% 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_667__5374526_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:32:00.963

% Could-be-implicit typings (4)
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (26)
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_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    minus_174331535omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    plus_p1547158847omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
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__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Modules_Oadditive_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    additi1900403525omplex : (complex > complex) > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_v_c____, type,
    c : complex).
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_x____, type,
    x : complex).
thf(sy_v_y____, type,
    y : complex).

% Relevant facts (129)
thf(fact_0_nc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ p)))))). % nc
thf(fact_1_th, axiom,
    ((![X : complex]: ((poly_complex2 @ q @ (minus_minus_complex @ X @ c)) = (poly_complex2 @ pa @ X))))). % th
thf(fact_2_less_Oprems, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ pa)))))). % less.prems
thf(fact_3_that, axiom,
    ((fundam1158420650omplex @ (poly_complex2 @ q)))). % that
thf(fact_4_q_I1_J, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ pa)))). % q(1)
thf(fact_5_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_6_q_I2_J, axiom,
    ((![X : complex]: ((poly_complex2 @ q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))). % q(2)
thf(fact_7__092_060open_062poly_Ap_Ax_A_061_Apoly_Aq_A_Ix_A_N_Ac_J_092_060close_062, axiom,
    (((poly_complex2 @ pa @ x) = (poly_complex2 @ q @ (minus_minus_complex @ x @ c))))). % \<open>poly p x = poly q (x - c)\<close>
thf(fact_8__092_060open_062poly_Aq_A_Ix_A_N_Ac_J_A_061_Apoly_Aq_A_Iy_A_N_Ac_J_092_060close_062, axiom,
    (((poly_complex2 @ q @ (minus_minus_complex @ x @ c)) = (poly_complex2 @ q @ (minus_minus_complex @ y @ c))))). % \<open>poly q (x - c) = poly q (y - c)\<close>
thf(fact_9_calculation, axiom,
    (((poly_complex2 @ pa @ x) = (poly_complex2 @ q @ (minus_minus_complex @ y @ c))))). % calculation
thf(fact_10_poly__diff, axiom,
    ((![P : poly_complex, Q : poly_complex, X2 : complex]: ((poly_complex2 @ (minus_174331535omplex @ P @ Q) @ X2) = (minus_minus_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q @ X2)))))). % poly_diff
thf(fact_11_c, axiom,
    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ c)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % c
thf(fact_12__092_060open_062_092_060exists_062q_O_Apsize_Aq_A_061_Apsize_Ap_A_092_060and_062_A_I_092_060forall_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_092_060close_062, axiom,
    ((?[Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ pa)) & (![X : complex]: ((poly_complex2 @ Q2 @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))))). % \<open>\<exists>q. psize q = psize p \<and> (\<forall>x. poly q x = poly p (c + x))\<close>
thf(fact_13__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062q_O_A_092_060lbrakk_062psize_Aq_A_061_Apsize_Ap_059_A_092_060forall_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ pa)) => (~ ((![X : complex]: ((poly_complex2 @ Q2 @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))))))))). % \<open>\<And>thesis. (\<And>q. \<lbrakk>psize q = psize p; \<forall>x. poly q x = poly p (c + x)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_14_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_15_diff__eq__diff__eq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: (((minus_minus_complex @ A @ B) = (minus_minus_complex @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_16_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ C) @ B) = (minus_minus_complex @ (minus_minus_complex @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_O_A_092_060forall_062w_O_Acmod_A_Ipoly_Ap_Ac_J_A_092_060le_062_Acmod_A_Ipoly_Ap_Aw_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![C2 : complex]: (~ ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ C2)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W))))))))))). % \<open>\<And>thesis. (\<And>c. \<forall>w. cmod (poly p c) \<le> cmod (poly p w) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_18_less_Ohyps, axiom,
    ((![P : poly_complex]: ((ord_less_nat @ (fundam1709708056omplex @ P) @ (fundam1709708056omplex @ pa)) => ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex))))))). % less.hyps
thf(fact_19_additive_Odiff, axiom,
    ((![F : complex > complex, X2 : complex, Y : complex]: ((additi1900403525omplex @ F) => ((F @ (minus_minus_complex @ X2 @ Y)) = (minus_minus_complex @ (F @ X2) @ (F @ Y))))))). % additive.diff
thf(fact_20_add__left__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_21_add__right__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_22_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_23_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_24_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_25_add__cancel__left__left, axiom,
    ((![B : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) = (B = zero_zero_complex))))). % add_cancel_left_left
thf(fact_26_add__cancel__left__right, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex))))). % add_cancel_left_right
thf(fact_27_add__cancel__right__left, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex))))). % add_cancel_right_left
thf(fact_28_add__cancel__right__right, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex))))). % add_cancel_right_right
