% 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_1078__5378052_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:45.700

% Could-be-implicit typings (10)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_J, type,
    poly_poly_poly_a : $tType).
thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_J, type,
    set_poly_poly_a : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    poly_poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    poly_poly_a : $tType).
thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_Itf__a_J_J, type,
    set_poly_a : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Set__Oset_Itf__a_J, type,
    set_a : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (72)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Nat__Onat, type,
    fundam170929432ly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Polynomial__Opoly_Itf__a_J, type,
    fundam1343031620poly_a : poly_poly_a > poly_a > poly_poly_a).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001tf__a, type,
    fundam1358810038poly_a : poly_a > a > poly_a).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Nat__Onat, type,
    fundam1567013434ze_nat : poly_nat > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Polynomial__Opoly_Itf__a_J, type,
    fundam1032801442poly_a : poly_poly_a > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001tf__a, type,
    fundam247907092size_a : poly_a > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    minus_minus_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    minus_154650241poly_a : poly_poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_Itf__a_J, type,
    minus_minus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Ominus__class_Ominus_001tf__a, type,
    minus_minus_a : a > a > a).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    one_one_poly_nat : poly_nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    one_one_poly_poly_a : poly_poly_a).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_Itf__a_J, type,
    one_one_poly_a : poly_a).
thf(sy_c_Groups_Oone__class_Oone_001tf__a, type,
    one_one_a : a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_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__Nat__Onat_J_J, type,
    zero_z1059985641ly_nat : poly_poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_J, type,
    zero_z2064990175poly_a : poly_poly_poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    zero_z2096148049poly_a : poly_poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J, type,
    zero_zero_poly_a : poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
thf(sy_c_Int_Oring__1__class_OInts_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    ring_11454639307poly_a : set_poly_poly_a).
thf(sy_c_Int_Oring__1__class_OInts_001t__Polynomial__Opoly_Itf__a_J, type,
    ring_1_Ints_poly_a : set_poly_a).
thf(sy_c_Int_Oring__1__class_OInts_001tf__a, type,
    ring_1_Ints_a : set_a).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    neg_nu1613852873poly_a : poly_poly_a > poly_poly_a).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Polynomial__Opoly_Itf__a_J, type,
    neg_nu1855370811poly_a : poly_a > poly_a).
thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001tf__a, type,
    neg_nu976519853_inc_a : a > a).
thf(sy_c_Orderings_Oord__class_Oless_001t__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_Ocontent_001t__Nat__Onat, type,
    content_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Nat__Onat, type,
    degree_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    degree_poly_nat : poly_poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    degree_poly_poly_a : poly_poly_poly_a > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_Itf__a_J, type,
    degree_poly_a : poly_poly_a > nat).
thf(sy_c_Polynomial_Odegree_001tf__a, type,
    degree_a : poly_a > nat).
thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat, type,
    is_zero_nat : poly_nat > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_Itf__a_J, type,
    is_zero_poly_a : poly_poly_a > $o).
thf(sy_c_Polynomial_Ois__zero_001tf__a, type,
    is_zero_a : poly_a > $o).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    poly_poly_poly_a2 : poly_poly_poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_poly_a2 : poly_poly_a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001tf__a, type,
    poly_a2 : poly_a > a > a).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Nat__Onat, type,
    coeff_nat : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    coeff_poly_nat : poly_poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    coeff_poly_poly_a : poly_poly_poly_a > nat > poly_poly_a).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_Itf__a_J, type,
    coeff_poly_a : poly_poly_a > nat > poly_a).
thf(sy_c_Polynomial_Opoly_Ocoeff_001tf__a, type,
    coeff_a : poly_a > nat > a).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Nat__Onat, type,
    poly_cutoff_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_cutoff_poly_nat : nat > poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    poly_c1841332160poly_a : nat > poly_poly_poly_a > poly_poly_poly_a).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_cutoff_poly_a : nat > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Opoly__cutoff_001tf__a, type,
    poly_cutoff_a : nat > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly__shift_001t__Nat__Onat, type,
    poly_shift_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__shift_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_shift_poly_a : nat > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Opoly__shift_001tf__a, type,
    poly_shift_a : nat > poly_a > poly_a).
thf(sy_c_Polynomial_Opos__poly_001t__Nat__Onat, type,
    pos_poly_nat : poly_nat > $o).
thf(sy_c_Polynomial_Oprimitive__part_001t__Nat__Onat, type,
    primitive_part_nat : poly_nat > poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Nat__Onat, type,
    reflect_poly_nat : poly_nat > poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    reflec781175074ly_nat : poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    reflec581648976poly_a : poly_poly_poly_a > poly_poly_poly_a).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_Itf__a_J, type,
    reflect_poly_poly_a : poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Oreflect__poly_001tf__a, type,
    reflect_poly_a : poly_a > poly_a).
thf(sy_c_Polynomial_Osynthetic__div_001t__Nat__Onat, type,
    synthetic_div_nat : poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Osynthetic__div_001t__Polynomial__Opoly_Itf__a_J, type,
    synthetic_div_poly_a : poly_poly_a > poly_a > poly_poly_a).
thf(sy_c_Polynomial_Osynthetic__div_001tf__a, type,
    synthetic_div_a : poly_a > a > poly_a).
thf(sy_c_member_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    member_poly_poly_a : poly_poly_a > set_poly_poly_a > $o).
thf(sy_c_member_001t__Polynomial__Opoly_Itf__a_J, type,
    member_poly_a : poly_a > set_poly_a > $o).
thf(sy_c_member_001tf__a, type,
    member_a : a > set_a > $o).
thf(sy_v_x, type,
    x : a).

