% 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_921__5376720_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:34:10.507

% Could-be-implicit typings (7)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    poly_p1267267526omplex : $tType).
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__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    poly_poly_nat : $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 (64)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Complex__Ocomplex, type,
    fundam1201687030omplex : poly_complex > complex > poly_complex).
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_It__Complex__Ocomplex_J, type,
    fundam1307691262omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
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_It__Complex__Ocomplex_J, type,
    fundam1956464160omplex : poly_poly_complex > nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
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__Complex__Ocomplex_J, type,
    one_one_poly_complex : poly_complex).
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_It__Complex__Ocomplex_J_J, type,
    one_on1331105667omplex : poly_poly_complex).
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_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_It__Complex__Ocomplex_J_J_J, type,
    zero_z1200043727omplex : poly_p1267267526omplex).
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_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_Odegree_001t__Nat__Onat, type,
    degree_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    degree_poly_complex : poly_poly_complex > nat).
thf(sy_c_Polynomial_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
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_It__Complex__Ocomplex_J, type,
    is_zero_poly_complex : poly_poly_complex > $o).
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_Oorder_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    order_1735763309omplex : poly_poly_complex > poly_p1267267526omplex > nat).
thf(sy_c_Polynomial_OpCons_001t__Complex__Ocomplex, type,
    pCons_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Nat__Onat, type,
    pCons_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    pCons_poly_complex : poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    pCons_poly_nat : poly_nat > poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    pCons_1087637536omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex).
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_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_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
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__Complex__Ocomplex_J, type,
    poly_c622223248omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__shift_001t__Complex__Ocomplex, type,
    poly_shift_complex : nat > poly_complex > poly_complex).
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_It__Complex__Ocomplex_J, type,
    poly_s558570093omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Complex__Ocomplex, type,
    reflect_poly_complex : poly_complex > poly_complex).
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__Complex__Ocomplex_J, type,
    reflec309385472omplex : poly_poly_complex > poly_poly_complex).
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_It__Complex__Ocomplex_J_J, type,
    reflec1997789704omplex : poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_c_Polynomial_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > poly_complex).
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_It__Complex__Ocomplex_J, type,
    synthe1985144195omplex : poly_poly_complex > poly_complex > poly_poly_complex).
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_thesis____, type,
    thesis : $o).

% Relevant facts (237)
thf(fact_0_n0, axiom,
    ((~ ((na = zero_zero_nat))))). % n0
thf(fact_1_assms_I2_J, axiom,
    (((degree_complex @ p) = n))). % assms(2)
thf(fact_2_True, axiom,
    (((degree_complex @ s) = zero_zero_nat))). % True
thf(fact_3_False, axiom,
    ((~ ((qa = zero_z1746442943omplex))))). % False
thf(fact_4_sne, axiom,
    ((~ ((s = zero_z1746442943omplex))))). % sne
thf(fact_5_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_6_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_7_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_8_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_9_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_10_pCons__eq__0__iff, axiom,
    ((![A : poly_nat, P : poly_poly_nat]: (((pCons_poly_nat @ A @ P) = zero_z1059985641ly_nat) = (((A = zero_zero_poly_nat)) & ((P = zero_z1059985641ly_nat))))))). % pCons_eq_0_iff
thf(fact_11_pCons__eq__0__iff, axiom,
    ((![A : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A @ P) = zero_z1200043727omplex) = (((A = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_12_pCons__eq__0__iff, axiom,
