% Mizar problem: t29_pdiff_7,pdiff_7,1591,5 
include('/home/mptp/mizwrk/7.13.01_4.181.1147/MPTP2/pl/../AxiomsThf/SET010^0.ax').
thf(n1_type, type, 1: $i).
thf(k10_xtuple_0_type, type, k10_xtuple_0: $i > $i).
thf(k12_finseq_1_type, type, k12_finseq_1: $i > $i > $i).
thf(k13_finseq_1_type, type, k13_finseq_1: $i > $i).
thf(k1_card_1_type, type, k1_card_1: $i > $i).
thf(k1_euclid_type, type, k1_euclid: $i > $i).
thf(k1_finseq_1_type, type, k1_finseq_1: $i > $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_pdiff_1_type, type, k1_pdiff_1: $i > $i > $i).
thf(k1_relset_1_type, type, k1_relset_1: $i > $i > $i).
thf(k1_rvsum_1_type, type, k1_rvsum_1: $i > $i).
thf(k1_seq_1_type, type, k1_seq_1: $i > $i > $i).
thf(k1_tarski_type, type, k1_tarski: $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_finseq_1_type, type, k2_finseq_1: $i > $i).
thf(k2_funct_1_type, type, k2_funct_1: $i > $i).
thf(k2_tarski_type, type, k2_tarski: $i > $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k3_finseq_1_type, type, k3_finseq_1: $i > $i).
thf(k3_finseq_2_type, type, k3_finseq_2: $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_pdiff_1_type, type, k3_pdiff_1: $i > $i > $i).
thf(k3_relat_1_type, type, k3_relat_1: $i > $i > $i).
thf(k4_finseq_2_type, type, k4_finseq_2: $i > $i > $i).
thf(k4_numbers_type, type, k4_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_tarski_type, type, k4_tarski: $i > $i > $i).
thf(k5_finseq_1_type, type, k5_finseq_1: $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k7_partfun1_type, type, k7_partfun1: $i > $i > $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(m1_finseq_1_type, type, m1_finseq_1: $i > $i > $o).
thf(m1_finseq_2_type, type, m1_finseq_2: $i > $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(m2_finseq_1_type, type, m2_finseq_1: $i > $i > $o).
thf(m2_finseq_2_type, type, m2_finseq_2: $i > $i > $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $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_relset_1_type, type, r2_relset_1: $i > $i > $i > $i > $o).
thf(v10_valued_2_type, type, v10_valued_2: $i > $o).
thf(v11_valued_2_type, type, v11_valued_2: $i > $o).
thf(v12_valued_2_type, type, v12_valued_2: $i > $o).
thf(v1_card_1_type, type, v1_card_1: $i > $o).
thf(v1_finseq_1_type, type, v1_finseq_1: $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_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_valued_0_type, type, v1_valued_0: $i > $o).
thf(v1_valued_2_type, type, v1_valued_2: $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_xtuple_0_type, type, v1_xtuple_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(v1_xxreal_2_type, type, v1_xxreal_2: $i > $o).
thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_finseq_1_type, type, v2_finseq_1: $i > $o).
thf(v2_funct_1_type, type, v2_funct_1: $i > $o).
thf(v2_funct_2_type, type, v2_funct_2: $i > $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_valued_0_type, type, v2_valued_0: $i > $o).
thf(v2_valued_2_type, type, v2_valued_2: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v2_xxreal_2_type, type, v2_xxreal_2: $i > $o).
thf(v3_card_1_type, type, v3_card_1: $i > $i > $o).
thf(v3_finseq_1_type, type, v3_finseq_1: $i > $o).
thf(v3_funct_1_type, type, v3_funct_1: $i > $o).
thf(v3_funct_2_type, type, v3_funct_2: $i > $i > $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_valued_2_type, type, v3_valued_2: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(v3_xxreal_2_type, type, v3_xxreal_2: $i > $o).
thf(v4_funct_1_type, type, v4_funct_1: $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(v4_valued_2_type, type, v4_valued_2: $i > $o).
thf(v4_xxreal_2_type, type, v4_xxreal_2: $i > $o).
thf(v5_membered_type, type, v5_membered: $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(v5_valued_2_type, type, v5_valued_2: $i > $o).
thf(v5_xxreal_2_type, type, v5_xxreal_2: $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v6_valued_0_type, type, v6_valued_0: $i > $o).
thf(v6_valued_2_type, type, v6_valued_2: $i > $o).
thf(v6_xxreal_2_type, type, v6_xxreal_2: $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(v7_valued_2_type, type, v7_valued_2: $i > $o).
thf(v8_valued_0_type, type, v8_valued_0: $i > $o).
thf(v8_valued_2_type, type, v8_valued_2: $i > $o).
thf(v9_valued_2_type, type, v9_valued_2: $i > $o).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(cc10_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc10_finseq_1)).
thf(cc10_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k4_numbers) )  =>  (v5_membered @ A) ) ) , file(membered, cc10_membered)).
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(cc10_valued_2, axiom,  (! [A: $i] :  ( (v2_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_valued_2 @ B) ) ) ) ) , file(valued_2, cc10_valued_2)).
thf(cc10_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v1_xxreal_2 @ A) )  =>  ( (v3_membered @ A)  &  (v3_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc10_xxreal_2)).
thf(cc11_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc11_finseq_1)).
thf(cc11_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k5_numbers) )  =>  (v6_membered @ A) ) ) , file(membered, cc11_membered)).
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(cc11_valued_2, axiom,  (! [A: $i] :  ( (v3_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_valued_2 @ B) ) ) ) ) , file(valued_2, cc11_valued_2)).
thf(cc11_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v2_xxreal_2 @ A) )  =>  ( (v3_membered @ A)  &  (v4_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc11_xxreal_2)).
thf(cc12_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) ) , file(finseq_1, cc12_finseq_1)).
thf(cc12_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc12_membered)).
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(cc12_valued_2, axiom,  (! [A: $i] :  ( (v4_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_2 @ B) ) ) ) ) , file(valued_2, cc12_valued_2)).
thf(cc12_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v5_membered @ A)  &  (v1_finset_1 @ A) ) ) ) , file(xxreal_2, cc12_xxreal_2)).
thf(cc13_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc13_membered)).
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(cc13_valued_2, axiom,  (! [A: $i] :  ( (v5_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_valued_2 @ B) ) ) ) ) , file(valued_2, cc13_valued_2)).
thf(cc13_xxreal_2, axiom,  (! [A: $i] :  ( ( (v6_membered @ A)  &  (v4_xxreal_2 @ A) )  =>  ( (v6_membered @ A)  &  ( (v1_finset_1 @ A)  &  (v4_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc13_xxreal_2)).
thf(cc14_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc14_membered)).