% Relevant facts (227)
thf(fact_0_poly__0, axiom,
    ((![X : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X) = zero_zero_poly_nat)))). % poly_0
thf(fact_1_poly__0, axiom,
    ((![X : poly_poly_a]: ((poly_poly_poly_a2 @ zero_z2064990175poly_a @ X) = zero_z2096148049poly_a)))). % poly_0
thf(fact_2_poly__0, axiom,
    ((![X : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X) = zero_zero_poly_a)))). % poly_0
thf(fact_3_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_4_poly__0, axiom,
    ((![X : a]: ((poly_a2 @ zero_zero_poly_a @ X) = zero_zero_a)))). % poly_0
thf(fact_5_zero__reorient, axiom,
    ((![X : poly_nat]: ((zero_zero_poly_nat = X) = (X = zero_zero_poly_nat))))). % zero_reorient
thf(fact_6_zero__reorient, axiom,
    ((![X : poly_poly_a]: ((zero_z2096148049poly_a = X) = (X = zero_z2096148049poly_a))))). % zero_reorient
thf(fact_7_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_8_zero__reorient, axiom,
    ((![X : poly_a]: ((zero_zero_poly_a = X) = (X = zero_zero_poly_a))))). % zero_reorient
thf(fact_9_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_10_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_nat]: (((poly_poly_nat2 @ (reflec781175074ly_nat @ P) @ zero_zero_poly_nat) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_11_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_poly_a]: (((poly_poly_poly_a2 @ (reflec581648976poly_a @ P) @ zero_z2096148049poly_a) = zero_z2096148049poly_a) = (P = zero_z2064990175poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_12_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_a]: (((poly_a2 @ (reflect_poly_a @ P) @ zero_zero_a) = zero_zero_a) = (P = zero_zero_poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_13_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_a]: (((poly_poly_a2 @ (reflect_poly_poly_a @ P) @ zero_zero_poly_a) = zero_zero_poly_a) = (P = zero_z2096148049poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_14_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_nat]: (((poly_nat2 @ (reflect_poly_nat @ P) @ zero_zero_nat) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_15_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_16_offset__poly__0, axiom,
    ((![H : poly_a]: ((fundam1343031620poly_a @ zero_z2096148049poly_a @ H) = zero_z2096148049poly_a)))). % offset_poly_0
thf(fact_17_offset__poly__0, axiom,
    ((![H : a]: ((fundam1358810038poly_a @ zero_zero_poly_a @ H) = zero_zero_poly_a)))). % offset_poly_0
thf(fact_18_offset__poly__eq__0__iff, axiom,
    ((![P : poly_nat, H : nat]: (((fundam170929432ly_nat @ P @ H) = zero_zero_poly_nat) = (P = zero_zero_poly_nat))))). % offset_poly_eq_0_iff
thf(fact_19_offset__poly__eq__0__iff, axiom,
    ((![P : poly_poly_a, H : poly_a]: (((fundam1343031620poly_a @ P @ H) = zero_z2096148049poly_a) = (P = zero_z2096148049poly_a))))). % offset_poly_eq_0_iff
thf(fact_20_offset__poly__eq__0__iff, axiom,
    ((![P : poly_a, H : a]: (((fundam1358810038poly_a @ P @ H) = zero_zero_poly_a) = (P = zero_zero_poly_a))))). % offset_poly_eq_0_iff
thf(fact_21_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_22_reflect__poly__0, axiom,
    (((reflect_poly_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % reflect_poly_0
thf(fact_23_reflect__poly__0, axiom,
    (((reflect_poly_a @ zero_zero_poly_a) = zero_zero_poly_a))). % reflect_poly_0
thf(fact_24_psize__eq__0__iff, axiom,
    ((![P : poly_a]: (((fundam247907092size_a @ P) = zero_zero_nat) = (P = zero_zero_poly_a))))). % psize_eq_0_iff
thf(fact_25_psize__eq__0__iff, axiom,
    ((![P : poly_nat]: (((fundam1567013434ze_nat @ P) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % psize_eq_0_iff
thf(fact_26_psize__eq__0__iff, axiom,
    ((![P : poly_poly_a]: (((fundam1032801442poly_a @ P) = zero_zero_nat) = (P = zero_z2096148049poly_a))))). % psize_eq_0_iff
thf(fact_27_is__zero__null, axiom,
    ((is_zero_a = (^[P2 : poly_a]: (P2 = zero_zero_poly_a))))). % is_zero_null
thf(fact_28_is__zero__null, axiom,
    ((is_zero_nat = (^[P2 : poly_nat]: (P2 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_29_is__zero__null, axiom,
    ((is_zero_poly_a = (^[P2 : poly_poly_a]: (P2 = zero_z2096148049poly_a))))). % is_zero_null
thf(fact_30_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_cutoff_0
thf(fact_31_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_32_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_cutoff_0
thf(fact_33_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_nat]: (((coeff_poly_nat @ (reflec781175074ly_nat @ P) @ zero_zero_nat) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_34_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_poly_a]: (((coeff_poly_poly_a @ (reflec581648976poly_a @ P) @ zero_zero_nat) = zero_z2096148049poly_a) = (P = zero_z2064990175poly_a))))). % coeff_0_reflect_poly_0_iff
thf(fact_35_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_nat]: (((coeff_nat @ (reflect_poly_nat @ P) @ zero_zero_nat) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_36_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_a]: (((coeff_poly_a @ (reflect_poly_poly_a @ P) @ zero_zero_nat) = zero_zero_poly_a) = (P = zero_z2096148049poly_a))))). % coeff_0_reflect_poly_0_iff
