% 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_142__5368796_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:27:25.708

% Could-be-implicit typings (5)
thf(ty_n_t__Set__Oset_It__Real__Oreal_J, type,
    set_real : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (31)
thf(sy_c_Complex_Ocomplex_OComplex, type,
    complex2 : real > real > complex).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex, type,
    abs_abs_complex : complex > complex).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
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__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
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__Num__Onum, type,
    times_times_num : num > num > num).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_real : real > real).
thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex, type,
    neg_nu1648888445omplex : complex > complex).
thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal, type,
    neg_numeral_dbl_real : real > real).
thf(sy_c_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex, type,
    numera632737353omplex : num > complex).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > real).
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__Num__Onum, type,
    ord_less_eq_num : num > num > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_x____, type,
    x : real).
thf(sy_v_y____, type,
    y : real).
thf(sy_v_z, type,
    z : complex).

% Relevant facts (212)
thf(fact_0__092_060open_0622_A_K_Ay_A_092_060le_062_A1_092_060close_062, axiom,
    ((ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ y) @ one_one_real))). % \<open>2 * y \<le> 1\<close>
thf(fact_1__092_060open_062_N_A1_A_092_060le_062_A2_A_K_Ay_092_060close_062, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ y)))). % \<open>- 1 \<le> 2 * y\<close>
thf(fact_2__092_060open_0622_A_K_Ax_A_092_060le_062_A1_092_060close_062, axiom,
    ((ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ x) @ one_one_real))). % \<open>2 * x \<le> 1\<close>
thf(fact_3__092_060open_062_N_A1_A_092_060le_062_A2_A_K_Ax_092_060close_062, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ x)))). % \<open>- 1 \<le> 2 * x\<close>
thf(fact_4_numeral__le__one__iff, axiom,
    ((![N : num]: ((ord_less_eq_real @ (numeral_numeral_real @ N) @ one_one_real) = (ord_less_eq_num @ N @ one))))). % numeral_le_one_iff
thf(fact_5_numeral__le__one__iff, axiom,
    ((![N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ N) @ one_one_nat) = (ord_less_eq_num @ N @ one))))). % numeral_le_one_iff
thf(fact_6_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numera632737353omplex @ N) = one_one_complex) = (N = one))))). % numeral_eq_one_iff
thf(fact_7_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_real @ N) = one_one_real) = (N = one))))). % numeral_eq_one_iff
thf(fact_8_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_9_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_complex = (numera632737353omplex @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_10_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_real = (numeral_numeral_real @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_11_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_12_abs__numeral, axiom,
    ((![N : num]: ((abs_abs_real @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ N))))). % abs_numeral
thf(fact_13_abs__1, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_1
thf(fact_14_abs__1, axiom,
    (((abs_abs_complex @ one_one_complex) = one_one_complex))). % abs_1
thf(fact_15_abs__mult__self__eq, axiom,
    ((![A : real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A))))). % abs_mult_self_eq
thf(fact_16_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_17_semiring__norm_I83_J, axiom,
    ((![N : num]: (~ ((one = (bit0 @ N))))))). % semiring_norm(83)
thf(fact_18_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (times_times_real @ (numeral_numeral_real @ W) @ Z)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ V @ W)) @ Z))))). % mult_numeral_left_semiring_numeral
