% Mizar problem: t3_csspace3,csspace3,300,5 
include('Axioms/SET010^0.ax').
thf(n0_type, type, 0: $i).
thf(n1_type, type, 1: $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_nat_1_type, type, k1_nat_1: $i > $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_seq_2_type, type, k1_seq_2: $i > $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_numbers_type, type, k2_numbers: $i).
thf(k2_series_1_type, type, k2_series_1: $i > $i).
thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k3_funct_2_type, type, k3_funct_2: $i > $i > $i > $i > $i).
thf(k3_numbers_type, type, k3_numbers: $i).
thf(k3_series_1_type, type, k3_series_1: $i > $i).
thf(k4_numbers_type, type, k4_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_series_1_type, type, k4_series_1: $i > $i).
thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $i > $i).
thf(k54_valued_1_type, type, k54_valued_1: $i > $i).
thf(k55_valued_1_type, type, k55_valued_1: $i > $i > $i > $i).
thf(k5_complex1_type, type, k5_complex1: $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k5_ordinal1_type, type, k5_ordinal1: $i).
thf(k6_xcmplx_0_type, type, k6_xcmplx_0: $i > $i > $i).
thf(k9_complex1_type, type, k9_complex1: $i > $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
thf(r2_tarski_type, type, r2_tarski: $i > $i > $o).
thf(v10_ordinal1_type, type, v10_ordinal1: $i > $o).
thf(v1_comseq_2_type, type, v1_comseq_2: $i > $o).
thf(v1_finset_1_type, type, v1_finset_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o).
thf(v1_int_1_type, type, v1_int_1: $i > $o).
thf(v1_membered_type, type, v1_membered: $i > $o).
thf(v1_ordinal1_type, type, v1_ordinal1: $i > $o).
thf(v1_partfun1_type, type, v1_partfun1: $i > $i > $o).
thf(v1_rat_1_type, type, v1_rat_1: $i > $o).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_seq_2_type, type, v1_seq_2: $i > $o).
thf(v1_series_1_type, type, v1_series_1: $i > $o).
thf(v1_setfam_1_type, type, v1_setfam_1: $i > $o).
thf(v1_subset_1_type, type, v1_subset_1: $i > $i > $o).
thf(v1_valued_0_type, type, v1_valued_0: $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_comseq_2_type, type, v2_comseq_2: $i > $o).
thf(v2_comseq_3_type, type, v2_comseq_3: $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_seq_2_type, type, v2_seq_2: $i > $o).
thf(v2_valued_0_type, type, v2_valued_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_valued_0_type, type, v3_valued_0: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(v4_membered_type, type, v4_membered: $i > $o).
thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o).
thf(v4_valued_0_type, type, v4_valued_0: $i > $o).
thf(v5_membered_type, type, v5_membered: $i > $o).
thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o).
thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o).
thf(v5_valued_0_type, type, v5_valued_0: $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v6_valued_0_type, type, v6_valued_0: $i > $o).
thf(v7_membered_type, type, v7_membered: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_valued_0_type, type, v7_valued_0: $i > $o).
thf(v8_ordinal1_type, type, v8_ordinal1: $i > $o).
thf(v8_valued_0_type, type, v8_valued_0: $i > $o).
thf(v9_ordinal1_type, type, v9_ordinal1: $i > $o).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(asymmetry_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ~ ( ( (r2_tarski @ B)  @ A) ) ) ) , file(tarski, r2_tarski)).
thf(cc10_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_int_1 @ B) ) ) ) ) , file(membered, cc10_membered)).
thf(cc10_ordinal1, axiom,  (! [A: $i] :  ( (v6_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1)).
thf(cc10_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_valued_0 @ B) ) ) ) ) , file(valued_0, cc10_valued_0)).
thf(cc11_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc11_membered)).
thf(cc11_ordinal1, axiom,  (! [A: $i] :  ( (v8_ordinal1 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc11_ordinal1)).
thf(cc11_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_valued_0 @ B) ) ) ) ) , file(valued_0, cc11_valued_0)).
thf(cc12_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_membered @ A) ) ) , file(membered, cc12_membered)).
thf(cc12_ordinal1, axiom,  (! [A: $i] :  ( (v8_ordinal1 @ A)  =>  (v1_zfmisc_1 @ A) ) ) , file(ordinal1, cc12_ordinal1)).
thf(cc12_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_valued_0 @ B) ) ) ) ) , file(valued_0, cc12_valued_0)).
thf(cc13_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_membered @ B) ) ) ) ) , file(membered, cc13_membered)).
