% 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_1028__5377616_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:23.641

% 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 (41)
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_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    one_on1411366565ly_nat : poly_poly_nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    times_1246143675omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    times_times_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    times_1460995011omplex : poly_poly_complex > poly_poly_complex > 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_Nat_OSuc, type,
    suc : nat > nat).
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_Odegree_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    degree_poly_nat : poly_poly_nat > 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_Power_Opower__class_Opower_001t__Complex__Ocomplex, type,
    power_power_complex : complex > nat > complex).
thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat, type,
    power_power_nat : nat > nat > nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    power_184595776omplex : poly_complex > nat > poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    power_power_poly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    power_432682568omplex : poly_poly_complex > nat > poly_poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    power_1336127338ly_nat : poly_poly_nat > nat > poly_poly_nat).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat, type,
    divide_divide_nat : nat > nat > nat).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    divide1187762952omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    divide350004240omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_v_k____, type,
    k : complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).

% Relevant facts (246)
thf(fact_0_k_I2_J, axiom,
    ((~ ((k = zero_zero_complex))))). % k(2)
thf(fact_1_dp_I2_J, axiom,
    (((degree_complex @ p) = zero_zero_nat))). % dp(2)
thf(fact_2_dp_I1_J, axiom,
    ((~ ((p = zero_z1746442943omplex))))). % dp(1)
thf(fact_3_k_I1_J, axiom,
    ((p = (pCons_complex @ k @ zero_z1746442943omplex)))). % k(1)
thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062k_O_A_092_060lbrakk_062p_A_061_A_091_058k_058_093_059_Ak_A_092_060noteq_062_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![K : complex]: ((p = (pCons_complex @ K @ zero_z1746442943omplex)) => (K = zero_zero_complex))))))). % \<open>\<And>thesis. (\<And>k. \<lbrakk>p = [:k:]; k \<noteq> 0\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_5_nonzero__divide__mult__cancel__left, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ (times_times_complex @ A @ B)) = (divide1210191872omplex @ one_one_complex @ B)))))). % nonzero_divide_mult_cancel_left
thf(fact_6_nonzero__divide__mult__cancel__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ B @ (times_times_complex @ A @ B)) = (divide1210191872omplex @ one_one_complex @ A)))))). % nonzero_divide_mult_cancel_right
thf(fact_7_one__poly__eq__simps_I2_J, axiom,
    (((pCons_poly_nat @ one_one_poly_nat @ zero_z1059985641ly_nat) = one_on1411366565ly_nat))). % one_poly_eq_simps(2)
thf(fact_8_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_9_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_10_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_11_one__poly__eq__simps_I1_J, axiom,
    ((one_on1411366565ly_nat = (pCons_poly_nat @ one_one_poly_nat @ zero_z1059985641ly_nat)))). % one_poly_eq_simps(1)
thf(fact_12_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_13_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_14_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_15_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_16_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_17_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_18_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_19_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_20_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_21_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_22_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_23_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_24_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_25_divide__eq__1__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = one_one_complex) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_26_div__self, axiom,
    ((![A : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((divide1187762952omplex @ A @ A) = one_one_poly_complex))))). % div_self
thf(fact_27_div__self, axiom,
    ((![A : poly_poly_complex]: ((~ ((A = zero_z1040703943omplex))) => ((divide350004240omplex @ A @ A) = one_on1331105667omplex))))). % div_self
thf(fact_28_div__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % div_self
thf(fact_29_div__self, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ A @ A) = one_one_nat))))). % div_self
thf(fact_30_one__eq__divide__iff, axiom,
    ((![A : complex, B : complex]: ((one_one_complex = (divide1210191872omplex @ A @ B)) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_31_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_32_divide__self__if, axiom,
    ((![A : complex]: (((A = zero_zero_complex) => ((divide1210191872omplex @ A @ A) = zero_zero_complex)) & ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex)))))). % divide_self_if