thf(fact_19_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z : nat]: ((times_times_nat @ (numeral_numeral_nat @ V) @ (times_times_nat @ (numeral_numeral_nat @ W) @ Z)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ V @ W)) @ Z))))). % mult_numeral_left_semiring_numeral
thf(fact_20_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z : complex]: ((times_times_complex @ (numera632737353omplex @ V) @ (times_times_complex @ (numera632737353omplex @ W) @ Z)) = (times_times_complex @ (numera632737353omplex @ (times_times_num @ V @ W)) @ Z))))). % mult_numeral_left_semiring_numeral
thf(fact_21_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_22_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_23_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_complex @ (numera632737353omplex @ M) @ (numera632737353omplex @ N)) = (numera632737353omplex @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_24_mult_Oleft__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ one_one_complex @ A) = A)))). % mult.left_neutral
thf(fact_25_mult_Oleft__neutral, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % mult.left_neutral
thf(fact_26_mult_Oleft__neutral, axiom,
    ((![A : nat]: ((times_times_nat @ one_one_nat @ A) = A)))). % mult.left_neutral
thf(fact_27_mult_Oright__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ A @ one_one_complex) = A)))). % mult.right_neutral
thf(fact_28_mult_Oright__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.right_neutral
thf(fact_29_mult_Oright__neutral, axiom,
    ((![A : nat]: ((times_times_nat @ A @ one_one_nat) = A)))). % mult.right_neutral
thf(fact_30_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_31_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_32_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numera632737353omplex @ M) = (numera632737353omplex @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_33_semiring__norm_I87_J, axiom,
    ((![M : num, N : num]: (((bit0 @ M) = (bit0 @ N)) = (M = N))))). % semiring_norm(87)
thf(fact_34_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_35_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_36_neg__equal__iff__equal, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_37_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_38_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_39_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_40_abs__abs, axiom,
    ((![A : complex]: ((abs_abs_complex @ (abs_abs_complex @ A)) = (abs_abs_complex @ A))))). % abs_abs
thf(fact_41_neg__le__iff__le, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ B))))). % neg_le_iff_le
thf(fact_42_mult__minus__right, axiom,
    ((![A : real, B : real]: ((times_times_real @ A @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (times_times_real @ A @ B)))))). % mult_minus_right
thf(fact_43_mult__minus__right, axiom,
    ((![A : complex, B : complex]: ((times_times_complex @ A @ (uminus1204672759omplex @ B)) = (uminus1204672759omplex @ (times_times_complex @ A @ B)))))). % mult_minus_right
thf(fact_44_minus__mult__minus, axiom,
    ((![A : real, B : real]: ((times_times_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (times_times_real @ A @ B))))). % minus_mult_minus
thf(fact_45_minus__mult__minus, axiom,
    ((![A : complex, B : complex]: ((times_times_complex @ (uminus1204672759omplex @ A) @ (uminus1204672759omplex @ B)) = (times_times_complex @ A @ B))))). % minus_mult_minus
thf(fact_46_mult__minus__left, axiom,
    ((![A : real, B : real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (uminus_uminus_real @ (times_times_real @ A @ B)))))). % mult_minus_left
thf(fact_47_mult__minus__left, axiom,
    ((![A : complex, B : complex]: ((times_times_complex @ (uminus1204672759omplex @ A) @ B) = (uminus1204672759omplex @ (times_times_complex @ A @ B)))))). % mult_minus_left
thf(fact_48_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_49_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_50_abs__minus__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus_cancel
