% Mizar problem: t23_fintopo7,fintopo7,1651,7 
include('Axioms/SET010^0.ax').
thf(n1_type, type, np__1: $i).
thf(g1_fintopo2_type, type, g1_fintopo2: $i > $i > $i).
thf(k1_cantor_1_type, type, k1_cantor_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_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k3_tarski_type, type, k3_tarski: $i > $i).
thf(k3_xboole_0_type, type, k3_xboole_0: $i > $i > $i).
thf(k4_fintopo7_type, type, k4_fintopo7: $i > $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k5_ordinal1_type, type, k5_ordinal1: $i).
thf(k5_setfam_1_type, type, k5_setfam_1: $i > $i > $i).
thf(k9_subset_1_type, type, k9_subset_1: $i > $i > $i > $i).
thf(u1_fintopo2_type, type, u1_fintopo2: $i > $i).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(l1_fintopo2_type, type, l1_fintopo2: $i > $o).
thf(l1_struct_0_type, type, l1_struct_0: $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(r2_tarski_type, type, r2_tarski: $i > $i > $o).
thf(v13_struct_0_type, type, v13_struct_0: $i > $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_fintopo2_type, type, v1_fintopo2: $i > $o).
thf(v1_fintopo7_type, type, v1_fintopo7: $i > $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_subset_1_type, type, v1_subset_1: $i > $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_card_1_type, type, v2_card_1: $i > $o).
thf(v2_fintopo7_type, type, v2_fintopo7: $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_struct_0_type, type, v2_struct_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v3_card_1_type, type, v3_card_1: $i > $i > $o).
thf(v3_fintopo7_type, type, v3_fintopo7: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v4_fintopo7_type, type, v4_fintopo7: $i > $o).
thf(v4_membered_type, type, v4_membered: $i > $o).
thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o).
thf(v5_membered_type, type, v5_membered: $i > $o).
thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o).
thf(v6_fintopo7_type, type, v6_fintopo7: $i > $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v7_fintopo7_type, type, v7_fintopo7: $i > $i > $o).
thf(v7_membered_type, type, v7_membered: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_struct_0_type, type, v7_struct_0: $i > $o).
thf(v8_struct_0_type, type, v8_struct_0: $i > $o).
thf(abstractness_v1_fintopo2, axiom,  (! [A: $i] :  ( (l1_fintopo2 @ A)  =>  ( (v1_fintopo2 @ A)  =>  (A =  ( (g1_fintopo2 @  (u1_struct_0 @ A) )  @  (u1_fintopo2 @ A) ) ) ) ) ) , file(fintopo2, v1_fintopo2)).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(asymmetry_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ~ ( ( (r2_tarski @ B)  @ A) ) ) ) , file(tarski, r2_tarski)).
thf(cc10_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] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_int_1 @ B) ) ) ) ) , file(membered, cc10_membered)).
thf(cc10_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) )  =>  ( (v13_struct_0 @ A)  @ np__1) ) ) ) , file(struct_0, cc10_struct_0)).
thf(cc11_card_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_card_1 @ A) )  =>  (! [B: $i] :  ( ( (v3_card_1 @ B)  @ A)  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(card_1, cc11_card_1)).
thf(cc11_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc11_membered)).
thf(cc11_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ np__1)  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc11_struct_0)).
thf(cc12_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_membered @ A) ) ) , file(membered, cc12_membered)).
thf(cc13_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_membered @ B) ) ) ) ) , file(membered, cc13_membered)).
thf(cc14_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_membered @ B) ) ) ) ) , file(membered, cc14_membered)).
thf(cc15_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_membered @ B) ) ) ) ) , file(membered, cc15_membered)).
thf(cc16_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_membered @ B) ) ) ) ) , file(membered, cc16_membered)).
thf(cc17_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_membered @ B) ) ) ) ) , file(membered, cc17_membered)).
thf(cc17_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc17_struct_0)).
thf(cc18_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_membered @ B) ) ) ) ) , file(membered, cc18_membered)).
thf(cc19_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_membered @ A) ) ) , file(membered, cc19_membered)).
thf(cc1_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(card_1, cc1_card_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_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_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  (v7_struct_0 @ A) ) ) ) , file(struct_0, cc1_struct_0)).
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_zfmisc_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_zfmisc_1 @ A) ) ) , file(zfmisc_1, cc1_zfmisc_1)).
thf(cc2_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc2_card_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_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_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc2_struct_0)).