thf(cc13_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  ~ ( (v8_ordinal1 @ A) ) ) ) , file(ordinal1, cc13_ordinal1)).
thf(cc13_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k3_numbers) ) ) ) ) , file(valued_0, cc13_valued_0)).
thf(cc14_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_membered @ B) ) ) ) ) , file(membered, cc14_membered)).
thf(cc14_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc14_ordinal1)).
thf(cc14_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k4_numbers) ) ) ) ) , file(valued_0, cc14_valued_0)).
thf(cc15_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_membered @ B) ) ) ) ) , file(membered, cc15_membered)).
thf(cc15_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v9_ordinal1 @ A) ) ) ) , file(ordinal1, cc15_ordinal1)).
thf(cc15_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_0, cc15_valued_0)).
thf(cc16_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_membered @ B) ) ) ) ) , file(membered, cc16_membered)).
thf(cc16_ordinal1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v10_ordinal1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ~ ( (v8_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, cc16_ordinal1)).
thf(cc16_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_valued_0 @ C) ) ) ) ) , file(valued_0, cc16_valued_0)).
thf(cc17_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_membered @ B) ) ) ) ) , file(membered, cc17_membered)).
thf(cc17_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v10_ordinal1 @ A) )  =>  (v1_setfam_1 @ A) ) ) , file(ordinal1, cc17_ordinal1)).
thf(cc17_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v2_valued_0 @ C) ) ) ) ) , file(valued_0, cc17_valued_0)).
thf(cc18_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_membered @ B) ) ) ) ) , file(membered, cc18_membered)).
thf(cc18_ordinal1, axiom,  (! [A: $i] :  ( (v10_ordinal1 @ A)  =>  ~ ( (v1_setfam_1 @ A) ) ) ) , file(ordinal1, cc18_ordinal1)).
thf(cc18_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v3_valued_0 @ C) ) ) ) ) , file(valued_0, cc18_valued_0)).
thf(cc19_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_membered @ A) ) ) , file(membered, cc19_membered)).
thf(cc19_ordinal1, axiom,  (! [A: $i] :  ( (v1_setfam_1 @ A)  =>  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc19_ordinal1)).
thf(cc19_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k3_numbers) ) ) ) ) , file(valued_0, cc19_valued_0)).
thf(cc1_comseq_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k2_numbers) ) )  =>  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  (v2_comseq_2 @ A) ) )  =>  ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  (v1_comseq_2 @ A) ) ) ) ) ) , file(comseq_2, cc1_comseq_2)).
thf(cc1_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_partfun1 @ C)  @ A)  =>  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) , file(funct_2, cc1_funct_2)).
thf(cc1_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (v5_membered @ A) ) ) , file(membered, cc1_membered)).
thf(cc1_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)).
thf(cc1_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1)).
thf(cc1_seq_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_comseq_2 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v1_seq_2 @ A)  &  (v2_seq_2 @ A) ) ) ) ) ) ) , file(seq_2, cc1_seq_2)).
thf(cc1_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_xboole_0 @ B) ) ) ) ) , file(subset_1, cc1_subset_1)).
thf(cc1_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) ) ) ) , file(valued_0, cc1_valued_0)).
thf(cc1_xcmplx_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc1_xcmplx_0)).
thf(cc1_xreal_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)).
thf(cc20_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (v10_ordinal1 @ A) ) ) , file(ordinal1, cc20_ordinal1)).
thf(cc20_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k4_numbers) ) ) ) ) , file(valued_0, cc20_valued_0)).
thf(cc21_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v4_valued_0 @ C) ) ) ) ) , file(valued_0, cc21_valued_0)).
thf(cc22_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_zfmisc_1 @ A)  &  (v2_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) ) ) ) ) , file(valued_0, cc22_valued_0)).
thf(cc23_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v7_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc23_valued_0)).
thf(cc24_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc24_valued_0)).
thf(cc28_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k2_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) ) ) ) , file(valued_0, cc28_valued_0)).
thf(cc2_comseq_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k2_numbers) ) )  =>  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  ~ ( (v1_comseq_2 @ A) ) ) )  =>  ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  ~ ( (v2_comseq_2 @ A) ) ) ) ) ) ) , file(comseq_2, cc2_comseq_2)).
thf(cc2_funct_2, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc2_funct_2)).
thf(cc2_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (v4_membered @ A) ) ) , file(membered, cc2_membered)).
thf(cc2_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) )  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)).
thf(cc2_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relset_1, cc2_relset_1)).
