% Mizar problem: e4_52_3,topgen_2,1539,19 
include('Axioms/SET010^1.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_52_type,type,( c1_52__topgen_2: $i )).
thf(c1_52_3_type,type,( c1_52_3__topgen_2: $i )).
thf(c2_52_type,type,( c2_52__topgen_2: $i )).
thf(c7_52_type,type,( c7_52__topgen_2: $i )).
thf(c8_52_type,type,( c8_52__topgen_2: $i )).
thf(c9_52_type,type,( c9_52__topgen_2: $i )).
thf(g1_pre_topc_type,type,( g1_pre_topc: $i > $i > $i )).
thf(k10_eqrel_1_type,type,( k10_eqrel_1: $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_cantor_1_type,type,( k2_cantor_1: $i > $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k3_subset_1_type,type,( k3_subset_1: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_subset_1_type,type,( k4_subset_1: $i > $i > $i > $i )).
thf(k4_xboole_0_type,type,( k4_xboole_0: $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k5_topgen_2_type,type,( k5_topgen_2: $i > $i > $i )).
thf(k6_domain_1_type,type,( k6_domain_1: $i > $i > $i )).
thf(k7_subset_1_type,type,( k7_subset_1: $i > $i > $i > $i )).
thf(u1_pre_topc_type,type,( u1_pre_topc: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_pre_topc_type,type,( l1_pre_topc: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(m1_eqrel_1_type,type,( m1_eqrel_1: $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(r1_tarski_type,type,( r1_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_card_5_type,type,( v1_card_5: $i > $o )).
thf(v1_compts_1_type,type,( v1_compts_1: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_pre_topc_type,type,( v1_pre_topc: $i > $o )).
thf(v1_setfam_1_type,type,( v1_setfam_1: $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_topgen_2_type,type,( v1_topgen_2: $i > $o )).
thf(v1_tops_1_type,type,( v1_tops_1: $i > $i > $o )).
thf(v1_tops_2_type,type,( v1_tops_2: $i > $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_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_compts_1_type,type,( v2_compts_1: $i > $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_pre_topc_type,type,( v2_pre_topc: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_tops_1_type,type,( v2_tops_1: $i > $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_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_pre_topc_type,type,( v3_pre_topc: $i > $i > $o )).
thf(v3_tops_1_type,type,( v3_tops_1: $i > $i > $o )).
thf(v4_pre_topc_type,type,( v4_pre_topc: $i > $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v6_pre_topc_type,type,( v6_pre_topc: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_pre_topc_type,type,( v7_pre_topc: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_pre_topc_type,type,( v8_pre_topc: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(cc6_card_fil,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v2_card_1 @ A ) ) => ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ( v1_card_5 @ A ) ) ) ),file(card_fil,cc6_card_fil)).
thf(rc2_card_fil,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v2_card_1 @ A ) ) ),file(card_fil,rc2_card_fil)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(cc2_topgen_2,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ~ ( v1_topgen_2 @ A ) => ~ ( v8_struct_0 @ A ) ) ) ),file(topgen_2,cc2_topgen_2)).
thf(cc4_card_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc4_card_1)).
thf(cc7_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v7_pre_topc @ A ) => ( v6_pre_topc @ A ) ) ) ),file(pre_topc,cc7_pre_topc)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(fc4_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
thf(fc5_card_1,axiom,( v2_card_1 @ k4_ordinal1 ),file(card_1,fc5_card_1)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc7_card_1,axiom,( ~ ( v1_finset_1 @ k4_ordinal1 ) ),file(card_1,fc7_card_1)).
thf(rc2_eqrel_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_eqrel_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_setfam_1 @ B ) ) ) ),file(eqrel_1,rc2_eqrel_1)).
thf(rc2_topgen_2,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ( v2_pre_topc @ A ) & ~ ( v1_topgen_2 @ A ) ) ),file(topgen_2,rc2_topgen_2)).