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_zfmisc_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(zfmisc_1, cc2_zfmisc_1)).
thf(cc3_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc3_card_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_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(cc4_card_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc4_card_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_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  &  (v8_struct_0 @ A) ) ) ) ) , file(struct_0, cc4_struct_0)).
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(cc5_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc5_card_1)).
thf(cc5_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  =>  ( (v1_partfun1 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) ) , file(funct_2, cc5_funct_2)).
thf(cc5_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v1_membered @ A) ) ) , file(membered, cc5_membered)).
thf(cc5_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v8_struct_0 @ A) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ~ ( (v8_struct_0 @ A) ) ) ) ) ) , file(struct_0, cc5_struct_0)).
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(cc6_card_1, axiom,  (! [A: $i] :  ( ( (v3_ordinal1 @ A)  &  (v1_finset_1 @ A) )  =>  (v7_ordinal1 @ A) ) ) , file(card_1, cc6_card_1)).
thf(cc6_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc6_membered)).
thf(cc6_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v7_struct_0 @ A)  =>  (v8_struct_0 @ A) ) ) ) , file(struct_0, cc6_struct_0)).
thf(cc7_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ k5_ordinal1)  =>  (v1_xboole_0 @ A) ) ) , file(card_1, cc7_card_1)).
thf(cc7_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc7_membered)).
thf(cc7_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v8_struct_0 @ A) )  =>  ~ ( (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc7_struct_0)).
thf(cc8_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (v3_card_1 @ A)  @ k5_ordinal1) ) ) , file(card_1, cc8_card_1)).
thf(cc8_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc8_membered)).
thf(cc8_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  ( (v13_struct_0 @ A)  @ k5_ordinal1) ) ) ) , file(struct_0, cc8_struct_0)).
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_funct_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, cc9_funct_2)).
thf(cc9_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_rat_1 @ B) ) ) ) ) , file(membered, cc9_membered)).
thf(cc9_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ k5_ordinal1)  =>  (v2_struct_0 @ A) ) ) ) , file(struct_0, cc9_struct_0)).
thf(commutativity_k3_xboole_0, axiom,  (! [A: $i, B: $i] :  ( ( (k3_xboole_0 @ A)  @ B)  =  ( (k3_xboole_0 @ B)  @ A) ) ) , file(xboole_0, k3_xboole_0)).
thf(commutativity_k9_subset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ A) )  =>  ( ( ( (k9_subset_1 @ A)  @ B)  @ C)  =  ( ( (k9_subset_1 @ A)  @ C)  @ B) ) ) ) , file(subset_1, k9_subset_1)).
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(d11_fintopo7, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  ( (k4_fintopo7 @ A)  =  ( ( (replSep1 @  (^ [B: $i] :  ( ( (v1_fintopo7 @ B)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) )  @  (^ [B: $i] : B) )  @  (^ [B: $i] : $true) ) ) ) ) , file(fintopo7, d11_fintopo7)).
thf(d1_cantor_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  =>  ( (C =  ( (k1_cantor_1 @ A)  @ B) )  <=>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @ A) )  =>  ( ( (r2_tarski @ D)  @ C)  <=>  (? [E: $i] :  ( ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  &  ( ( (r1_tarski @ E)  @ B)  &  (D =  ( (k5_setfam_1 @ A)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(cantor_1, d1_cantor_1)).
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(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_g1_fintopo2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) ) ) ) ) )  =>  ( (v1_fintopo2 @  ( (g1_fintopo2 @ A)  @ B) )  &  (l1_fintopo2 @  ( (g1_fintopo2 @ A)  @ B) ) ) ) ) , file(fintopo2, g1_fintopo2)).
thf(dt_k1_cantor_1, axiom,  (! [A: $i, B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  =>  ( (m1_subset_1 @  ( (k1_cantor_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) ) ) ) , file(cantor_1, k1_cantor_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_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)).
thf(dt_k3_tarski, axiom, $true, file(tarski, k3_tarski)).
thf(dt_k3_xboole_0, axiom, $true, file(xboole_0, k3_xboole_0)).
thf(dt_k4_fintopo7, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  (k4_fintopo7 @ A) ) )  &  ( (m1_subset_1 @  (k4_fintopo7 @ A) )  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) ) ) , file(fintopo7, k4_fintopo7)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k5_ordinal1, axiom, $true, file(ordinal1, k5_ordinal1)).
thf(dt_k5_setfam_1, axiom,  (! [A: $i, B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  =>  ( (m1_subset_1 @  ( (k5_setfam_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(setfam_1, k5_setfam_1)).
thf(dt_k9_subset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ A) )  =>  ( (m1_subset_1 @  ( ( (k9_subset_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, k9_subset_1)).