    ((![A : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A @ P) = zero_z1040703943omplex) = (((A = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_13_pCons__eq__0__iff, axiom,
    ((![A : nat, P : poly_nat]: (((pCons_nat @ A @ P) = zero_zero_poly_nat) = (((A = zero_zero_nat)) & ((P = zero_zero_poly_nat))))))). % pCons_eq_0_iff
thf(fact_14_pCons__eq__0__iff, axiom,
    ((![A : complex, P : poly_complex]: (((pCons_complex @ A @ P) = zero_z1746442943omplex) = (((A = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_15_pCons__induct, axiom,
    ((![P2 : poly_poly_nat > $o, P : poly_poly_nat]: ((P2 @ zero_z1059985641ly_nat) => ((![A2 : poly_nat, P3 : poly_poly_nat]: (((~ ((A2 = zero_zero_poly_nat))) | (~ ((P3 = zero_z1059985641ly_nat)))) => ((P2 @ P3) => (P2 @ (pCons_poly_nat @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_16_pCons__induct, axiom,
    ((![P2 : poly_p1267267526omplex > $o, P : poly_p1267267526omplex]: ((P2 @ zero_z1200043727omplex) => ((![A2 : poly_poly_complex, P3 : poly_p1267267526omplex]: (((~ ((A2 = zero_z1040703943omplex))) | (~ ((P3 = zero_z1200043727omplex)))) => ((P2 @ P3) => (P2 @ (pCons_1087637536omplex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_17_pCons__induct, axiom,
    ((![P2 : poly_poly_complex > $o, P : poly_poly_complex]: ((P2 @ zero_z1040703943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex]: (((~ ((A2 = zero_z1746442943omplex))) | (~ ((P3 = zero_z1040703943omplex)))) => ((P2 @ P3) => (P2 @ (pCons_poly_complex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_18_pCons__induct, axiom,
    ((![P2 : poly_nat > $o, P : poly_nat]: ((P2 @ zero_zero_poly_nat) => ((![A2 : nat, P3 : poly_nat]: (((~ ((A2 = zero_zero_nat))) | (~ ((P3 = zero_zero_poly_nat)))) => ((P2 @ P3) => (P2 @ (pCons_nat @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_19_pCons__induct, axiom,
    ((![P2 : poly_complex > $o, P : poly_complex]: ((P2 @ zero_z1746442943omplex) => ((![A2 : complex, P3 : poly_complex]: (((~ ((A2 = zero_zero_complex))) | (~ ((P3 = zero_z1746442943omplex)))) => ((P2 @ P3) => (P2 @ (pCons_complex @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_20_pCons__eq__iff, axiom,
    ((![A : nat, P : poly_nat, B : nat, Q : poly_nat]: (((pCons_nat @ A @ P) = (pCons_nat @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_21_pCons__eq__iff, axiom,
    ((![A : poly_complex, P : poly_poly_complex, B : poly_complex, Q : poly_poly_complex]: (((pCons_poly_complex @ A @ P) = (pCons_poly_complex @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_22_pCons__eq__iff, axiom,
    ((![A : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A @ P) = (pCons_complex @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_23_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_complex > $o, P : poly_complex, Q : poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A2 : complex, P3 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A2 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_24_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_nat > $o, P : poly_complex, Q : poly_nat]: ((P2 @ zero_z1746442943omplex @ zero_zero_poly_nat) => ((![A2 : complex, P3 : poly_complex, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_25_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_poly_complex > $o, P : poly_complex, Q : poly_poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1040703943omplex) => ((![A2 : complex, P3 : poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A2 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_26_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_complex > $o, P : poly_nat, Q : poly_complex]: ((P2 @ zero_zero_poly_nat @ zero_z1746442943omplex) => ((![A2 : nat, P3 : poly_nat, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_27_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_nat > $o, P : poly_nat, Q : poly_nat]: ((P2 @ zero_zero_poly_nat @ zero_zero_poly_nat) => ((![A2 : nat, P3 : poly_nat, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_28_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_poly_complex > $o, P : poly_nat, Q : poly_poly_complex]: ((P2 @ zero_zero_poly_nat @ zero_z1040703943omplex) => ((![A2 : nat, P3 : poly_nat, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_29_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_complex > $o, P : poly_poly_complex, Q : poly_complex]: ((P2 @ zero_z1040703943omplex @ zero_z1746442943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A2 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_30_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_nat > $o, P : poly_poly_complex, Q : poly_nat]: ((P2 @ zero_z1040703943omplex @ zero_zero_poly_nat) => ((![A2 : poly_complex, P3 : poly_poly_complex, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_31_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_poly_complex > $o, P : poly_poly_complex, Q : poly_poly_complex]: ((P2 @ zero_z1040703943omplex @ zero_z1040703943omplex) => ((![A2 : poly_complex, P3 : poly_poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A2 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_32_pderiv_Oinduct, axiom,