thf(fact_37_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_a]: (((coeff_a @ (reflect_poly_a @ P) @ zero_zero_nat) = zero_zero_a) = (P = zero_zero_poly_a))))). % coeff_0_reflect_poly_0_iff
thf(fact_38_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_shift_0
thf(fact_39_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_40_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_shift_0
thf(fact_41_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_nat]: ((~ (((coeff_poly_nat @ P @ zero_zero_nat) = zero_zero_poly_nat))) => ((reflec781175074ly_nat @ (reflec781175074ly_nat @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_42_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_poly_a]: ((~ (((coeff_poly_poly_a @ P @ zero_zero_nat) = zero_z2096148049poly_a))) => ((reflec581648976poly_a @ (reflec581648976poly_a @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_43_reflect__poly__reflect__poly, axiom,
    ((![P : poly_nat]: ((~ (((coeff_nat @ P @ zero_zero_nat) = zero_zero_nat))) => ((reflect_poly_nat @ (reflect_poly_nat @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_44_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_a]: ((~ (((coeff_poly_a @ P @ zero_zero_nat) = zero_zero_poly_a))) => ((reflect_poly_poly_a @ (reflect_poly_poly_a @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_45_reflect__poly__reflect__poly, axiom,
    ((![P : poly_a]: ((~ (((coeff_a @ P @ zero_zero_nat) = zero_zero_a))) => ((reflect_poly_a @ (reflect_poly_a @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_46_zero__natural_Orsp, axiom,
    ((zero_zero_nat = zero_zero_nat))). % zero_natural.rsp
thf(fact_47_content__eq__zero__iff, axiom,
    ((![P : poly_nat]: (((content_nat @ P) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % content_eq_zero_iff
thf(fact_48_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_49_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_poly_a @ zero_z2064990175poly_a @ N) = zero_z2096148049poly_a)))). % coeff_0
thf(fact_50_coeff__0, axiom,
    ((![N : nat]: ((coeff_a @ zero_zero_poly_a @ N) = zero_zero_a)))). % coeff_0
thf(fact_51_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_52_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_a @ zero_z2096148049poly_a @ N) = zero_zero_poly_a)))). % coeff_0
thf(fact_53_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_54_zero__poly_Orep__eq, axiom,
    (((coeff_poly_nat @ zero_z1059985641ly_nat) = (^[Uu : nat]: zero_zero_poly_nat)))). % zero_poly.rep_eq
thf(fact_55_zero__poly_Orep__eq, axiom,
    (((coeff_poly_poly_a @ zero_z2064990175poly_a) = (^[Uu : nat]: zero_z2096148049poly_a)))). % zero_poly.rep_eq
thf(fact_56_zero__poly_Orep__eq, axiom,
    (((coeff_a @ zero_zero_poly_a) = (^[Uu : nat]: zero_zero_a)))). % zero_poly.rep_eq
thf(fact_57_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_58_zero__poly_Orep__eq, axiom,
    (((coeff_poly_a @ zero_z2096148049poly_a) = (^[Uu : nat]: zero_zero_poly_a)))). % zero_poly.rep_eq
thf(fact_59_poly__0__coeff__0, axiom,
    ((![P : poly_a]: ((poly_a2 @ P @ zero_zero_a) = (coeff_a @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_60_poly__0__coeff__0, axiom,
    ((![P : poly_poly_a]: ((poly_poly_a2 @ P @ zero_zero_poly_a) = (coeff_poly_a @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_61_poly__0__coeff__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ P @ zero_zero_nat) = (coeff_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_62_poly__0__coeff__0, axiom,
    ((![P : poly_poly_nat]: ((poly_poly_nat2 @ P @ zero_zero_poly_nat) = (coeff_poly_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_63_poly__0__coeff__0, axiom,
    ((![P : poly_poly_poly_a]: ((poly_poly_poly_a2 @ P @ zero_z2096148049poly_a) = (coeff_poly_poly_a @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_64_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_nat]: ((poly_poly_nat2 @ (reflec781175074ly_nat @ P) @ zero_zero_poly_nat) = (coeff_poly_nat @ P @ (degree_poly_nat @ P)))))). % poly_reflect_poly_0
thf(fact_65_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_poly_a]: ((poly_poly_poly_a2 @ (reflec581648976poly_a @ P) @ zero_z2096148049poly_a) = (coeff_poly_poly_a @ P @ (degree_poly_poly_a @ P)))))). % poly_reflect_poly_0
thf(fact_66_poly__reflect__poly__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ (reflect_poly_nat @ P) @ zero_zero_nat) = (coeff_nat @ P @ (degree_nat @ P)))))). % poly_reflect_poly_0
thf(fact_67_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_a]: ((poly_poly_a2 @ (reflect_poly_poly_a @ P) @ zero_zero_poly_a) = (coeff_poly_a @ P @ (degree_poly_a @ P)))))). % poly_reflect_poly_0
thf(fact_68_poly__reflect__poly__0, axiom,
    ((![P : poly_a]: ((poly_a2 @ (reflect_poly_a @ P) @ zero_zero_a) = (coeff_a @ P @ (degree_a @ P)))))). % poly_reflect_poly_0
thf(fact_69_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_a @ N @ one_one_poly_a) = zero_zero_poly_a)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_a @ N @ one_one_poly_a) = one_one_poly_a)))))). % poly_cutoff_1
