% Mizar problem: s4_stirl2_1,stirl2_1,1211,6 
include('Axioms/SET010^1.ax').
thf(n1_type, type, np__1: $i).
thf(f1_s4_stirl2_1_type, type, f1_s4_stirl2_1: $i).
thf(f2_s4_stirl2_1_type, type, f2_s4_stirl2_1: $i).
thf(f3_s4_stirl2_1_type, type, f3_s4_stirl2_1: $i).
thf(f4_s4_stirl2_1_type, type, f4_s4_stirl2_1: $i).
thf(k10_xtuple_0_type, type, k10_xtuple_0: $i > $i).
thf(k1_card_1_type, type, k1_card_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_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_partfun1_type, type, k2_partfun1: $i > $i > $i > $i > $i).
thf(k2_relset_1_type, type, k2_relset_1: $i > $i > $i).
thf(k2_xboole_0_type, type, k2_xboole_0: $i > $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k3_numbers_type, type, k3_numbers: $i).
thf(k4_numbers_type, type, k4_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_xboole_0_type, type, k4_xboole_0: $i > $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k5_relat_1_type, type, k5_relat_1: $i > $i > $i).
thf(k6_subset_1_type, type, k6_subset_1: $i > $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(p1_s4_stirl2_1_type, type, p1_s4_stirl2_1: $i > $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(v1_afinsq_1_type, type, v1_afinsq_1: $i > $o).
thf(v1_card_1_type, type, v1_card_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_ordinal1_type, type, v1_ordinal1: $i > $o).
thf(v1_partfun1_type, type, v1_partfun1: $i > $i > $o).
thf(v1_rat_1_type, type, v1_rat_1: $i > $o).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_setfam_1_type, type, v1_setfam_1: $i > $o).
thf(v1_subset_1_type, type, v1_subset_1: $i > $i > $o).
thf(v1_valued_0_type, type, v1_valued_0: $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(v1_xxreal_2_type, type, v1_xxreal_2: $i > $o).
thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_card_1_type, type, v2_card_1: $i > $o).
thf(v2_finset_1_type, type, v2_finset_1: $i > $o).
thf(v2_funct_1_type, type, v2_funct_1: $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_relat_1_type, type, v2_relat_1: $i > $o).
thf(v2_valued_0_type, type, v2_valued_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v2_xxreal_2_type, type, v2_xxreal_2: $i > $o).
thf(v3_card_1_type, type, v3_card_1: $i > $i > $o).
thf(v3_funct_1_type, type, v3_funct_1: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_relat_1_type, type, v3_relat_1: $i > $o).
thf(v3_valued_0_type, type, v3_valued_0: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(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_partfun3_type, type, v4_partfun3: $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_xxreal_2_type, type, v4_xxreal_2: $i > $o).
thf(v5_finset_1_type, type, v5_finset_1: $i > $o).
thf(v5_membered_type, type, v5_membered: $i > $o).
thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o).
thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o).
thf(v5_valued_0_type, type, v5_valued_0: $i > $o).
thf(v5_xxreal_2_type, type, v5_xxreal_2: $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v6_valued_0_type, type, v6_valued_0: $i > $o).
thf(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(v8_valued_0_type, type, v8_valued_0: $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_card_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) )  =>  ( (v3_card_1 @ A)  @ np__1) ) ) , file(card_1, cc10_card_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_ordinal1, axiom,  (! [A: $i] :  ( (v6_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1)).
thf(cc10_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_valued_0 @ B) ) ) ) ) , file(valued_0, cc10_valued_0)).
thf(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_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_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_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_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_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_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_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_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_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(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(cc1_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_xboole_0 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(afinsq_1, cc1_afinsq_1)).
thf(cc1_afinsq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v7_ordinal1 @ A)  &  (v6_membered @ A) ) ) ) , file(afinsq_2, cc1_afinsq_2)).
thf(cc1_binop_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k3_numbers)  =>  (v1_rat_1 @ A) ) ) , file(binop_2, cc1_binop_2)).
thf(cc1_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(card_1, cc1_card_1)).
thf(cc1_finset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_finset_1 @ A) ) ) , file(finset_1, cc1_finset_1)).
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_int_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_numbers)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc1_int_1)).
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_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)).
thf(cc1_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_relat_1 @ A) ) ) , file(relat_1, cc1_relat_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_stirl2_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(stirl2_1, cc1_stirl2_1)).
thf(cc1_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_xboole_0 @ B) ) ) ) ) , file(subset_1, cc1_subset_1)).
thf(cc1_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) ) ) ) , file(valued_0, cc1_valued_0)).
thf(cc1_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(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(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(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(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(cc25_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  (v6_membered @ A) ) ) , file(membered, cc25_membered)).
thf(cc26_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_membered @ A) ) ) , file(membered, cc26_membered)).
thf(cc2_afinsq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) ) ) ) ) ) ) , file(afinsq_1, cc2_afinsq_1)).
thf(cc2_afinsq_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_partfun3 @ A) ) ) ) , file(afinsq_2, cc2_afinsq_2)).
thf(cc2_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc2_card_1)).
thf(cc2_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_finset_1 @ B) ) ) ) ) , file(finset_1, cc2_finset_1)).