thf(fact_33_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_34_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_35_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_36_mult__cancel__right, axiom,
    ((![A : poly_poly_complex, C : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A @ C) = (times_1460995011omplex @ B @ C)) = (((C = zero_z1040703943omplex)) | ((A = B))))))). % mult_cancel_right
thf(fact_37_mult__cancel__right, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A @ C) = (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((A = B))))))). % mult_cancel_right
thf(fact_38_mult__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_right
thf(fact_39_mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_right
thf(fact_40_mult__cancel__left, axiom,
    ((![C : poly_poly_complex, A : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ C @ A) = (times_1460995011omplex @ C @ B)) = (((C = zero_z1040703943omplex)) | ((A = B))))))). % mult_cancel_left
thf(fact_41_mult__cancel__left, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: (((times_1246143675omplex @ C @ A) = (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((A = B))))))). % mult_cancel_left
thf(fact_42_mult__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_left
thf(fact_43_mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_left
thf(fact_44_mult__eq__0__iff, axiom,
    ((![A : poly_nat, B : poly_nat]: (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat) = (((A = zero_zero_poly_nat)) | ((B = zero_zero_poly_nat))))))). % mult_eq_0_iff
thf(fact_45_mult__eq__0__iff, axiom,
    ((![A : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A @ B) = zero_z1040703943omplex) = (((A = zero_z1040703943omplex)) | ((B = zero_z1040703943omplex))))))). % mult_eq_0_iff
thf(fact_46_mult__eq__0__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex) = (((A = zero_z1746442943omplex)) | ((B = zero_z1746442943omplex))))))). % mult_eq_0_iff
thf(fact_47_mult__eq__0__iff, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = (((A = zero_zero_nat)) | ((B = zero_zero_nat))))))). % mult_eq_0_iff
thf(fact_48_mult__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_49_mult__zero__right, axiom,
    ((![A : poly_nat]: ((times_times_poly_nat @ A @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % mult_zero_right
thf(fact_50_mult__zero__right, axiom,
    ((![A : poly_poly_complex]: ((times_1460995011omplex @ A @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % mult_zero_right
thf(fact_51_mult__zero__right, axiom,
    ((![A : poly_complex]: ((times_1246143675omplex @ A @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % mult_zero_right
thf(fact_52_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_53_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_54_mult__zero__left, axiom,
    ((![A : poly_nat]: ((times_times_poly_nat @ zero_zero_poly_nat @ A) = zero_zero_poly_nat)))). % mult_zero_left
thf(fact_55_mult__zero__left, axiom,
    ((![A : poly_poly_complex]: ((times_1460995011omplex @ zero_z1040703943omplex @ A) = zero_z1040703943omplex)))). % mult_zero_left
thf(fact_56_mult__zero__left, axiom,
    ((![A : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ A) = zero_z1746442943omplex)))). % mult_zero_left
thf(fact_57_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_58_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_59_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_60_divide__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_right
thf(fact_61_divide__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((divide1210191872omplex @ C @ A) = (divide1210191872omplex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_left
thf(fact_62_div__by__0, axiom,
    ((![A : poly_complex]: ((divide1187762952omplex @ A @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % div_by_0
thf(fact_63_div__by__0, axiom,
    ((![A : poly_poly_complex]: ((divide350004240omplex @ A @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % div_by_0
thf(fact_64_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_65_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_66_divide__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % divide_eq_0_iff
thf(fact_67_div__0, axiom,
    ((![A : poly_complex]: ((divide1187762952omplex @ zero_z1746442943omplex @ A) = zero_z1746442943omplex)))). % div_0
thf(fact_68_div__0, axiom,
    ((![A : poly_poly_complex]: ((divide350004240omplex @ zero_z1040703943omplex @ A) = zero_z1040703943omplex)))). % div_0
thf(fact_69_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_70_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_71_times__divide__eq__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ A @ (divide1210191872omplex @ B @ C)) = (divide1210191872omplex @ (times_times_complex @ A @ B) @ C))))). % times_divide_eq_right
thf(fact_72_divide__divide__eq__right, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ A @ (divide1210191872omplex @ B @ C)) = (divide1210191872omplex @ (times_times_complex @ A @ C) @ B))))). % divide_divide_eq_right
thf(fact_73_divide__divide__eq__left, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ A @ B) @ C) = (divide1210191872omplex @ A @ (times_times_complex @ B @ C)))))). % divide_divide_eq_left
thf(fact_74_times__divide__eq__left, axiom,