thf(fact_70_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_nat @ N @ one_one_poly_nat) = zero_zero_poly_nat)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_nat @ N @ one_one_poly_nat) = one_one_poly_nat)))))). % poly_cutoff_1
thf(fact_71_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_poly_a @ N @ one_one_poly_poly_a) = zero_z2096148049poly_a)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_poly_a @ N @ one_one_poly_poly_a) = one_one_poly_poly_a)))))). % poly_cutoff_1
thf(fact_72_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_nat]: ((~ (((coeff_poly_nat @ P @ zero_zero_nat) = zero_zero_poly_nat))) => ((degree_poly_nat @ (reflec781175074ly_nat @ P)) = (degree_poly_nat @ P)))))). % degree_reflect_poly_eq
thf(fact_73_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_poly_a]: ((~ (((coeff_poly_poly_a @ P @ zero_zero_nat) = zero_z2096148049poly_a))) => ((degree_poly_poly_a @ (reflec581648976poly_a @ P)) = (degree_poly_poly_a @ P)))))). % degree_reflect_poly_eq
thf(fact_74_degree__reflect__poly__eq, axiom,
    ((![P : poly_nat]: ((~ (((coeff_nat @ P @ zero_zero_nat) = zero_zero_nat))) => ((degree_nat @ (reflect_poly_nat @ P)) = (degree_nat @ P)))))). % degree_reflect_poly_eq
thf(fact_75_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_a]: ((~ (((coeff_poly_a @ P @ zero_zero_nat) = zero_zero_poly_a))) => ((degree_poly_a @ (reflect_poly_poly_a @ P)) = (degree_poly_a @ P)))))). % degree_reflect_poly_eq
thf(fact_76_degree__reflect__poly__eq, axiom,
    ((![P : poly_a]: ((~ (((coeff_a @ P @ zero_zero_nat) = zero_zero_a))) => ((degree_a @ (reflect_poly_a @ P)) = (degree_a @ P)))))). % degree_reflect_poly_eq
thf(fact_77_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_a @ N @ one_one_poly_a) = one_one_poly_a)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_a @ N @ one_one_poly_a) = zero_zero_poly_a)))))). % poly_shift_1
thf(fact_78_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_nat @ N @ one_one_poly_nat) = one_one_poly_nat)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_nat @ N @ one_one_poly_nat) = zero_zero_poly_nat)))))). % poly_shift_1
thf(fact_79_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_poly_a @ N @ one_one_poly_poly_a) = one_one_poly_poly_a)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_poly_a @ N @ one_one_poly_poly_a) = zero_z2096148049poly_a)))))). % poly_shift_1
thf(fact_80_coeff__poly__cutoff, axiom,
    ((![K : nat, N : nat, P : poly_a]: (((ord_less_nat @ K @ N) => ((coeff_a @ (poly_cutoff_a @ N @ P) @ K) = (coeff_a @ P @ K))) & ((~ ((ord_less_nat @ K @ N))) => ((coeff_a @ (poly_cutoff_a @ N @ P) @ K) = zero_zero_a)))))). % coeff_poly_cutoff
thf(fact_81_coeff__poly__cutoff, axiom,
    ((![K : nat, N : nat, P : poly_poly_a]: (((ord_less_nat @ K @ N) => ((coeff_poly_a @ (poly_cutoff_poly_a @ N @ P) @ K) = (coeff_poly_a @ P @ K))) & ((~ ((ord_less_nat @ K @ N))) => ((coeff_poly_a @ (poly_cutoff_poly_a @ N @ P) @ K) = zero_zero_poly_a)))))). % coeff_poly_cutoff
thf(fact_82_coeff__poly__cutoff, axiom,
    ((![K : nat, N : nat, P : poly_nat]: (((ord_less_nat @ K @ N) => ((coeff_nat @ (poly_cutoff_nat @ N @ P) @ K) = (coeff_nat @ P @ K))) & ((~ ((ord_less_nat @ K @ N))) => ((coeff_nat @ (poly_cutoff_nat @ N @ P) @ K) = zero_zero_nat)))))). % coeff_poly_cutoff
thf(fact_83_coeff__poly__cutoff, axiom,
    ((![K : nat, N : nat, P : poly_poly_nat]: (((ord_less_nat @ K @ N) => ((coeff_poly_nat @ (poly_cutoff_poly_nat @ N @ P) @ K) = (coeff_poly_nat @ P @ K))) & ((~ ((ord_less_nat @ K @ N))) => ((coeff_poly_nat @ (poly_cutoff_poly_nat @ N @ P) @ K) = zero_zero_poly_nat)))))). % coeff_poly_cutoff
thf(fact_84_coeff__poly__cutoff, axiom,
    ((![K : nat, N : nat, P : poly_poly_poly_a]: (((ord_less_nat @ K @ N) => ((coeff_poly_poly_a @ (poly_c1841332160poly_a @ N @ P) @ K) = (coeff_poly_poly_a @ P @ K))) & ((~ ((ord_less_nat @ K @ N))) => ((coeff_poly_poly_a @ (poly_c1841332160poly_a @ N @ P) @ K) = zero_z2096148049poly_a)))))). % coeff_poly_cutoff
thf(fact_85_coeff__0__reflect__poly, axiom,
    ((![P : poly_nat]: ((coeff_nat @ (reflect_poly_nat @ P) @ zero_zero_nat) = (coeff_nat @ P @ (degree_nat @ P)))))). % coeff_0_reflect_poly
thf(fact_86_coeff__0__reflect__poly, axiom,
    ((![P : poly_poly_a]: ((coeff_poly_a @ (reflect_poly_poly_a @ P) @ zero_zero_nat) = (coeff_poly_a @ P @ (degree_poly_a @ P)))))). % coeff_0_reflect_poly
thf(fact_87_coeff__0__reflect__poly, axiom,
    ((![P : poly_a]: ((coeff_a @ (reflect_poly_a @ P) @ zero_zero_nat) = (coeff_a @ P @ (degree_a @ P)))))). % coeff_0_reflect_poly
thf(fact_88_leading__coeff__0__iff, axiom,
    ((![P : poly_a]: (((coeff_a @ P @ (degree_a @ P)) = zero_zero_a) = (P = zero_zero_poly_a))))). % leading_coeff_0_iff
thf(fact_89_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_a]: (((coeff_poly_a @ P @ (degree_poly_a @ P)) = zero_zero_poly_a) = (P = zero_z2096148049poly_a))))). % leading_coeff_0_iff
thf(fact_90_leading__coeff__0__iff, axiom,
    ((![P : poly_nat]: (((coeff_nat @ P @ (degree_nat @ P)) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % leading_coeff_0_iff