thf(cc2_seq_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v1_seq_2 @ A)  &  (v2_seq_2 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_comseq_2 @ A) ) ) ) ) ) , file(seq_2, cc2_seq_2)).
thf(cc2_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( ~ ( ( (v1_subset_1 @ B)  @ A) )  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) ) , file(subset_1, cc2_subset_1)).
thf(cc2_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc2_valued_0)).
thf(cc2_xcmplx_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc2_xcmplx_0)).
thf(cc2_xreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0)).
thf(cc30_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k1_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc30_valued_0)).
thf(cc31_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_ordinal1) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0)).
thf(cc3_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc3_funct_2)).
thf(cc3_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (v3_membered @ A) ) ) , file(membered, cc3_membered)).
thf(cc3_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)).
thf(cc3_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc3_relset_1)).
thf(cc3_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc3_subset_1)).
thf(cc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc3_valued_0)).
thf(cc3_xcmplx_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k2_numbers)  =>  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc3_xcmplx_0)).
thf(cc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)).
thf(cc4_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  =>  ( (v1_partfun1 @ B)  @ A) ) ) ) ) , file(funct_2, cc4_funct_2)).
thf(cc4_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v2_membered @ A) ) ) , file(membered, cc4_membered)).
thf(cc4_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1)).
thf(cc4_seq_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) )  =>  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  (v2_comseq_2 @ A) ) )  =>  ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  (v1_comseq_2 @ A) ) ) ) ) ) , file(seq_2, cc4_seq_2)).
thf(cc4_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc4_subset_1)).
thf(cc4_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc4_valued_0)).
thf(cc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc5_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  =>  ( (v1_partfun1 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) ) , file(funct_2, cc5_funct_2)).
thf(cc5_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v1_membered @ A) ) ) , file(membered, cc5_membered)).
thf(cc5_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
thf(cc5_subset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_zfmisc_1 @ B) ) ) ) ) , file(subset_1, cc5_subset_1)).
thf(cc5_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) ) ) ) , file(valued_0, cc5_valued_0)).
thf(cc6_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc6_membered)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) ) ) ) , file(valued_0, cc6_valued_0)).
thf(cc7_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc7_membered)).
thf(cc7_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc7_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc7_valued_0)).
thf(cc8_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc8_membered)).
thf(cc8_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc8_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc8_valued_0)).
thf(cc9_funct_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, cc9_funct_2)).
thf(cc9_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_rat_1 @ B) ) ) ) ) , file(membered, cc9_membered)).
thf(cc9_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1)).
thf(cc9_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0)).
thf(commutativity_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k4_ordinal1) )  =>  ( (= @  ( (k1_nat_1 @ A)  @ B) )  @  ( (k1_nat_1 @ B)  @ A) ) ) ) , file(nat_1, k1_nat_1)).
thf(commutativity_k2_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xcmplx_0, k2_xcmplx_0)).
thf(connectedness_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( ( (r1_xxreal_0 @ A)  @ B)  |  ( (r1_xxreal_0 @ B)  @ A) ) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(d1_absvalue, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( ( ( (r1_xxreal_0 @ k5_numbers)  @ A)  =>  ( (= @  (k9_complex1 @ A) )  @ A) )  &  ( ~ ( ( (r1_xxreal_0 @ k5_numbers)  @ A) )  =>  ( (= @  (k9_complex1 @ A) )  @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(absvalue, d1_absvalue)).
thf(d1_series_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ( (v1_partfun1 @ A)  @ k4_ordinal1)  &  (v1_valued_0 @ A) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k4_ordinal1)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ k4_ordinal1)  &  (v1_valued_0 @ B) ) ) ) )  =>  ( ( (= @ B)  @  (k2_series_1 @ A) )  <=>  ( ( (= @  ( (k1_funct_1 @ B)  @ k5_numbers) )  @  ( (k1_funct_1 @ A)  @ k5_numbers) )  &  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  ( (= @  ( (k1_funct_1 @ B)  @  ( (k1_nat_1 @ C)  @ 1) ) )  @  ( (k2_xcmplx_0 @  ( (k1_funct_1 @ B)  @ C) )  @  ( (k1_funct_1 @ A)  @  ( (k1_nat_1 @ C)  @ 1) ) ) ) ) ) ) ) ) ) ) ) , file(series_1, d1_series_1)).
thf(d2_series_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) )  =>  ( (v1_series_1 @ A)  <=>  (v2_comseq_2 @  (k3_series_1 @ A) ) ) ) ) , file(series_1, d2_series_1)).