    ((![P2 : poly_complex > $o, A0 : poly_complex]: ((![A2 : complex, P3 : poly_complex]: (((~ ((P3 = zero_z1746442943omplex))) => (P2 @ P3)) => (P2 @ (pCons_complex @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_33_pderiv_Oinduct, axiom,
    ((![P2 : poly_nat > $o, A0 : poly_nat]: ((![A2 : nat, P3 : poly_nat]: (((~ ((P3 = zero_zero_poly_nat))) => (P2 @ P3)) => (P2 @ (pCons_nat @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_34_pderiv_Oinduct, axiom,
    ((![P2 : poly_poly_complex > $o, A0 : poly_poly_complex]: ((![A2 : poly_complex, P3 : poly_poly_complex]: (((~ ((P3 = zero_z1040703943omplex))) => (P2 @ P3)) => (P2 @ (pCons_poly_complex @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_35_pne, axiom,
    ((~ ((pa = zero_z1746442943omplex))))). % pne
thf(fact_36_offset__poly__single, axiom,
    ((![A : complex, H : complex]: ((fundam1201687030omplex @ (pCons_complex @ A @ zero_z1746442943omplex) @ H) = (pCons_complex @ A @ zero_z1746442943omplex))))). % offset_poly_single
thf(fact_37_offset__poly__single, axiom,
    ((![A : nat, H : nat]: ((fundam170929432ly_nat @ (pCons_nat @ A @ zero_zero_poly_nat) @ H) = (pCons_nat @ A @ zero_zero_poly_nat))))). % offset_poly_single
thf(fact_38_offset__poly__single, axiom,
    ((![A : poly_complex, H : poly_complex]: ((fundam1307691262omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex) @ H) = (pCons_poly_complex @ A @ zero_z1040703943omplex))))). % offset_poly_single
thf(fact_39_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A2 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_40_pCons__cases, axiom,
    ((![P : poly_nat]: (~ ((![A2 : nat, Q2 : poly_nat]: (~ ((P = (pCons_nat @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_41_pCons__cases, axiom,
    ((![P : poly_poly_complex]: (~ ((![A2 : poly_complex, Q2 : poly_poly_complex]: (~ ((P = (pCons_poly_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_42_pderiv_Ocases, axiom,
    ((![X : poly_complex]: (~ ((![A2 : complex, P3 : poly_complex]: (~ ((X = (pCons_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_43_pderiv_Ocases, axiom,
    ((![X : poly_nat]: (~ ((![A2 : nat, P3 : poly_nat]: (~ ((X = (pCons_nat @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_44_pderiv_Ocases, axiom,
    ((![X : poly_poly_complex]: (~ ((![A2 : poly_complex, P3 : poly_poly_complex]: (~ ((X = (pCons_poly_complex @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_45_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_46_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_47_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_48_zero__reorient, axiom,
    ((![X : poly_nat]: ((zero_zero_poly_nat = X) = (X = zero_zero_poly_nat))))). % zero_reorient
thf(fact_49_zero__reorient, axiom,
    ((![X : poly_poly_complex]: ((zero_z1040703943omplex = X) = (X = zero_z1040703943omplex))))). % zero_reorient
thf(fact_50_assms_I3_J, axiom,
    ((~ ((n = zero_zero_nat))))). % assms(3)
thf(fact_51_dpn, axiom,
    (((degree_complex @ pa) = na))). % dpn
thf(fact_52_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_53_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_54_degree__0, axiom,
    (((degree_poly_complex @ zero_z1040703943omplex) = zero_zero_nat))). % degree_0
thf(fact_55_pq0, axiom,
    ((![X2 : complex]: (((poly_complex2 @ pa @ X2) = zero_zero_complex) => ((poly_complex2 @ qa @ X2) = zero_zero_complex))))). % pq0
thf(fact_56_degree__offset__poly, axiom,
    ((![P : poly_complex, H : complex]: ((degree_complex @ (fundam1201687030omplex @ P @ H)) = (degree_complex @ P))))). % degree_offset_poly
thf(fact_57_offset__poly__eq__0__iff, axiom,
    ((![P : poly_complex, H : complex]: (((fundam1201687030omplex @ P @ H) = zero_z1746442943omplex) = (P = zero_z1746442943omplex))))). % offset_poly_eq_0_iff
thf(fact_58_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_59_offset__poly__eq__0__iff, axiom,
    ((![P : poly_poly_complex, H : poly_complex]: (((fundam1307691262omplex @ P @ H) = zero_z1040703943omplex) = (P = zero_z1040703943omplex))))). % offset_poly_eq_0_iff
thf(fact_60_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_61_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_62_offset__poly__0, axiom,
    ((![H : poly_complex]: ((fundam1307691262omplex @ zero_z1040703943omplex @ H) = zero_z1040703943omplex)))). % offset_poly_0
thf(fact_63_degree__eq__zeroE, axiom,
    ((![P : poly_complex]: (((degree_complex @ P) = zero_zero_nat) => (~ ((![A2 : complex]: (~ ((P = (pCons_complex @ A2 @ zero_z1746442943omplex))))))))))). % degree_eq_zeroE