thf(fact_51_abs__minus, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus
thf(fact_52_abs__minus, axiom,
    ((![A : complex]: ((abs_abs_complex @ (uminus1204672759omplex @ A)) = (abs_abs_complex @ A))))). % abs_minus
thf(fact_53_semiring__norm_I13_J, axiom,
    ((![M : num, N : num]: ((times_times_num @ (bit0 @ M) @ (bit0 @ N)) = (bit0 @ (bit0 @ (times_times_num @ M @ N))))))). % semiring_norm(13)
thf(fact_54_semiring__norm_I11_J, axiom,
    ((![M : num]: ((times_times_num @ M @ one) = M)))). % semiring_norm(11)
thf(fact_55_semiring__norm_I12_J, axiom,
    ((![N : num]: ((times_times_num @ one @ N) = N)))). % semiring_norm(12)
thf(fact_56_semiring__norm_I71_J, axiom,
    ((![M : num, N : num]: ((ord_less_eq_num @ (bit0 @ M) @ (bit0 @ N)) = (ord_less_eq_num @ M @ N))))). % semiring_norm(71)
thf(fact_57_semiring__norm_I68_J, axiom,
    ((![N : num]: (ord_less_eq_num @ one @ N)))). % semiring_norm(68)
thf(fact_58_mult__minus1__right, axiom,
    ((![Z : real]: ((times_times_real @ Z @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ Z))))). % mult_minus1_right
thf(fact_59_mult__minus1__right, axiom,
    ((![Z : complex]: ((times_times_complex @ Z @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ Z))))). % mult_minus1_right
thf(fact_60_mult__minus1, axiom,
    ((![Z : real]: ((times_times_real @ (uminus_uminus_real @ one_one_real) @ Z) = (uminus_uminus_real @ Z))))). % mult_minus1
thf(fact_61_mult__minus1, axiom,
    ((![Z : complex]: ((times_times_complex @ (uminus1204672759omplex @ one_one_complex) @ Z) = (uminus1204672759omplex @ Z))))). % mult_minus1
thf(fact_62_abs__neg__one, axiom,
    (((abs_abs_real @ (uminus_uminus_real @ one_one_real)) = one_one_real))). % abs_neg_one
thf(fact_63_abs__neg__numeral, axiom,
    ((![N : num]: ((abs_abs_real @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ N))))). % abs_neg_numeral
thf(fact_64_num__double, axiom,
    ((![N : num]: ((times_times_num @ (bit0 @ one) @ N) = (bit0 @ N))))). % num_double
thf(fact_65_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_66_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_67_semiring__norm_I69_J, axiom,
    ((![M : num]: (~ ((ord_less_eq_num @ (bit0 @ M) @ one)))))). % semiring_norm(69)
thf(fact_68_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ one_one_real)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_69_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ one_one_complex)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_70_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_71_Collect__mem__eq, axiom,
    ((![A2 : set_real]: ((collect_real @ (^[X : real]: (member_real @ X @ A2))) = A2)))). % Collect_mem_eq
thf(fact_72_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_73_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus1204672759omplex @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_74_mult__neg__numeral__simps_I1_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ (times_times_num @ M @ N)))))). % mult_neg_numeral_simps(1)
thf(fact_75_mult__neg__numeral__simps_I1_J, axiom,
    ((![M : num, N : num]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (numera632737353omplex @ (times_times_num @ M @ N)))))). % mult_neg_numeral_simps(1)
thf(fact_76_mult__neg__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(2)
thf(fact_77_mult__neg__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ (numera632737353omplex @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(2)
thf(fact_78_mult__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(3)
thf(fact_79_mult__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((times_times_complex @ (numera632737353omplex @ M) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (uminus1204672759omplex @ (numera632737353omplex @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(3)
thf(fact_80_semiring__norm_I170_J, axiom,
    ((![V : num, W : num, Y : real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ V)) @ (times_times_real @ (numeral_numeral_real @ W) @ Y)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ V @ W))) @ Y))))). % semiring_norm(170)