thf(dt_l1_fintopo2, axiom,  (! [A: $i] :  ( (l1_fintopo2 @ A)  =>  (l1_struct_0 @ A) ) ) , file(fintopo2, l1_fintopo2)).
thf(dt_l1_struct_0, axiom, $true, file(struct_0, l1_struct_0)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_u1_fintopo2, axiom,  (! [A: $i] :  ( (l1_fintopo2 @ A)  =>  ( (v1_funct_1 @  (u1_fintopo2 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_fintopo2 @ A) )  @  (u1_struct_0 @ A) )  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( (m1_subset_1 @  (u1_fintopo2 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) ) ) ) ) ) , file(fintopo2, u1_fintopo2)).
thf(dt_u1_struct_0, axiom, $true, file(struct_0, u1_struct_0)).
thf(existence_l1_fintopo2, axiom,  (? [A: $i] :  (l1_fintopo2 @ A) ) , file(fintopo2, l1_fintopo2)).
thf(existence_l1_struct_0, axiom,  (? [A: $i] :  (l1_struct_0 @ A) ) , file(struct_0, l1_struct_0)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(fc10_membered, axiom,  (! [A: $i] :  ( (v1_rat_1 @ A)  =>  (v4_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc10_membered)).
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(fc11_membered, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v5_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc11_membered)).
thf(fc12_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) ) , file(card_1, fc12_card_1)).
thf(fc12_membered, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v6_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc12_membered)).
thf(fc13_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, fc13_card_1)).
thf(fc14_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, fc14_card_1)).
thf(fc16_card_1, axiom,  (! [A: $i] :  ( (v3_card_1 @  (k1_tarski @ A) )  @ np__1) ) , file(card_1, fc16_card_1)).
thf(fc19_struct_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_card_1 @ A)  &  ( ( (v13_struct_0 @ B)  @ A)  &  (l1_struct_0 @ B) ) )  =>  ( (v3_card_1 @  (u1_struct_0 @ B) )  @ A) ) ) , file(struct_0, fc19_struct_0)).
thf(fc1_struct_0, axiom,  (! [A: $i] :  ( ( (v2_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc1_struct_0)).
thf(fc1_subset_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, fc1_subset_1)).
thf(fc1_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc1_zfmisc_1, axiom,  (! [A: $i] :  (v1_zfmisc_1 @  (k1_tarski @ A) ) ) , file(zfmisc_1, fc1_zfmisc_1)).
thf(fc2_fintopo7, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  (k4_fintopo7 @ A) ) )  &  ( (v6_fintopo7 @  (k4_fintopo7 @ A) )  @ A) ) ) ) , file(fintopo7, fc2_fintopo7)).
thf(fc2_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 @  ( (k3_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc2_relset_1)).
thf(fc2_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc2_struct_0)).
thf(fc2_xboole_0, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_tarski @ A) ) ) ) , file(xboole_0, fc2_xboole_0)).
thf(fc2_zfmisc_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ B)  =>  (v1_xboole_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(zfmisc_1, fc2_zfmisc_1)).
thf(fc31_membered, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ A)  =>  (v1_membered @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc31_membered)).
thf(fc32_membered, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ A)  =>  (v1_membered @  ( (k3_xboole_0 @ B)  @ A) ) ) ) , file(membered, fc32_membered)).
thf(fc33_membered, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ A)  =>  (v2_membered @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc33_membered)).
thf(fc34_membered, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ A)  =>  (v2_membered @  ( (k3_xboole_0 @ B)  @ A) ) ) ) , file(membered, fc34_membered)).
thf(fc35_membered, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ A)  =>  (v3_membered @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc35_membered)).
thf(fc36_membered, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ A)  =>  (v3_membered @  ( (k3_xboole_0 @ B)  @ A) ) ) ) , file(membered, fc36_membered)).
thf(fc37_membered, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ A)  =>  (v4_membered @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc37_membered)).
thf(fc38_membered, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ A)  =>  (v4_membered @  ( (k3_xboole_0 @ B)  @ A) ) ) ) , file(membered, fc38_membered)).
thf(fc39_membered, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ A)  =>  (v5_membered @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc39_membered)).
thf(fc3_zfmisc_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(zfmisc_1, fc3_zfmisc_1)).
thf(fc40_membered, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ A)  =>  (v5_membered @  ( (k3_xboole_0 @ B)  @ A) ) ) ) , file(membered, fc40_membered)).
thf(fc41_membered, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ A)  =>  (v6_membered @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(membered, fc41_membered)).