thf(fact_64_degree__eq__zeroE, axiom,
    ((![P : poly_nat]: (((degree_nat @ P) = zero_zero_nat) => (~ ((![A2 : nat]: (~ ((P = (pCons_nat @ A2 @ zero_zero_poly_nat))))))))))). % degree_eq_zeroE
thf(fact_65_degree__eq__zeroE, axiom,
    ((![P : poly_poly_complex]: (((degree_poly_complex @ P) = zero_zero_nat) => (~ ((![A2 : poly_complex]: (~ ((P = (pCons_poly_complex @ A2 @ zero_z1040703943omplex))))))))))). % degree_eq_zeroE
thf(fact_66_degree__pCons__0, axiom,
    ((![A : complex]: ((degree_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_67_degree__pCons__0, axiom,
    ((![A : nat]: ((degree_nat @ (pCons_nat @ A @ zero_zero_poly_nat)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_68_degree__pCons__0, axiom,
    ((![A : poly_complex]: ((degree_poly_complex @ (pCons_poly_complex @ A @ zero_z1040703943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_69_assms_I1_J, axiom,
    ((![X2 : complex]: (((poly_complex2 @ p @ X2) = zero_zero_complex) => ((poly_complex2 @ q @ X2) = zero_zero_complex))))). % assms(1)
thf(fact_70_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_71_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_72_psize__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((fundam1956464160omplex @ P) = zero_zero_nat) = (P = zero_z1040703943omplex))))). % psize_eq_0_iff
thf(fact_73_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_complex, C : complex]: (((synthe151143547omplex @ P @ C) = zero_z1746442943omplex) = ((degree_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_74_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_75_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_poly_complex, C : poly_complex]: (((synthe1985144195omplex @ P @ C) = zero_z1040703943omplex) = ((degree_poly_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_76_degree__pCons__eq__if, axiom,
    ((![P : poly_complex, A : complex]: (((P = zero_z1746442943omplex) => ((degree_complex @ (pCons_complex @ A @ P)) = zero_zero_nat)) & ((~ ((P = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A @ P)) = (suc @ (degree_complex @ P)))))))). % degree_pCons_eq_if
thf(fact_77_degree__pCons__eq__if, axiom,
    ((![P : poly_nat, A : nat]: (((P = zero_zero_poly_nat) => ((degree_nat @ (pCons_nat @ A @ P)) = zero_zero_nat)) & ((~ ((P = zero_zero_poly_nat))) => ((degree_nat @ (pCons_nat @ A @ P)) = (suc @ (degree_nat @ P)))))))). % degree_pCons_eq_if
thf(fact_78_degree__pCons__eq__if, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: (((P = zero_z1040703943omplex) => ((degree_poly_complex @ (pCons_poly_complex @ A @ P)) = zero_zero_nat)) & ((~ ((P = zero_z1040703943omplex))) => ((degree_poly_complex @ (pCons_poly_complex @ A @ P)) = (suc @ (degree_poly_complex @ P)))))))). % degree_pCons_eq_if
thf(fact_79_is__zero__null, axiom,
    ((is_zero_complex = (^[P4 : poly_complex]: (P4 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_80_is__zero__null, axiom,
    ((is_zero_nat = (^[P4 : poly_nat]: (P4 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_81_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P4 : poly_poly_complex]: (P4 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_82_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_83_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_84_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_c622223248omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_85_oa, axiom,
    ((~ (((order_complex @ a @ pa) = zero_zero_nat))))). % oa
thf(fact_86__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,
    ((~ ((![A2 : complex]: (~ (((poly_complex2 @ pa @ A2) = zero_zero_complex)))))))). % \<open>\<And>thesis. (\<And>a. poly p a = 0 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_87_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_88_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_89_poly__shift__0, axiom,
    ((![N : nat]: ((poly_s558570093omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_shift_0
thf(fact_90_a, axiom,
    (((poly_complex2 @ pa @ a) = zero_zero_complex))). % a
thf(fact_91_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_92_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_93_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_94_poly__0, axiom,
    ((![X : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X) = zero_zero_poly_nat)))). % poly_0
thf(fact_95_poly__0, axiom,
    ((![X : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X) = zero_z1040703943omplex)))). % poly_0
thf(fact_96_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_97_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_98_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_99_synthetic__div__pCons, axiom,