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_int_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc2_int_1)).
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_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) )  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)).
thf(cc2_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_relat_1 @ B) ) ) ) ) , file(relat_1, cc2_relat_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_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( ~ ( ( (v1_subset_1 @ B)  @ A) )  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) ) , file(subset_1, cc2_subset_1)).
thf(cc2_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc2_valued_0)).
thf(cc2_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(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(cc3_afinsq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( (v1_finset_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) ) ) ) ) ) , file(afinsq_1, cc3_afinsq_1)).
thf(cc3_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc3_card_1)).
thf(cc3_finset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_finset_1 @ A)  =>  (! [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_funct_2 @ C)  @ A)  @ B)  &  (v1_finset_1 @ C) ) ) ) ) ) ) ) , file(finset_1, cc3_finset_1)).
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_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(int_1, cc3_int_1)).
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_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)).
thf(cc3_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_relat_1 @ A) ) ) ) , file(relat_1, cc3_relat_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_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc3_subset_1)).
thf(cc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc3_valued_0)).
thf(cc3_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_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k1_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k1_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v3_valued_0 @ A) ) ) ) ) ) ) ) , file(afinsq_1, cc4_afinsq_1)).
thf(cc4_card_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc4_card_1)).
thf(cc4_finset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(finset_1, cc4_finset_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_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) ) , file(relat_1, cc4_relat_1)).
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_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc4_subset_1)).
thf(cc4_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc4_valued_0)).
thf(cc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(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_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k5_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k5_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v4_valued_0 @ A) ) ) ) ) ) ) ) , file(afinsq_1, cc5_afinsq_1)).
thf(cc5_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc5_card_1)).
thf(cc5_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_zfmisc_1 @ A) ) ) ) , file(finset_1, cc5_finset_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_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v1_membered @ A) ) ) , file(membered, cc5_membered)).
thf(cc5_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
thf(cc5_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v4_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc5_relat_1)).
thf(cc5_subset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_zfmisc_1 @ B) ) ) ) ) , file(subset_1, cc5_subset_1)).
thf(cc5_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) ) ) ) , file(valued_0, cc5_valued_0)).
thf(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_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_xboole_0 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) , file(afinsq_1, cc6_afinsq_1)).
thf(cc6_card_1, axiom,  (! [A: $i] :  ( ( (v3_ordinal1 @ A)  &  (v1_finset_1 @ A) )  =>  (v7_ordinal1 @ A) ) ) , file(card_1, cc6_card_1)).
thf(cc6_finset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_finset_1 @ A) ) ) , file(finset_1, cc6_finset_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_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v5_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc6_relat_1)).
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_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_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) ) ) , file(afinsq_1, cc7_afinsq_1)).
thf(cc7_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ k1_xboole_0)  =>  (v1_xboole_0 @ A) ) ) , file(card_1, cc7_card_1)).
thf(cc7_finset_1, axiom,  (! [A: $i] :  ( (v5_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finset_1 @ B) ) ) ) ) , file(finset_1, cc7_finset_1)).
thf(cc7_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v4_funct_1 @ A) ) ) , file(funct_1, cc7_funct_1)).
thf(cc7_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc7_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) ) ) ) ) ) ) , file(relat_1, cc7_relat_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_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_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) ) ) , file(afinsq_1, cc8_afinsq_1)).
thf(cc8_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (v3_card_1 @ A)  @ k1_xboole_0) ) ) , file(card_1, cc8_card_1)).
thf(cc8_finset_1, axiom,  (! [A: $i] :  ( (v5_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_finset_1 @ B) ) ) ) ) , file(finset_1, cc8_finset_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_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc8_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) ) ) ) ) ) ) , file(relat_1, cc8_relat_1)).
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_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_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(afinsq_1, cc9_afinsq_1)).
thf(cc9_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ np__1)  =>  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) ) ) ) , file(card_1, cc9_card_1)).
thf(cc9_finset_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_finset_1 @ A) ) ) ) , file(finset_1, cc9_finset_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_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1)).
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_xxreal_2, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  ( (v6_membered @ A)  &  (v3_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc9_xxreal_2)).
thf(commutativity_k2_xboole_0, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k2_xboole_0 @ A)  @ B) )  @  ( (k2_xboole_0 @ B)  @ A) ) ) , file(xboole_0, k2_xboole_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_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (= @ B)  @  (k1_tarski @ A) )  <=>  (! [C: $i] :  ( ( (r2_hidden @ C)  @ B)  <=>  ( (= @ C)  @ A) ) ) ) ) ) , file(tarski, d1_tarski)).
thf(d2_xboole_0, axiom,  ( (= @ k1_xboole_0)  @  (eps @  (^ [A: $i] :  (v1_xboole_0 @ A) ) ) ) , file(xboole_0, d2_xboole_0)).