    ((![B : complex, C : complex, A : complex]: ((times_times_complex @ (divide1210191872omplex @ B @ C) @ A) = (divide1210191872omplex @ (times_times_complex @ B @ A) @ C))))). % times_divide_eq_left
thf(fact_75_div__by__1, axiom,
    ((![A : poly_complex]: ((divide1187762952omplex @ A @ one_one_poly_complex) = A)))). % div_by_1
thf(fact_76_div__by__1, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ one_one_complex) = A)))). % div_by_1
thf(fact_77_div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % div_by_1
thf(fact_78_mult__cancel__right2, axiom,
    ((![A : poly_poly_complex, C : poly_poly_complex]: (((times_1460995011omplex @ A @ C) = C) = (((C = zero_z1040703943omplex)) | ((A = one_on1331105667omplex))))))). % mult_cancel_right2
thf(fact_79_mult__cancel__right2, axiom,
    ((![A : poly_complex, C : poly_complex]: (((times_1246143675omplex @ A @ C) = C) = (((C = zero_z1746442943omplex)) | ((A = one_one_poly_complex))))))). % mult_cancel_right2
thf(fact_80_mult__cancel__right2, axiom,
    ((![A : complex, C : complex]: (((times_times_complex @ A @ C) = C) = (((C = zero_zero_complex)) | ((A = one_one_complex))))))). % mult_cancel_right2
thf(fact_81_mult__cancel__right1, axiom,
    ((![C : poly_poly_complex, B : poly_poly_complex]: ((C = (times_1460995011omplex @ B @ C)) = (((C = zero_z1040703943omplex)) | ((B = one_on1331105667omplex))))))). % mult_cancel_right1
thf(fact_82_mult__cancel__right1, axiom,
    ((![C : poly_complex, B : poly_complex]: ((C = (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((B = one_one_poly_complex))))))). % mult_cancel_right1
thf(fact_83_mult__cancel__right1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_right1
thf(fact_84_mult__cancel__left2, axiom,
    ((![C : poly_poly_complex, A : poly_poly_complex]: (((times_1460995011omplex @ C @ A) = C) = (((C = zero_z1040703943omplex)) | ((A = one_on1331105667omplex))))))). % mult_cancel_left2
thf(fact_85_mult__cancel__left2, axiom,
    ((![C : poly_complex, A : poly_complex]: (((times_1246143675omplex @ C @ A) = C) = (((C = zero_z1746442943omplex)) | ((A = one_one_poly_complex))))))). % mult_cancel_left2
thf(fact_86_mult__cancel__left2, axiom,
    ((![C : complex, A : complex]: (((times_times_complex @ C @ A) = C) = (((C = zero_zero_complex)) | ((A = one_one_complex))))))). % mult_cancel_left2
thf(fact_87_mult__cancel__left1, axiom,
    ((![C : poly_poly_complex, B : poly_poly_complex]: ((C = (times_1460995011omplex @ C @ B)) = (((C = zero_z1040703943omplex)) | ((B = one_on1331105667omplex))))))). % mult_cancel_left1
thf(fact_88_mult__cancel__left1, axiom,
    ((![C : poly_complex, B : poly_complex]: ((C = (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((B = one_one_poly_complex))))))). % mult_cancel_left1
thf(fact_89_mult__cancel__left1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_left1
thf(fact_90_nonzero__mult__divide__mult__cancel__right2, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right2
thf(fact_91_nonzero__mult__div__cancel__right, axiom,
    ((![B : poly_poly_complex, A : poly_poly_complex]: ((~ ((B = zero_z1040703943omplex))) => ((divide350004240omplex @ (times_1460995011omplex @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_92_nonzero__mult__div__cancel__right, axiom,
    ((![B : poly_complex, A : poly_complex]: ((~ ((B = zero_z1746442943omplex))) => ((divide1187762952omplex @ (times_1246143675omplex @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_93_nonzero__mult__div__cancel__right, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_94_nonzero__mult__div__cancel__right, axiom,
    ((![B : nat, A : nat]: ((~ ((B = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ B) = A))))). % nonzero_mult_div_cancel_right
thf(fact_95_nonzero__mult__divide__mult__cancel__right, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_right
thf(fact_96_nonzero__mult__divide__mult__cancel__left2, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ B @ C)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left2
thf(fact_97_nonzero__mult__div__cancel__left, axiom,
    ((![A : poly_poly_complex, B : poly_poly_complex]: ((~ ((A = zero_z1040703943omplex))) => ((divide350004240omplex @ (times_1460995011omplex @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_98_nonzero__mult__div__cancel__left, axiom,
    ((![A : poly_complex, B : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((divide1187762952omplex @ (times_1246143675omplex @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_99_nonzero__mult__div__cancel__left, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_100_nonzero__mult__div__cancel__left, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B))))). % nonzero_mult_div_cancel_left
thf(fact_101_nonzero__mult__divide__mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B)))))). % nonzero_mult_divide_mult_cancel_left
thf(fact_102_mult__divide__mult__cancel__left__if, axiom,
    ((![C : complex, A : complex, B : complex]: (((C = zero_zero_complex) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = zero_zero_complex)) & ((~ ((C = zero_zero_complex))) => ((divide1210191872omplex @ (times_times_complex @ C @ A) @ (times_times_complex @ C @ B)) = (divide1210191872omplex @ A @ B))))))). % mult_divide_mult_cancel_left_if
thf(fact_103_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_104_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_105_degree__0, axiom,
    (((degree_poly_complex @ zero_z1040703943omplex) = zero_zero_nat))). % degree_0