thf(fact_81_semiring__norm_I170_J, axiom,
    ((![V : num, W : num, Y : complex]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ V)) @ (times_times_complex @ (numera632737353omplex @ W) @ Y)) = (times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ (times_times_num @ V @ W))) @ Y))))). % semiring_norm(170)
thf(fact_82_semiring__norm_I171_J, axiom,
    ((![V : num, W : num, Y : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ W)) @ Y)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ V @ W))) @ Y))))). % semiring_norm(171)
thf(fact_83_semiring__norm_I171_J, axiom,
    ((![V : num, W : num, Y : complex]: ((times_times_complex @ (numera632737353omplex @ V) @ (times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ W)) @ Y)) = (times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ (times_times_num @ V @ W))) @ Y))))). % semiring_norm(171)
thf(fact_84_semiring__norm_I172_J, axiom,
    ((![V : num, W : num, Y : real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ V)) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ W)) @ Y)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ V @ W)) @ Y))))). % semiring_norm(172)
thf(fact_85_semiring__norm_I172_J, axiom,
    ((![V : num, W : num, Y : complex]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ V)) @ (times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ W)) @ Y)) = (times_times_complex @ (numera632737353omplex @ (times_times_num @ V @ W)) @ Y))))). % semiring_norm(172)
thf(fact_86_neg__numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (ord_less_eq_num @ N @ M))))). % neg_numeral_le_iff
thf(fact_87_not__neg__one__le__neg__numeral__iff, axiom,
    ((![M : num]: ((~ ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ M))))) = (~ ((M = one))))))). % not_neg_one_le_neg_numeral_iff
thf(fact_88_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_89_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_90_equation__minus__iff, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = (B = (uminus1204672759omplex @ A)))))). % equation_minus_iff
thf(fact_91_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_92_minus__equation__iff, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((uminus1204672759omplex @ B) = A))))). % minus_equation_iff
thf(fact_93_le__num__One__iff, axiom,
    ((![X2 : num]: ((ord_less_eq_num @ X2 @ one) = (X2 = one))))). % le_num_One_iff
thf(fact_94_le__imp__neg__le, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % le_imp_neg_le
thf(fact_95_minus__le__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ A))))). % minus_le_iff
thf(fact_96_le__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A)))))). % le_minus_iff
thf(fact_97_minus__mult__commute, axiom,
    ((![A : real, B : real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ A @ (uminus_uminus_real @ B)))))). % minus_mult_commute
thf(fact_98_minus__mult__commute, axiom,
    ((![A : complex, B : complex]: ((times_times_complex @ (uminus1204672759omplex @ A) @ B) = (times_times_complex @ A @ (uminus1204672759omplex @ B)))))). % minus_mult_commute
thf(fact_99_square__eq__iff, axiom,
    ((![A : real, B : real]: (((times_times_real @ A @ A) = (times_times_real @ B @ B)) = (((A = B)) | ((A = (uminus_uminus_real @ B)))))))). % square_eq_iff
thf(fact_100_square__eq__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ A) = (times_times_complex @ B @ B)) = (((A = B)) | ((A = (uminus1204672759omplex @ B)))))))). % square_eq_iff
thf(fact_101_one__neq__neg__one, axiom,
    ((~ ((one_one_real = (uminus_uminus_real @ one_one_real)))))). % one_neq_neg_one
thf(fact_102_one__neq__neg__one, axiom,
    ((~ ((one_one_complex = (uminus1204672759omplex @ one_one_complex)))))). % one_neq_neg_one
thf(fact_103_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numeral_numeral_real @ M) = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % numeral_neq_neg_numeral
thf(fact_104_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numera632737353omplex @ M) = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % numeral_neq_neg_numeral