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(dt_f1_s4_stirl2_1, axiom, $true, file(stirl2_1, f1_s4_stirl2_1)).
thf(dt_f2_s4_stirl2_1, axiom, $true, file(stirl2_1, f2_s4_stirl2_1)).
thf(dt_f3_s4_stirl2_1, axiom, $true, file(stirl2_1, f3_s4_stirl2_1)).
thf(dt_f4_s4_stirl2_1, axiom, $true, file(stirl2_1, f4_s4_stirl2_1)).
thf(dt_k10_xtuple_0, axiom, $true, file(xtuple_0, k10_xtuple_0)).
thf(dt_k1_card_1, axiom,  (! [A: $i] :  (v1_card_1 @  (k1_card_1 @ A) ) ) , file(card_1, k1_card_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_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_partfun1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( (v1_funct_1 @  ( ( ( (k2_partfun1 @ A)  @ B)  @ C)  @ D) )  &  ( (m1_subset_1 @  ( ( ( (k2_partfun1 @ A)  @ B)  @ C)  @ D) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) ) , file(partfun1, k2_partfun1)).
thf(dt_k2_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (m1_subset_1 @  ( (k2_relset_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(relset_1, k2_relset_1)).
thf(dt_k2_xboole_0, axiom, $true, file(xboole_0, k2_xboole_0)).
thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)).
thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)).
thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k4_xboole_0, axiom, $true, file(xboole_0, k4_xboole_0)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k5_relat_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @ A)  =>  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) , file(relat_1, k5_relat_1)).
thf(dt_k6_subset_1, axiom,  (! [A: $i, B: $i] :  ( (m1_subset_1 @  ( (k6_subset_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) , file(subset_1, k6_subset_1)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
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_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
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(fc10_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(card_1, fc10_card_1)).
thf(fc10_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  (v1_setfam_1 @  (k10_xtuple_0 @ A) ) ) ) , file(funct_1, fc10_funct_1)).
thf(fc10_membered, axiom,  (! [A: $i] :  ( (v1_rat_1 @ A)  =>  (v4_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc10_membered)).
thf(fc10_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc10_relat_1)).
thf(fc10_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) ) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relset_1, fc10_relset_1)).
thf(fc10_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(subset_1, fc10_subset_1)).
thf(fc10_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ k3_numbers) ) )  =>  ( (v5_relat_1 @  ( (k2_xboole_0 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc10_valued_0)).
thf(fc11_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) , file(card_1, fc11_card_1)).
thf(fc11_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) )  &  ( (m1_subset_1 @ B)  @  (k9_xtuple_0 @ A) ) )  =>  ~ ( (v1_xboole_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc11_funct_1)).
thf(fc11_membered, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v5_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc11_membered)).
thf(fc11_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) , file(relat_1, fc11_relat_1)).
thf(fc11_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ k4_numbers) ) )  =>  ( (v5_relat_1 @  ( (k2_xboole_0 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc11_valued_0)).
thf(fc11_xxreal_2, axiom,  ( ~ ( (v3_xxreal_2 @ k1_numbers) )  &  ~ ( (v4_xxreal_2 @ k1_numbers) ) ) , file(xxreal_2, fc11_xxreal_2)).
thf(fc12_finset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_finset_1 @ A)  =>  (v1_finset_1 @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(finset_1, fc12_finset_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(fc12_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  &  ( (v1_relat_1 @ B)  &  (v4_valued_0 @ B) ) )  =>  (v4_valued_0 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc12_valued_0)).
thf(fc13_card_1, axiom,  (! [A: $i] :  ( (v3_card_1 @  (k1_tarski @ A) )  @ np__1) ) , file(card_1, fc13_card_1)).
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(fc14_card_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_card_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) )  =>  ( (v3_card_1 @  (k9_xtuple_0 @ B) )  @ A) ) ) , file(card_1, fc14_card_1)).
thf(fc14_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_finset_1 @ A)  &  (v1_finset_1 @ B) )  =>  (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(finset_1, fc14_finset_1)).
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_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  &  (v1_relat_1 @ B) )  =>  (v1_valued_0 @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc14_valued_0)).
thf(fc16_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ B) )  =>  ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc16_relat_1)).
thf(fc16_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  &  (v1_relat_1 @ B) )  =>  (v2_valued_0 @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc16_valued_0)).
thf(fc17_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) , file(finset_1, fc17_finset_1)).
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_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc17_relat_1)).