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(cc14_valued_2, axiom,  (! [A: $i] :  ( (v6_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_valued_2 @ B) ) ) ) ) , file(valued_2, cc14_valued_2)).
thf(cc14_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  (v3_membered @ A) ) ) ) , file(xxreal_2, cc14_xxreal_2)).
thf(cc15_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_rat_1 @ B) ) ) ) ) , file(membered, cc15_membered)).
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(cc15_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_valued_0 @ B) ) ) ) ) , file(valued_2, cc15_valued_2)).
thf(cc15_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v2_membered @ A)  &  (v6_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc15_xxreal_2)).
thf(cc16_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_int_1 @ B) ) ) ) ) , file(membered, cc16_membered)).
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(cc16_valued_2, axiom,  (! [A: $i] :  ( (v2_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v2_valued_0 @ B) ) ) ) ) , file(valued_2, cc16_valued_2)).
thf(cc16_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v1_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) , file(xxreal_2, cc16_xxreal_2)).
thf(cc17_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc17_membered)).
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(cc17_valued_2, axiom,  (! [A: $i] :  ( (v3_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_valued_0 @ B) ) ) ) ) , file(valued_2, cc17_valued_2)).
thf(cc17_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v2_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) , file(xxreal_2, cc17_xxreal_2)).
thf(cc18_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_membered @ A) ) ) , file(membered, cc18_membered)).
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(cc18_valued_2, axiom,  (! [A: $i] :  ( (v4_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ( (v5_relat_1 @ B)  @ k3_numbers) ) ) ) ) , file(valued_2, cc18_valued_2)).
thf(cc19_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_membered @ B) ) ) ) ) , file(membered, cc19_membered)).
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(cc19_valued_2, axiom,  (! [A: $i] :  ( (v5_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ( (v5_relat_1 @ B)  @ k4_numbers) ) ) ) ) , file(valued_2, cc19_valued_2)).
thf(cc1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  =>  ( (v3_card_1 @ B)  @ A) ) ) ) ) , file(euclid, cc1_euclid)).
thf(cc1_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc1_finseq_1)).
thf(cc1_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  ( (k4_finseq_2 @ B)  @ A) )  =>  ( (v3_card_1 @ C)  @ B) ) ) ) ) , file(finseq_2, cc1_finseq_2)).
thf(cc1_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_funct_1 @ A) ) ) , file(funct_1, cc1_funct_1)).
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_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_ordinal1 @ A)  &  (v7_ordinal1 @ A) ) ) ) , file(nat_1, cc1_nat_1)).
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_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_valued_2, axiom,  (! [A: $i] :  ( (v6_valued_2 @ A)  =>  (v5_valued_2 @ A) ) ) , file(valued_2, cc1_valued_2)).
thf(cc1_xcmplx_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (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_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_membered @ B) ) ) ) ) , file(membered, cc20_membered)).
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(cc20_valued_2, axiom,  (! [A: $i] :  ( (v6_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_2, cc20_valued_2)).
thf(cc21_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_membered @ B) ) ) ) ) , file(membered, cc21_membered)).
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(cc21_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v7_valued_2 @ B) ) ) ) ) ) ) ) , file(valued_2, cc21_valued_2)).
thf(cc22_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_membered @ B) ) ) ) ) , file(membered, cc22_membered)).
thf(cc22_valued_0, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_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(cc22_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v12_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v11_valued_2 @ A) ) ) ) , file(valued_2, cc22_valued_2)).
thf(cc23_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_membered @ B) ) ) ) ) , file(membered, cc23_membered)).
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(cc23_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v11_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v10_valued_2 @ A) ) ) ) , file(valued_2, cc23_valued_2)).
thf(cc24_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_membered @ B) ) ) ) ) , file(membered, cc24_membered)).
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(cc24_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v10_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v9_valued_2 @ A) ) ) ) , file(valued_2, cc24_valued_2)).
thf(cc25_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  (v6_membered @ A) ) ) , file(membered, cc25_membered)).
thf(cc25_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v9_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v8_valued_2 @ A) ) ) ) , file(valued_2, cc25_valued_2)).
thf(cc26_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_membered @ A) ) ) , file(membered, cc26_membered)).
thf(cc26_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v9_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v7_valued_2 @ A) ) ) ) , file(valued_2, cc26_valued_2)).
thf(cc27_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v12_valued_2 @ A) ) ) ) , file(valued_2, cc27_valued_2)).
thf(cc28_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v1_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v7_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc28_valued_2)).
thf(cc29_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v2_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v8_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc29_valued_2)).
thf(cc2_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finseq_1, cc2_finseq_1)).
thf(cc2_finseq_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (v4_funct_1 @ B) ) ) ) , file(finseq_2, cc2_finseq_2)).
thf(cc2_funct_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) ) ) ) , file(funct_1, cc2_funct_1)).
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_nat_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ~ ( (v3_xxreal_0 @ A) ) ) ) , file(nat_1, cc2_nat_1)).
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_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_valued_2, axiom,  (! [A: $i] :  ( (v5_valued_2 @ A)  =>  (v4_valued_2 @ A) ) ) , file(valued_2, cc2_valued_2)).
thf(cc2_xcmplx_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (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(cc2_xxreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, cc2_xxreal_0)).
thf(cc2_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) )  =>  ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_2 @ A)  &  (v2_xxreal_2 @ A) ) ) ) ) ) , file(xxreal_2, cc2_xxreal_2)).
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(cc30_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v3_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v9_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc30_valued_2)).
thf(cc31_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k5_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0)).
thf(cc31_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v4_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v10_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc31_valued_2)).
thf(cc32_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v5_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v11_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc32_valued_2)).
thf(cc33_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v6_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v12_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc33_valued_2)).
thf(cc3_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v5_relat_1 @ B)  @ A) ) ) ) , file(finseq_1, cc3_finseq_1)).
thf(cc3_finseq_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (v3_finseq_1 @ B) ) ) ) , file(finseq_2, cc3_finseq_2)).
thf(cc3_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_funct_1 @ B) ) ) ) ) , file(funct_1, cc3_funct_1)).
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_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc3_nat_1)).
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_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_valued_2, axiom,  (! [A: $i] :  ( (v4_valued_2 @ A)  =>  (v3_valued_2 @ A) ) ) , file(valued_2, cc3_valued_2)).
thf(cc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)).
thf(cc3_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0)).
thf(cc3_xxreal_2, axiom,  (! [A: $i] :  ( ( (v6_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) )  =>  ( (v6_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc3_xxreal_2)).
thf(cc4_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc4_finseq_1)).
thf(cc4_funct_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc4_funct_1)).