thf(fact_91_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_nat]: (((coeff_poly_nat @ P @ (degree_poly_nat @ P)) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % leading_coeff_0_iff
thf(fact_92_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_poly_a]: (((coeff_poly_poly_a @ P @ (degree_poly_poly_a @ P)) = zero_z2096148049poly_a) = (P = zero_z2064990175poly_a))))). % leading_coeff_0_iff
thf(fact_93_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_94_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_95_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_96_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_97_reflect__poly__1, axiom,
    (((reflect_poly_nat @ one_one_poly_nat) = one_one_poly_nat))). % reflect_poly_1
thf(fact_98_reflect__poly__1, axiom,
    (((reflect_poly_poly_a @ one_one_poly_poly_a) = one_one_poly_poly_a))). % reflect_poly_1
thf(fact_99_reflect__poly__1, axiom,
    (((reflect_poly_a @ one_one_poly_a) = one_one_poly_a))). % reflect_poly_1
thf(fact_100_degree__0, axiom,
    (((degree_a @ zero_zero_poly_a) = zero_zero_nat))). % degree_0
thf(fact_101_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_102_degree__0, axiom,
    (((degree_poly_a @ zero_z2096148049poly_a) = zero_zero_nat))). % degree_0
thf(fact_103_poly__1, axiom,
    ((![X : a]: ((poly_a2 @ one_one_poly_a @ X) = one_one_a)))). % poly_1
thf(fact_104_poly__1, axiom,
    ((![X : poly_a]: ((poly_poly_a2 @ one_one_poly_poly_a @ X) = one_one_poly_a)))). % poly_1
thf(fact_105_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_106_content__1, axiom,
    (((content_nat @ one_one_poly_nat) = one_one_nat))). % content_1
thf(fact_107_lead__coeff__1, axiom,
    (((coeff_nat @ one_one_poly_nat @ (degree_nat @ one_one_poly_nat)) = one_one_nat))). % lead_coeff_1
thf(fact_108_linorder__neqE__nat, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % linorder_neqE_nat
thf(fact_109_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_110_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_111_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_112_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_113_less__not__refl2, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ N @ M2) => (~ ((M2 = N))))))). % less_not_refl2
thf(fact_114_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_115_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_116_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_117_less__degree__imp, axiom,
    ((![N : nat, P : poly_a]: ((ord_less_nat @ N @ (degree_a @ P)) => (?[I : nat]: ((ord_less_nat @ N @ I) & (~ (((coeff_a @ P @ I) = zero_zero_a))))))))). % less_degree_imp
thf(fact_118_less__degree__imp, axiom,
    ((![N : nat, P : poly_poly_a]: ((ord_less_nat @ N @ (degree_poly_a @ P)) => (?[I : nat]: ((ord_less_nat @ N @ I) & (~ (((coeff_poly_a @ P @ I) = zero_zero_poly_a))))))))). % less_degree_imp
thf(fact_119_less__degree__imp, axiom,
    ((![N : nat, P : poly_nat]: ((ord_less_nat @ N @ (degree_nat @ P)) => (?[I : nat]: ((ord_less_nat @ N @ I) & (~ (((coeff_nat @ P @ I) = zero_zero_nat))))))))). % less_degree_imp
thf(fact_120_less__degree__imp, axiom,
    ((![N : nat, P : poly_poly_nat]: ((ord_less_nat @ N @ (degree_poly_nat @ P)) => (?[I : nat]: ((ord_less_nat @ N @ I) & (~ (((coeff_poly_nat @ P @ I) = zero_zero_poly_nat))))))))). % less_degree_imp
thf(fact_121_less__degree__imp, axiom,
    ((![N : nat, P : poly_poly_poly_a]: ((ord_less_nat @ N @ (degree_poly_poly_a @ P)) => (?[I : nat]: ((ord_less_nat @ N @ I) & (~ (((coeff_poly_poly_a @ P @ I) = zero_z2096148049poly_a))))))))). % less_degree_imp
thf(fact_122_coeff__eq__0, axiom,
    ((![P : poly_a, N : nat]: ((ord_less_nat @ (degree_a @ P) @ N) => ((coeff_a @ P @ N) = zero_zero_a))))). % coeff_eq_0
thf(fact_123_coeff__eq__0, axiom,
    ((![P : poly_poly_a, N : nat]: ((ord_less_nat @ (degree_poly_a @ P) @ N) => ((coeff_poly_a @ P @ N) = zero_zero_poly_a))))). % coeff_eq_0
thf(fact_124_coeff__eq__0, axiom,
    ((![P : poly_nat, N : nat]: ((ord_less_nat @ (degree_nat @ P) @ N) => ((coeff_nat @ P @ N) = zero_zero_nat))))). % coeff_eq_0
thf(fact_125_coeff__eq__0, axiom,
    ((![P : poly_poly_nat, N : nat]: ((ord_less_nat @ (degree_poly_nat @ P) @ N) => ((coeff_poly_nat @ P @ N) = zero_zero_poly_nat))))). % coeff_eq_0
thf(fact_126_coeff__eq__0, axiom,
    ((![P : poly_poly_poly_a, N : nat]: ((ord_less_nat @ (degree_poly_poly_a @ P) @ N) => ((coeff_poly_poly_a @ P @ N) = zero_z2096148049poly_a))))). % coeff_eq_0
thf(fact_127_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_128_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_129_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_130_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_131_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_132_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_133_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_134_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_135_gr__implies__not0, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_136_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_137_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_138_degree__offset__poly, axiom,