thf(d3_series_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) )  =>  ( (= @  (k4_series_1 @ A) )  @  (k1_seq_2 @  (k3_series_1 @ A) ) ) ) ) , file(series_1, d3_series_1)).
thf(d6_seq_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) )  =>  ( (v2_comseq_2 @ A)  <=>  (? [B: $i] :  ( (v1_xreal_0 @ B)  &  (! [C: $i] :  ( (v1_xreal_0 @ C)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ C)  @ k5_numbers) )  &  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (? [E: $i] :  ( (v7_ordinal1 @ E)  &  ( ( (r1_xxreal_0 @ D)  @ E)  &  ( (r1_xxreal_0 @ C)  @  (k9_complex1 @  ( (k6_xcmplx_0 @  ( (k1_funct_1 @ A)  @ E) )  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(seq_2, d6_seq_2)).
thf(d7_seq_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) )  =>  ( (v2_comseq_2 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (= @ B)  @  (k1_seq_2 @ A) )  <=>  (! [C: $i] :  ( (v1_xreal_0 @ C)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ C)  @ k5_numbers) )  &  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (? [E: $i] :  ( (v7_ordinal1 @ E)  &  ( ( (r1_xxreal_0 @ D)  @ E)  &  ( (r1_xxreal_0 @ C)  @  (k9_complex1 @  ( (k6_xcmplx_0 @  ( (k1_funct_1 @ A)  @ E) )  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(seq_2, d7_seq_2)).
thf(d9_comseq_3, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k2_numbers) ) ) ) )  =>  ( (v2_comseq_3 @ A)  <=>  (v1_series_1 @  ( ( (k55_valued_1 @ k4_ordinal1)  @ k2_numbers)  @ A) ) ) ) ) , file(comseq_3, d9_comseq_3)).
thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k4_ordinal1) )  =>  ( (m1_subset_1 @  ( (k1_nat_1 @ A)  @ B) )  @ k4_ordinal1) ) ) , file(nat_1, k1_nat_1)).
thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)).
thf(dt_k1_seq_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) )  =>  (v1_xreal_0 @  (k1_seq_2 @ A) ) ) ) , file(seq_2, k1_seq_2)).
thf(dt_k1_xboole_0, axiom, $true, file(xboole_0, k1_xboole_0)).
thf(dt_k1_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)).
thf(dt_k2_numbers, axiom, $true, file(numbers, k2_numbers)).
thf(dt_k2_series_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ( (v1_partfun1 @ A)  @ k4_ordinal1)  &  (v1_valued_0 @ A) ) ) ) )  =>  ( (v1_relat_1 @  (k2_series_1 @ A) )  &  ( ( (v4_relat_1 @  (k2_series_1 @ A) )  @ k4_ordinal1)  &  ( (v1_funct_1 @  (k2_series_1 @ A) )  &  ( ( (v1_partfun1 @  (k2_series_1 @ A) )  @ k4_ordinal1)  &  (v1_valued_0 @  (k2_series_1 @ A) ) ) ) ) ) ) ) , file(series_1, k2_series_1)).
thf(dt_k2_xcmplx_0, axiom, $true, file(xcmplx_0, k2_xcmplx_0)).
thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)).
thf(dt_k3_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @ B) ) ) , file(funct_2, k3_funct_2)).
thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)).
thf(dt_k3_series_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) )  =>  ( (v1_funct_1 @  (k3_series_1 @ A) )  &  ( ( ( (v1_funct_2 @  (k3_series_1 @ A) )  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @  (k3_series_1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) ) ) ) , file(series_1, k3_series_1)).
thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k4_series_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) )  =>  (v1_xreal_0 @  (k4_series_1 @ A) ) ) ) , file(series_1, k4_series_1)).
thf(dt_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(dt_k54_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ A) )  &  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  (v3_valued_0 @  (k54_valued_1 @ A) ) ) ) ) ) , file(valued_1, k54_valued_1)).
thf(dt_k55_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( (v1_funct_1 @  ( ( (k55_valued_1 @ A)  @ B)  @ C) )  &  ( (m1_subset_1 @  ( ( (k55_valued_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ k1_numbers) ) ) ) ) ) , file(valued_1, k55_valued_1)).
thf(dt_k5_complex1, axiom,  ( (m1_subset_1 @ k5_complex1)  @ k2_numbers) , file(complex1, k5_complex1)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(dt_k5_ordinal1, axiom, $true, file(ordinal1, k5_ordinal1)).