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_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_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_valued_2, axiom,  (! [A: $i] :  ( (v3_valued_2 @ A)  =>  (v1_valued_2 @ A) ) ) , file(valued_2, cc4_valued_2)).
thf(cc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc4_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc4_xxreal_0)).
thf(cc4_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ( (v3_xxreal_2 @ A)  &  (v4_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc4_xxreal_2)).
thf(cc5_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) , file(finseq_1, cc5_finseq_1)).
thf(cc5_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) )  =>  ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(funct_1, cc5_funct_1)).
thf(cc5_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v3_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( (v2_funct_1 @ C)  &  ( (v2_funct_2 @ C)  @ B) ) ) ) ) ) ) , file(funct_2, cc5_funct_2)).
thf(cc5_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v1_membered @ A) ) ) , file(membered, cc5_membered)).
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(cc5_valued_2, axiom,  (! [A: $i] :  ( (v3_valued_2 @ A)  =>  (v2_valued_2 @ A) ) ) , file(valued_2, cc5_valued_2)).
thf(cc5_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc5_xxreal_0)).
thf(cc5_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  ( (v3_xxreal_2 @ A)  &  (v4_xxreal_2 @ A) ) )  =>  ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc5_xxreal_2)).
thf(cc6_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) , file(finseq_1, cc6_finseq_1)).
thf(cc6_funct_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc6_funct_1)).
thf(cc6_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( (v2_funct_1 @ C)  &  ( (v2_funct_2 @ C)  @ B) ) )  =>  ( (v1_funct_1 @ C)  &  ( ( (v3_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) , file(funct_2, cc6_funct_2)).
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(cc6_valued_2, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_valued_2 @ A) ) ) , file(valued_2, cc6_valued_2)).
thf(cc6_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc6_xxreal_0)).
thf(cc6_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v1_finset_1 @ A) )  =>  ( (v3_membered @ A)  &  (v5_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc6_xxreal_2)).
thf(cc7_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) , file(finseq_1, cc7_finseq_1)).
thf(cc7_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v4_funct_1 @ A) ) ) , file(funct_1, cc7_funct_1)).
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(cc7_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (v4_funct_1 @ A) ) ) , file(valued_2, cc7_valued_2)).
thf(cc7_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) )  =>  ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc7_xxreal_0)).
thf(cc7_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_xxreal_2 @ A) ) )  =>  ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v2_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc7_xxreal_2)).
thf(cc8_finseq_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_finseq_1 @ A) ) ) , file(finseq_1, cc8_finseq_1)).
thf(cc8_funct_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, cc8_funct_1)).
thf(cc8_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, cc8_funct_2)).
thf(cc8_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  =>  (v3_membered @ A) ) ) , file(membered, cc8_membered)).
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(cc8_valued_2, axiom,  (! [A: $i] :  ( (v2_valued_2 @ A)  =>  (v4_funct_1 @ A) ) ) , file(valued_2, cc8_valued_2)).
thf(cc8_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc8_xxreal_0)).
thf(cc8_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_xxreal_2 @ A) ) )  =>  ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc8_xxreal_2)).
thf(cc9_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (v4_funct_1 @ A) ) ) , file(finseq_1, cc9_finseq_1)).
thf(cc9_funct_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_funct_1 @ B) ) ) ) ) , file(funct_1, cc9_funct_1)).
thf(cc9_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k3_numbers) )  =>  (v4_membered @ A) ) ) , file(membered, cc9_membered)).
thf(cc9_valued_0, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0)).
thf(cc9_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_valued_2 @ B) ) ) ) ) , file(valued_2, cc9_valued_2)).
thf(cc9_xxreal_2, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  ( (v6_membered @ A)  &  (v3_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc9_xxreal_2)).
thf(commutativity_k2_tarski, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k2_tarski @ A)  @ B) )  @  ( (k2_tarski @ B)  @ A) ) ) , file(tarski, k2_tarski)).
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(d10_xboole_0, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (= @ A)  @ B)  <=>  ( ( (r1_tarski @ A)  @ B)  &  ( (r1_tarski @ B)  @ A) ) ) ) ) , file(xboole_0, d10_xboole_0)).
thf(d1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k1_euclid @ A) )  @  ( (k4_finseq_2 @ A)  @ k1_numbers) ) ) ) , file(euclid, d1_euclid)).
thf(d1_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k1_finseq_1 @ A) )  @  ( ( (replSep1 @  (^ [B: $i] :  ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers) ) )  @  (^ [B: $i] : B) )  @  (^ [B: $i] :  ( ( (r1_xxreal_0 @ 1)  @ B)  &  ( (r1_xxreal_0 @ B)  @ A) ) ) ) ) ) ) , file(finseq_1, d1_finseq_1)).
thf(d2_xboole_0, axiom,  ( (= @ k1_xboole_0)  @  (eps @  (^ [A: $i] :  (v1_xboole_0 @ A) ) ) ) , file(xboole_0, d2_xboole_0)).
thf(d3_pdiff_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) )  =>  ( (= @  ( (k3_pdiff_1 @ A)  @ B) )  @  ( (k3_relat_1 @ B)  @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) ) ) ) ) ) ) , file(pdiff_1, d3_pdiff_1)).
thf(d3_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r1_tarski @ A)  @ B)  <=>  (! [C: $i] :  ( ( (r2_hidden @ C)  @ A)  =>  ( (r2_hidden @ C)  @ B) ) ) ) ) ) , file(tarski, d3_tarski)).
thf(d4_finseq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (= @  ( (k4_finseq_2 @ A)  @ B) )  @  ( ( (replSep1 @  (^ [C: $i] :  ( ( (m2_finseq_2 @ C)  @ B)  @  (k3_finseq_2 @ B) ) ) )  @  (^ [C: $i] : C) )  @  (^ [C: $i] :  ( (= @  (k3_finseq_1 @ C) )  @ A) ) ) ) ) ) ) , file(finseq_2, d4_finseq_2)).
thf(d5_finseq_1, axiom,  (! [A: $i] :  ( (= @  (k5_finseq_1 @ A) )  @  (k1_tarski @  ( (k4_tarski @ 1)  @ A) ) ) ) , file(finseq_1, d5_finseq_1)).
thf(d5_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k4_tarski @ A)  @ B) )  @  ( (k2_tarski @  ( (k2_tarski @ A)  @ B) )  @  (k1_tarski @ A) ) ) ) ) , file(tarski, d5_tarski)).