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_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  &  (v1_relat_1 @ B) )  =>  (v3_valued_0 @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc18_valued_0)).
thf(fc19_finset_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_finset_1 @ A) )  =>  (v1_finset_1 @  (k9_xtuple_0 @ A) ) ) ) , file(finset_1, fc19_finset_1)).
thf(fc19_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v3_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  (v1_xboole_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(funct_1, fc19_funct_1)).
thf(fc1_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  (v7_ordinal1 @  (k9_xtuple_0 @ A) ) ) ) , file(afinsq_1, fc1_afinsq_1)).
thf(fc1_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (v1_xboole_0 @  (k1_card_1 @ A) )  &  (v1_card_1 @  (k1_card_1 @ A) ) ) ) ) , file(card_1, fc1_card_1)).
thf(fc1_finset_1, axiom,  (! [A: $i] :  (v1_finset_1 @  (k1_tarski @ A) ) ) , file(finset_1, fc1_finset_1)).
thf(fc1_relset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  &  ( (v1_relat_1 @ C)  &  ( (v4_relat_1 @ C)  @ A) ) )  =>  ( (v4_relat_1 @  ( (k2_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc1_relset_1)).
thf(fc1_subset_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, fc1_subset_1)).
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_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc20_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  &  (v1_relat_1 @ B) )  =>  ( (v5_relat_1 @  ( (k4_xboole_0 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc20_valued_0)).
thf(fc22_finset_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_finset_1 @ A) )  =>  (v1_finset_1 @  (k10_xtuple_0 @ A) ) ) ) , file(finset_1, fc22_finset_1)).
thf(fc22_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  &  (v1_relat_1 @ B) )  =>  ( (v5_relat_1 @  ( (k4_xboole_0 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc22_valued_0)).
thf(fc23_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_relat_1 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v3_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc23_relat_1)).
thf(fc24_relat_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  (v1_relat_1 @ A) )  =>  (v1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc24_relat_1)).
thf(fc24_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  &  (v1_relat_1 @ B) )  =>  (v4_valued_0 @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc24_valued_0)).
thf(fc25_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v1_membered @ A)  &  (v1_membered @ B) )  =>  (v1_membered @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc25_membered)).
thf(fc25_relat_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  (v1_relat_1 @ A) )  =>  (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) , file(relat_1, fc25_relat_1)).
thf(fc26_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_finset_1 @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ B)  @ A) )  &  (v1_finset_1 @  ( (k5_relat_1 @ B)  @ A) ) ) ) ) , file(finset_1, fc26_finset_1)).
thf(fc26_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v2_membered @ A)  &  (v2_membered @ B) )  =>  (v2_membered @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc26_membered)).
thf(fc26_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v5_relat_1 @ C)  @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  &  ( (v5_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ B) ) ) ) , file(relat_1, fc26_relat_1)).
thf(fc27_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_finset_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ B)  @ A) )  &  (v1_finset_1 @  ( (k5_relat_1 @ B)  @ A) ) ) ) ) , file(finset_1, fc27_finset_1)).
thf(fc27_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v3_membered @ A)  &  (v3_membered @ B) )  =>  (v3_membered @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc27_membered)).
thf(fc27_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v4_relat_1 @ C)  @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  &  ( ( (v4_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ A)  &  ( (v4_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ B) ) ) ) ) , file(relat_1, fc27_relat_1)).
thf(fc28_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v4_membered @ A)  &  (v4_membered @ B) )  =>  (v4_membered @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc28_membered)).
thf(fc29_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v5_membered @ A)  &  (v5_membered @ B) )  =>  (v5_membered @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc29_membered)).
thf(fc2_afinsq_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  &  (v7_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_finset_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(afinsq_1, fc2_afinsq_1)).
thf(fc2_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @  (k1_card_1 @ A) ) )  &  (v1_card_1 @  (k1_card_1 @ A) ) ) ) ) , file(card_1, fc2_card_1)).
thf(fc2_relat_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @ A)  =>  (v1_relat_1 @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(relat_1, fc2_relat_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(fc30_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v5_finset_1 @  (k1_tarski @ A) ) ) ) , file(finset_1, fc30_finset_1)).
thf(fc30_membered, axiom,  (! [A: $i, B: $i] :  ( ( (v6_membered @ A)  &  (v6_membered @ B) )  =>  (v6_membered @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc30_membered)).
thf(fc31_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v5_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) , file(finset_1, fc31_finset_1)).
thf(fc33_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v5_finset_1 @ A)  &  (v5_finset_1 @ B) )  =>  (v5_finset_1 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(finset_1, fc33_finset_1)).
thf(fc35_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finset_1 @ A) ) )  =>  (v1_finset_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(finset_1, fc35_finset_1)).
thf(fc36_finset_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_finset_1 @ A) )  =>  (v5_finset_1 @  (k10_xtuple_0 @ A) ) ) ) , file(finset_1, fc36_finset_1)).
thf(fc3_membered, axiom,  (v3_membered @ k1_numbers) , file(membered, fc3_membered)).
thf(fc3_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_relat_1 @ B) )  =>  (v1_relat_1 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(relat_1, fc3_relat_1)).
thf(fc3_relset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  &  (v1_relat_1 @ C) )  =>  ( (v4_relat_1 @  ( (k4_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc3_relset_1)).