thf(fact_106_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_107_degree__1, axiom,
    (((degree_nat @ one_one_poly_nat) = zero_zero_nat))). % degree_1
thf(fact_108_divide__poly__0, axiom,
    ((![F : poly_complex]: ((divide1187762952omplex @ F @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % divide_poly_0
thf(fact_109_divide__poly__0, axiom,
    ((![F : poly_poly_complex]: ((divide350004240omplex @ F @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % divide_poly_0
thf(fact_110_poly__div__mult__right, axiom,
    ((![X : poly_complex, Y : poly_complex, Z : poly_complex]: ((divide1187762952omplex @ X @ (times_1246143675omplex @ Y @ Z)) = (divide1187762952omplex @ (divide1187762952omplex @ X @ Y) @ Z))))). % poly_div_mult_right
thf(fact_111_divide__poly, axiom,
    ((![G : poly_poly_complex, F : poly_poly_complex]: ((~ ((G = zero_z1040703943omplex))) => ((divide350004240omplex @ (times_1460995011omplex @ F @ G) @ G) = F))))). % divide_poly
thf(fact_112_divide__poly, axiom,
    ((![G : poly_complex, F : poly_complex]: ((~ ((G = zero_z1746442943omplex))) => ((divide1187762952omplex @ (times_1246143675omplex @ F @ G) @ G) = F))))). % divide_poly
thf(fact_113_degree__power__eq, axiom,
    ((![P : poly_poly_complex, N : nat]: ((~ ((P = zero_z1040703943omplex))) => ((degree_poly_complex @ (power_432682568omplex @ P @ N)) = (times_times_nat @ N @ (degree_poly_complex @ P))))))). % degree_power_eq
thf(fact_114_degree__power__eq, axiom,
    ((![P : poly_complex, N : nat]: ((~ ((P = zero_z1746442943omplex))) => ((degree_complex @ (power_184595776omplex @ P @ N)) = (times_times_nat @ N @ (degree_complex @ P))))))). % degree_power_eq
thf(fact_115_pderiv_Ocases, axiom,
    ((![X : poly_complex]: (~ ((![A2 : complex, P2 : poly_complex]: (~ ((X = (pCons_complex @ A2 @ P2)))))))))). % pderiv.cases
thf(fact_116_pderiv_Ocases, axiom,
    ((![X : poly_nat]: (~ ((![A2 : nat, P2 : poly_nat]: (~ ((X = (pCons_nat @ A2 @ P2)))))))))). % pderiv.cases
thf(fact_117_pderiv_Ocases, axiom,
    ((![X : poly_poly_complex]: (~ ((![A2 : poly_complex, P2 : poly_poly_complex]: (~ ((X = (pCons_poly_complex @ A2 @ P2)))))))))). % pderiv.cases
thf(fact_118_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A2 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_119_pCons__cases, axiom,
    ((![P : poly_nat]: (~ ((![A2 : nat, Q2 : poly_nat]: (~ ((P = (pCons_nat @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_120_pCons__cases, axiom,
    ((![P : poly_poly_complex]: (~ ((![A2 : poly_complex, Q2 : poly_poly_complex]: (~ ((P = (pCons_poly_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_121_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_122_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_123_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_124_degree__pCons__0, axiom,
    ((![A : complex]: ((degree_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_125_degree__pCons__0, axiom,
    ((![A : nat]: ((degree_nat @ (pCons_nat @ A @ zero_zero_poly_nat)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_126_degree__pCons__0, axiom,
    ((![A : poly_complex]: ((degree_poly_complex @ (pCons_poly_complex @ A @ zero_z1040703943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_127_degree__mult__eq__0, axiom,
    ((![P : poly_nat, Q : poly_nat]: (((degree_nat @ (times_times_poly_nat @ P @ Q)) = zero_zero_nat) = (((P = zero_zero_poly_nat)) | ((((Q = zero_zero_poly_nat)) | ((((~ ((P = zero_zero_poly_nat)))) & ((((~ ((Q = zero_zero_poly_nat)))) & (((((degree_nat @ P) = zero_zero_nat)) & (((degree_nat @ Q) = zero_zero_nat))))))))))))))). % degree_mult_eq_0
thf(fact_128_degree__mult__eq__0, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex]: (((degree_poly_complex @ (times_1460995011omplex @ P @ Q)) = zero_zero_nat) = (((P = zero_z1040703943omplex)) | ((((Q = zero_z1040703943omplex)) | ((((~ ((P = zero_z1040703943omplex)))) & ((((~ ((Q = zero_z1040703943omplex)))) & (((((degree_poly_complex @ P) = zero_zero_nat)) & (((degree_poly_complex @ Q) = zero_zero_nat))))))))))))))). % degree_mult_eq_0
thf(fact_129_degree__mult__eq__0, axiom,
    ((![P : poly_complex, Q : poly_complex]: (((degree_complex @ (times_1246143675omplex @ P @ Q)) = zero_zero_nat) = (((P = zero_z1746442943omplex)) | ((((Q = zero_z1746442943omplex)) | ((((~ ((P = zero_z1746442943omplex)))) & ((((~ ((Q = zero_z1746442943omplex)))) & (((((degree_complex @ P) = zero_zero_nat)) & (((degree_complex @ Q) = zero_zero_nat))))))))))))))). % degree_mult_eq_0
thf(fact_130_mult__right__cancel, axiom,
    ((![C : poly_poly_complex, A : poly_poly_complex, B : poly_poly_complex]: ((~ ((C = zero_z1040703943omplex))) => (((times_1460995011omplex @ A @ C) = (times_1460995011omplex @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_131_mult__right__cancel, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => (((times_1246143675omplex @ A @ C) = (times_1246143675omplex @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_132_mult__right__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_133_mult__right__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_134_mult__left__cancel, axiom,
    ((![C : poly_poly_complex, A : poly_poly_complex, B : poly_poly_complex]: ((~ ((C = zero_z1040703943omplex))) => (((times_1460995011omplex @ C @ A) = (times_1460995011omplex @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_135_mult__left__cancel, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => (((times_1246143675omplex @ C @ A) = (times_1246143675omplex @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_136_mult__left__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_137_mult__left__cancel, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_138_no__zero__divisors, axiom,