thf(d6_partfun1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  (! [C: $i] :  ( ( (r2_hidden @ C)  @  (k9_xtuple_0 @ B) )  =>  ( (= @  ( ( (k7_partfun1 @ A)  @ B)  @ C) )  @  ( (k1_funct_1 @ B)  @ C) ) ) ) ) ) ) , file(partfun1, d6_partfun1)).
thf(dt_k10_xtuple_0, axiom, $true, file(xtuple_0, k10_xtuple_0)).
thf(dt_k12_finseq_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (m2_finseq_1 @  ( (k12_finseq_1 @ A)  @ B) )  @ A) ) ) , file(finseq_1, k12_finseq_1)).
thf(dt_k13_finseq_1, axiom, $true, file(finseq_1, k13_finseq_1)).
thf(dt_k1_card_1, axiom,  (! [A: $i] :  (v1_card_1 @  (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)).
thf(dt_k1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  (k1_euclid @ A) )  @ k1_numbers) ) ) , file(euclid, k1_euclid)).
thf(dt_k1_finseq_1, axiom, $true, file(finseq_1, k1_finseq_1)).
thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)).
thf(dt_k1_pdiff_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  ( (v1_funct_1 @  ( (k1_pdiff_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k1_pdiff_1 @ A)  @ B) )  @  (k1_euclid @ B) )  @ k1_numbers)  &  ( (m1_subset_1 @  ( (k1_pdiff_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ B) )  @ k1_numbers) ) ) ) ) ) ) , file(pdiff_1, k1_pdiff_1)).
thf(dt_k1_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (m1_subset_1 @  ( (k1_relset_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(relset_1, k1_relset_1)).
thf(dt_k1_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (m1_subset_1 @  (k1_rvsum_1 @ A) )  @  (k1_zfmisc_1 @ k1_numbers) ) ) ) , file(rvsum_1, k1_rvsum_1)).
thf(dt_k1_seq_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( (m1_subset_1 @  ( (k1_seq_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(seq_1, k1_seq_1)).
thf(dt_k1_tarski, axiom, $true, file(tarski, k1_tarski)).
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_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_subset_1 @  (k2_finseq_1 @ A) )  @  (k1_zfmisc_1 @ k5_numbers) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(dt_k2_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  ( (v1_relat_1 @  (k2_funct_1 @ A) )  &  (v1_funct_1 @  (k2_funct_1 @ A) ) ) ) ) , file(funct_1, k2_funct_1)).
thf(dt_k2_tarski, axiom, $true, file(tarski, k2_tarski)).
thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)).
thf(dt_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( ( (m2_subset_1 @  (k3_finseq_1 @ A) )  @ k1_numbers)  @ k5_numbers) ) ) , file(finseq_1, k3_finseq_1)).
thf(dt_k3_finseq_2, axiom,  (! [A: $i] :  ( (m1_finseq_2 @  (k3_finseq_2 @ A) )  @ A) ) , file(finseq_2, k3_finseq_2)).
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_pdiff_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (v1_funct_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_pdiff_1 @ A)  @ B) )  &  ( (m1_subset_1 @  ( (k3_pdiff_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ 1) ) ) ) ) ) ) , file(pdiff_1, k3_pdiff_1)).
thf(dt_k3_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) ) ) , file(relat_1, k3_relat_1)).
thf(dt_k4_finseq_2, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  ( (k4_finseq_2 @ A)  @ B) )  @ B) ) ) , file(finseq_2, k4_finseq_2)).
thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k4_tarski, axiom, $true, file(tarski, k4_tarski)).
thf(dt_k5_finseq_1, axiom, $true, file(finseq_1, k5_finseq_1)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k7_partfun1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  ( (m1_subset_1 @  ( ( (k7_partfun1 @ A)  @ B)  @ C) )  @ A) ) ) , file(partfun1, k7_partfun1)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_m1_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) , file(finseq_1, m1_finseq_1)).
thf(dt_m1_finseq_2, axiom, $true, file(finseq_2, m1_finseq_2)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  =>  ( (v1_funct_1 @ B)  &  ( (v1_finseq_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) ) ) ) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(dt_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ A)  @ B)  =>  ( (m2_finseq_1 @ C)  @ A) ) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(dt_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  =>  ( (m1_subset_1 @ C)  @ A) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(existence_m1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_finseq_1 @ B)  @ A) ) ) , file(finseq_1, m1_finseq_1)).
thf(existence_m1_finseq_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_finseq_2 @ B)  @ A) ) ) , file(finseq_2, m1_finseq_2)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(existence_m2_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m2_finseq_1 @ B)  @ A) ) ) , file(finseq_1, m2_finseq_1)).
thf(existence_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (? [C: $i] :  ( ( (m2_finseq_2 @ C)  @ A)  @ B) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(existence_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (? [C: $i] :  ( ( (m2_subset_1 @ C)  @ A)  @ B) ) ) ) , file(subset_1, m2_subset_1)).
thf(fc108_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v4_relat_1 @ A)  @ k5_numbers) )  =>  (v6_membered @  (k9_xtuple_0 @ A) ) ) ) , file(valued_1, fc108_valued_1)).
thf(fc10_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_valued_2 @  (k1_euclid @ A) ) ) ) , file(euclid, fc10_euclid)).
thf(fc10_membered, axiom,  (! [A: $i] :  ( (v1_rat_1 @ A)  =>  (v4_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc10_membered)).
thf(fc11_membered, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v5_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc11_membered)).
thf(fc11_xxreal_2, axiom,  ( ~ ( (v3_xxreal_2 @ k1_numbers) )  &  ~ ( (v4_xxreal_2 @ k1_numbers) ) ) , file(xxreal_2, fc11_xxreal_2)).
thf(fc12_finseq_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k13_finseq_1 @ A) ) ) ) , file(finseq_1, fc12_finseq_1)).
thf(fc12_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) )  =>  (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) , file(funct_1, fc12_funct_1)).
thf(fc12_membered, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v6_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc12_membered)).
thf(fc13_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) )  =>  ~ ( (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) ) , file(funct_1, fc13_funct_1)).
thf(fc13_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_membered @  ( (k2_tarski @ A)  @ B) ) ) ) , file(membered, fc13_membered)).
thf(fc14_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (v4_funct_1 @  (k1_tarski @ A) ) ) ) , file(funct_1, fc14_funct_1)).
thf(fc14_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  (v2_membered @  ( (k2_tarski @ A)  @ B) ) ) ) , file(membered, fc14_membered)).
thf(fc14_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v1_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ D)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ D)  @ B) ) ) ) ) , file(valued_2, fc14_valued_2)).