thf(fc42_membered, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ A)  =>  (v6_membered @  ( (k3_xboole_0 @ B)  @ A) ) ) ) , file(membered, fc42_membered)).
thf(fc4_zfmisc_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_zfmisc_1 @ A)  &  (v1_zfmisc_1 @ B) )  =>  (v1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(zfmisc_1, fc4_zfmisc_1)).
thf(fc59_membered, axiom,  (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)).
thf(fc5_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 @  ( (k3_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc5_relset_1)).
thf(fc6_card_1, axiom,  (v1_card_1 @ k4_ordinal1) , file(card_1, fc6_card_1)).
thf(fc6_membered, axiom,  (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)).
thf(fc6_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc6_struct_0)).
thf(fc7_card_1, axiom,  (v2_card_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_struct_0, axiom,  (! [A: $i] :  ( ( (v7_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc7_struct_0)).
thf(fc8_membered, axiom,  (! [A: $i] :  ( (v1_xxreal_0 @ A)  =>  (v2_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc8_membered)).
thf(fc8_struct_0, axiom,  (! [A: $i] :  ( ( (v8_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_finset_1 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc8_struct_0)).
thf(fc9_card_1, axiom,  ~ ( (v1_finset_1 @ k4_ordinal1) ) , file(card_1, fc9_card_1)).
thf(fc9_membered, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v3_membered @  (k1_tarski @ A) ) ) ) , file(membered, fc9_membered)).
thf(fc9_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_finset_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc9_struct_0)).
thf(free_g1_fintopo2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) ) ) ) ) )  =>  (! [C: $i, D: $i] :  ( ( ( (g1_fintopo2 @ A)  @ B)  =  ( (g1_fintopo2 @ C)  @ D) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) , file(fintopo2, g1_fintopo2)).
thf(idempotence_k3_xboole_0, axiom,  (! [A: $i, B: $i] :  ( ( (k3_xboole_0 @ A)  @ A)  = A) ) , file(xboole_0, k3_xboole_0)).
thf(idempotence_k9_subset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ A) )  =>  ( ( ( (k9_subset_1 @ A)  @ B)  @ B)  = B) ) ) , file(subset_1, k9_subset_1)).
thf(rc1_card_1, axiom,  (? [A: $i] :  (v1_card_1 @ A) ) , file(card_1, rc1_card_1)).
thf(rc1_fintopo2, axiom,  (? [A: $i] :  ( (l1_fintopo2 @ A)  &  (v1_fintopo2 @ A) ) ) , file(fintopo2, rc1_fintopo2)).
thf(rc1_fintopo7, axiom,  (? [A: $i] :  ( (l1_fintopo2 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  (v4_fintopo7 @ A) ) ) ) ) ) ) , file(fintopo7, rc1_fintopo7)).
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_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_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)).
thf(rc1_zfmisc_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) ) ) , file(zfmisc_1, rc1_zfmisc_1)).
thf(rc21_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc21_struct_0)).
thf(rc22_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc22_struct_0)).
thf(rc23_struct_0, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (l1_struct_0 @ B)  &  ( (v13_struct_0 @ B)  @ A) ) ) ) ) , file(struct_0, rc23_struct_0)).
thf(rc2_fintopo2, axiom,  (? [A: $i] :  ( (l1_fintopo2 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  (v1_fintopo2 @ A) ) ) ) , file(fintopo2, rc2_fintopo2)).
thf(rc2_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc2_membered)).
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_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)).
thf(rc2_zfmisc_1, axiom,  (? [A: $i] :  ~ ( (v1_zfmisc_1 @ A) ) ) , file(zfmisc_1, rc2_zfmisc_1)).
thf(rc3_card_1, axiom,  (? [A: $i] :  ~ ( (v1_finset_1 @ A) ) ) , file(card_1, rc3_card_1)).
thf(rc3_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v6_membered @ A)  &  (v7_membered @ A) ) ) ) , file(membered, rc3_membered)).
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(rc4_fintopo7, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( (v1_fintopo7 @ B)  @ A) ) ) ) ) , file(fintopo7, rc4_fintopo7)).
thf(rc4_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(struct_0, rc4_struct_0)).
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(rc5_fintopo7, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( (v6_fintopo7 @ B)  @ A) ) ) ) ) , file(fintopo7, rc5_fintopo7)).
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(rc6_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, rc6_card_1)).
thf(rc6_fintopo7, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( (v7_fintopo7 @ B)  @ A) ) ) ) ) , file(fintopo7, rc6_fintopo7)).