    ((![P : poly_a, H : a]: ((degree_a @ (fundam1358810038poly_a @ P @ H)) = (degree_a @ P))))). % degree_offset_poly
thf(fact_139_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_nat]: ((~ ((P = zero_z1059985641ly_nat))) => (~ (((coeff_poly_nat @ P @ (degree_poly_nat @ P)) = zero_zero_poly_nat))))))). % leading_coeff_neq_0
thf(fact_140_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_poly_a]: ((~ ((P = zero_z2064990175poly_a))) => (~ (((coeff_poly_poly_a @ P @ (degree_poly_poly_a @ P)) = zero_z2096148049poly_a))))))). % leading_coeff_neq_0
thf(fact_141_leading__coeff__neq__0, axiom,
    ((![P : poly_a]: ((~ ((P = zero_zero_poly_a))) => (~ (((coeff_a @ P @ (degree_a @ P)) = zero_zero_a))))))). % leading_coeff_neq_0
thf(fact_142_leading__coeff__neq__0, axiom,
    ((![P : poly_nat]: ((~ ((P = zero_zero_poly_nat))) => (~ (((coeff_nat @ P @ (degree_nat @ P)) = zero_zero_nat))))))). % leading_coeff_neq_0
thf(fact_143_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_a]: ((~ ((P = zero_z2096148049poly_a))) => (~ (((coeff_poly_a @ P @ (degree_poly_a @ P)) = zero_zero_poly_a))))))). % leading_coeff_neq_0
thf(fact_144_not__one__less__zero, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ zero_zero_nat))))). % not_one_less_zero
thf(fact_145_zero__less__one, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % zero_less_one
thf(fact_146_less__numeral__extra_I1_J, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % less_numeral_extra(1)
thf(fact_147_less__one, axiom,
    ((![N : nat]: ((ord_less_nat @ N @ one_one_nat) = (N = zero_zero_nat))))). % less_one
thf(fact_148_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_149_zero__neq__one, axiom,
    ((~ ((zero_zero_a = one_one_a))))). % zero_neq_one
thf(fact_150_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_a = one_one_poly_a))))). % zero_neq_one
thf(fact_151_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_152_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_153_zero__neq__one, axiom,
    ((~ ((zero_z2096148049poly_a = one_one_poly_poly_a))))). % zero_neq_one
thf(fact_154_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ one_one_nat))))). % less_numeral_extra(4)
thf(fact_155_one__natural_Orsp, axiom,
    ((one_one_nat = one_one_nat))). % one_natural.rsp
thf(fact_156_content__primitive__part, axiom,
    ((![P : poly_nat]: ((~ ((P = zero_zero_poly_nat))) => ((content_nat @ (primitive_part_nat @ P)) = one_one_nat))))). % content_primitive_part
thf(fact_157_primitive__part__0, axiom,
    (((primitive_part_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % primitive_part_0
thf(fact_158_primitive__part__eq__0__iff, axiom,
    ((![P : poly_nat]: (((primitive_part_nat @ P) = zero_zero_poly_nat) = (P = zero_zero_poly_nat))))). % primitive_part_eq_0_iff
thf(fact_159_primitive__part__prim, axiom,
    ((![P : poly_nat]: (((content_nat @ P) = one_one_nat) => ((primitive_part_nat @ P) = P))))). % primitive_part_prim
thf(fact_160_pos__poly__def, axiom,
    ((pos_poly_nat = (^[P2 : poly_nat]: (ord_less_nat @ zero_zero_nat @ (coeff_nat @ P2 @ (degree_nat @ P2))))))). % pos_poly_def
thf(fact_161_not__pos__poly__0, axiom,
    ((~ ((pos_poly_nat @ zero_zero_poly_nat))))). % not_pos_poly_0
thf(fact_162_Ints__0, axiom,
    ((member_a @ zero_zero_a @ ring_1_Ints_a))). % Ints_0
thf(fact_163_Ints__0, axiom,
    ((member_poly_a @ zero_zero_poly_a @ ring_1_Ints_poly_a))). % Ints_0
thf(fact_164_Ints__0, axiom,
    ((member_poly_poly_a @ zero_z2096148049poly_a @ ring_11454639307poly_a))). % Ints_0
thf(fact_165_dbl__inc__simps_I2_J, axiom,
    (((neg_nu976519853_inc_a @ zero_zero_a) = one_one_a))). % dbl_inc_simps(2)
thf(fact_166_dbl__inc__simps_I2_J, axiom,
    (((neg_nu1855370811poly_a @ zero_zero_poly_a) = one_one_poly_a))). % dbl_inc_simps(2)
thf(fact_167_dbl__inc__simps_I2_J, axiom,
    (((neg_nu1613852873poly_a @ zero_z2096148049poly_a) = one_one_poly_poly_a))). % dbl_inc_simps(2)
thf(fact_168_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_a, C : a]: (((synthetic_div_a @ P @ C) = zero_zero_poly_a) = ((degree_a @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_169_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_nat, C : nat]: (((synthetic_div_nat @ P @ C) = zero_zero_poly_nat) = ((degree_nat @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_170_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_poly_a, C : poly_a]: (((synthetic_div_poly_a @ P @ C) = zero_z2096148049poly_a) = ((degree_poly_a @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_171_coeff__reflect__poly, axiom,
    ((![P : poly_poly_nat, N : nat]: (((ord_less_nat @ (degree_poly_nat @ P) @ N) => ((coeff_poly_nat @ (reflec781175074ly_nat @ P) @ N) = zero_zero_poly_nat)) & ((~ ((ord_less_nat @ (degree_poly_nat @ P) @ N))) => ((coeff_poly_nat @ (reflec781175074ly_nat @ P) @ N) = (coeff_poly_nat @ P @ (minus_minus_nat @ (degree_poly_nat @ P) @ N)))))))). % coeff_reflect_poly
thf(fact_172_coeff__reflect__poly, axiom,