thf(fc15_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  (v4_funct_1 @  ( (k2_tarski @ A)  @ B) ) ) ) , file(funct_1, fc15_funct_1)).
thf(fc15_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v3_membered @  ( (k2_tarski @ A)  @ B) ) ) ) , file(membered, fc15_membered)).
thf(fc15_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v2_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ D)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ D)  @ B) ) ) ) ) , file(valued_2, fc15_valued_2)).
thf(fc16_finseq_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k5_finseq_1 @ A) ) ) ) , file(finseq_1, fc16_finseq_1)).
thf(fc16_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v1_rat_1 @ A)  &  (v1_rat_1 @ B) )  =>  (v4_membered @  ( (k2_tarski @ A)  @ B) ) ) ) , file(membered, fc16_membered)).
thf(fc16_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v1_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  (v1_valued_0 @  ( (k1_funct_1 @ D)  @ B) ) ) ) , file(valued_2, fc16_valued_2)).
thf(fc17_funct_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v4_funct_1 @ A)  &  ( (v1_relat_1 @ C)  &  ( ( (v5_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ C)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ C)  @ B) ) ) ) ) , file(funct_1, fc17_funct_1)).
thf(fc17_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v1_int_1 @ A)  &  (v1_int_1 @ B) )  =>  (v5_membered @  ( (k2_tarski @ A)  @ B) ) ) ) , file(membered, fc17_membered)).
thf(fc17_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v2_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  (v2_valued_0 @  ( (k1_funct_1 @ D)  @ B) ) ) ) , file(valued_2, fc17_valued_2)).
thf(fc17_xxreal_2, axiom,  (v6_xxreal_2 @ k1_numbers) , file(xxreal_2, fc17_xxreal_2)).
thf(fc18_funct_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ~ ( (v1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) ) , file(funct_1, fc18_funct_1)).
thf(fc18_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  (v6_membered @  ( (k2_tarski @ A)  @ B) ) ) ) , file(membered, fc18_membered)).
thf(fc18_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v3_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  (v3_valued_0 @  ( (k1_funct_1 @ D)  @ B) ) ) ) , file(valued_2, fc18_valued_2)).
thf(fc19_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v4_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  ( (v5_relat_1 @  ( (k1_funct_1 @ D)  @ B) )  @ k3_numbers) ) ) , file(valued_2, fc19_valued_2)).
thf(fc1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ~ ( (v1_xboole_0 @  (k1_euclid @ A) ) ) ) ) , file(euclid, fc1_euclid)).
thf(fc1_finseq_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  (v1_xboole_0 @ A) )  =>  (v1_xboole_0 @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, fc1_finseq_1)).
thf(fc1_finseq_5, axiom,  (! [A: $i] :  (v1_zfmisc_1 @  (k5_finseq_1 @ A) ) ) , file(finseq_5, fc1_finseq_5)).
thf(fc1_funct_1, axiom,  (! [A: $i, B: $i] :  (v1_funct_1 @  (k1_tarski @  ( (k4_tarski @ A)  @ B) ) ) ) , file(funct_1, fc1_funct_1)).
thf(fc1_numbers, axiom,  ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)).
thf(fc1_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (v1_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc1_valued_0)).
thf(fc1_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (v1_valued_2 @  (k1_tarski @ A) ) ) ) , file(valued_2, fc1_valued_2)).
thf(fc1_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc1_xtuple_0, axiom,  (! [A: $i, B: $i] :  (v1_xtuple_0 @  ( (k4_tarski @ A)  @ B) ) ) , file(xtuple_0, fc1_xtuple_0)).
thf(fc20_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v5_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  ( (v5_relat_1 @  ( (k1_funct_1 @ D)  @ B) )  @ k4_numbers) ) ) , file(valued_2, fc20_valued_2)).
thf(fc21_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v6_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  (v4_valued_0 @  ( (k1_funct_1 @ D)  @ B) ) ) ) , file(valued_2, fc21_valued_2)).
thf(fc22_finseq_1, axiom,  (! [A: $i] :  (v4_funct_1 @  (k13_finseq_1 @ A) ) ) , file(finseq_1, fc22_finseq_1)).
thf(fc23_finseq_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) )  =>  ~ ( (v1_xboole_0 @  (k1_finseq_1 @ A) ) ) ) ) , file(finseq_1, fc23_finseq_1)).
thf(fc24_finseq_1, axiom,  (! [A: $i] :  ( (v3_card_1 @  (k5_finseq_1 @ A) )  @ 1) ) , file(finseq_1, fc24_finseq_1)).
thf(fc27_finseq_1, axiom,  (! [A: $i] :  (v3_finseq_1 @  (k13_finseq_1 @ A) ) ) , file(finseq_1, fc27_finseq_1)).
thf(fc29_finseq_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v3_finseq_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) )  =>  (v1_finseq_1 @  ( (k1_funct_1 @ B)  @ C) ) ) ) , file(finseq_1, fc29_finseq_1)).
thf(fc2_finseq_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) )  =>  ~ ( (v1_xboole_0 @  (k1_finseq_1 @ A) ) ) ) ) , file(finseq_1, fc2_finseq_1)).
thf(fc2_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc2_funct_1)).
thf(fc2_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (v2_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc2_valued_0)).
thf(fc2_xboole_0, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_tarski @ A) ) ) ) , file(xboole_0, fc2_xboole_0)).
thf(fc34_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v7_valued_2 @ A) )  =>  (v1_valued_2 @  (k10_xtuple_0 @ A) ) ) ) , file(valued_2, fc34_valued_2)).
thf(fc35_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v8_valued_2 @ A) )  =>  (v2_valued_2 @  (k10_xtuple_0 @ A) ) ) ) , file(valued_2, fc35_valued_2)).
thf(fc36_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v9_valued_2 @ A) )  =>  (v3_valued_2 @  (k10_xtuple_0 @ A) ) ) ) , file(valued_2, fc36_valued_2)).
thf(fc37_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v10_valued_2 @ A) )  =>  (v4_valued_2 @  (k10_xtuple_0 @ A) ) ) ) , file(valued_2, fc37_valued_2)).
thf(fc38_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v11_valued_2 @ A) )  =>  (v5_valued_2 @  (k10_xtuple_0 @ A) ) ) ) , file(valued_2, fc38_valued_2)).
thf(fc39_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v12_valued_2 @ A) )  =>  (v6_valued_2 @  (k10_xtuple_0 @ A) ) ) ) , file(valued_2, fc39_valued_2)).
thf(fc3_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, fc3_finseq_1)).
