% Mizar problem: s1_compl_sp,compl_sp,2478,6 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(f1_s1_compl_sp_type,type,( f1_s1_compl_sp: $i )).
thf(g1_orders_2_type,type,( g1_orders_2: $i > $i > $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_domain_1_type,type,( k1_domain_1: $i > $i > $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_relat_1_type,type,( k1_relat_1: $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_1: $i > $i > $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_wellord1_type,type,( k1_wellord1: $i > $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_tarski_type,type,( k2_tarski: $i > $i > $i )).
thf(k2_wellord1_type,type,( k2_wellord1: $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_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_rfunct_3_type,type,( k3_rfunct_3: $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_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_partfun1_type,type,( k4_partfun1: $i > $i > $i )).
thf(k4_subset_1_type,type,( k4_subset_1: $i > $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k5_relat_1_type,type,( k5_relat_1: $i > $i > $i )).
thf(k5_setfam_1_type,type,( k5_setfam_1: $i > $i > $i )).
thf(k6_domain_1_type,type,( k6_domain_1: $i > $i > $i )).
thf(k9_setfam_1_type,type,( k9_setfam_1: $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(u1_orders_2_type,type,( u1_orders_2: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_orders_2_type,type,( l1_orders_2: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(m1_rfunct_3_type,type,( m1_rfunct_3: $i > $i > $i > $o )).
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_s1_compl_sp_type,type,( p1_s1_compl_sp: $i > $i > $o )).
thf(r1_relat_2_type,type,( r1_relat_2: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r1_wellfnd1_type,type,( r1_wellfnd1: $i > $i > $i > $i > $o )).
thf(r1_wellord1_type,type,( r1_wellord1: $i > $i > $o )).
thf(r2_wellord1_type,type,( r2_wellord1: $i > $i > $o )).
thf(r4_relat_2_type,type,( r4_relat_2: $i > $i > $o )).
thf(r6_relat_2_type,type,( r6_relat_2: $i > $i > $o )).
thf(r8_relat_2_type,type,( r8_relat_2: $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_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_orders_2_type,type,( v1_orders_2: $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_wellfnd1_type,type,( v1_wellfnd1: $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_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_wellord1_type,type,( v2_wellord1: $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_membered_type,type,( v3_membered: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $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_membered_type,type,( v6_membered: $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_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v1_orders_2 @ A ) => ( = @ A @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ) ),file(orders_2,v1_orders_2)).
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_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_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),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_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xcmplx_0 @ B ) ) ) ),file(membered,cc12_membered)).
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(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_membered)).
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(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_membered)).
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_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] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
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(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_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc1_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_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc1_zfmisc_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,cc1_zfmisc_1)).
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(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(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(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(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(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_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_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc2_funct_2)).
thf(cc2_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
thf(cc2_nat_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ~ ( v3_xxreal_0 @ A ) ) ),file(nat_1,cc2_nat_1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc2_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_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_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_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_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc3_funct_2)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_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_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(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_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(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(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_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(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(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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_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(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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_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(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_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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v13_struct_0 @ A @ k1_xboole_0 ) ) ) ),file(struct_0,cc8_struct_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(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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ k1_xboole_0 ) => ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc9_struct_0)).
thf(commutativity_k2_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ B @ A ) ) ),file(tarski,k2_tarski)).
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(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_k4_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) => ( = @ ( k4_subset_1 @ A @ B @ C ) @ ( k4_subset_1 @ A @ C @ B ) ) ) ),file(subset_1,k4_subset_1)).
thf(d1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ~ ( = @ B @ k1_xboole_0 ) => ( ( v1_funct_2 @ C @ A @ B ) <=> ( = @ A @ ( k1_relset_1 @ A @ C ) ) ) ) & ( ( = @ B @ k1_xboole_0 ) => ( ( v1_funct_2 @ C @ A @ B ) <=> ( = @ C @ k1_xboole_0 ) ) ) ) ) ),file(funct_2,d1_funct_2)).