    ((![A : complex, P : poly_complex, C : complex]: ((synthe151143547omplex @ (pCons_complex @ A @ P) @ C) = (pCons_complex @ (poly_complex2 @ P @ C) @ (synthe151143547omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_100_synthetic__div__pCons, axiom,
    ((![A : nat, P : poly_nat, C : nat]: ((synthetic_div_nat @ (pCons_nat @ A @ P) @ C) = (pCons_nat @ (poly_nat2 @ P @ C) @ (synthetic_div_nat @ P @ C)))))). % synthetic_div_pCons
thf(fact_101_synthetic__div__pCons, axiom,
    ((![A : poly_complex, P : poly_poly_complex, C : poly_complex]: ((synthe1985144195omplex @ (pCons_poly_complex @ A @ P) @ C) = (pCons_poly_complex @ (poly_poly_complex2 @ P @ C) @ (synthe1985144195omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_102_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_103_order__0I, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: ((~ (((poly_poly_complex2 @ P @ A) = zero_z1746442943omplex))) => ((order_poly_complex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_104_order__0I, axiom,
    ((![P : poly_complex, A : complex]: ((~ (((poly_complex2 @ P @ A) = zero_zero_complex))) => ((order_complex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_105_order__0I, axiom,
    ((![P : poly_p1267267526omplex, A : poly_poly_complex]: ((~ (((poly_p282434315omplex @ P @ A) = zero_z1040703943omplex))) => ((order_1735763309omplex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_106_order__root, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: (((poly_poly_complex2 @ P @ A) = zero_z1746442943omplex) = (((P = zero_z1040703943omplex)) | ((~ (((order_poly_complex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_107_order__root, axiom,
    ((![P : poly_complex, A : complex]: (((poly_complex2 @ P @ A) = zero_zero_complex) = (((P = zero_z1746442943omplex)) | ((~ (((order_complex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_108_order__root, axiom,
    ((![P : poly_p1267267526omplex, A : poly_poly_complex]: (((poly_p282434315omplex @ P @ A) = zero_z1040703943omplex) = (((P = zero_z1200043727omplex)) | ((~ (((order_1735763309omplex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_109_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X3 : poly_complex]: ((poly_poly_complex2 @ P @ X3) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_110_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X3 : complex]: ((poly_complex2 @ P @ X3) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_111_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X3 : poly_poly_complex]: ((poly_p282434315omplex @ P @ X3) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_112_psize__def, axiom,
    ((fundam1709708056omplex = (^[P4 : poly_complex]: (if_nat @ (P4 = zero_z1746442943omplex) @ zero_zero_nat @ (suc @ (degree_complex @ P4))))))). % psize_def
thf(fact_113_psize__def, axiom,
    ((fundam1567013434ze_nat = (^[P4 : poly_nat]: (if_nat @ (P4 = zero_zero_poly_nat) @ zero_zero_nat @ (suc @ (degree_nat @ P4))))))). % psize_def
thf(fact_114_psize__def, axiom,
    ((fundam1956464160omplex = (^[P4 : poly_poly_complex]: (if_nat @ (P4 = zero_z1040703943omplex) @ zero_zero_nat @ (suc @ (degree_poly_complex @ P4))))))). % psize_def
thf(fact_115_fundamental__theorem__of__algebra__alt, axiom,
    ((![P : poly_complex]: ((~ ((?[A2 : complex, L : poly_complex]: ((~ ((A2 = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (P = (pCons_complex @ A2 @ L))))))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra_alt
thf(fact_116_degree__pCons__eq, axiom,
    ((![P : poly_complex, A : complex]: ((~ ((P = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A @ P)) = (suc @ (degree_complex @ P))))))). % degree_pCons_eq
thf(fact_117_degree__pCons__eq, axiom,
    ((![P : poly_nat, A : nat]: ((~ ((P = zero_zero_poly_nat))) => ((degree_nat @ (pCons_nat @ A @ P)) = (suc @ (degree_nat @ P))))))). % degree_pCons_eq
thf(fact_118_degree__pCons__eq, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: ((~ ((P = zero_z1040703943omplex))) => ((degree_poly_complex @ (pCons_poly_complex @ A @ P)) = (suc @ (degree_poly_complex @ P))))))). % degree_pCons_eq
thf(fact_119_oop, axiom,
    ((![A : complex]: (ord_less_eq_nat @ (order_complex @ A @ pa) @ na)))). % oop
thf(fact_120_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_121_nat_Oinject, axiom,
    ((![X22 : nat, Y2 : nat]: (((suc @ X22) = (suc @ Y2)) = (X22 = Y2))))). % nat.inject
thf(fact_122_exists__least__lemma, axiom,
    ((![P2 : nat > $o]: ((~ ((P2 @ zero_zero_nat))) => ((?[X_1 : nat]: (P2 @ X_1)) => (?[N2 : nat]: ((~ ((P2 @ N2))) & (P2 @ (suc @ N2))))))))). % exists_least_lemma
thf(fact_123_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_124_bot__nat__0_Oextremum, axiom,
    ((![A : nat]: (ord_less_eq_nat @ zero_zero_nat @ A)))). % bot_nat_0.extremum
thf(fact_125_le0, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % le0
thf(fact_126_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_127_lift__Suc__antimono__le, axiom,