thf(fact_105_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (numeral_numeral_real @ N))))))). % neg_numeral_neq_numeral
thf(fact_106_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus1204672759omplex @ (numera632737353omplex @ M)) = (numera632737353omplex @ N))))))). % neg_numeral_neq_numeral
thf(fact_107_abs__eq__iff, axiom,
    ((![X2 : real, Y : real]: (((abs_abs_real @ X2) = (abs_abs_real @ Y)) = (((X2 = Y)) | ((X2 = (uminus_uminus_real @ Y)))))))). % abs_eq_iff
thf(fact_108_mult_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((times_times_real @ B @ (times_times_real @ A @ C)) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.left_commute
thf(fact_109_mult_Oleft__commute, axiom,
    ((![B : nat, A : nat, C : nat]: ((times_times_nat @ B @ (times_times_nat @ A @ C)) = (times_times_nat @ A @ (times_times_nat @ B @ C)))))). % mult.left_commute
thf(fact_110_mult_Ocommute, axiom,
    ((times_times_real = (^[A3 : real]: (^[B2 : real]: (times_times_real @ B2 @ A3)))))). % mult.commute
thf(fact_111_mult_Ocommute, axiom,
    ((times_times_nat = (^[A3 : nat]: (^[B2 : nat]: (times_times_nat @ B2 @ A3)))))). % mult.commute
thf(fact_112_mult_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.assoc
thf(fact_113_mult_Oassoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C)))))). % mult.assoc
thf(fact_114_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_115_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_116_one__reorient, axiom,
    ((![X2 : real]: ((one_one_real = X2) = (X2 = one_one_real))))). % one_reorient
thf(fact_117_one__reorient, axiom,
    ((![X2 : nat]: ((one_one_nat = X2) = (X2 = one_one_nat))))). % one_reorient
thf(fact_118_one__reorient, axiom,
    ((![X2 : complex]: ((one_one_complex = X2) = (X2 = one_one_complex))))). % one_reorient
thf(fact_119_le__minus__one__simps_I2_J, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ one_one_real))). % le_minus_one_simps(2)
thf(fact_120_le__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))))). % le_minus_one_simps(4)
thf(fact_121_not__numeral__le__neg__numeral, axiom,
    ((![M : num, N : num]: (~ ((ord_less_eq_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % not_numeral_le_neg_numeral
thf(fact_122_neg__numeral__le__numeral, axiom,
    ((![M : num, N : num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N))))). % neg_numeral_le_numeral
thf(fact_123_square__eq__1__iff, axiom,
    ((![X2 : real]: (((times_times_real @ X2 @ X2) = one_one_real) = (((X2 = one_one_real)) | ((X2 = (uminus_uminus_real @ one_one_real)))))))). % square_eq_1_iff
thf(fact_124_square__eq__1__iff, axiom,
    ((![X2 : complex]: (((times_times_complex @ X2 @ X2) = one_one_complex) = (((X2 = one_one_complex)) | ((X2 = (uminus1204672759omplex @ one_one_complex)))))))). % square_eq_1_iff
thf(fact_125_numeral__times__minus__swap, axiom,
    ((![W : num, X2 : real]: ((times_times_real @ (numeral_numeral_real @ W) @ (uminus_uminus_real @ X2)) = (times_times_real @ X2 @ (uminus_uminus_real @ (numeral_numeral_real @ W))))))). % numeral_times_minus_swap
thf(fact_126_numeral__times__minus__swap, axiom,
    ((![W : num, X2 : complex]: ((times_times_complex @ (numera632737353omplex @ W) @ (uminus1204672759omplex @ X2)) = (times_times_complex @ X2 @ (uminus1204672759omplex @ (numera632737353omplex @ W))))))). % numeral_times_minus_swap
thf(fact_127_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_real = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % one_neq_neg_numeral
thf(fact_128_one__neq__neg__numeral, axiom,
    ((![N : num]: (~ ((one_one_complex = (uminus1204672759omplex @ (numera632737353omplex @ N)))))))). % one_neq_neg_numeral
thf(fact_129_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numeral_numeral_real @ N) = (uminus_uminus_real @ one_one_real))))))). % numeral_neq_neg_one
thf(fact_130_numeral__neq__neg__one, axiom,
    ((![N : num]: (~ (((numera632737353omplex @ N) = (uminus1204672759omplex @ one_one_complex))))))). % numeral_neq_neg_one
thf(fact_131_abs__ge__minus__self, axiom,
    ((![A : real]: (ord_less_eq_real @ (uminus_uminus_real @ A) @ (abs_abs_real @ A))))). % abs_ge_minus_self