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_wellfnd1,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v1_wellfnd1 @ A ) <=> ( r1_wellord1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(wellfnd1,d2_wellfnd1)).
thf(d3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( = @ B @ ( k10_xtuple_0 @ A ) ) <=> ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ? [D: $i] : ( ( r2_hidden @ D @ ( k9_xtuple_0 @ A ) ) & ( = @ C @ ( k1_funct_1 @ A @ D ) ) ) ) ) ) ),file(funct_1,d3_funct_1)).
thf(d3_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_tarski @ A @ B ) <=> ! [C: $i] : ( ( r2_hidden @ C @ A ) => ( r2_hidden @ C @ B ) ) ) ),file(tarski,d3_tarski)).
thf(d3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( = @ C @ ( k2_xboole_0 @ A @ B ) ) <=> ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ A ) | ( r2_hidden @ D @ B ) ) ) ) ),file(xboole_0,d3_xboole_0)).
thf(d4_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( ( = @ B @ ( k3_tarski @ A ) ) <=> ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ? [D: $i] : ( ( r2_hidden @ C @ D ) & ( r2_hidden @ D @ A ) ) ) ) ),file(tarski,d4_tarski)).
thf(d5_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k4_tarski @ A @ B ) @ ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ) ),file(tarski,d5_tarski)).
thf(d5_wellfnd1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_orders_2 @ A ) ) => ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( k3_rfunct_3 @ ( u1_struct_0 @ A ) @ B ) ) @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( k3_rfunct_3 @ ( u1_struct_0 @ A ) @ B ) ) @ B ) ) ) ) => ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) ) => ( ( r1_wellfnd1 @ A @ B @ C @ D ) <=> ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) ) => ( = @ ( k1_funct_1 @ D @ E ) @ ( k1_binop_1 @ C @ E @ ( k5_relat_1 @ D @ ( k1_wellord1 @ ( u1_orders_2 @ A ) @ E ) ) ) ) ) ) ) ) ) ) ),file(wellfnd1,d5_wellfnd1)).
thf(d5_wellord1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( r2_wellord1 @ A @ B ) <=> ( ( r1_relat_2 @ A @ B ) & ( r8_relat_2 @ A @ B ) & ( r4_relat_2 @ A @ B ) & ( r6_relat_2 @ A @ B ) & ( r1_wellord1 @ A @ B ) ) ) ) ),file(wellord1,d5_wellord1)).
thf(d6_relat_2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( r6_relat_2 @ A @ B ) <=> ! [C: $i] : ! [D: $i] : ~ ( ( r2_hidden @ C @ B ) & ( r2_hidden @ D @ B ) & ~ ( = @ C @ D ) & ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) & ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ) ),file(relat_2,d6_relat_2)).
thf(d6_wellord1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( = @ ( k2_wellord1 @ A @ B ) @ ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ B @ B ) ) ) ) ),file(wellord1,d6_wellord1)).
thf(dt_f1_s1_compl_sp,axiom,( ~ ( v1_xboole_0 @ f1_s1_compl_sp ) ),file(compl_sp,f1_s1_compl_sp)).
thf(dt_g1_orders_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) ) & ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ) ),file(orders_2,g1_orders_2)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k1_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ B ) ) => ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(domain_1,k1_domain_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_relat_1,axiom,( $true ),file(relat_1,k1_relat_1)).
thf(dt_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( m1_subset_1 @ ( k1_relset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k1_relset_1)).
thf(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
thf(dt_k1_wellord1,axiom,( $true ),file(wellord1,k1_wellord1)).
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_tarski,axiom,( $true ),file(tarski,k2_tarski)).
thf(dt_k2_wellord1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k2_wellord1 @ A @ B ) ) ) ),file(wellord1,k2_wellord1)).
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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k3_rfunct_3,axiom,( ! [A: $i] : ! [B: $i] : ( m1_rfunct_3 @ ( k3_rfunct_3 @ A @ B ) @ A @ B ) ),file(rfunct_3,k3_rfunct_3)).
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_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k4_partfun1,axiom,( $true ),file(partfun1,k4_partfun1)).
thf(dt_k4_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) => ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(subset_1,k4_subset_1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
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_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_k6_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(domain_1,k6_domain_1)).
thf(dt_k9_setfam_1,axiom,( ! [A: $i] : ( m1_subset_1 @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(setfam_1,k9_setfam_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_l1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( l1_struct_0 @ A ) ) ),file(orders_2,l1_orders_2)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_m1_rfunct_3,axiom,( $true ),file(rfunct_3,m1_rfunct_3)).