    ((![F : nat > nat, N : nat, N3 : nat]: ((![N2 : nat]: (ord_less_eq_nat @ (F @ (suc @ N2)) @ (F @ N2))) => ((ord_less_eq_nat @ N @ N3) => (ord_less_eq_nat @ (F @ N3) @ (F @ N))))))). % lift_Suc_antimono_le
thf(fact_128_lift__Suc__mono__le, axiom,
    ((![F : nat > nat, N : nat, N3 : nat]: ((![N2 : nat]: (ord_less_eq_nat @ (F @ N2) @ (F @ (suc @ N2)))) => ((ord_less_eq_nat @ N @ N3) => (ord_less_eq_nat @ (F @ N) @ (F @ N3))))))). % lift_Suc_mono_le
thf(fact_129_transitive__stepwise__le, axiom,
    ((![M : nat, N : nat, R : nat > nat > $o]: ((ord_less_eq_nat @ M @ N) => ((![X4 : nat]: (R @ X4 @ X4)) => ((![X4 : nat, Y : nat, Z : nat]: ((R @ X4 @ Y) => ((R @ Y @ Z) => (R @ X4 @ Z)))) => ((![N2 : nat]: (R @ N2 @ (suc @ N2))) => (R @ M @ N)))))))). % transitive_stepwise_le
thf(fact_130_nat__induct__at__least, axiom,
    ((![M : nat, N : nat, P2 : nat > $o]: ((ord_less_eq_nat @ M @ N) => ((P2 @ M) => ((![N2 : nat]: ((ord_less_eq_nat @ M @ N2) => ((P2 @ N2) => (P2 @ (suc @ N2))))) => (P2 @ N))))))). % nat_induct_at_least
thf(fact_131_full__nat__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N2 : nat]: ((![M2 : nat]: ((ord_less_eq_nat @ (suc @ M2) @ N2) => (P2 @ M2))) => (P2 @ N2))) => (P2 @ N))))). % full_nat_induct
thf(fact_132_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_133_Suc__n__not__le__n, axiom,
    ((![N : nat]: (~ ((ord_less_eq_nat @ (suc @ N) @ N)))))). % Suc_n_not_le_n
thf(fact_134_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_135_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_136_le__SucI, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ M @ (suc @ N)))))). % le_SucI
thf(fact_137_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_138_Suc__leD, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ (suc @ M) @ N) => (ord_less_eq_nat @ M @ N))))). % Suc_leD
thf(fact_139_bot__nat__0_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat))))). % bot_nat_0.extremum_uniqueI
thf(fact_140_bot__nat__0_Oextremum__unique, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat))))). % bot_nat_0.extremum_unique
thf(fact_141_le__0__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_0_eq
thf(fact_142_less__eq__nat_Osimps_I1_J, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % less_eq_nat.simps(1)
thf(fact_143_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_144_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_145_eq__imp__le, axiom,
    ((![M : nat, N : nat]: ((M = N) => (ord_less_eq_nat @ M @ N))))). % eq_imp_le
thf(fact_146_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_147_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_148_Nat_Oex__has__greatest__nat, axiom,
    ((![P2 : nat > $o, K : nat, B : nat]: ((P2 @ K) => ((![Y : nat]: ((P2 @ Y) => (ord_less_eq_nat @ Y @ B))) => (?[X4 : nat]: ((P2 @ X4) & (![Y3 : nat]: ((P2 @ Y3) => (ord_less_eq_nat @ Y3 @ X4)))))))))). % Nat.ex_has_greatest_nat
thf(fact_149_zero__le, axiom,
    ((![X : nat]: (ord_less_eq_nat @ zero_zero_nat @ X)))). % zero_le
thf(fact_150_Suc__inject, axiom,
    ((![X : nat, Y4 : nat]: (((suc @ X) = (suc @ Y4)) => (X = Y4))))). % Suc_inject
thf(fact_151_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_152_degree__pCons__le, axiom,
    ((![A : nat, P : poly_nat]: (ord_less_eq_nat @ (degree_nat @ (pCons_nat @ A @ P)) @ (suc @ (degree_nat @ P)))))). % degree_pCons_le
thf(fact_153_degree__pCons__le, axiom,
    ((![A : poly_complex, P : poly_poly_complex]: (ord_less_eq_nat @ (degree_poly_complex @ (pCons_poly_complex @ A @ P)) @ (suc @ (degree_poly_complex @ P)))))). % degree_pCons_le
thf(fact_154_degree__pCons__le, axiom,
    ((![A : complex, P : poly_complex]: (ord_less_eq_nat @ (degree_complex @ (pCons_complex @ A @ P)) @ (suc @ (degree_complex @ P)))))). % degree_pCons_le
thf(fact_155_order__degree, axiom,
    ((![P : poly_complex, A : complex]: ((~ ((P = zero_z1746442943omplex))) => (ord_less_eq_nat @ (order_complex @ A @ P) @ (degree_complex @ P)))))). % order_degree
thf(fact_156_order__degree, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: ((~ ((P = zero_z1040703943omplex))) => (ord_less_eq_nat @ (order_poly_complex @ A @ P) @ (degree_poly_complex @ P)))))). % order_degree
thf(fact_157_nat_Odistinct_I1_J, axiom,
    ((![X22 : nat]: (~ ((zero_zero_nat = (suc @ X22))))))). % nat.distinct(1)
thf(fact_158_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_159_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_160_nat_OdiscI, axiom,
    ((![Nat : nat, X22 : nat]: ((Nat = (suc @ X22)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_161_nat__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N2 : nat]: ((P2 @ N2) => (P2 @ (suc @ N2)))) => (P2 @ N)))))). % nat_induct
thf(fact_162_diff__induct, axiom,
    ((![P2 : nat > nat > $o, M : nat, N : nat]: ((![X4 : nat]: (P2 @ X4 @ zero_zero_nat)) => ((![Y : nat]: (P2 @ zero_zero_nat @ (suc @ Y))) => ((![X4 : nat, Y : nat]: ((P2 @ X4 @ Y) => (P2 @ (suc @ X4) @ (suc @ Y)))) => (P2 @ M @ N))))))). % diff_induct