thf(fact_132_abs__le__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) = (((ord_less_eq_real @ A @ B)) & ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B))))))). % abs_le_iff
thf(fact_133_abs__le__D2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ (uminus_uminus_real @ A) @ B))))). % abs_le_D2
thf(fact_134_abs__leI, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) => (ord_less_eq_real @ (abs_abs_real @ A) @ B)))))). % abs_leI
thf(fact_135_not__one__le__neg__numeral, axiom,
    ((![M : num]: (~ ((ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)))))))). % not_one_le_neg_numeral
thf(fact_136_not__numeral__le__neg__one, axiom,
    ((![M : num]: (~ ((ord_less_eq_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ one_one_real))))))). % not_numeral_le_neg_one
thf(fact_137_neg__numeral__le__neg__one, axiom,
    ((![M : num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ one_one_real))))). % neg_numeral_le_neg_one
thf(fact_138_neg__one__le__numeral, axiom,
    ((![M : num]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ M))))). % neg_one_le_numeral
thf(fact_139_neg__numeral__le__one, axiom,
    ((![M : num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ one_one_real)))). % neg_numeral_le_one
thf(fact_140_mult__1s__ring__1_I1_J, axiom,
    ((![B : real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ one)) @ B) = (uminus_uminus_real @ B))))). % mult_1s_ring_1(1)
thf(fact_141_mult__1s__ring__1_I1_J, axiom,
    ((![B : complex]: ((times_times_complex @ (uminus1204672759omplex @ (numera632737353omplex @ one)) @ B) = (uminus1204672759omplex @ B))))). % mult_1s_ring_1(1)
thf(fact_142_mult__1s__ring__1_I2_J, axiom,
    ((![B : real]: ((times_times_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ one))) = (uminus_uminus_real @ B))))). % mult_1s_ring_1(2)
thf(fact_143_mult__1s__ring__1_I2_J, axiom,
    ((![B : complex]: ((times_times_complex @ B @ (uminus1204672759omplex @ (numera632737353omplex @ one))) = (uminus1204672759omplex @ B))))). % mult_1s_ring_1(2)
thf(fact_144_uminus__numeral__One, axiom,
    (((uminus_uminus_real @ (numeral_numeral_real @ one)) = (uminus_uminus_real @ one_one_real)))). % uminus_numeral_One
thf(fact_145_uminus__numeral__One, axiom,
    (((uminus1204672759omplex @ (numera632737353omplex @ one)) = (uminus1204672759omplex @ one_one_complex)))). % uminus_numeral_One
thf(fact_146_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_147_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_nat @ one_one_nat @ one_one_nat))). % le_numeral_extra(4)
thf(fact_148_mult_Ocomm__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ A @ one_one_complex) = A)))). % mult.comm_neutral
thf(fact_149_mult_Ocomm__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.comm_neutral
thf(fact_150_mult_Ocomm__neutral, axiom,
    ((![A : nat]: ((times_times_nat @ A @ one_one_nat) = A)))). % mult.comm_neutral
thf(fact_151_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : complex]: ((times_times_complex @ one_one_complex @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_152_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_153_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : nat]: ((times_times_nat @ one_one_nat @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_154_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_155_abs__le__D1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B))))). % abs_le_D1
thf(fact_156_abs__mult, axiom,
    ((![A : complex, B : complex]: ((abs_abs_complex @ (times_times_complex @ A @ B)) = (times_times_complex @ (abs_abs_complex @ A) @ (abs_abs_complex @ B)))))). % abs_mult
thf(fact_157_abs__mult, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_mult
thf(fact_158_abs__one, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_one
thf(fact_159_one__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ N))))). % one_le_numeral
thf(fact_160_one__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ N))))). % one_le_numeral
thf(fact_161_mult__numeral__1__right, axiom,