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(dt_u1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( m1_subset_1 @ ( u1_orders_2 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ) ) ),file(orders_2,u1_orders_2)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(existence_l1_orders_2,axiom,( ? [A: $i] : ( l1_orders_2 @ A ) ),file(orders_2,l1_orders_2)).
thf(existence_l1_struct_0,axiom,( ? [A: $i] : ( l1_struct_0 @ A ) ),file(struct_0,l1_struct_0)).
thf(existence_m1_rfunct_3,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( m1_rfunct_3 @ C @ A @ B ) ),file(rfunct_3,m1_rfunct_3)).
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(fc108_valued_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) ) => ( v6_membered @ ( k9_xtuple_0 @ A ) ) ) ),file(valued_1,fc108_valued_1)).
thf(fc10_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_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ B ) => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc10_finset_1)).
thf(fc10_membered,axiom,( ! [A: $i] : ( ( v1_rat_1 @ A ) => ( v4_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc10_membered)).
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(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_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc11_finset_1)).
thf(fc11_membered,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v5_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc11_membered)).
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] : ( v3_card_1 @ ( k1_tarski @ A ) @ np__1 ) ),file(card_1,fc13_card_1)).
thf(fc13_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( v1_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc13_membered)).
thf(fc14_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_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( v2_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc14_membered)).
thf(fc15_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v3_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc15_membered)).
thf(fc16_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_rat_1 @ A ) & ( v1_rat_1 @ B ) ) => ( v4_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc16_membered)).
thf(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_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v5_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc17_membered)).
thf(fc18_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( v6_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc18_membered)).
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_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_finset_1,axiom,( ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ) ),file(finset_1,fc1_finset_1)).
thf(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
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_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] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ) ),file(zfmisc_1,fc1_zfmisc_1)).
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(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(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(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(fc28_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ) ),file(finset_1,fc28_finset_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_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),file(finset_1,fc2_finset_1)).
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] : ( v1_zfmisc_1 @ ( k1_tarski @ A ) ) ),file(zfmisc_1,fc2_zfmisc_1)).
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(fc31_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_membered @ A ) => ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc31_membered)).
thf(fc32_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v5_finset_1 @ ( k2_tarski @ A @ B ) ) ) ),file(finset_1,fc32_finset_1)).
thf(fc32_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_membered @ A ) => ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),file(membered,fc32_membered)).
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(fc33_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v2_membered @ A ) => ( v2_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc33_membered)).
thf(fc34_finset_1,axiom,( ! [A: $i] : ( ( ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) => ( v1_finset_1 @ ( k3_tarski @ A ) ) ) ),file(finset_1,fc34_finset_1)).
thf(fc34_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v2_membered @ A ) => ( v2_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),file(membered,fc34_membered)).
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(fc35_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v3_membered @ A ) => ( v3_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc35_membered)).
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(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_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
thf(fc3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ) ),file(xboole_0,fc3_xboole_0)).
thf(fc3_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ B ) => ( 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_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
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_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(fc4_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(zfmisc_1,fc4_zfmisc_1)).
thf(fc56_membered,axiom,( v7_membered @ k1_numbers ),file(membered,fc56_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_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(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(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,( ~ ( 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_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_numbers,axiom,( ~ ( v1_finset_1 @ k1_numbers ) ),file(numbers,fc8_numbers)).
thf(fc8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) => ( v1_relat_1 @ ( k9_xtuple_0 @ D ) ) ) ),file(relset_1,fc8_relset_1)).
thf(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,( ! [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_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_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_orders_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ! [C: $i] : ! [D: $i] : ( ( = @ ( g1_orders_2 @ A @ B ) @ ( g1_orders_2 @ C @ D ) ) => ( ( = @ A @ C ) & ( = @ B @ D ) ) ) ) ),file(orders_2,g1_orders_2)).
thf(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
thf(idempotence_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k3_xboole_0)).
thf(idempotence_k4_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) => ( = @ ( k4_subset_1 @ A @ B @ B ) @ B ) ) ),file(subset_1,k4_subset_1)).