thf(fact_163_zero__induct, axiom,
    ((![P2 : nat > $o, K : nat]: ((P2 @ K) => ((![N2 : nat]: ((P2 @ (suc @ N2)) => (P2 @ N2))) => (P2 @ zero_zero_nat)))))). % zero_induct
thf(fact_164_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_165_Zero__neq__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_neq_Suc
thf(fact_166_Zero__not__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_not_Suc
thf(fact_167_old_Onat_Oexhaust, axiom,
    ((![Y4 : nat]: ((~ ((Y4 = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y4 = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_168_old_Onat_Oinducts, axiom,
    ((![P2 : nat > $o, Nat : nat]: ((P2 @ zero_zero_nat) => ((![Nat3 : nat]: ((P2 @ Nat3) => (P2 @ (suc @ Nat3)))) => (P2 @ Nat)))))). % old.nat.inducts
thf(fact_169_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M4 : nat]: (N = (suc @ M4))))))). % not0_implies_Suc
thf(fact_170_order__refl, axiom,
    ((![X : nat]: (ord_less_eq_nat @ X @ X)))). % order_refl
thf(fact_171_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_172_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat))). % le_numeral_extra(3)
thf(fact_173_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((poly_poly_complex2 @ (reflec309385472omplex @ P) @ zero_z1746442943omplex) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_174_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_175_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_complex]: (((poly_complex2 @ (reflect_poly_complex @ P) @ zero_zero_complex) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_176_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_177_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((poly_p282434315omplex @ (reflec1997789704omplex @ P) @ zero_z1040703943omplex) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_178_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_complex @ N @ one_one_poly_complex) = zero_z1746442943omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_complex @ N @ one_one_poly_complex) = one_one_poly_complex)))))). % poly_cutoff_1
thf(fact_179_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_180_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_c622223248omplex @ N @ one_on1331105667omplex) = zero_z1040703943omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_c622223248omplex @ N @ one_on1331105667omplex) = one_on1331105667omplex)))))). % poly_cutoff_1
thf(fact_181_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_182_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_183_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_184_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_185_poly__1, axiom,
    ((![X : complex]: ((poly_complex2 @ one_one_poly_complex @ X) = one_one_complex)))). % poly_1
thf(fact_186_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_187_reflect__poly__const, axiom,
    ((![A : complex]: ((reflect_poly_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = (pCons_complex @ A @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_188_reflect__poly__const, axiom,
    ((![A : nat]: ((reflect_poly_nat @ (pCons_nat @ A @ zero_zero_poly_nat)) = (pCons_nat @ A @ zero_zero_poly_nat))))). % reflect_poly_const
thf(fact_189_reflect__poly__const, axiom,
    ((![A : poly_complex]: ((reflec309385472omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex)) = (pCons_poly_complex @ A @ zero_z1040703943omplex))))). % reflect_poly_const
thf(fact_190_order__1__eq__0, axiom,
    ((![X : complex]: ((order_complex @ X @ one_one_poly_complex) = zero_zero_nat)))). % order_1_eq_0
thf(fact_191_one__poly__eq__simps_I2_J, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % one_poly_eq_simps(2)
thf(fact_192_one__poly__eq__simps_I2_J, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % one_poly_eq_simps(2)
thf(fact_193_one__poly__eq__simps_I2_J, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % one_poly_eq_simps(2)
thf(fact_194_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_complex = (pCons_complex @ one_one_complex @ zero_z1746442943omplex)))). % one_poly_eq_simps(1)
thf(fact_195_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_nat = (pCons_nat @ one_one_nat @ zero_zero_poly_nat)))). % one_poly_eq_simps(1)
thf(fact_196_one__poly__eq__simps_I1_J, axiom,
    ((one_on1331105667omplex = (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex)))). % one_poly_eq_simps(1)
thf(fact_197_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_nat @ one_one_nat @ one_one_nat))). % le_numeral_extra(4)
thf(fact_198_constant__def, axiom,
    ((fundam1158420650omplex = (^[F2 : complex > complex]: (![X3 : complex]: (![Y5 : complex]: ((F2 @ X3) = (F2 @ Y5)))))))). % constant_def