thf(fact_29_add__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_left
thf(fact_30_add__le__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_right
thf(fact_31_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_32_diff__zero, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_zero
thf(fact_33_diff__0__right, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A)))). % diff_0_right
thf(fact_34_diff__self, axiom,
    ((![A : complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex)))). % diff_self
thf(fact_35_add__less__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ B))))). % add_less_cancel_left
thf(fact_36_add__less__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_nat @ A @ B))))). % add_less_cancel_right
thf(fact_37_add__diff__cancel__right_H, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_38_add__diff__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ C) @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_right
thf(fact_39_add__diff__cancel__left_H, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_40_add__diff__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ C @ A) @ (plus_plus_complex @ C @ B)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_left
thf(fact_41_diff__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_42_add__diff__cancel, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_43_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_44_poly__add, axiom,
    ((![P : poly_complex, Q : poly_complex, X2 : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P @ Q) @ X2) = (plus_plus_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q @ X2)))))). % poly_add
thf(fact_45_add__le__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel1
thf(fact_46_add__le__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel2
thf(fact_47_le__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel1
thf(fact_48_le__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel2
thf(fact_49_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_50_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_51_add__less__same__cancel1, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ B) = (ord_less_nat @ A @ zero_zero_nat))))). % add_less_same_cancel1
thf(fact_52_add__less__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat))))). % add_less_same_cancel2
thf(fact_53_less__add__same__cancel1, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B))))). % less_add_same_cancel1
thf(fact_54_less__add__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B))))). % less_add_same_cancel2
thf(fact_55_diff__ge__0__iff__ge, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_56_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_57_add__mono__thms__linordered__field_I5_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_nat @ I @ J) & (ord_less_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(5)
thf(fact_58_add__mono__thms__linordered__field_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (ord_less_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(4)
thf(fact_59_add__mono__thms__linordered__field_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(4)
thf(fact_60_add__mono__thms__linordered__field_I3_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_nat @ I @ J) & (ord_less_eq_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(3)
thf(fact_61_add__mono__thms__linordered__field_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(3)
thf(fact_62_add__mono__thms__linordered__field_I2_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (ord_less_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(2)
thf(fact_63_add__mono__thms__linordered__field_I1_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_nat @ I @ J) & (K = L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(1)
thf(fact_64_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (K = L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_65_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_66_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_67_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_68_additive_Oadd, axiom,
    ((![F : complex > complex, X2 : complex, Y : complex]: ((additi1900403525omplex @ F) => ((F @ (plus_plus_complex @ X2 @ Y)) = (plus_plus_complex @ (F @ X2) @ (F @ Y))))))). % additive.add
thf(fact_69_additive__def, axiom,
    ((additi1900403525omplex = (^[F2 : complex > complex]: (![X3 : complex]: (![Y2 : complex]: ((F2 @ (plus_plus_complex @ X3 @ Y2)) = (plus_plus_complex @ (F2 @ X3) @ (F2 @ Y2))))))))). % additive_def
thf(fact_70_additive_Ozero, axiom,
    ((![F : complex > complex]: ((additi1900403525omplex @ F) => ((F @ zero_zero_complex) = zero_zero_complex))))). % additive.zero
thf(fact_71_additive_Ointro, axiom,
    ((![F : complex > complex]: ((![X4 : complex, Y3 : complex]: ((F @ (plus_plus_complex @ X4 @ Y3)) = (plus_plus_complex @ (F @ X4) @ (F @ Y3)))) => (additi1900403525omplex @ F))))). % additive.intro
thf(fact_72_group__cancel_Oadd1, axiom,
    ((![A2 : complex, K : complex, A : complex, B : complex]: ((A2 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A2 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_73_group__cancel_Oadd2, axiom,
    ((![B2 : complex, K : complex, B : complex, A : complex]: ((B2 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B2) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_74_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_75_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_76_add_Oassoc, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.assoc