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_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_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_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_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_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_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc2_valued_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) ) ),file(valued_1,rc2_valued_1)).
thf(rc2_wellfnd1,axiom,( ? [A: $i] : ( ( l1_orders_2 @ A ) & ~ ( v2_struct_0 @ A ) & ( v1_wellfnd1 @ A ) ) ),file(wellfnd1,rc2_wellfnd1)).
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_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_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_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(rc3_valued_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(valued_1,rc3_valued_1)).
thf(rc3_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc3_xreal_0)).
thf(rc3_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(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_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(rc4_valued_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v3_card_1 @ A @ np__1 ) ) ),file(valued_1,rc4_valued_1)).
thf(rc4_xreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc4_xreal_0)).
thf(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(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_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_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_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_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(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(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(redefinition_k1_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ B ) ) => ( = @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k4_tarski @ C @ D ) ) ) ),file(domain_1,k1_domain_1)).
thf(redefinition_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k1_relset_1 @ A @ B ) @ ( k9_xtuple_0 @ B ) ) ) ),file(relset_1,k1_relset_1)).
thf(redefinition_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_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_k3_rfunct_3,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_rfunct_3 @ A @ B ) @ ( k4_partfun1 @ A @ B ) ) ),file(rfunct_3,k3_rfunct_3)).
thf(redefinition_k4_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) => ( = @ ( k4_subset_1 @ A @ B @ C ) @ ( k2_xboole_0 @ B @ C ) ) ) ),file(subset_1,k4_subset_1)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
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_k6_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( = @ ( k6_domain_1 @ A @ B ) @ ( k1_tarski @ B ) ) ) ),file(domain_1,k6_domain_1)).
thf(redefinition_k9_setfam_1,axiom,( ! [A: $i] : ( = @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),file(setfam_1,k9_setfam_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(t11_wellfnd1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_orders_2 @ A ) ) => ( ( v1_wellfnd1 @ A ) <=> ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( k3_rfunct_3 @ ( u1_struct_0 @ A ) @ B ) ) @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( k3_rfunct_3 @ ( u1_struct_0 @ A ) @ B ) ) @ B ) ) ) ) => ? [D: $i] : ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) ) ) & ( r1_wellfnd1 @ A @ B @ C @ D ) ) ) ) ) ) ),file(wellfnd1,t11_wellfnd1)).
thf(t17_wellord2,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( r2_wellord1 @ B @ A ) ) ),file(wellord2,t17_wellord2)).
thf(t17_xboole_1,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ) ),file(xboole_1,t17_xboole_1)).
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_pcomps_2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( r2_wellord1 @ A @ B ) => ( ( r2_wellord1 @ ( k2_wellord1 @ A @ B ) @ B ) & ( = @ B @ ( k1_relat_1 @ ( k2_wellord1 @ A @ B ) ) ) ) ) ) ),file(pcomps_2,t1_pcomps_2)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t1_wellord1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( v1_relat_1 @ C ) => ( ( r2_hidden @ A @ ( k1_wellord1 @ C @ B ) ) <=> ( ~ ( = @ A @ B ) & ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) ) ) ) ),file(wellord1,t1_wellord1)).
thf(t1_xboole_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r1_tarski @ A @ B ) & ( r1_tarski @ B @ C ) ) => ( r1_tarski @ A @ C ) ) ),file(xboole_1,t1_xboole_1)).
thf(t29_wellord1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( v1_relat_1 @ C ) => ( ( ( v2_wellord1 @ C ) & ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) & ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) ) => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) <=> ( r1_tarski @ ( k1_wellord1 @ C @ A ) @ ( k1_wellord1 @ C @ B ) ) ) ) ) ),file(wellord1,t29_wellord1)).
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_hidden @ A @ B ) ) ) ),file(subset,t2_subset)).
thf(t31_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_tarski @ ( k1_tarski @ A ) @ B ) <=> ( r2_hidden @ A @ B ) ) ),file(zfmisc_1,t31_zfmisc_1)).