    ((![A : poly_nat, B : poly_nat]: ((~ ((A = zero_zero_poly_nat))) => ((~ ((B = zero_zero_poly_nat))) => (~ (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat)))))))). % no_zero_divisors
thf(fact_139_no__zero__divisors, axiom,
    ((![A : poly_poly_complex, B : poly_poly_complex]: ((~ ((A = zero_z1040703943omplex))) => ((~ ((B = zero_z1040703943omplex))) => (~ (((times_1460995011omplex @ A @ B) = zero_z1040703943omplex)))))))). % no_zero_divisors
thf(fact_140_no__zero__divisors, axiom,
    ((![A : poly_complex, B : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((~ ((B = zero_z1746442943omplex))) => (~ (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex)))))))). % no_zero_divisors
thf(fact_141_no__zero__divisors, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((~ ((B = zero_zero_nat))) => (~ (((times_times_nat @ A @ B) = zero_zero_nat)))))))). % no_zero_divisors
thf(fact_142_no__zero__divisors, axiom,
    ((![A : complex, B : complex]: ((~ ((A = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (~ (((times_times_complex @ A @ B) = zero_zero_complex)))))))). % no_zero_divisors
thf(fact_143_divisors__zero, axiom,
    ((![A : poly_nat, B : poly_nat]: (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat) => ((A = zero_zero_poly_nat) | (B = zero_zero_poly_nat)))))). % divisors_zero
thf(fact_144_divisors__zero, axiom,
    ((![A : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A @ B) = zero_z1040703943omplex) => ((A = zero_z1040703943omplex) | (B = zero_z1040703943omplex)))))). % divisors_zero
thf(fact_145_divisors__zero, axiom,
    ((![A : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex) => ((A = zero_z1746442943omplex) | (B = zero_z1746442943omplex)))))). % divisors_zero
thf(fact_146_divisors__zero, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((A = zero_zero_nat) | (B = zero_zero_nat)))))). % divisors_zero
thf(fact_147_divisors__zero, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) => ((A = zero_zero_complex) | (B = zero_zero_complex)))))). % divisors_zero
thf(fact_148_mult__not__zero, axiom,
    ((![A : poly_nat, B : poly_nat]: ((~ (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat))) => ((~ ((A = zero_zero_poly_nat))) & (~ ((B = zero_zero_poly_nat)))))))). % mult_not_zero
thf(fact_149_mult__not__zero, axiom,
    ((![A : poly_poly_complex, B : poly_poly_complex]: ((~ (((times_1460995011omplex @ A @ B) = zero_z1040703943omplex))) => ((~ ((A = zero_z1040703943omplex))) & (~ ((B = zero_z1040703943omplex)))))))). % mult_not_zero
thf(fact_150_mult__not__zero, axiom,
    ((![A : poly_complex, B : poly_complex]: ((~ (((times_1246143675omplex @ A @ B) = zero_z1746442943omplex))) => ((~ ((A = zero_z1746442943omplex))) & (~ ((B = zero_z1746442943omplex)))))))). % mult_not_zero
thf(fact_151_mult__not__zero, axiom,
    ((![A : nat, B : nat]: ((~ (((times_times_nat @ A @ B) = zero_zero_nat))) => ((~ ((A = zero_zero_nat))) & (~ ((B = zero_zero_nat)))))))). % mult_not_zero
thf(fact_152_mult__not__zero, axiom,
    ((![A : complex, B : complex]: ((~ (((times_times_complex @ A @ B) = zero_zero_complex))) => ((~ ((A = zero_zero_complex))) & (~ ((B = zero_zero_complex)))))))). % mult_not_zero
thf(fact_153_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_154_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_155_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_156_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_157_zero__neq__one, axiom,
    ((~ ((zero_z1040703943omplex = one_on1331105667omplex))))). % zero_neq_one
thf(fact_158_divide__divide__eq__left_H, axiom,
    ((![A : complex, B : complex, C : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ A @ B) @ C) = (divide1210191872omplex @ A @ (times_times_complex @ C @ B)))))). % divide_divide_eq_left'
thf(fact_159_divide__divide__times__eq, axiom,
    ((![X : complex, Y : complex, Z : complex, W : complex]: ((divide1210191872omplex @ (divide1210191872omplex @ X @ Y) @ (divide1210191872omplex @ Z @ W)) = (divide1210191872omplex @ (times_times_complex @ X @ W) @ (times_times_complex @ Y @ Z)))))). % divide_divide_times_eq
thf(fact_160_times__divide__times__eq, axiom,
    ((![X : complex, Y : complex, Z : complex, W : complex]: ((times_times_complex @ (divide1210191872omplex @ X @ Y) @ (divide1210191872omplex @ Z @ W)) = (divide1210191872omplex @ (times_times_complex @ X @ Z) @ (times_times_complex @ Y @ W)))))). % times_divide_times_eq
thf(fact_161_pderiv_Oinduct, axiom,
    ((![P3 : poly_complex > $o, A0 : poly_complex]: ((![A2 : complex, P2 : poly_complex]: (((~ ((P2 = zero_z1746442943omplex))) => (P3 @ P2)) => (P3 @ (pCons_complex @ A2 @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_162_pderiv_Oinduct, axiom,
    ((![P3 : poly_nat > $o, A0 : poly_nat]: ((![A2 : nat, P2 : poly_nat]: (((~ ((P2 = zero_zero_poly_nat))) => (P3 @ P2)) => (P3 @ (pCons_nat @ A2 @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_163_pderiv_Oinduct, axiom,