    ((![A : real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A)))). % mult_numeral_1_right
thf(fact_162_mult__numeral__1__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A)))). % mult_numeral_1_right
thf(fact_163_mult__numeral__1__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ (numera632737353omplex @ one)) = A)))). % mult_numeral_1_right
thf(fact_164_mult__numeral__1, axiom,
    ((![A : real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A)))). % mult_numeral_1
thf(fact_165_mult__numeral__1, axiom,
    ((![A : nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A)))). % mult_numeral_1
thf(fact_166_mult__numeral__1, axiom,
    ((![A : complex]: ((times_times_complex @ (numera632737353omplex @ one) @ A) = A)))). % mult_numeral_1
thf(fact_167_numeral__One, axiom,
    (((numeral_numeral_real @ one) = one_one_real))). % numeral_One
thf(fact_168_numeral__One, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numeral_One
thf(fact_169_numeral__One, axiom,
    (((numera632737353omplex @ one) = one_one_complex))). % numeral_One
thf(fact_170_dbl__simps_I4_J, axiom,
    (((neg_numeral_dbl_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one)))))). % dbl_simps(4)
thf(fact_171_dbl__simps_I4_J, axiom,
    (((neg_nu1648888445omplex @ (uminus1204672759omplex @ one_one_complex)) = (uminus1204672759omplex @ (numera632737353omplex @ (bit0 @ one)))))). % dbl_simps(4)
thf(fact_172_real__minus__mult__self__le, axiom,
    ((![U : real, X2 : real]: (ord_less_eq_real @ (uminus_uminus_real @ (times_times_real @ U @ U)) @ (times_times_real @ X2 @ X2))))). % real_minus_mult_self_le
thf(fact_173_dbl__simps_I3_J, axiom,
    (((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one))))). % dbl_simps(3)
thf(fact_174_dbl__simps_I3_J, axiom,
    (((neg_nu1648888445omplex @ one_one_complex) = (numera632737353omplex @ (bit0 @ one))))). % dbl_simps(3)
thf(fact_175_z, axiom,
    ((z = (complex2 @ x @ y)))). % z
thf(fact_176_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_177_verit__minus__simplify_I4_J, axiom,
    ((![B : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_178__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_Ay_O_Az_A_061_AComplex_Ax_Ay_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![X3 : real, Y2 : real]: (~ ((z = (complex2 @ X3 @ Y2))))))))). % \<open>\<And>thesis. (\<And>x y. z = Complex x y \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_179_verit__eq__simplify_I8_J, axiom,
    ((![X22 : num, Y22 : num]: (((bit0 @ X22) = (bit0 @ Y22)) = (X22 = Y22))))). % verit_eq_simplify(8)
thf(fact_180_dbl__simps_I5_J, axiom,
    ((![K : num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ K)) = (numeral_numeral_real @ (bit0 @ K)))))). % dbl_simps(5)
thf(fact_181_dbl__simps_I5_J, axiom,
    ((![K : num]: ((neg_nu1648888445omplex @ (numera632737353omplex @ K)) = (numera632737353omplex @ (bit0 @ K)))))). % dbl_simps(5)
thf(fact_182_dbl__simps_I1_J, axiom,
    ((![K : num]: ((neg_numeral_dbl_real @ (uminus_uminus_real @ (numeral_numeral_real @ K))) = (uminus_uminus_real @ (neg_numeral_dbl_real @ (numeral_numeral_real @ K))))))). % dbl_simps(1)
thf(fact_183_dbl__simps_I1_J, axiom,
    ((![K : num]: ((neg_nu1648888445omplex @ (uminus1204672759omplex @ (numera632737353omplex @ K))) = (uminus1204672759omplex @ (neg_nu1648888445omplex @ (numera632737353omplex @ K))))))). % dbl_simps(1)
thf(fact_184_md, axiom,
    (((real_V638595069omplex @ z) = one_one_real))). % md
thf(fact_185_verit__la__disequality, axiom,
    ((![A : real, B : real]: ((A = B) | ((~ ((ord_less_eq_real @ A @ B))) | (~ ((ord_less_eq_real @ B @ A)))))))). % verit_la_disequality
thf(fact_186_verit__la__disequality, axiom,
    ((![A : num, B : num]: ((A = B) | ((~ ((ord_less_eq_num @ A @ B))) | (~ ((ord_less_eq_num @ B @ A)))))))). % verit_la_disequality
thf(fact_187_verit__la__disequality, axiom,
    ((![A : nat, B : nat]: ((A = B) | ((~ ((ord_less_eq_nat @ A @ B))) | (~ ((ord_less_eq_nat @ B @ A)))))))). % verit_la_disequality
thf(fact_188_verit__negate__coefficient_I3_J, axiom,
    ((![A : real, B : real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B)))))). % verit_negate_coefficient(3)
