_cases
thf(fact_158_eq__refl, axiom,
    ((![X3 : nat, Y2 : nat]: ((X3 = Y2) => (ord_less_eq_nat @ X3 @ Y2))))). % eq_refl
thf(fact_159_linear, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ Y2) | (ord_less_eq_nat @ Y2 @ X3))))). % linear
thf(fact_160_antisym, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ Y2) => ((ord_less_eq_nat @ Y2 @ X3) => (X3 = Y2)))))). % antisym
thf(fact_161_eq__iff, axiom,
    (((^[Y5 : nat]: (^[Z2 : nat]: (Y5 = Z2))) = (^[X : nat]: (^[Y : nat]: (((ord_less_eq_nat @ X @ Y)) & ((ord_less_eq_nat @ Y @ X)))))))). % eq_iff
thf(fact_162_ord__le__eq__subst, axiom,
    ((![A2 : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A2 @ B) => (((F2 @ B) = C) => ((![X4 : nat, Y3 : nat]: ((ord_less_eq_nat @ X4 @ Y3) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_eq_nat @ (F2 @ A2) @ C))))))). % ord_le_eq_subst
thf(fact_163_ord__eq__le__subst, axiom,
    ((![A2 : nat, F2 : nat > nat, B : nat, C : nat]: ((A2 = (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y3 : nat]: ((ord_less_eq_nat @ X4 @ Y3) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_eq_nat @ A2 @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_164_order__subst2, axiom,
    ((![A2 : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A2 @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X4 : nat, Y3 : nat]: ((ord_less_eq_nat @ X4 @ Y3) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y3)))) => (ord_less_eq_nat @ (F2 @ A2) @ C))))))). % order_subst2

% Conjectures (1)
thf(conj_0, conjecture,
    ((~ ((x = a))))).