    ((![P3 : poly_poly_complex > $o, A0 : poly_poly_complex]: ((![A2 : poly_complex, P2 : poly_poly_complex]: (((~ ((P2 = zero_z1040703943omplex))) => (P3 @ P2)) => (P3 @ (pCons_poly_complex @ A2 @ P2)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_164_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_complex > $o, P : poly_complex, Q : poly_complex]: ((P3 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A2 : complex, P2 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A2 @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_165_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_nat > $o, P : poly_complex, Q : poly_nat]: ((P3 @ zero_z1746442943omplex @ zero_zero_poly_nat) => ((![A2 : complex, P2 : poly_complex, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A2 @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_166_poly__induct2, axiom,
    ((![P3 : poly_complex > poly_poly_complex > $o, P : poly_complex, Q : poly_poly_complex]: ((P3 @ zero_z1746442943omplex @ zero_z1040703943omplex) => ((![A2 : complex, P2 : poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_complex @ A2 @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_167_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_complex > $o, P : poly_nat, Q : poly_complex]: ((P3 @ zero_zero_poly_nat @ zero_z1746442943omplex) => ((![A2 : nat, P2 : poly_nat, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A2 @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_168_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_nat > $o, P : poly_nat, Q : poly_nat]: ((P3 @ zero_zero_poly_nat @ zero_zero_poly_nat) => ((![A2 : nat, P2 : poly_nat, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A2 @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_169_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_poly_complex > $o, P : poly_nat, Q : poly_poly_complex]: ((P3 @ zero_zero_poly_nat @ zero_z1040703943omplex) => ((![A2 : nat, P2 : poly_nat, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_nat @ A2 @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_170_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_complex > $o, P : poly_poly_complex, Q : poly_complex]: ((P3 @ zero_z1040703943omplex @ zero_z1746442943omplex) => ((![A2 : poly_complex, P2 : poly_poly_complex, B2 : complex, Q2 : poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A2 @ P2) @ (pCons_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_171_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_nat > $o, P : poly_poly_complex, Q : poly_nat]: ((P3 @ zero_z1040703943omplex @ zero_zero_poly_nat) => ((![A2 : poly_complex, P2 : poly_poly_complex, B2 : nat, Q2 : poly_nat]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A2 @ P2) @ (pCons_nat @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_172_poly__induct2, axiom,
    ((![P3 : poly_poly_complex > poly_poly_complex > $o, P : poly_poly_complex, Q : poly_poly_complex]: ((P3 @ zero_z1040703943omplex @ zero_z1040703943omplex) => ((![A2 : poly_complex, P2 : poly_poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P3 @ P2 @ Q2) => (P3 @ (pCons_poly_complex @ A2 @ P2) @ (pCons_poly_complex @ B2 @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_173_mult__poly__0__right, axiom,
    ((![P : poly_nat]: ((times_times_poly_nat @ P @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % mult_poly_0_right
thf(fact_174_mult__poly__0__right, axiom,
    ((![P : poly_poly_complex]: ((times_1460995011omplex @ P @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % mult_poly_0_right
thf(fact_175_mult__poly__0__right, axiom,
    ((![P : poly_complex]: ((times_1246143675omplex @ P @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % mult_poly_0_right
thf(fact_176_mult__poly__0__left, axiom,
    ((![Q : poly_nat]: ((times_times_poly_nat @ zero_zero_poly_nat @ Q) = zero_zero_poly_nat)))). % mult_poly_0_left
thf(fact_177_mult__poly__0__left, axiom,
    ((![Q : poly_poly_complex]: ((times_1460995011omplex @ zero_z1040703943omplex @ Q) = zero_z1040703943omplex)))). % mult_poly_0_left
thf(fact_178_mult__poly__0__left, axiom,
    ((![Q : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ Q) = zero_z1746442943omplex)))). % mult_poly_0_left
thf(fact_179_nonzero__eq__divide__eq, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => ((A = (divide1210191872omplex @ B @ C)) = ((times_times_complex @ A @ C) = B)))))). % nonzero_eq_divide_eq
thf(fact_180_nonzero__divide__eq__eq, axiom,
    ((![C : complex, B : complex, A : complex]: ((~ ((C = zero_zero_complex))) => (((divide1210191872omplex @ B @ C) = A) = (B = (times_times_complex @ A @ C))))))). % nonzero_divide_eq_eq
thf(fact_181_eq__divide__imp, axiom,
    ((![C : complex, A : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A @ C) = B) => (A = (divide1210191872omplex @ B @ C))))))). % eq_divide_imp
thf(fact_182_divide__eq__imp, axiom,
    ((![C : complex, B : complex, A : complex]: ((~ ((C = zero_zero_complex))) => ((B = (times_times_complex @ A @ C)) => ((divide1210191872omplex @ B @ C) = A)))))). % divide_eq_imp
thf(fact_183_eq__divide__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((A = (divide1210191872omplex @ B @ C)) = (((((~ ((C = zero_zero_complex)))) => (((times_times_complex @ A @ C) = B)))) & ((((C = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % eq_divide_eq
thf(fact_184_divide__eq__eq, axiom,
    ((![B : complex, C : complex, A : complex]: (((divide1210191872omplex @ B @ C) = A) = (((((~ ((C = zero_zero_complex)))) => ((B = (times_times_complex @ A @ C))))) & ((((C = zero_zero_complex)) => ((A = zero_zero_complex))))))))). % divide_eq_eq
thf(fact_185_frac__eq__eq, axiom,