thf(dt_k6_xcmplx_0, axiom, $true, file(xcmplx_0, k6_xcmplx_0)).
thf(dt_k9_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xreal_0 @  (k9_complex1 @ A) ) ) ) , file(complex1, k9_complex1)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(fc100_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k54_valued_1 @ C) )  &  ( (v1_partfun1 @  (k54_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc100_valued_1)).
thf(fc101_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k54_valued_1 @ C) )  &  ( (v1_partfun1 @  (k54_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc101_valued_1)).
thf(fc10_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(subset_1, fc10_subset_1)).
thf(fc10_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc10_xreal_0)).
thf(fc114_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ B) )  &  ( ( (v4_relat_1 @  (k54_valued_1 @ B) )  @ A)  &  ( (v1_funct_1 @  (k54_valued_1 @ B) )  &  (v3_valued_0 @  (k54_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc114_valued_1)).
thf(fc118_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ B) )  &  ( (v1_funct_1 @  (k54_valued_1 @ B) )  &  ( ( (v1_partfun1 @  (k54_valued_1 @ B) )  @ A)  &  (v3_valued_0 @  (k54_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc118_valued_1)).
thf(fc11_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc11_xreal_0)).
thf(fc12_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc12_xreal_0)).
thf(fc13_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc13_xreal_0)).
thf(fc14_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc14_xreal_0)).
thf(fc15_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  ~ ( (v3_xxreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc15_xreal_0)).
thf(fc16_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  ~ ( (v2_xxreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc16_xreal_0)).
thf(fc17_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc17_xreal_0)).
thf(fc18_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc18_xreal_0)).
thf(fc19_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc19_xreal_0)).
thf(fc1_membered, axiom,  (v1_membered @ k2_numbers) , file(membered, fc1_membered)).
thf(fc1_numbers, axiom,  ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)).
thf(fc1_subset_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, fc1_subset_1)).
thf(fc1_valued_1, axiom,  (! [A: $i] :  ( (v1_rat_1 @ A)  =>  ( (v1_xreal_0 @  (k9_complex1 @ A) )  &  (v1_rat_1 @  (k9_complex1 @ A) ) ) ) ) , file(valued_1, fc1_valued_1)).
thf(fc1_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc20_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc20_xreal_0)).
thf(fc21_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc21_xreal_0)).
thf(fc22_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc22_xreal_0)).
thf(fc2_numbers, axiom,  ~ ( (v1_xboole_0 @ k2_numbers) ) , file(numbers, fc2_numbers)).
thf(fc2_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc2_xcmplx_0)).
thf(fc3_membered, axiom,  (v3_membered @ k1_numbers) , file(membered, fc3_membered)).
thf(fc3_numbers, axiom,  ~ ( (v1_xboole_0 @ k3_numbers) ) , file(numbers, fc3_numbers)).
thf(fc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  (v1_xreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc3_xreal_0)).
thf(fc4_membered, axiom,  (v4_membered @ k3_numbers) , file(membered, fc4_membered)).
thf(fc4_numbers, axiom,  ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers)).
thf(fc4_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc4_xcmplx_0)).
thf(fc55_membered, axiom,  (v7_membered @ k2_numbers) , file(membered, fc55_membered)).
thf(fc56_membered, axiom,  (v7_membered @ k1_numbers) , file(membered, fc56_membered)).
thf(fc57_membered, axiom,  (v7_membered @ k3_numbers) , file(membered, fc57_membered)).
thf(fc58_membered, axiom,  (v7_membered @ k4_numbers) , file(membered, fc58_membered)).
thf(fc59_membered, axiom,  (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)).
thf(fc5_membered, axiom,  (v5_membered @ k4_numbers) , file(membered, fc5_membered)).
thf(fc5_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc5_xreal_0)).
thf(fc61_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (v1_xcmplx_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc61_valued_0)).
thf(fc62_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) )  =>  (v1_xxreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc62_valued_0)).
thf(fc63_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  (v1_xreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc63_valued_0)).
thf(fc64_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_rat_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc64_valued_0)).
thf(fc65_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_int_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc65_valued_0)).
thf(fc66_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) )  =>  (v7_ordinal1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc66_valued_0)).
thf(fc6_membered, axiom,  (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)).
thf(fc6_numbers, axiom,  ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_seq_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  ( (v2_comseq_2 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k2_numbers) ) ) ) ) )  =>  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  ( ( ( (v1_funct_2 @  (k54_valued_1 @ A) )  @ k4_ordinal1)  @ k1_numbers)  &  (v2_comseq_2 @  (k54_valued_1 @ A) ) ) ) ) ) , file(seq_2, fc6_seq_2)).