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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (v3_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc3_valued_0)).
thf(fc3_xboole_0, axiom,  (! [A: $i, B: $i] :  ~ ( (v1_xboole_0 @  ( (k2_tarski @ A)  @ B) ) ) ) , file(xboole_0, fc3_xboole_0)).
thf(fc40_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v7_valued_2 @ A) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) , file(valued_2, fc40_valued_2)).
thf(fc41_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v8_valued_2 @ A) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) , file(valued_2, fc41_valued_2)).
thf(fc42_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v7_valued_2 @ A) ) )  =>  (v1_valued_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_2, fc42_valued_2)).
thf(fc43_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v8_valued_2 @ A) ) )  =>  (v2_valued_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_2, fc43_valued_2)).
thf(fc44_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v9_valued_2 @ A) ) )  =>  (v3_valued_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_2, fc44_valued_2)).
thf(fc45_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v10_valued_2 @ A) ) )  =>  ( (v5_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_2, fc45_valued_2)).
thf(fc46_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v11_valued_2 @ A) ) )  =>  ( (v5_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_2, fc46_valued_2)).
thf(fc47_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v12_valued_2 @ A) ) )  =>  (v4_valued_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_2, fc47_valued_2)).
thf(fc4_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_card_1 @  (k1_finseq_1 @ A) )  @ A) ) ) , file(finseq_1, fc4_finseq_1)).
thf(fc4_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (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 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ C) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ C) )  @ A)  @ B) ) ) ) , file(funct_2, fc4_funct_2)).
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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (v4_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc4_valued_0)).
thf(fc4_xtuple_0, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) , file(xtuple_0, fc4_xtuple_0)).
thf(fc55_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v1_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc55_valued_0)).
thf(fc56_membered, axiom,  (v7_membered @ k1_numbers) , file(membered, fc56_membered)).
thf(fc56_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v2_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v2_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc56_valued_0)).
thf(fc57_membered, axiom,  (v7_membered @ k3_numbers) , file(membered, fc57_membered)).
thf(fc57_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v3_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc57_valued_0)).
thf(fc58_membered, axiom,  (v7_membered @ k4_numbers) , file(membered, fc58_membered)).
thf(fc58_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ k3_numbers) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  @ k3_numbers) ) ) ) , file(valued_0, fc58_valued_0)).
thf(fc59_membered, axiom,  (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)).
thf(fc59_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ k4_numbers) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  @ k4_numbers) ) ) ) , file(valued_0, fc59_valued_0)).
thf(fc5_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k4_finseq_2 @ A)  @ B) ) ) ) ) , file(finseq_2, fc5_finseq_2)).
thf(fc5_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ B)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ B) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ C) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ C) )  @ A)  @ B) ) ) ) , file(funct_2, fc5_funct_2)).
thf(fc5_membered, axiom,  (v5_membered @ k4_numbers) , file(membered, fc5_membered)).
thf(fc5_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (v5_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc5_valued_0)).
thf(fc5_xtuple_0, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) , file(xtuple_0, fc5_xtuple_0)).
thf(fc60_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v4_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v4_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc60_valued_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_finseq_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k5_finseq_1 @ A) )  &  (v1_funct_1 @  (k5_finseq_1 @ A) ) ) ) , file(finseq_1, fc6_finseq_1)).
thf(fc6_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k2_funct_1 @ A) )  &  ( (v1_funct_1 @  (k2_funct_1 @ A) )  &  (v2_funct_1 @  (k2_funct_1 @ A) ) ) ) ) ) , file(funct_1, fc6_funct_1)).
thf(fc6_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( (v2_funct_2 @ B)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) )  &  ( (v1_funct_1 @ C)  &  ( ( (v2_funct_2 @ C)  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ C)  @ B) )  &  ( (v2_funct_2 @  ( (k3_relat_1 @ C)  @ B) )  @ A) ) ) ) , file(funct_2, fc6_funct_2)).
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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (v6_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc6_valued_0)).
thf(fc7_finseq_1, axiom,  (! [A: $i] :  (v1_finseq_1 @  (k5_finseq_1 @ A) ) ) , file(finseq_1, fc7_finseq_1)).
thf(fc7_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v2_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v2_funct_1 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc7_funct_1)).
thf(fc7_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  &  ( ( ( (v3_funct_2 @ B)  @ A)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ A)  &  ( ( ( (v3_funct_2 @ C)  @ A)  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ B)  @ C) )  &  ( ( ( (v1_funct_2 @  ( (k3_relat_1 @ B)  @ C) )  @ A)  @ A)  &  ( ( (v3_funct_2 @  ( (k3_relat_1 @ B)  @ C) )  @ A)  @ A) ) ) ) ) , file(funct_2, fc7_funct_2)).
thf(fc7_membered, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc7_membered)).
thf(fc7_numbers, axiom,  ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers)).
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_euclid, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_finseq_1 @  ( (k4_finseq_2 @ A)  @ B) ) ) ) , file(euclid, fc8_euclid)).
thf(fc8_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ B)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ C) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ E) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ E) )  @ A)  @ C) ) ) ) , file(funct_2, fc8_funct_2)).
thf(fc8_membered, axiom,  (! [A: $i] :  ( (v1_xxreal_0 @ A)  =>  (v2_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc8_membered)).
thf(fc8_nat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  &  ( ( (v4_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  @ B)  &  (v1_funct_1 @  ( (k3_relat_1 @ A)  @ C) ) ) ) ) ) ) , file(nat_1, fc8_nat_1)).
thf(fc8_numbers, axiom,  ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers)).
thf(fc8_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C) ) )  =>  (v1_relat_1 @  (k9_xtuple_0 @ D) ) ) ) , file(relset_1, fc8_relset_1)).
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(fc91_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v5_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc91_valued_0)).
thf(fc92_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v7_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v7_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc92_valued_0)).
thf(fc93_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v6_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v5_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc93_valued_0)).
thf(fc94_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v8_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v7_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc94_valued_0)).
thf(fc95_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v6_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc95_valued_0)).
thf(fc96_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v6_valued_0 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(valued_0, fc96_valued_0)).
thf(fc97_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v8_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc97_valued_0)).
thf(fc98_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v8_valued_0 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(valued_0, fc98_valued_0)).
thf(fc9_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_finseq_1 @  (k1_euclid @ A) ) ) ) , file(euclid, fc9_euclid)).
thf(fc9_membered, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v3_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc9_membered)).
thf(fc9_nat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  &  ( (v1_partfun1 @  ( (k3_relat_1 @ A)  @ C) )  @ k5_numbers) ) ) ) , file(nat_1, fc9_nat_1)).