    ((![Y : complex, Z : complex, X : complex, W : complex]: ((~ ((Y = zero_zero_complex))) => ((~ ((Z = zero_zero_complex))) => (((divide1210191872omplex @ X @ Y) = (divide1210191872omplex @ W @ Z)) = ((times_times_complex @ X @ Z) = (times_times_complex @ W @ Y)))))))). % frac_eq_eq
thf(fact_186_right__inverse__eq, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => (((divide1210191872omplex @ A @ B) = one_one_complex) = (A = B)))))). % right_inverse_eq
thf(fact_187_pCons__induct, axiom,
    ((![P3 : poly_poly_nat > $o, P : poly_poly_nat]: ((P3 @ zero_z1059985641ly_nat) => ((![A2 : poly_nat, P2 : poly_poly_nat]: (((~ ((A2 = zero_zero_poly_nat))) | (~ ((P2 = zero_z1059985641ly_nat)))) => ((P3 @ P2) => (P3 @ (pCons_poly_nat @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_188_pCons__induct, axiom,
    ((![P3 : poly_p1267267526omplex > $o, P : poly_p1267267526omplex]: ((P3 @ zero_z1200043727omplex) => ((![A2 : poly_poly_complex, P2 : poly_p1267267526omplex]: (((~ ((A2 = zero_z1040703943omplex))) | (~ ((P2 = zero_z1200043727omplex)))) => ((P3 @ P2) => (P3 @ (pCons_1087637536omplex @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_189_pCons__induct, axiom,
    ((![P3 : poly_complex > $o, P : poly_complex]: ((P3 @ zero_z1746442943omplex) => ((![A2 : complex, P2 : poly_complex]: (((~ ((A2 = zero_zero_complex))) | (~ ((P2 = zero_z1746442943omplex)))) => ((P3 @ P2) => (P3 @ (pCons_complex @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_190_pCons__induct, axiom,
    ((![P3 : poly_nat > $o, P : poly_nat]: ((P3 @ zero_zero_poly_nat) => ((![A2 : nat, P2 : poly_nat]: (((~ ((A2 = zero_zero_nat))) | (~ ((P2 = zero_zero_poly_nat)))) => ((P3 @ P2) => (P3 @ (pCons_nat @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_191_pCons__induct, axiom,
    ((![P3 : poly_poly_complex > $o, P : poly_poly_complex]: ((P3 @ zero_z1040703943omplex) => ((![A2 : poly_complex, P2 : poly_poly_complex]: (((~ ((A2 = zero_z1746442943omplex))) | (~ ((P2 = zero_z1040703943omplex)))) => ((P3 @ P2) => (P3 @ (pCons_poly_complex @ A2 @ P2))))) => (P3 @ P)))))). % pCons_induct
thf(fact_192_pCons__one, axiom,
    (((pCons_poly_nat @ one_one_poly_nat @ zero_z1059985641ly_nat) = one_on1411366565ly_nat))). % pCons_one
thf(fact_193_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_194_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_195_pCons__one, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % pCons_one
thf(fact_196_degree__linear__power, axiom,
    ((![A : poly_nat, N : nat]: ((degree_poly_nat @ (power_1336127338ly_nat @ (pCons_poly_nat @ A @ (pCons_poly_nat @ one_one_poly_nat @ zero_z1059985641ly_nat)) @ N)) = N)))). % degree_linear_power
thf(fact_197_degree__linear__power, axiom,
    ((![A : nat, N : nat]: ((degree_nat @ (power_power_poly_nat @ (pCons_nat @ A @ (pCons_nat @ one_one_nat @ zero_zero_poly_nat)) @ N)) = N)))). % degree_linear_power
thf(fact_198_degree__linear__power, axiom,
    ((![A : poly_complex, N : nat]: ((degree_poly_complex @ (power_432682568omplex @ (pCons_poly_complex @ A @ (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex)) @ N)) = N)))). % degree_linear_power
thf(fact_199_degree__linear__power, axiom,
    ((![A : complex, N : nat]: ((degree_complex @ (power_184595776omplex @ (pCons_complex @ A @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex)) @ N)) = N)))). % degree_linear_power
thf(fact_200_div__mult__mult1__if, axiom,
    ((![C : nat, A : nat, B : nat]: (((C = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = zero_zero_nat)) & ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (divide_divide_nat @ A @ B))))))). % div_mult_mult1_if
thf(fact_201_div__mult__mult2, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) = (divide_divide_nat @ A @ B)))))). % div_mult_mult2
thf(fact_202_div__mult__mult1, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (divide_divide_nat @ A @ B)))))). % div_mult_mult1
thf(fact_203_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_204_power__one, axiom,
    ((![N : nat]: ((power_power_poly_nat @ one_one_poly_nat @ N) = one_one_poly_nat)))). % power_one
thf(fact_205_power__one, axiom,
    ((![N : nat]: ((power_184595776omplex @ one_one_poly_complex @ N) = one_one_poly_complex)))). % power_one
thf(fact_206_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_207_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_208__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062p_A_061_A0_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062p_A_092_060noteq_062_A0_059_Adegree_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060And_062n_O_A_092_060lbrakk_062p_A_092_060noteq_062_A0_059_Adegree_Ap_A_061_ASuc_An_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    (((~ ((p = zero_z1746442943omplex))) => (((~ ((p = zero_z1746442943omplex))) => (~ (((degree_complex @ p) = zero_zero_nat)))) => (~ (((~ ((p = zero_z1746442943omplex))) => (![N2 : nat]: (~ (((degree_complex @ p) = (suc @ N2)))))))))))). % \<open>\<And>thesis. \<lbrakk>p = 0 \<Longrightarrow> thesis; \<lbrakk>p \<noteq> 0; degree p = 0\<rbrakk> \<Longrightarrow> thesis; \<And>n. \<lbrakk>p \<noteq> 0; degree p = Suc n\<rbrakk> \<Longrightarrow> thesis\<rbrakk> \<Longrightarrow> thesis\<close>
thf(fact_209_mult_Oright__neutral, axiom,
    ((![A : poly_nat]: ((times_times_poly_nat @ A @ one_one_poly_nat) = A)))). % mult.right_neutral
thf(fact_210_mult_Oright__neutral, axiom,