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(fc43_membered, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ A)  =>  (v1_membered @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc43_membered)).
thf(fc43_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc43_valued_0)).
thf(fc44_membered, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ A)  =>  (v2_membered @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc44_membered)).
thf(fc44_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v2_valued_0 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc44_valued_0)).
thf(fc45_membered, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ A)  =>  (v3_membered @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc45_membered)).
thf(fc45_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc45_valued_0)).
thf(fc46_membered, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ A)  =>  (v4_membered @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc46_membered)).
thf(fc46_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @ k3_numbers) ) ) ) , file(valued_0, fc46_valued_0)).
thf(fc47_membered, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ A)  =>  (v5_membered @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc47_membered)).
thf(fc47_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @ k4_numbers) ) ) ) , file(valued_0, fc47_valued_0)).
thf(fc48_membered, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ A)  =>  (v6_membered @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc48_membered)).
thf(fc48_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v4_valued_0 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc48_valued_0)).
thf(fc4_card_1, axiom,  (v1_card_1 @ k4_ordinal1) , file(card_1, fc4_card_1)).
thf(fc4_membered, axiom,  (v4_membered @ k3_numbers) , file(membered, fc4_membered)).
thf(fc4_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  =>  (v3_ordinal1 @  (k9_xtuple_0 @ A) ) ) ) , file(ordinal1, fc4_ordinal1)).
thf(fc4_relset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  &  ( (v1_relat_1 @ C)  &  ( (v5_relat_1 @ C)  @ A) ) )  =>  ( (v5_relat_1 @  ( (k2_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc4_relset_1)).
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_xboole_0, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ~ ( (v1_xboole_0 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) ) , file(xboole_0, fc4_xboole_0)).
thf(fc56_membered, axiom,  (v7_membered @ k1_numbers) , file(membered, fc56_membered)).
thf(fc57_membered, axiom,  (v7_membered @ k3_numbers) , file(membered, fc57_membered)).
thf(fc58_membered, axiom,  (v7_membered @ k4_numbers) , file(membered, fc58_membered)).
thf(fc59_membered, axiom,  (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)).
thf(fc5_card_1, axiom,  (v2_card_1 @ k4_ordinal1) , file(card_1, fc5_card_1)).
thf(fc5_membered, axiom,  (v5_membered @ k4_numbers) , file(membered, fc5_membered)).
thf(fc5_ordinal1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  &  (v3_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @  (k10_xtuple_0 @ A) )  &  (v5_ordinal1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) ) , file(ordinal1, fc5_ordinal1)).
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_xboole_0, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ~ ( (v1_xboole_0 @  ( (k2_xboole_0 @ B)  @ A) ) ) ) ) , file(xboole_0, fc5_xboole_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_card_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  ( (v1_finset_1 @  (k1_card_1 @ A) )  &  (v1_card_1 @  (k1_card_1 @ A) ) ) ) ) , file(card_1, fc6_card_1)).
thf(fc6_membered, axiom,  (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) , file(relat_1, fc6_relat_1)).
thf(fc6_relset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  &  (v1_relat_1 @ C) )  =>  ( (v5_relat_1 @  ( (k4_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc6_relset_1)).
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_card_1, axiom,  ~ ( (v1_finset_1 @ k4_ordinal1) ) , file(card_1, fc7_card_1)).
thf(fc7_membered, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc7_membered)).
thf(fc7_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  &  ( (v1_relat_1 @ B)  &  (v1_valued_0 @ B) ) )  =>  (v1_valued_0 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc7_valued_0)).
thf(fc85_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (v1_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc85_valued_0)).
thf(fc86_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (v2_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc86_valued_0)).
thf(fc87_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (v3_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc87_valued_0)).
thf(fc88_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc88_valued_0)).
thf(fc89_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc89_valued_0)).
thf(fc8_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ( ~ ( (v1_finset_1 @  (k1_card_1 @ A) ) )  &  (v1_card_1 @  (k1_card_1 @ A) ) ) ) ) , file(card_1, fc8_card_1)).
thf(fc8_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc8_funct_1)).
thf(fc8_membered, axiom,  (! [A: $i] :  ( (v1_xxreal_0 @ A)  =>  (v2_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc8_membered)).
thf(fc8_relat_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  =>  ~ ( (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) ) , file(relat_1, fc8_relat_1)).
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(fc8_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  &  ( (v1_relat_1 @ B)  &  (v2_valued_0 @ B) ) )  =>  (v2_valued_0 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc8_valued_0)).