thf(fc9_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @  ( (k2_zfmisc_1 @ B)  @ C) ) ) )  =>  (v1_relat_1 @  (k10_xtuple_0 @ D) ) ) ) , file(relset_1, fc9_relset_1)).
thf(ie1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (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) ) ) )  =>  ( (= @  ( ( (k7_partfun1 @ B)  @ C)  @ D) )  @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) ) ) ) , file(funct_2, ie1_funct_2)).
thf(projectivity_k1_card_1, axiom,  (! [A: $i] :  ( (= @  (k1_card_1 @  (k1_card_1 @ A) ) )  @  (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)).
thf(projectivity_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (= @  (k3_finseq_1 @  (k3_finseq_1 @ A) ) )  @  (k3_finseq_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)).
thf(rc1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) ) ) , file(finseq_1, rc1_finseq_1)).
thf(rc1_finseq_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) , file(finseq_2, rc1_finseq_2)).
thf(rc1_finseq_5, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v2_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) ) , file(finseq_5, rc1_finseq_5)).
thf(rc1_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) , file(funct_1, rc1_funct_1)).
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_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_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_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) , file(valued_1, rc1_valued_1)).
thf(rc1_valued_2, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_valued_2 @ A) ) ) , file(valued_2, rc1_valued_2)).
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(rc1_xtuple_0, axiom,  (? [A: $i] :  (v1_xtuple_0 @ A) ) , file(xtuple_0, rc1_xtuple_0)).
thf(rc1_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc1_xxreal_0)).
thf(rc1_xxreal_2, axiom,  (? [A: $i] :  ( (v1_membered @ A)  &  ( (v2_membered @ A)  &  ( (v3_membered @ A)  &  ( (v4_membered @ A)  &  ( (v5_membered @ A)  &  ( (v6_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_2 @ A)  &  (v2_xxreal_2 @ A) ) ) ) ) ) ) ) ) ) , file(xxreal_2, rc1_xxreal_2)).
thf(rc2_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_xboole_0 @ B)  &  ( (v1_finset_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc2_finseq_1)).
thf(rc2_finseq_5, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v2_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(finseq_5, rc2_finseq_5)).
thf(rc2_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) ) ) , file(funct_1, rc2_funct_1)).
thf(rc2_funct_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  &  ( ( (v3_funct_2 @ B)  @ A)  @ A) ) ) ) ) ) ) ) ) ) , file(funct_2, rc2_funct_2)).
thf(rc2_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc2_membered)).
thf(rc2_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_ordinal1 @ A) ) ) ) , file(nat_1, rc2_nat_1)).
thf(rc2_valued_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v3_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) ) ) ) ) , file(valued_0, rc2_valued_0)).
thf(rc2_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(valued_1, rc2_valued_1)).
thf(rc2_valued_2, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v12_valued_2 @ A) ) ) ) , file(valued_2, rc2_valued_2)).
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_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc2_xcmplx_0)).
thf(rc2_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc2_xreal_0)).
thf(rc2_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) , file(xxreal_0, rc2_xxreal_0)).
thf(rc2_xxreal_2, axiom,  (? [A: $i] :  ( (v6_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) ) , file(xxreal_2, rc2_xxreal_2)).
thf(rc3_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) , file(finseq_1, rc3_finseq_1)).
thf(rc3_finseq_5, axiom,  (? [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) , file(finseq_5, rc3_finseq_5)).
thf(rc3_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v6_membered @ A)  &  (v7_membered @ A) ) ) ) , file(membered, rc3_membered)).
thf(rc3_valued_0, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ( (v1_partfun1 @ A)  @ k5_numbers)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (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)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) ) ) ) , file(valued_1, rc3_valued_1)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc3_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) , file(xxreal_0, rc3_xxreal_0)).
thf(rc3_xxreal_2, axiom,  (? [A: $i] :  ( (v1_membered @ A)  &  ( (v2_membered @ A)  &  ( (v3_membered @ A)  &  ( (v4_membered @ A)  &  ( (v5_membered @ A)  &  ( (v6_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_2 @ A)  &  (v5_xxreal_2 @ A) ) ) ) ) ) ) ) ) ) , file(xxreal_2, rc3_xxreal_2)).
thf(rc4_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) , file(finseq_1, rc4_finseq_1)).
thf(rc4_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v3_funct_1 @ B)  &  ( ( (v1_funct_2 @ B)  @ k5_numbers)  @ A) ) ) ) ) ) ) ) ) , file(valued_0, rc4_valued_0)).
thf(rc4_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v3_card_1 @ A)  @ 1) ) ) ) ) ) , file(valued_1, rc4_valued_1)).
thf(rc4_xreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc4_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, rc4_xxreal_0)).
thf(rc4_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) , file(xxreal_2, rc4_xxreal_2)).
thf(rc5_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) ) ) , file(funct_1, rc5_funct_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_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( (v1_xxreal_2 @ A)  &  ( (v2_xxreal_2 @ A)  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc5_xxreal_2)).
thf(rc6_finseq_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc6_finseq_1)).
thf(rc6_funct_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  (v1_funct_1 @ C) ) ) ) ) ) , file(funct_1, rc6_funct_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(rc6_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xxreal_2 @ A) )  &  ( (v2_xxreal_2 @ A)  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc6_xxreal_2)).
thf(rc7_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( ( (v3_card_1 @ B)  @ A)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc7_finseq_1)).
thf(rc7_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_funct_1 @ A) ) ) , file(funct_1, rc7_funct_1)).
thf(rc7_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( (v1_xxreal_2 @ A)  &  ( ~ ( (v2_xxreal_2 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc7_xxreal_2)).
thf(rc8_finseq_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_finseq_1 @ A) ) ) , file(finseq_1, rc8_finseq_1)).
thf(rc8_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xxreal_2 @ A) )  &  ( ~ ( (v2_xxreal_2 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) ) ) , file(xxreal_2, rc8_xxreal_2)).
thf(rc9_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) , file(finseq_1, rc9_finseq_1)).
thf(redefinition_k12_finseq_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (= @  ( (k12_finseq_1 @ A)  @ B) )  @  (k5_finseq_1 @ B) ) ) ) , file(finseq_1, k12_finseq_1)).
thf(redefinition_k1_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (= @  ( (k1_relset_1 @ A)  @ B) )  @  (k9_xtuple_0 @ B) ) ) ) , file(relset_1, k1_relset_1)).
thf(redefinition_k1_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (= @  (k1_rvsum_1 @ A) )  @  (k10_xtuple_0 @ A) ) ) ) , file(rvsum_1, k1_rvsum_1)).
thf(redefinition_k1_seq_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( (= @  ( (k1_seq_1 @ A)  @ B) )  @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(seq_1, k1_seq_1)).
thf(redefinition_k2_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k2_finseq_1 @ A) )  @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(redefinition_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (= @  (k3_finseq_1 @ A) )  @  (k1_card_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)).
thf(redefinition_k3_finseq_2, axiom,  (! [A: $i] :  ( (= @  (k3_finseq_2 @ A) )  @  (k13_finseq_1 @ A) ) ) , file(finseq_2, k3_finseq_2)).