    ((![A : poly_complex]: ((times_1246143675omplex @ A @ one_one_poly_complex) = A)))). % mult.right_neutral
thf(fact_211_mult_Oright__neutral, axiom,
    ((![A : nat]: ((times_times_nat @ A @ one_one_nat) = A)))). % mult.right_neutral
thf(fact_212_mult_Oright__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ A @ one_one_complex) = A)))). % mult.right_neutral
thf(fact_213_mult_Oleft__neutral, axiom,
    ((![A : poly_nat]: ((times_times_poly_nat @ one_one_poly_nat @ A) = A)))). % mult.left_neutral
thf(fact_214_mult_Oleft__neutral, axiom,
    ((![A : poly_complex]: ((times_1246143675omplex @ one_one_poly_complex @ A) = A)))). % mult.left_neutral
thf(fact_215_mult_Oleft__neutral, axiom,
    ((![A : nat]: ((times_times_nat @ one_one_nat @ A) = A)))). % mult.left_neutral
thf(fact_216_mult_Oleft__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ one_one_complex @ A) = A)))). % mult.left_neutral
thf(fact_217_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_218_power__Suc__0, axiom,
    ((![N : nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ N) = (suc @ zero_zero_nat))))). % power_Suc_0
thf(fact_219_nat__power__eq__Suc__0__iff, axiom,
    ((![X : nat, M : nat]: (((power_power_nat @ X @ M) = (suc @ zero_zero_nat)) = (((M = zero_zero_nat)) | ((X = (suc @ zero_zero_nat)))))))). % nat_power_eq_Suc_0_iff
thf(fact_220_div__by__Suc__0, axiom,
    ((![M : nat]: ((divide_divide_nat @ M @ (suc @ zero_zero_nat)) = M)))). % div_by_Suc_0
thf(fact_221_div__mult2__eq, axiom,
    ((![M : nat, N : nat, Q : nat]: ((divide_divide_nat @ M @ (times_times_nat @ N @ Q)) = (divide_divide_nat @ (divide_divide_nat @ M @ N) @ Q))))). % div_mult2_eq
thf(fact_222_one__eq__mult__iff, axiom,
    ((![M : nat, N : nat]: (((suc @ zero_zero_nat) = (times_times_nat @ M @ N)) = (((M = (suc @ zero_zero_nat))) & ((N = (suc @ zero_zero_nat)))))))). % one_eq_mult_iff
thf(fact_223_mult__eq__1__iff, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = (suc @ zero_zero_nat)) = (((M = (suc @ zero_zero_nat))) & ((N = (suc @ zero_zero_nat)))))))). % mult_eq_1_iff
thf(fact_224_nat__mult__div__cancel__disj, axiom,
    ((![K2 : nat, M : nat, N : nat]: (((K2 = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ K2 @ M) @ (times_times_nat @ K2 @ N)) = zero_zero_nat)) & ((~ ((K2 = zero_zero_nat))) => ((divide_divide_nat @ (times_times_nat @ K2 @ M) @ (times_times_nat @ K2 @ N)) = (divide_divide_nat @ M @ N))))))). % nat_mult_div_cancel_disj
thf(fact_225_nat_Oinject, axiom,
    ((![X2 : nat, Y2 : nat]: (((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))). % nat.inject
thf(fact_226_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_227_mult__is__0, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = zero_zero_nat) = (((M = zero_zero_nat)) | ((N = zero_zero_nat))))))). % mult_is_0
thf(fact_228_mult__0__right, axiom,
    ((![M : nat]: ((times_times_nat @ M @ zero_zero_nat) = zero_zero_nat)))). % mult_0_right
thf(fact_229_mult__cancel1, axiom,
    ((![K2 : nat, M : nat, N : nat]: (((times_times_nat @ K2 @ M) = (times_times_nat @ K2 @ N)) = (((M = N)) | ((K2 = zero_zero_nat))))))). % mult_cancel1
thf(fact_230_mult__cancel2, axiom,
    ((![M : nat, K2 : nat, N : nat]: (((times_times_nat @ M @ K2) = (times_times_nat @ N @ K2)) = (((M = N)) | ((K2 = zero_zero_nat))))))). % mult_cancel2
thf(fact_231_nat__mult__eq__1__iff, axiom,
    ((![M : nat, N : nat]: (((times_times_nat @ M @ N) = one_one_nat) = (((M = one_one_nat)) & ((N = one_one_nat))))))). % nat_mult_eq_1_iff
thf(fact_232_nat__1__eq__mult__iff, axiom,
    ((![M : nat, N : nat]: ((one_one_nat = (times_times_nat @ M @ N)) = (((M = one_one_nat)) & ((N = one_one_nat))))))). % nat_1_eq_mult_iff
thf(fact_233_Suc__inject, axiom,
    ((![X : nat, Y : nat]: (((suc @ X) = (suc @ Y)) => (X = Y))))). % Suc_inject
thf(fact_234_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_235_nat__mult__1__right, axiom,
    ((![N : nat]: ((times_times_nat @ N @ one_one_nat) = N)))). % nat_mult_1_right
thf(fact_236_nat__mult__1, axiom,
    ((![N : nat]: ((times_times_nat @ one_one_nat @ N) = N)))). % nat_mult_1
thf(fact_237_nat_Odistinct_I1_J, axiom,
    ((![X2 : nat]: (~ ((zero_zero_nat = (suc @ X2))))))). % nat.distinct(1)
thf(fact_238_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_239_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_240_nat_OdiscI, axiom,
    ((![Nat : nat, X2 : nat]: ((Nat = (suc @ X2)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_241_nat__induct, axiom,
    ((![P3 : nat > $o, N : nat]: ((P3 @ zero_zero_nat) => ((![N2 : nat]: ((P3 @ N2) => (P3 @ (suc @ N2)))) => (P3 @ N)))))). % nat_induct
thf(fact_242_One__nat__def, axiom,
    ((one_one_nat = (suc @ zero_zero_nat)))). % One_nat_def
thf(fact_243_diff__induct, axiom,
    ((![P3 : nat > nat > $o, M : nat, N : nat]: ((![X3 : nat]: (P3 @ X3 @ zero_zero_nat)) => ((![Y3 : nat]: (P3 @ zero_zero_nat @ (suc @ Y3))) => ((![X3 : nat, Y3 : nat]: ((P3 @ X3 @ Y3) => (P3 @ (suc @ X3) @ (suc @ Y3)))) => (P3 @ M @ N))))))). % diff_induct
thf(fact_244_zero__induct, axiom,
    ((![P3 : nat > $o, K2 : nat]: ((P3 @ K2) => ((![N2 : nat]: ((P3 @ (suc @ N2)) => (P3 @ N2))) => (P3 @ zero_zero_nat)))))). % zero_induct
thf(fact_245_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero

% Conjectures (1)
thf(conj_0, conjecture,
    (((power_184595776omplex @ q @ (degree_complex @ p)) = (times_1246143675omplex @ p @ (pCons_complex @ (divide1210191872omplex @ one_one_complex @ k) @ zero_z1746442943omplex))))).