thf(fc6_xcmplx_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_ordinal1 @ A) )  &  (v1_xcmplx_0 @ A) )  =>  ( ~ ( (v8_ordinal1 @  (k4_xcmplx_0 @ A) ) )  &  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(xcmplx_0, fc6_xcmplx_0)).
thf(fc7_numbers, axiom,  ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers)).
thf(fc7_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc7_xreal_0)).
thf(fc85_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (v1_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc85_valued_0)).
thf(fc86_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (v2_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc86_valued_0)).
thf(fc87_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (v3_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc87_valued_0)).
thf(fc88_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc88_valued_0)).
thf(fc89_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc89_valued_0)).
thf(fc8_numbers, axiom,  ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers)).
thf(fc8_ordinal1, axiom,  (v7_ordinal1 @ k5_ordinal1) , file(ordinal1, fc8_ordinal1)).
thf(fc90_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (v4_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc90_valued_0)).
thf(fc97_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ A) )  &  ( ( (v5_relat_1 @  (k54_valued_1 @ A) )  @ k3_numbers)  &  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  (v3_valued_0 @  (k54_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc97_valued_1)).
thf(fc98_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ A) )  &  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  ( (v3_valued_0 @  (k54_valued_1 @ A) )  &  (v4_valued_0 @  (k54_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc98_valued_1)).
thf(fc99_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k54_valued_1 @ C) )  &  ( (v1_partfun1 @  (k54_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc99_valued_1)).
thf(fc9_numbers, axiom,  ~ ( (v1_finset_1 @ k2_numbers) ) , file(numbers, fc9_numbers)).
thf(fc9_ordinal1, axiom,  (v8_ordinal1 @ k5_ordinal1) , file(ordinal1, fc9_ordinal1)).
thf(fc9_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc9_xreal_0)).
thf(involutiveness_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ A) ) )  @ A) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(projectivity_k54_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (= @  (k54_valued_1 @  (k54_valued_1 @ A) ) )  @  (k54_valued_1 @ A) ) ) ) , file(valued_1, k54_valued_1)).
thf(projectivity_k55_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( (= @  ( ( (k55_valued_1 @ A)  @ B)  @  ( ( (k55_valued_1 @ A)  @ B)  @ C) ) )  @  ( ( (k55_valued_1 @ A)  @ B)  @ C) ) ) ) , file(valued_1, k55_valued_1)).
thf(projectivity_k9_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  (k9_complex1 @  (k9_complex1 @ A) ) )  @  (k9_complex1 @ A) ) ) ) , file(complex1, k9_complex1)).
thf(rc10_ordinal1, axiom,  (? [A: $i] :  (v8_ordinal1 @ A) ) , file(ordinal1, rc10_ordinal1)).
thf(rc11_ordinal1, axiom,  (? [A: $i] :  ~ ( (v8_ordinal1 @ A) ) ) , file(ordinal1, rc11_ordinal1)).
thf(rc12_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, rc12_ordinal1)).
thf(rc13_ordinal1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v9_ordinal1 @ A) ) ) , file(ordinal1, rc13_ordinal1)).
thf(rc14_ordinal1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ~ ( (v9_ordinal1 @ A) ) ) ) , file(ordinal1, rc14_ordinal1)).
thf(rc1_comseq_2, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k2_numbers) ) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( ( (v5_relat_1 @ A)  @ k2_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_partfun1 @ A)  @ k4_ordinal1)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  ( (v1_valued_0 @ A)  &  (v1_comseq_2 @ A) ) ) ) ) ) ) ) ) ) ) , file(comseq_2, rc1_comseq_2)).
thf(rc1_funct_2, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, rc1_funct_2)).
thf(rc1_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc1_membered)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) , file(ordinal1, rc1_ordinal1)).
thf(rc1_relset_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_xboole_0 @ C)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) ) ) , file(relset_1, rc1_relset_1)).
thf(rc1_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(subset_1, rc1_subset_1)).
thf(rc1_valued_0, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, rc1_valued_0)).
thf(rc1_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)).
thf(rc1_xcmplx_0, axiom,  (? [A: $i] :  (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc1_xcmplx_0)).
thf(rc1_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)).
thf(rc2_comseq_2, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k2_numbers) ) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( ( (v5_relat_1 @ A)  @ k2_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_partfun1 @ A)  @ k4_ordinal1)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  ( (v1_valued_0 @ A)  &  (v2_comseq_2 @ A) ) ) ) ) ) ) ) ) ) ) , file(comseq_2, rc2_comseq_2)).