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_k5_numbers, axiom,  ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  <=>  ( (m1_finseq_1 @ B)  @ A) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(redefinition_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(redefinition_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(redefinition_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ D)  <=>  ( (= @ C)  @ D) ) ) ) , file(relset_1, r2_relset_1)).
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(reflexivity_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ C) ) ) , file(relset_1, r2_relset_1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom,  ( (r1_xxreal_0 @ 1)  @ 1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r1)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ 1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( ( (v2_xxreal_0 @ 1)  &  ( ( (m2_subset_1 @ 1)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ 1)  @ k5_numbers)  &  ( (m1_subset_1 @ 1)  @ k1_numbers) ) ) , file(numerals, spc1_numerals)).
thf(symmetry_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ D)  =>  ( ( ( (r2_relset_1 @ A)  @ B)  @ D)  @ C) ) ) ) , file(relset_1, r2_relset_1)).
thf(t12_funct_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( ( (r2_hidden @ A)  @  (k9_xtuple_0 @  ( (k3_relat_1 @ C)  @ B) ) )  =>  ( (= @  ( (k1_funct_1 @  ( (k3_relat_1 @ C)  @ B) )  @ A) )  @  ( (k1_funct_1 @ B)  @  ( (k1_funct_1 @ C)  @ A) ) ) ) ) ) ) ) ) , file(funct_1, t12_funct_1)).
thf(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_pdiff_1, axiom,  ( (! [A: $i] :  ( ( ( (m2_subset_1 @ A)  @ k1_numbers)  @ k5_numbers)  =>  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  ( ( (r2_hidden @ A)  @  (k2_finseq_1 @ B) )  =>  ( ( (= @  ( (k1_relset_1 @  (k1_euclid @ B) )  @  ( (k1_pdiff_1 @ A)  @ B) ) )  @  (k1_euclid @ B) )  &  ( (= @  (k1_rvsum_1 @  ( (k1_pdiff_1 @ A)  @ B) ) )  @ k1_numbers) ) ) ) ) ) )  &  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( ( (= @  ( (k1_seq_1 @  ( (k1_pdiff_1 @ 1)  @ 1) )  @  ( (k12_finseq_1 @ k1_numbers)  @ A) ) )  @ A)  &  ( (= @  ( (k1_funct_1 @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) )  @ A) )  @  ( (k12_finseq_1 @ k1_numbers)  @ A) ) ) ) ) ) , file(pdiff_1, t1_pdiff_1)).
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_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t27_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( (v1_relat_1 @ B)  =>  ( ( (r1_tarski @  (k10_xtuple_0 @ A) )  @  (k9_xtuple_0 @ B) )  =>  ( (= @  (k9_xtuple_0 @  ( (k3_relat_1 @ A)  @ B) ) )  @  (k9_xtuple_0 @ A) ) ) ) ) ) ) , file(relat_1, t27_relat_1)).
thf(t2_pdiff_1, axiom,  ( ( (v1_funct_1 @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) )  &  ( ( ( (v1_funct_2 @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) )  @ k1_numbers)  @  (k1_euclid @ 1) )  &  ( (m1_subset_1 @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (k1_euclid @ 1) ) ) ) ) )  &  ( (v2_funct_1 @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) )  &  ( ( (= @  (k9_xtuple_0 @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) ) )  @ k1_numbers)  &  ( ( (= @  (k10_xtuple_0 @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) ) )  @  (k1_euclid @ 1) )  &  (? [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k1_numbers)  @  (k1_euclid @ 1) )  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (k1_euclid @ 1) ) ) ) ) )  &  ( ( ( (v3_funct_2 @ A)  @ k1_numbers)  @  (k1_euclid @ 1) )  &  ( (= @  (k2_funct_1 @  ( (k1_pdiff_1 @ 1)  @ 1) ) )  @ A) ) ) ) ) ) ) ) , file(pdiff_1, t2_pdiff_1)).
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_hidden @ 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(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_hidden @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t5_partfun1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( (= @  ( (k1_relset_1 @ A)  @ C) )  @  ( (k1_relset_1 @ A)  @ D) )  &  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @ A)  =>  ( ( (r2_hidden @ E)  @  ( (k1_relset_1 @ A)  @ C) )  =>  ( (= @  ( (k1_funct_1 @ C)  @ E) )  @  ( (k1_funct_1 @ D)  @ E) ) ) ) ) )  =>  ( (= @ C)  @ D) ) ) ) ) ) ) ) , file(partfun1, t5_partfun1)).
thf(t5_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (v3_xxreal_0 @ A)  |  (v2_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t5_real)).
thf(t5_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_hidden @ 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)  =>  ( (v1_xboole_0 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ 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(t97_finseq_2, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( ( (v3_card_1 @ B)  @ 1)  &  ( (m2_finseq_1 @ B)  @ A) )  =>  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @ A)  &  ( (= @ B)  @  ( (k12_finseq_1 @ A)  @ C) ) ) ) ) ) ) ) , file(finseq_2, t97_finseq_2)).
thf(s3_partfun1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i > $i] :  (! [D: $i > $o] :  ( (! [E: $i] :  ( (D @ E)  =>  ( (r2_hidden @  (C @ E) )  @ B) ) )  =>  (? [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (! [F: $i] :  ( ( (r2_hidden @ F)  @  ( (k1_relset_1 @ A)  @ E) )  <=>  ( ( (r2_hidden @ F)  @ A)  &  (D @ F) ) ) )  &  (! [F: $i] :  ( ( (r2_hidden @ F)  @  ( (k1_relset_1 @ A)  @ E) )  =>  ( (= @  ( (k1_funct_1 @ E)  @ F) )  @  (C @ F) ) ) ) ) ) ) ) ) ) ) ) , file(partfun1, s3_partfun1)).
thf(t29_pdiff_7, conjecture,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ A)  @ k5_numbers) )  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ 1) ) ) ) )  =>  (? [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) )  &  ( ( ( (r2_relset_1 @  (k1_euclid @ A) )  @  (k1_euclid @ 1) )  @ B)  @  ( (k3_pdiff_1 @ A)  @ C) ) ) ) ) ) ) ) , file(pdiff_7, t29_pdiff_7)).