thf(fact_199_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_200_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_201_pCons__one, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % pCons_one
thf(fact_202_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_203_degree__reflect__poly__le, axiom,
    ((![P : poly_complex]: (ord_less_eq_nat @ (degree_complex @ (reflect_poly_complex @ P)) @ (degree_complex @ P))))). % degree_reflect_poly_le
thf(fact_204_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_205_dual__order_Oeq__iff, axiom,
    (((^[Y6 : nat]: (^[Z2 : nat]: (Y6 = Z2))) = (^[A3 : nat]: (^[B3 : nat]: (((ord_less_eq_nat @ B3 @ A3)) & ((ord_less_eq_nat @ A3 @ B3)))))))). % dual_order.eq_iff
thf(fact_206_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_207_linorder__wlog, axiom,
    ((![P2 : nat > nat > $o, A : nat, B : nat]: ((![A2 : nat, B2 : nat]: ((ord_less_eq_nat @ A2 @ B2) => (P2 @ A2 @ B2))) => ((![A2 : nat, B2 : nat]: ((P2 @ B2 @ A2) => (P2 @ A2 @ B2))) => (P2 @ A @ B)))))). % linorder_wlog
thf(fact_208_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_209_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_210_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_211_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_212_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_213_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y6 : nat]: (^[Z2 : nat]: (Y6 = Z2))) = (^[A3 : nat]: (^[B3 : nat]: (((ord_less_eq_nat @ A3 @ B3)) & ((ord_less_eq_nat @ B3 @ A3)))))))). % order_class.order.eq_iff
thf(fact_214_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_215_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_216_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_217_le__cases, axiom,
    ((![X : nat, Y4 : nat]: ((~ ((ord_less_eq_nat @ X @ Y4))) => (ord_less_eq_nat @ Y4 @ X))))). % le_cases
thf(fact_218_eq__refl, axiom,
    ((![X : nat, Y4 : nat]: ((X = Y4) => (ord_less_eq_nat @ X @ Y4))))). % eq_refl
thf(fact_219_linear, axiom,
    ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) | (ord_less_eq_nat @ Y4 @ X))))). % linear
thf(fact_220_antisym, axiom,
    ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => ((ord_less_eq_nat @ Y4 @ X) => (X = Y4)))))). % antisym
thf(fact_221_eq__iff, axiom,
    (((^[Y6 : nat]: (^[Z2 : nat]: (Y6 = Z2))) = (^[X3 : nat]: (^[Y5 : nat]: (((ord_less_eq_nat @ X3 @ Y5)) & ((ord_less_eq_nat @ Y5 @ X3)))))))). % eq_iff
thf(fact_222_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (((F @ B) = C) => ((![X4 : nat, Y : nat]: ((ord_less_eq_nat @ X4 @ Y) => (ord_less_eq_nat @ (F @ X4) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_223_ord__eq__le__subst, axiom,
    ((![A : nat, F : nat > nat, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y : nat]: ((ord_less_eq_nat @ X4 @ Y) => (ord_less_eq_nat @ (F @ X4) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_224_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) => ((![X4 : nat, Y : nat]: ((ord_less_eq_nat @ X4 @ Y) => (ord_less_eq_nat @ (F @ X4) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % order_subst2
thf(fact_225_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) => ((![X4 : nat, Y : nat]: ((ord_less_eq_nat @ X4 @ Y) => (ord_less_eq_nat @ (F @ X4) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % order_subst1
thf(fact_226_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_complex @ N @ one_one_poly_complex) = one_one_poly_complex)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_complex @ N @ one_one_poly_complex) = zero_z1746442943omplex)))))). % poly_shift_1
thf(fact_227_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_228_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_s558570093omplex @ N @ one_on1331105667omplex) = one_on1331105667omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_s558570093omplex @ N @ one_on1331105667omplex) = zero_z1040703943omplex)))))). % poly_shift_1
thf(fact_229_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_nat @ one_one_nat @ zero_zero_nat))))). % not_one_le_zero
thf(fact_230_zero__le__one, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ one_one_nat))). % zero_le_one
thf(fact_231_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_232_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_233_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_234_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_235_zero__neq__one, axiom,
    ((~ ((zero_z1040703943omplex = one_on1331105667omplex))))). % zero_neq_one
thf(fact_236_One__nat__def, axiom,
    ((one_one_nat = (suc @ zero_zero_nat)))). % One_nat_def

% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T, axiom,
    ((![P2 : $o]: ((P2 = $true) | (P2 = $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 (2)
thf(conj_0, hypothesis,
    ((![K2 : complex]: ((s = (pCons_complex @ K2 @ zero_z1746442943omplex)) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