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(fc9_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) ) , file(card_1, fc9_card_1)).
thf(fc9_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_finset_1 @ A)  &  (v1_finset_1 @ B) )  =>  (v1_finset_1 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(finset_1, fc9_finset_1)).
thf(fc9_membered, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v3_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc9_membered)).
thf(fc9_relat_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  =>  ~ ( (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) ) , file(relat_1, fc9_relat_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(fc9_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  &  ( (v1_relat_1 @ B)  &  (v3_valued_0 @ B) ) )  =>  (v3_valued_0 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc9_valued_0)).
thf(idempotence_k2_xboole_0, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k2_xboole_0 @ A)  @ A) )  @ A) ) , file(xboole_0, k2_xboole_0)).
thf(ie1_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  ( (= @  (k1_card_1 @ A) )  @  (k9_xtuple_0 @ A) ) ) ) , file(afinsq_1, ie1_afinsq_1)).
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(rc1_afinsq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) ) ) ) ) , file(afinsq_1, rc1_afinsq_1)).
thf(rc1_afinsq_2, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_xboole_0 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v4_valued_0 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) ) ) ) ) , file(afinsq_2, rc1_afinsq_2)).
thf(rc1_card_1, axiom,  (? [A: $i] :  (v1_card_1 @ A) ) , file(card_1, rc1_card_1)).
thf(rc1_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) , file(finset_1, rc1_finset_1)).
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_int_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  ( (v1_xxreal_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xreal_0 @ A)  &  (v1_int_1 @ A) ) ) ) ) ) , file(int_1, rc1_int_1)).
thf(rc1_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc1_membered)).
thf(rc1_nat_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_ordinal1 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v1_xreal_0 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) ) ) ) ) ) , file(nat_1, rc1_nat_1)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc1_ordinal1)).
thf(rc1_relat_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) ) ) , file(relat_1, rc1_relat_1)).
thf(rc1_relset_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_xboole_0 @ C)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) ) ) , file(relset_1, rc1_relset_1)).
thf(rc1_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(subset_1, rc1_subset_1)).
thf(rc1_valued_0, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, rc1_valued_0)).
thf(rc1_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)).
thf(rc1_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_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_afinsq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_xboole_0 @ B)  &  (v1_finset_1 @ B) ) ) ) ) ) ) ) , file(afinsq_1, rc2_afinsq_1)).
thf(rc2_card_1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) , file(card_1, rc2_card_1)).
thf(rc2_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(finset_1, rc2_finset_1)).
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_int_1, axiom,  (? [A: $i] :  (v1_int_1 @ A) ) , file(int_1, rc2_int_1)).
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_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc2_ordinal1)).
thf(rc2_relat_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) , file(relat_1, rc2_relat_1)).
thf(rc2_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  (v1_xboole_0 @ B) ) ) ) , file(subset_1, rc2_subset_1)).
thf(rc2_valued_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_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_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_afinsq_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) ) ) ) , file(afinsq_1, rc3_afinsq_1)).
thf(rc3_card_1, axiom,  (? [A: $i] :  ~ ( (v1_finset_1 @ A) ) ) , file(card_1, rc3_card_1)).
thf(rc3_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finset_1, rc3_finset_1)).
thf(rc3_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) , file(funct_1, rc3_funct_1)).
thf(rc3_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v6_membered @ A)  &  (v7_membered @ A) ) ) ) , file(membered, rc3_membered)).
thf(rc3_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_ordinal1 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v1_xreal_0 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) ) ) ) ) ) ) , file(nat_1, rc3_nat_1)).
thf(rc3_ordinal1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v5_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, rc3_ordinal1)).
thf(rc3_relat_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relat_1, rc3_relat_1)).
thf(rc3_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc3_subset_1)).
thf(rc3_valued_0, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ 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_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_afinsq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) ) ) , file(afinsq_1, rc4_afinsq_1)).
thf(rc4_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_finset_1 @ B) ) ) ) ) ) , file(card_1, rc4_card_1)).
thf(rc4_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(funct_1, rc4_funct_1)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc4_subset_1)).
thf(rc4_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_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_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v3_card_1 @ B)  @ A) ) ) ) , file(card_1, rc5_card_1)).
thf(rc5_finset_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)  &  (v1_finset_1 @ C) ) ) ) ) ) ) , file(finset_1, rc5_finset_1)).