thf(fact_189_complete__real, axiom,
    ((![S : set_real]: ((?[X4 : real]: (member_real @ X4 @ S)) => ((?[Z2 : real]: (![X3 : real]: ((member_real @ X3 @ S) => (ord_less_eq_real @ X3 @ Z2)))) => (?[Y2 : real]: ((![X4 : real]: ((member_real @ X4 @ S) => (ord_less_eq_real @ X4 @ Y2))) & (![Z2 : real]: ((![X3 : real]: ((member_real @ X3 @ S) => (ord_less_eq_real @ X3 @ Z2))) => (ord_less_eq_real @ Y2 @ Z2)))))))))). % complete_real
thf(fact_190_verit__eq__simplify_I10_J, axiom,
    ((![X22 : num]: (~ ((one = (bit0 @ X22))))))). % verit_eq_simplify(10)
thf(fact_191_complex_Oinject, axiom,
    ((![X1 : real, X22 : real, Y1 : real, Y22 : real]: (((complex2 @ X1 @ X22) = (complex2 @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % complex.inject
thf(fact_192_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_193_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_194_that_I1_J, axiom,
    ((ord_less_eq_real @ one_one_real @ (real_V638595069omplex @ (plus_plus_complex @ z @ one_one_complex))))). % that(1)
thf(fact_195_that_I2_J, axiom,
    ((ord_less_eq_real @ one_one_real @ (real_V638595069omplex @ (minus_minus_complex @ z @ one_one_complex))))). % that(2)
thf(fact_196_complex__mod__minus__le__complex__mod, axiom,
    ((![X2 : complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V638595069omplex @ X2)) @ (real_V638595069omplex @ X2))))). % complex_mod_minus_le_complex_mod
thf(fact_197_mult__le__mono2, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (times_times_nat @ K @ I) @ (times_times_nat @ K @ J)))))). % mult_le_mono2
thf(fact_198_mult__le__mono1, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (times_times_nat @ I @ K) @ (times_times_nat @ J @ K)))))). % mult_le_mono1
thf(fact_199_mult__le__mono, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ K @ L) => (ord_less_eq_nat @ (times_times_nat @ I @ K) @ (times_times_nat @ J @ L))))))). % mult_le_mono
thf(fact_200_le__square, axiom,
    ((![M : nat]: (ord_less_eq_nat @ M @ (times_times_nat @ M @ M))))). % le_square
thf(fact_201_le__cube, axiom,
    ((![M : nat]: (ord_less_eq_nat @ M @ (times_times_nat @ M @ (times_times_nat @ M @ M)))))). % le_cube
thf(fact_202_nat__mult__1__right, axiom,
    ((![N : nat]: ((times_times_nat @ N @ one_one_nat) = N)))). % nat_mult_1_right
thf(fact_203_nat__mult__1, axiom,
    ((![N : nat]: ((times_times_nat @ one_one_nat @ N) = N)))). % nat_mult_1
thf(fact_204_complex_Oexhaust, axiom,
    ((![Y : complex]: (~ ((![X12 : real, X23 : real]: (~ ((Y = (complex2 @ X12 @ X23)))))))))). % complex.exhaust
thf(fact_205_complex__minus, axiom,
    ((![A : real, B : real]: ((uminus1204672759omplex @ (complex2 @ A @ B)) = (complex2 @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)))))). % complex_minus
thf(fact_206_norm__mult__numeral2, axiom,
    ((![A : real, W : num]: ((real_V646646907m_real @ (times_times_real @ A @ (numeral_numeral_real @ W))) = (times_times_real @ (real_V646646907m_real @ A) @ (numeral_numeral_real @ W)))))). % norm_mult_numeral2
thf(fact_207_norm__mult__numeral2, axiom,
    ((![A : complex, W : num]: ((real_V638595069omplex @ (times_times_complex @ A @ (numera632737353omplex @ W))) = (times_times_real @ (real_V638595069omplex @ A) @ (numeral_numeral_real @ W)))))). % norm_mult_numeral2
thf(fact_208_norm__mult__numeral1, axiom,
    ((![W : num, A : real]: ((real_V646646907m_real @ (times_times_real @ (numeral_numeral_real @ W) @ A)) = (times_times_real @ (numeral_numeral_real @ W) @ (real_V646646907m_real @ A)))))). % norm_mult_numeral1
thf(fact_209_norm__mult__numeral1, axiom,
    ((![W : num, A : complex]: ((real_V638595069omplex @ (times_times_complex @ (numera632737353omplex @ W) @ A)) = (times_times_real @ (numeral_numeral_real @ W) @ (real_V638595069omplex @ A)))))). % norm_mult_numeral1
thf(fact_210_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_211_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

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (abs_abs_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ x)) @ one_one_real))).