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(t45_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( r2_hidden @ C @ ( k4_partfun1 @ A @ B ) ) ) ),file(partfun1,t45_partfun1)).
thf(t46_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( r2_hidden @ C @ ( k4_partfun1 @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),file(partfun1,t46_partfun1)).
thf(t47_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ ( k5_relat_1 @ C @ B ) ) ) => ( = @ ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A ) @ ( k1_funct_1 @ C @ A ) ) ) ) ),file(funct_1,t47_funct_1)).
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(t4_wellord1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ( ( r2_wellord1 @ A @ ( k1_relat_1 @ A ) ) <=> ( v2_wellord1 @ A ) ) ) ),file(wellord1,t4_wellord1)).
thf(t57_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( v1_relat_1 @ C ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ ( k5_relat_1 @ C @ B ) ) ) <=> ( ( r2_hidden @ A @ B ) & ( r2_hidden @ A @ ( k9_xtuple_0 @ C ) ) ) ) ) ),file(relat_1,t57_relat_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(t70_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ B ) => ( r1_tarski @ ( k10_xtuple_0 @ ( k5_relat_1 @ B @ A ) ) @ ( k10_xtuple_0 @ B ) ) ) ),file(relat_1,t70_relat_1)).
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_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(t8_xboole_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r1_tarski @ A @ B ) & ( r1_tarski @ C @ B ) ) => ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),file(xboole_1,t8_xboole_1)).
thf(t9_xboole_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( r1_tarski @ A @ B ) => ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ) ),file(xboole_1,t9_xboole_1)).
thf(s1_binop_1,axiom,( ! [A: $i > $i > $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ! [E: $i] : ! [F: $i] : ~ ( ( r2_hidden @ E @ D ) & ( r2_hidden @ F @ C ) & ! [G: $i] : ~ ( ( r2_hidden @ G @ B ) & ( A @ E @ F @ G ) ) ) => ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ C ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ D @ C ) @ B ) ) ) & ! [F: $i] : ! [G: $i] : ( ( ( r2_hidden @ F @ D ) & ( r2_hidden @ G @ C ) ) => ( A @ F @ G @ ( k1_binop_1 @ E @ F @ G ) ) ) ) ) ),file(binop_1,s1_binop_1)).
thf(s2_wellfnd1,axiom,( ! [A: $i] : ! [B: $i > $o] : ! [C: $i] : ( ( ( B @ C ) & ( v1_wellfnd1 @ A ) ) => ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) & ( B @ D ) & ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) ) => ~ ( ~ ( = @ D @ E ) & ( B @ E ) & ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ E @ D ) @ ( u1_orders_2 @ A ) ) ) ) ) ) ),file(wellfnd1,s2_wellfnd1)).
thf(s3_wellfnd1,axiom,( ! [A: $i > $o] : ! [B: $i] : ( ( ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) => ( ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) => ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ D @ C ) @ ( u1_orders_2 @ B ) ) => ( ( = @ D @ C ) | ( A @ D ) ) ) ) => ( A @ C ) ) ) & ( v1_wellfnd1 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) => ( A @ C ) ) ) ),file(wellfnd1,s3_wellfnd1)).
thf(s1_compl_sp,conjecture,( ( ! [A: $i] : ( ( m1_subset_1 @ A @ f1_s1_compl_sp ) => ! [B: $i] : ( ( m1_subset_1 @ B @ f1_s1_compl_sp ) => ( ( p1_s1_compl_sp @ A @ B ) <=> ( p1_s1_compl_sp @ B @ A ) ) ) ) & ! [A: $i] : ( ( m1_subset_1 @ A @ f1_s1_compl_sp ) => ~ ( p1_s1_compl_sp @ A @ A ) ) ) => ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_compl_sp ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ f1_s1_compl_sp ) => ! [C: $i] : ( ( m1_subset_1 @ C @ f1_s1_compl_sp ) => ( ( ( r2_hidden @ B @ A ) & ( r2_hidden @ C @ A ) ) => ( ( = @ B @ C ) | ( p1_s1_compl_sp @ B @ C ) ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ f1_s1_compl_sp ) => ? [C: $i] : ( ( m1_subset_1 @ C @ f1_s1_compl_sp ) & ( r2_hidden @ C @ A ) & ~ ( p1_s1_compl_sp @ B @ C ) ) ) ) ),file(compl_sp,s1_compl_sp)).