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_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc5_subset_1)).
thf(rc5_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_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) , file(card_1, rc6_card_1)).
thf(rc6_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (? [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  (v1_finset_1 @ C) ) ) ) ) ) ) ) ) , file(finset_1, rc6_finset_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_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc6_subset_1)).
thf(rc6_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v4_valued_0 @ B) ) ) ) ) ) ) , file(valued_0, rc6_valued_0)).
thf(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_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v3_card_1 @ B)  @ np__1) ) ) ) ) , file(card_1, rc7_card_1)).
thf(rc7_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_zfmisc_1 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(finset_1, rc7_finset_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_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  (v5_finset_1 @ A) ) ) ) , file(finset_1, rc8_finset_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_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finset_1 @ A) ) ) ) ) , file(finset_1, rc9_finset_1)).
thf(rc9_funct_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, rc9_funct_1)).
thf(rd4_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  ( (= @  ( (k5_relat_1 @ A)  @  (k9_xtuple_0 @ A) ) )  @ A) ) ) , file(relat_1, rd4_relat_1)).
thf(rd5_relat_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @ A)  =>  ( (= @  ( (k5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @ B) )  @  ( (k5_relat_1 @ A)  @ B) ) ) ) , file(relat_1, rd5_relat_1)).
thf(rd8_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (= @  ( (k5_relat_1 @ B)  @ A) )  @ B) ) ) , file(relat_1, rd8_relat_1)).
thf(redefinition_k2_partfun1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( (= @  ( ( ( (k2_partfun1 @ A)  @ B)  @ C)  @ D) )  @  ( (k5_relat_1 @ C)  @ D) ) ) ) , file(partfun1, k2_partfun1)).
thf(redefinition_k2_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (= @  ( (k2_relset_1 @ A)  @ B) )  @  (k10_xtuple_0 @ B) ) ) ) , file(relset_1, k2_relset_1)).
thf(redefinition_k5_numbers, axiom,  ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k6_subset_1, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k6_subset_1 @ A)  @ B) )  @  ( (k4_xboole_0 @ A)  @ B) ) ) , file(subset_1, k6_subset_1)).
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(reflexivity_r1_tarski, axiom,  (! [A: $i, B: $i] :  ( (r1_tarski @ A)  @ A) ) , file(tarski, r1_tarski)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( ( (v2_xxreal_0 @ np__1)  &  ( ( (m2_subset_1 @ np__1)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__1)  @ k5_numbers)  &  ( (m1_subset_1 @ np__1)  @ k1_numbers) ) ) , file(numerals, spc1_numerals)).
thf(t1_boole, axiom,  (! [A: $i] :  ( (= @  ( (k2_xboole_0 @ A)  @ k1_xboole_0) )  @ A) ) , file(boole, t1_boole)).
thf(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
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_boole, axiom,  (! [A: $i] :  ( (= @  ( (k4_xboole_0 @ A)  @ k1_xboole_0) )  @ A) ) , file(boole, t3_boole)).
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(t40_xboole_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k4_xboole_0 @  ( (k2_xboole_0 @ A)  @ B) )  @ B) )  @  ( (k4_xboole_0 @ A)  @ B) ) ) ) , file(xboole_1, t40_xboole_1)).
thf(t4_boole, axiom,  (! [A: $i] :  ( (= @  ( (k4_xboole_0 @ k1_xboole_0)  @ A) )  @ k1_xboole_0) ) , file(boole, t4_boole)).
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(t59_zfmisc_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (= @  ( (k4_xboole_0 @  (k1_tarski @ A) )  @ B) )  @  (k1_tarski @ A) )  <=>  ~ ( ( (r2_hidden @ A)  @ B) ) ) ) ) , file(zfmisc_1, t59_zfmisc_1)).
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(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_xboole_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( (r1_tarski @ A)  @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(xboole_1, t7_xboole_1)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( ( (= @ A)  @ B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(s3_stirl2_1, axiom,  (! [A: $i > $i > $i > $o] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i > $i] :  (! [E: $i] :  (! [F: $i] :  ( ( (! [G: $i] :  ( ( (r2_hidden @ G)  @  ( (k6_subset_1 @ F)  @ E) )  =>  ( (r2_hidden @  (D @ G) )  @ C) ) )  &  ( ( ( (r1_tarski @ E)  @ F)  &  ( (r1_tarski @ B)  @ C) )  &  ( ( (v1_xboole_0 @ B)  =>  (v1_xboole_0 @ E) )  &  (! [G: $i] :  ( ( (v1_funct_1 @ G)  &  ( ( ( (v1_funct_2 @ G)  @ F)  @ C)  &  ( (m1_subset_1 @ G)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ F)  @ C) ) ) ) )  =>  ( (! [H: $i] :  ( ( (r2_hidden @ H)  @  ( (k6_subset_1 @ F)  @ E) )  =>  ( (= @  (D @ H) )  @  ( (k1_funct_1 @ G)  @ H) ) ) )  =>  ( ( ( (A @ G)  @ F)  @ C)  <=>  ( ( (A @  ( ( ( (k2_partfun1 @ F)  @ C)  @ G)  @ E) )  @ E)  @ B) ) ) ) ) ) ) )  =>  ( (= @  (k1_card_1 @  ( ( (replSep1 @  (^ [G: $i] :  ( (v1_funct_1 @ G)  &  ( ( ( (v1_funct_2 @ G)  @ E)  @ B)  &  ( (m1_subset_1 @ G)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ E)  @ B) ) ) ) ) ) )  @  (^ [G: $i] : G) )  @  (^ [G: $i] :  ( ( (A @ G)  @ E)  @ B) ) ) ) )  @  (k1_card_1 @  ( ( (replSep1 @  (^ [G: $i] :  ( (v1_funct_1 @ G)  &  ( ( ( (v1_funct_2 @ G)  @ F)  @ C)  &  ( (m1_subset_1 @ G)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ F)  @ C) ) ) ) ) ) )  @  (^ [G: $i] : G) )  @  (^ [G: $i] :  ( ( ( (A @ G)  @ F)  @ C)  &  ( ( (r1_tarski @  ( (k2_relset_1 @ C)  @  ( ( ( (k2_partfun1 @ F)  @ C)  @ G)  @ E) ) )  @ B)  &  (! [H: $i] :  ( ( (r2_hidden @ H)  @  ( (k6_subset_1 @ F)  @ E) )  =>  ( (= @  ( (k1_funct_1 @ G)  @ H) )  @  (D @ H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(stirl2_1, s3_stirl2_1)).