    ((![P : poly_poly_poly_a, N : nat]: (((ord_less_nat @ (degree_poly_poly_a @ P) @ N) => ((coeff_poly_poly_a @ (reflec581648976poly_a @ P) @ N) = zero_z2096148049poly_a)) & ((~ ((ord_less_nat @ (degree_poly_poly_a @ P) @ N))) => ((coeff_poly_poly_a @ (reflec581648976poly_a @ P) @ N) = (coeff_poly_poly_a @ P @ (minus_minus_nat @ (degree_poly_poly_a @ P) @ N)))))))). % coeff_reflect_poly
thf(fact_173_coeff__reflect__poly, axiom,
    ((![P : poly_nat, N : nat]: (((ord_less_nat @ (degree_nat @ P) @ N) => ((coeff_nat @ (reflect_poly_nat @ P) @ N) = zero_zero_nat)) & ((~ ((ord_less_nat @ (degree_nat @ P) @ N))) => ((coeff_nat @ (reflect_poly_nat @ P) @ N) = (coeff_nat @ P @ (minus_minus_nat @ (degree_nat @ P) @ N)))))))). % coeff_reflect_poly
thf(fact_174_coeff__reflect__poly, axiom,
    ((![P : poly_poly_a, N : nat]: (((ord_less_nat @ (degree_poly_a @ P) @ N) => ((coeff_poly_a @ (reflect_poly_poly_a @ P) @ N) = zero_zero_poly_a)) & ((~ ((ord_less_nat @ (degree_poly_a @ P) @ N))) => ((coeff_poly_a @ (reflect_poly_poly_a @ P) @ N) = (coeff_poly_a @ P @ (minus_minus_nat @ (degree_poly_a @ P) @ N)))))))). % coeff_reflect_poly
thf(fact_175_coeff__reflect__poly, axiom,
    ((![P : poly_a, N : nat]: (((ord_less_nat @ (degree_a @ P) @ N) => ((coeff_a @ (reflect_poly_a @ P) @ N) = zero_zero_a)) & ((~ ((ord_less_nat @ (degree_a @ P) @ N))) => ((coeff_a @ (reflect_poly_a @ P) @ N) = (coeff_a @ P @ (minus_minus_nat @ (degree_a @ P) @ N)))))))). % coeff_reflect_poly
thf(fact_176_diff__self, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % diff_self
thf(fact_177_diff__self, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % diff_self
thf(fact_178_diff__self, axiom,
    ((![A : poly_poly_a]: ((minus_154650241poly_a @ A @ A) = zero_z2096148049poly_a)))). % diff_self
thf(fact_179_diff__0__right, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_0_right
thf(fact_180_diff__0__right, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_0_right
thf(fact_181_diff__0__right, axiom,
    ((![A : poly_poly_a]: ((minus_154650241poly_a @ A @ zero_z2096148049poly_a) = A)))). % diff_0_right
thf(fact_182_zero__diff, axiom,
    ((![A : nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % zero_diff
thf(fact_183_diff__zero, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_zero
thf(fact_184_diff__zero, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_zero
thf(fact_185_diff__zero, axiom,
    ((![A : poly_nat]: ((minus_minus_poly_nat @ A @ zero_zero_poly_nat) = A)))). % diff_zero
thf(fact_186_diff__zero, axiom,
    ((![A : poly_poly_a]: ((minus_154650241poly_a @ A @ zero_z2096148049poly_a) = A)))). % diff_zero
thf(fact_187_diff__zero, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A)))). % diff_zero
thf(fact_188_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_189_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_190_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_nat]: ((minus_minus_poly_nat @ A @ A) = zero_zero_poly_nat)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_191_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_poly_a]: ((minus_154650241poly_a @ A @ A) = zero_z2096148049poly_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_192_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_193_diff__self__eq__0, axiom,
    ((![M2 : nat]: ((minus_minus_nat @ M2 @ M2) = zero_zero_nat)))). % diff_self_eq_0
thf(fact_194_diff__0__eq__0, axiom,
    ((![N : nat]: ((minus_minus_nat @ zero_zero_nat @ N) = zero_zero_nat)))). % diff_0_eq_0
thf(fact_195_coeff__diff, axiom,
    ((![P : poly_nat, Q : poly_nat, N : nat]: ((coeff_nat @ (minus_minus_poly_nat @ P @ Q) @ N) = (minus_minus_nat @ (coeff_nat @ P @ N) @ (coeff_nat @ Q @ N)))))). % coeff_diff
thf(fact_196_poly__diff, axiom,
    ((![P : poly_a, Q : poly_a, X : a]: ((poly_a2 @ (minus_minus_poly_a @ P @ Q) @ X) = (minus_minus_a @ (poly_a2 @ P @ X) @ (poly_a2 @ Q @ X)))))). % poly_diff
thf(fact_197_poly__diff, axiom,
    ((![P : poly_poly_a, Q : poly_poly_a, X : poly_a]: ((poly_poly_a2 @ (minus_154650241poly_a @ P @ Q) @ X) = (minus_minus_poly_a @ (poly_poly_a2 @ P @ X) @ (poly_poly_a2 @ Q @ X)))))). % poly_diff
thf(fact_198_synthetic__div__0, axiom,
    ((![C : a]: ((synthetic_div_a @ zero_zero_poly_a @ C) = zero_zero_poly_a)))). % synthetic_div_0
thf(fact_199_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_200_synthetic__div__0, axiom,
    ((![C : poly_a]: ((synthetic_div_poly_a @ zero_z2096148049poly_a @ C) = zero_z2096148049poly_a)))). % synthetic_div_0
thf(fact_201_diff__numeral__special_I9_J, axiom,
    (((minus_minus_a @ one_one_a @ one_one_a) = zero_zero_a))). % diff_numeral_special(9)
thf(fact_202_diff__numeral__special_I9_J, axiom,
    (((minus_minus_poly_a @ one_one_poly_a @ one_one_poly_a) = zero_zero_poly_a))). % diff_numeral_special(9)
thf(fact_203_diff__numeral__special_I9_J, axiom,
    (((minus_154650241poly_a @ one_one_poly_poly_a @ one_one_poly_poly_a) = zero_z2096148049poly_a))). % diff_numeral_special(9)
thf(fact_204_zero__less__diff, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ N @ M2)) = (ord_less_nat @ M2 @ N))))). % zero_less_diff
thf(fact_205_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : a]: (^[Z : a]: (Y2 = Z))) = (^[A2 : a]: (^[B : a]: ((minus_minus_a @ A2 @ B) = zero_zero_a)))))). % eq_iff_diff_eq_0