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(rc7_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v3_card_1 @ B)  @ A) ) ) ) , file(card_1, rc7_card_1)).
thf(rc7_fintopo7, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( ( (v6_fintopo7 @ B)  @ A)  &  ( (v7_fintopo7 @ B)  @ A) ) ) ) ) ) , file(fintopo7, rc7_fintopo7)).
thf(rc8_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, rc8_card_1)).
thf(rc9_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, rc9_card_1)).
thf(rd1_zfmisc_1, axiom,  (! [A: $i] :  ( (k3_tarski @  (k1_tarski @ A) )  = A) ) , file(zfmisc_1, rd1_zfmisc_1)).
thf(redefinition_k5_setfam_1, axiom,  (! [A: $i, B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  =>  ( ( (k5_setfam_1 @ A)  @ B)  =  (k3_tarski @ B) ) ) ) , file(setfam_1, k5_setfam_1)).
thf(redefinition_k9_subset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ A) )  =>  ( ( ( (k9_subset_1 @ A)  @ B)  @ C)  =  ( (k3_xboole_0 @ B)  @ C) ) ) ) , file(subset_1, k9_subset_1)).
thf(redefinition_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  <=>  ( (r2_hidden @ A)  @ B) ) ) , file(tarski, r2_tarski)).
thf(reflexivity_r1_tarski, axiom,  (! [A: $i, B: $i] :  ( (r1_tarski @ A)  @ A) ) , file(tarski, r1_tarski)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( (v2_xxreal_0 @ np__1)  &  ( (m1_subset_1 @ np__1)  @ k4_ordinal1) ) , file(numerals, spc1_numerals)).
thf(t14_fintopo7, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  ( ( (r2_tarski @ k1_xboole_0)  @  (k4_fintopo7 @ A) )  &  ( ( (r2_tarski @  (u1_struct_0 @ A) )  @  (k4_fintopo7 @ A) )  &  ( (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  =>  ( ( (r1_tarski @ B)  @  (k4_fintopo7 @ A) )  =>  ( (r2_tarski @  ( (k5_setfam_1 @  (u1_struct_0 @ A) )  @ B) )  @  (k4_fintopo7 @ A) ) ) ) )  &  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( ( (r2_tarski @ B)  @  (k4_fintopo7 @ A) )  &  ( (r2_tarski @ C)  @  (k4_fintopo7 @ A) ) )  =>  ( (r2_tarski @  ( ( (k9_subset_1 @  (u1_struct_0 @ A) )  @ B)  @ C) )  @  (k4_fintopo7 @ A) ) ) ) ) ) ) ) ) ) ) ) , file(fintopo7, t14_fintopo7)).
thf(t16_yellow_9, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_xboole_0 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) ) )  =>  ( ( (k1_cantor_1 @ A)  @ B)  =  (k1_tarski @ k1_xboole_0) ) ) ) ) , file(yellow_9, t16_yellow_9)).
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_tarski @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t2_boole, axiom,  (! [A: $i] :  ( ( (k3_xboole_0 @ A)  @ k1_xboole_0)  = k1_xboole_0) ) , file(boole, t2_boole)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_tarski @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t3_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ B) )  <=>  ( (r1_tarski @ A)  @ B) ) ) ) , file(subset, t3_subset)).
thf(t4_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_tarski @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t5_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) )  &  (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset)).
thf(t6_boole, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (A = k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(t77_zfmisc_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r1_tarski @ A)  @ B)  =>  ( (r1_tarski @  (k3_tarski @ A) )  @  (k3_tarski @ B) ) ) ) ) , file(zfmisc_1, t77_zfmisc_1)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( (A = B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(t23_fintopo7, conjecture,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_fintopo2 @ A)  &  ( (v2_fintopo7 @ A)  &  ( (v3_fintopo7 @ A)  &  ( (v4_fintopo7 @ A)  &  (l1_fintopo2 @ A) ) ) ) ) )  =>  (! [B: $i] :  ( ( ( (v6_fintopo7 @ B)  @ A)  &  ( ( (v7_fintopo7 @ B)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) )  =>  ( (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ B)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ B)  =>  (? [E: $i] :  ( ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @ B) )  &  ( ( (k3_xboole_0 @ C)  @ D)  =  (k3_tarski @ E) ) ) ) ) ) ) )  &  ( (u1_struct_0 @ A)  =  ( (k5_setfam_1 @  (u1_struct_0 @ A) )  @ B) ) ) ) ) ) ) , file(fintopo7, t23_fintopo7)).