thf(rc2_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc2_membered)).
thf(rc2_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc2_ordinal1)).
thf(rc2_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  (v1_xboole_0 @ B) ) ) ) , file(subset_1, rc2_subset_1)).
thf(rc2_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(valued_1, rc2_valued_1)).
thf(rc2_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)).
thf(rc2_xcmplx_0, axiom,  (? [A: $i] :  (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc2_xcmplx_0)).
thf(rc2_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc2_xreal_0)).
thf(rc3_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v6_membered @ A)  &  (v7_membered @ A) ) ) ) , file(membered, rc3_membered)).
thf(rc3_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc3_ordinal1)).
thf(rc3_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc3_subset_1)).
thf(rc3_valued_0, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k4_ordinal1) ) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( ( (v5_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_partfun1 @ A)  @ k4_ordinal1)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k4_ordinal1)  &  ( (v1_valued_0 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v4_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc3_valued_0)).
thf(rc3_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) ) ) ) , file(valued_1, rc3_valued_1)).
thf(rc3_xcmplx_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc3_xcmplx_0)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc4_subset_1)).
thf(rc4_xcmplx_0, axiom,  (? [A: $i] :  ( ~ ( (v8_ordinal1 @ A) )  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc4_xcmplx_0)).
thf(rc4_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc5_ordinal1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v5_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc5_subset_1)).
thf(rc5_valued_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( ( (v5_relat_1 @ B)  @ k3_numbers)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( (v1_valued_0 @ B)  &  ( (v2_valued_0 @ B)  &  ( (v3_valued_0 @ B)  &  (v4_valued_0 @ B) ) ) ) ) ) ) ) ) ) ) , file(valued_1, rc5_valued_1)).
thf(rc5_xcmplx_0, axiom,  (? [A: $i] :  ( ~ ( (v8_ordinal1 @ A) )  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc5_xcmplx_0)).
thf(rc5_xreal_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc5_xreal_0)).
thf(rc6_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc6_ordinal1)).
thf(rc6_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc6_subset_1)).
thf(rc6_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v4_valued_0 @ B) ) ) ) ) ) ) , file(valued_0, rc6_valued_0)).
thf(rc7_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc7_ordinal1)).
thf(rc8_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc8_ordinal1)).
thf(rc9_ordinal1, axiom,  (? [A: $i] :  (v8_ordinal1 @ A) ) , file(ordinal1, rc9_ordinal1)).
thf(redefinition_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k4_ordinal1) )  =>  ( (= @  ( (k1_nat_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k1_nat_1)).
thf(redefinition_k3_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (= @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @  ( (k1_funct_1 @ C)  @ D) ) ) ) , file(funct_2, k3_funct_2)).
thf(redefinition_k3_series_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k1_numbers) ) ) ) )  =>  ( (= @  (k3_series_1 @ A) )  @  (k2_series_1 @ A) ) ) ) , file(series_1, k3_series_1)).
thf(redefinition_k55_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( (= @  ( ( (k55_valued_1 @ A)  @ B)  @ C) )  @  (k54_valued_1 @ C) ) ) ) , file(valued_1, k55_valued_1)).
thf(redefinition_k5_complex1, axiom,  ( (= @ k5_complex1)  @ k5_ordinal1) , file(complex1, k5_complex1)).
thf(redefinition_k5_numbers, axiom,  ( (= @ k5_numbers)  @ k5_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  <=>  ( (r2_hidden @ A)  @ B) ) ) , file(tarski, r2_tarski)).
thf(reflexivity_r1_tarski, axiom,  (! [A: $i, B: $i] :  ( (r1_tarski @ A)  @ A) ) , file(tarski, r1_tarski)).