thf(s4_stirl2_1, conjecture,  ( ( ( (v1_xboole_0 @ f2_s4_stirl2_1)  =>  (v1_xboole_0 @ f1_s4_stirl2_1) )  &  ( ~ ( ( (r2_hidden @ f3_s4_stirl2_1)  @ f1_s4_stirl2_1) )  &  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @  ( (k2_xboole_0 @ f1_s4_stirl2_1)  @  (k1_tarski @ f3_s4_stirl2_1) ) )  @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) )  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_xboole_0 @ f1_s4_stirl2_1)  @  (k1_tarski @ f3_s4_stirl2_1) ) )  @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) ) ) ) ) )  =>  ( ( (= @  ( (k1_funct_1 @ A)  @ f3_s4_stirl2_1) )  @ f4_s4_stirl2_1)  =>  ( ( ( (p1_s4_stirl2_1 @ A)  @  ( (k2_xboole_0 @ f1_s4_stirl2_1)  @  (k1_tarski @ f3_s4_stirl2_1) ) )  @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) )  <=>  ( ( (p1_s4_stirl2_1 @  ( ( ( (k2_partfun1 @  ( (k2_xboole_0 @ f1_s4_stirl2_1)  @  (k1_tarski @ f3_s4_stirl2_1) ) )  @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) )  @ A)  @ f1_s4_stirl2_1) )  @ f1_s4_stirl2_1)  @ f2_s4_stirl2_1) ) ) ) ) ) )  =>  ( (= @  (k1_card_1 @  ( ( (replSep1 @  (^ [A: $i] :  ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ f1_s4_stirl2_1)  @ f2_s4_stirl2_1)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ f1_s4_stirl2_1)  @ f2_s4_stirl2_1) ) ) ) ) ) )  @  (^ [A: $i] : A) )  @  (^ [A: $i] :  ( ( (p1_s4_stirl2_1 @ A)  @ f1_s4_stirl2_1)  @ f2_s4_stirl2_1) ) ) ) )  @  (k1_card_1 @  ( ( (replSep1 @  (^ [A: $i] :  ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @  ( (k2_xboole_0 @ f1_s4_stirl2_1)  @  (k1_tarski @ f3_s4_stirl2_1) ) )  @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) )  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_xboole_0 @ f1_s4_stirl2_1)  @  (k1_tarski @ f3_s4_stirl2_1) ) )  @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) ) ) ) ) ) ) )  @  (^ [A: $i] : A) )  @  (^ [A: $i] :  ( ( ( (p1_s4_stirl2_1 @ A)  @  ( (k2_xboole_0 @ f1_s4_stirl2_1)  @  (k1_tarski @ f3_s4_stirl2_1) ) )  @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) )  &  ( ( (r1_tarski @  ( (k2_relset_1 @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) )  @  ( ( ( (k2_partfun1 @  ( (k2_xboole_0 @ f1_s4_stirl2_1)  @  (k1_tarski @ f3_s4_stirl2_1) ) )  @  ( (k2_xboole_0 @ f2_s4_stirl2_1)  @  (k1_tarski @ f4_s4_stirl2_1) ) )  @ A)  @ f1_s4_stirl2_1) ) )  @ f2_s4_stirl2_1)  &  ( (= @  ( (k1_funct_1 @ A)  @ f3_s4_stirl2_1) )  @ f4_s4_stirl2_1) ) ) ) ) ) ) ) , file(stirl2_1, s4_stirl2_1)).
thf(sethood_m1_subset_1, axiom, ( ! [A: $i] :  ( sethood @ ( ^ [X: $i] : (m1_subset_1 @ X @ A) ) ) ) , file(subset_1, m1_subset_1)).