thf(fact_206_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_a]: (^[Z : poly_a]: (Y2 = Z))) = (^[A2 : poly_a]: (^[B : poly_a]: ((minus_minus_poly_a @ A2 @ B) = zero_zero_poly_a)))))). % eq_iff_diff_eq_0
thf(fact_207_eq__iff__diff__eq__0, axiom,
    (((^[Y2 : poly_poly_a]: (^[Z : poly_poly_a]: (Y2 = Z))) = (^[A2 : poly_poly_a]: (^[B : poly_poly_a]: ((minus_154650241poly_a @ A2 @ B) = zero_z2096148049poly_a)))))). % eq_iff_diff_eq_0
thf(fact_208_minus__nat_Odiff__0, axiom,
    ((![M2 : nat]: ((minus_minus_nat @ M2 @ zero_zero_nat) = M2)))). % minus_nat.diff_0
thf(fact_209_diffs0__imp__equal, axiom,
    ((![M2 : nat, N : nat]: (((minus_minus_nat @ M2 @ N) = zero_zero_nat) => (((minus_minus_nat @ N @ M2) = zero_zero_nat) => (M2 = N)))))). % diffs0_imp_equal
thf(fact_210_diff__less__mono2, axiom,
    ((![M2 : nat, N : nat, L : nat]: ((ord_less_nat @ M2 @ N) => ((ord_less_nat @ M2 @ L) => (ord_less_nat @ (minus_minus_nat @ L @ N) @ (minus_minus_nat @ L @ M2))))))). % diff_less_mono2
thf(fact_211_less__imp__diff__less, axiom,
    ((![J : nat, K : nat, N : nat]: ((ord_less_nat @ J @ K) => (ord_less_nat @ (minus_minus_nat @ J @ N) @ K))))). % less_imp_diff_less
thf(fact_212_minus__poly_Orep__eq, axiom,
    ((![X : poly_nat, Xa : poly_nat]: ((coeff_nat @ (minus_minus_poly_nat @ X @ Xa)) = (^[N3 : nat]: (minus_minus_nat @ (coeff_nat @ X @ N3) @ (coeff_nat @ Xa @ N3))))))). % minus_poly.rep_eq
thf(fact_213_diff__commute, axiom,
    ((![I2 : nat, J : nat, K : nat]: ((minus_minus_nat @ (minus_minus_nat @ I2 @ J) @ K) = (minus_minus_nat @ (minus_minus_nat @ I2 @ K) @ J))))). % diff_commute
thf(fact_214_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : nat, C : nat, B2 : nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ C) @ B2) = (minus_minus_nat @ (minus_minus_nat @ A @ B2) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_215_diff__less, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ zero_zero_nat @ N) => ((ord_less_nat @ zero_zero_nat @ M2) => (ord_less_nat @ (minus_minus_nat @ M2 @ N) @ M2)))))). % diff_less
thf(fact_216_coeff__0__degree__minus__1, axiom,
    ((![Rrr : poly_a, Dr : nat]: (((coeff_a @ Rrr @ Dr) = zero_zero_a) => ((ord_less_eq_nat @ (degree_a @ Rrr) @ Dr) => (ord_less_eq_nat @ (degree_a @ Rrr) @ (minus_minus_nat @ Dr @ one_one_nat))))))). % coeff_0_degree_minus_1
thf(fact_217_coeff__0__degree__minus__1, axiom,
    ((![Rrr : poly_poly_a, Dr : nat]: (((coeff_poly_a @ Rrr @ Dr) = zero_zero_poly_a) => ((ord_less_eq_nat @ (degree_poly_a @ Rrr) @ Dr) => (ord_less_eq_nat @ (degree_poly_a @ Rrr) @ (minus_minus_nat @ Dr @ one_one_nat))))))). % coeff_0_degree_minus_1
thf(fact_218_coeff__0__degree__minus__1, axiom,
    ((![Rrr : poly_nat, Dr : nat]: (((coeff_nat @ Rrr @ Dr) = zero_zero_nat) => ((ord_less_eq_nat @ (degree_nat @ Rrr) @ Dr) => (ord_less_eq_nat @ (degree_nat @ Rrr) @ (minus_minus_nat @ Dr @ one_one_nat))))))). % coeff_0_degree_minus_1
thf(fact_219_coeff__0__degree__minus__1, axiom,
    ((![Rrr : poly_poly_nat, Dr : nat]: (((coeff_poly_nat @ Rrr @ Dr) = zero_zero_poly_nat) => ((ord_less_eq_nat @ (degree_poly_nat @ Rrr) @ Dr) => (ord_less_eq_nat @ (degree_poly_nat @ Rrr) @ (minus_minus_nat @ Dr @ one_one_nat))))))). % coeff_0_degree_minus_1
thf(fact_220_coeff__0__degree__minus__1, axiom,
    ((![Rrr : poly_poly_poly_a, Dr : nat]: (((coeff_poly_poly_a @ Rrr @ Dr) = zero_z2096148049poly_a) => ((ord_less_eq_nat @ (degree_poly_poly_a @ Rrr) @ Dr) => (ord_less_eq_nat @ (degree_poly_poly_a @ Rrr) @ (minus_minus_nat @ Dr @ one_one_nat))))))). % coeff_0_degree_minus_1
thf(fact_221_eq__zero__or__degree__less, axiom,
    ((![P : poly_a, N : nat]: ((ord_less_eq_nat @ (degree_a @ P) @ N) => (((coeff_a @ P @ N) = zero_zero_a) => ((P = zero_zero_poly_a) | (ord_less_nat @ (degree_a @ P) @ N))))))). % eq_zero_or_degree_less
thf(fact_222_eq__zero__or__degree__less, axiom,
    ((![P : poly_poly_a, N : nat]: ((ord_less_eq_nat @ (degree_poly_a @ P) @ N) => (((coeff_poly_a @ P @ N) = zero_zero_poly_a) => ((P = zero_z2096148049poly_a) | (ord_less_nat @ (degree_poly_a @ P) @ N))))))). % eq_zero_or_degree_less
thf(fact_223_eq__zero__or__degree__less, axiom,
    ((![P : poly_nat, N : nat]: ((ord_less_eq_nat @ (degree_nat @ P) @ N) => (((coeff_nat @ P @ N) = zero_zero_nat) => ((P = zero_zero_poly_nat) | (ord_less_nat @ (degree_nat @ P) @ N))))))). % eq_zero_or_degree_less
thf(fact_224_eq__zero__or__degree__less, axiom,
    ((![P : poly_poly_nat, N : nat]: ((ord_less_eq_nat @ (degree_poly_nat @ P) @ N) => (((coeff_poly_nat @ P @ N) = zero_zero_poly_nat) => ((P = zero_z1059985641ly_nat) | (ord_less_nat @ (degree_poly_nat @ P) @ N))))))). % eq_zero_or_degree_less
thf(fact_225_eq__zero__or__degree__less, axiom,
    ((![P : poly_poly_poly_a, N : nat]: ((ord_less_eq_nat @ (degree_poly_poly_a @ P) @ N) => (((coeff_poly_poly_a @ P @ N) = zero_z2096148049poly_a) => ((P = zero_z2064990175poly_a) | (ord_less_nat @ (degree_poly_poly_a @ P) @ N))))))). % eq_zero_or_degree_less
thf(fact_226_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq

% Conjectures (1)
thf(conj_0, conjecture,
    ((zero_zero_a = (poly_a2 @ zero_zero_poly_a @ x)))).