thf(reflexivity_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( (r1_xxreal_0 @ A)  @ A) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom,  ( (r1_xxreal_0 @ 0)  @ 0) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom,  ( (r1_xxreal_0 @ 0)  @ 1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ 0)  @  (k4_xcmplx_0 @ 1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ ( ( (r1_xxreal_0 @ 1)  @ 0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom,  ( (r1_xxreal_0 @ 1)  @ 1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ 1)  @  (k4_xcmplx_0 @ 1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ 1) )  @ 0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ 1) )  @ 1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ 1) )  @  (k4_xcmplx_0 @ 1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ 0)  @ 0) )  @ 0) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0)).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ 0)  @ 1) )  @ 1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ 0)  @  (k4_xcmplx_0 @ 1) ) )  @  (k4_xcmplx_0 @ 1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ 1)  @ 0) )  @ 1) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ 1)  @  (k4_xcmplx_0 @ 1) ) )  @ 0) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ 1) )  @ 0) )  @  (k4_xcmplx_0 @ 1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ 1) )  @ 1) )  @ 0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ 0)  @ 0) )  @ 0) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ 0)  @ 1) )  @  (k4_xcmplx_0 @ 1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ 0)  @  (k4_xcmplx_0 @ 1) ) )  @ 1) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ 1)  @ 0) )  @ 1) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ 1)  @ 1) )  @ 0) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ 1) )  @ 0) )  @  (k4_xcmplx_0 @ 1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ 1) )  @  (k4_xcmplx_0 @ 1) ) )  @ 0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)).
thf(rqRealNeg__k4_xcmplx_0__r0_r0, axiom,  ( (= @  (k4_xcmplx_0 @ 0) )  @ 0) , file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0)).
thf(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom,  ( (= @  (k4_xcmplx_0 @ 1) )  @  (k4_xcmplx_0 @ 1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)).
thf(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ 1) ) )  @ 1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)).
thf(spc0_boole, axiom,  (v1_xboole_0 @ 0) , file(boole, spc0_boole)).
thf(spc0_numerals, axiom,  ( (m1_subset_1 @ 0)  @ k4_ordinal1) , file(numerals, spc0_numerals)).
thf(spc1_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ B) ) )  @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(arithm, spc1_arithm)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ 1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( (v2_xxreal_0 @ 1)  &  ( (m1_subset_1 @ 1)  @ k4_ordinal1) ) , file(numerals, spc1_numerals)).
thf(spc6_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( (= @  ( (k2_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) )  @ C) )  @  ( (k2_xcmplx_0 @ A)  @  ( (k2_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc6_arithm)).
thf(spc8_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) ) )  @  (k4_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(arithm, spc8_arithm)).
thf(spc9_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) ) )  @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(arithm, spc9_arithm)).
thf(t18_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (! [B: $i] :  ( (= @  ( (k1_funct_1 @  (k54_valued_1 @ A) )  @ B) )  @  (k9_complex1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, t18_valued_1)).
thf(t1_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @ k5_numbers) )  @ A) ) ) , file(arithm, t1_arithm)).
thf(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v2_xxreal_0 @ A) )  =>  (v2_xxreal_0 @ B) ) ) ) ) ) , file(real, t1_real)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t2_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v3_xxreal_0 @ B) )  =>  (v3_xxreal_0 @ A) ) ) ) ) ) , file(real, t2_real)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_tarski @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t3_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v3_xxreal_0 @ A) )  &  (v3_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t3_real)).
thf(t3_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ B) )  <=>  ( (r1_tarski @ A)  @ B) ) ) ) , file(subset, t3_subset)).
thf(t44_complex1, axiom,  ( (= @  (k9_complex1 @ k5_numbers) )  @ k5_numbers) , file(complex1, t44_complex1)).
thf(t4_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k6_xcmplx_0 @ A)  @ k5_numbers) )  @ A) ) ) , file(arithm, t4_arithm)).
thf(t4_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v2_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t4_real)).
thf(t4_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_tarski @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t5_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v8_ordinal1 @ B)  |  ( (v3_xxreal_0 @ A)  |  (v2_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t5_real)).
thf(t5_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) )  &  (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset)).
thf(t6_boole, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (= @ A)  @ k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(t6_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v8_ordinal1 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ B) ) ) ) ) ) ) ) ) , file(real, t7_real)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( ( (= @ A)  @ B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(t8_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) ) ) ) , file(real, t8_real)).
thf(s2_nat_1, axiom,  (! [A: $i > $o] :  ( ( (A @ k5_numbers)  &  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( (A @ B)  =>  (A @  ( (k1_nat_1 @ B)  @ 1) ) ) ) ) )  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (A @ B) ) ) ) ) , file(nat_1, s2_nat_1)).
thf(t3_csspace3, conjecture,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k2_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k2_numbers) ) ) ) )  =>  ( (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( (= @  ( (k1_funct_1 @ A)  @ B) )  @ k5_complex1) ) )  =>  ( (v2_comseq_3 @ A)  &  ( (= @  (k4_series_1 @  ( ( (k55_valued_1 @ k4_ordinal1)  @ k2_numbers)  @ A) ) )  @ k5_numbers) ) ) ) ) , file(csspace3, t3_csspace3)).