thf(fact_77_add_Oleft__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_78_add_Oright__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_79_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A3 : complex]: (^[B3 : complex]: (plus_plus_complex @ B3 @ A3)))))). % add.commute
thf(fact_80_diff__le__eq, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B)))))). % diff_le_eq
thf(fact_81_le__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) = (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))))). % le_diff_eq
thf(fact_82_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_83_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_84_add_Oleft__commute, axiom,
    ((![B : complex, A : complex, C : complex]: ((plus_plus_complex @ B @ (plus_plus_complex @ A @ C)) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.left_commute
thf(fact_85_add__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_mono
thf(fact_86_add__neg__neg, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_neg_neg
thf(fact_87_add__pos__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_pos_pos
thf(fact_88_add__left__imp__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_89_canonically__ordered__monoid__add__class_OlessE, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((![C2 : nat]: ((B = (plus_plus_nat @ A @ C2)) => (C2 = zero_zero_nat))))))))). % canonically_ordered_monoid_add_class.lessE
thf(fact_90_add__right__imp__eq, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_91_le__iff__diff__le__0, axiom,
    ((ord_less_eq_real = (^[A3 : real]: (^[B3 : real]: (ord_less_eq_real @ (minus_minus_real @ A3 @ B3) @ zero_zero_real)))))). % le_iff_diff_le_0
thf(fact_92_add__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_left_mono
thf(fact_93_add__decreasing, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_94_add__increasing, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing
thf(fact_95_add__neg__nonpos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_neg_nonpos
thf(fact_96_add__neg__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_neg_nonpos
thf(fact_97_add__nonneg__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_nonneg_pos
thf(fact_98_add__nonneg__pos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_pos
thf(fact_99_add__nonpos__neg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_nonpos_neg
thf(fact_100_add__nonpos__neg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_neg
thf(fact_101_add__pos__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_pos_nonneg
thf(fact_102_add__pos__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_pos_nonneg
thf(fact_103_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_104_add__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_right_mono
thf(fact_105_add__decreasing2, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ C @ zero_zero_real) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_106_add__increasing2, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing2
thf(fact_107_add__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_108_add__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_nonpos
thf(fact_109_add__nonneg__eq__0__iff, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X2) => ((ord_less_eq_real @ zero_zero_real @ Y) => (((plus_plus_real @ X2 @ Y) = zero_zero_real) = (((X2 = zero_zero_real)) & ((Y = zero_zero_real))))))))). % add_nonneg_eq_0_iff
thf(fact_110_add__nonpos__eq__0__iff, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ zero_zero_real) => ((ord_less_eq_real @ Y @ zero_zero_real) => (((plus_plus_real @ X2 @ Y) = zero_zero_real) = (((X2 = zero_zero_real)) & ((Y = zero_zero_real))))))))). % add_nonpos_eq_0_iff
thf(fact_111_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_112_pos__add__strict, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))))))). % pos_add_strict
thf(fact_113_add__strict__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_strict_mono
thf(fact_114_add__le__less__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_le_less_mono
thf(fact_115_add__le__less__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_le_less_mono
thf(fact_116_add__less__le__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_less_le_mono
thf(fact_117_add__less__le__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_less_le_mono
thf(fact_118_gr__implies__not__zero, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_119_add__le__imp__le__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_left
thf(fact_120_add__le__imp__le__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_right
thf(fact_121_add__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)))))). % add_strict_left_mono
thf(fact_122_add__strict__increasing, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))))))). % add_strict_increasing
thf(fact_123_add__strict__increasing, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C))))))). % add_strict_increasing
thf(fact_124_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_125_add__strict__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)))))). % add_strict_right_mono
thf(fact_126_add__strict__increasing2, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))))))). % add_strict_increasing2
thf(fact_127_add__strict__increasing2, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C))))))). % add_strict_increasing2
thf(fact_128_add__less__imp__less__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ B))))). % add_less_imp_less_left

% Conjectures (1)
thf(conj_0, conjecture,
    (((poly_complex2 @ q @ (minus_minus_complex @ y @ c)) = (poly_complex2 @ pa @ y)))).