thf(rc4_eqrel_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_eqrel_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_setfam_1 @ B ) ) ) ),file(eqrel_1,rc4_eqrel_1)).
thf(rc9_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v7_pre_topc @ A ) ) ),file(pre_topc,rc9_pre_topc)).
thf(t1_numerals,axiom,( m1_subset_1 @ k1_xboole_0 @ k4_ordinal1 ),file(numerals,t1_numerals)).
thf(existence_m1_eqrel_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_eqrel_1 @ B @ A ) ),file(eqrel_1,m1_eqrel_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(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
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(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_m1_eqrel_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_eqrel_1 @ B @ A ) => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),file(eqrel_1,m1_eqrel_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(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_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(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(cc1_eqrel_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_eqrel_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ),file(eqrel_1,cc1_eqrel_1)).
thf(cc1_topgen_2,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v8_struct_0 @ A ) => ( v1_topgen_2 @ A ) ) ) ),file(topgen_2,cc1_topgen_2)).
thf(cc2_compts_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v8_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v2_compts_1 @ B @ A ) => ( v4_pre_topc @ B @ A ) ) ) ) ),file(compts_1,cc2_compts_1)).
thf(cc2_eqrel_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_eqrel_1 @ B @ A ) => ( v1_setfam_1 @ B ) ) ),file(eqrel_1,cc2_eqrel_1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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(cc3_compts_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ( v8_struct_0 @ A ) & ( v2_pre_topc @ A ) ) => ( ( v2_pre_topc @ A ) & ( v1_compts_1 @ A ) ) ) ) ),file(compts_1,cc3_compts_1)).
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(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_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_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v8_pre_topc @ A ) => ( v7_pre_topc @ A ) ) ) ),file(pre_topc,cc8_pre_topc)).
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(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(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_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_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_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(rc1_card_5,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_5,rc1_card_5)).
thf(rc1_compts_1,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v8_pre_topc @ A ) ) ),file(compts_1,rc1_compts_1)).
thf(rc1_topgen_2,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_tops_2 @ B @ A ) ) ) ),file(topgen_2,rc1_topgen_2)).
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_card_1,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_1,rc2_card_1)).
thf(rc2_compts_1,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v1_pre_topc @ A ) & ( v2_pre_topc @ A ) ) ),file(compts_1,rc2_compts_1)).
thf(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(rc4_compts_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_tops_2 @ B @ A ) ) ) ),file(compts_1,rc4_compts_1)).
thf(rc4_tops_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v1_tops_1 @ B @ A ) ) ) ),file(tops_1,rc4_tops_1)).
thf(free_g1_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ! [D: $i] : ( ( = @ ( g1_pre_topc @ A @ B ) @ ( g1_pre_topc @ C @ D ) ) => ( ( = @ A @ C ) & ( = @ B @ D ) ) ) ) ),file(pre_topc,g1_pre_topc)).
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(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
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(dt_g1_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) ) & ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ) ),file(pre_topc,g1_pre_topc)).
thf(dt_k10_eqrel_1,axiom,( ! [A: $i] : ( m1_eqrel_1 @ ( k10_eqrel_1 @ A ) @ A ) ),file(eqrel_1,k10_eqrel_1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
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_u1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),file(pre_topc,u1_pre_topc)).
thf(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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(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(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_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_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v3_tops_1 @ B @ A ) => ( v2_tops_1 @ B @ A ) ) ) ) ),file(tops_1,cc4_tops_1)).
thf(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc5_compts_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v2_struct_0 @ A ) => ( v8_pre_topc @ A ) ) ) ),file(compts_1,cc5_compts_1)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc5_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( ( v4_pre_topc @ B @ A ) & ( v2_tops_1 @ B @ A ) ) => ( v3_tops_1 @ B @ A ) ) ) ) ),file(tops_1,cc5_tops_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_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc6_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( ( v3_pre_topc @ B @ A ) & ( v3_tops_1 @ B @ A ) ) => ( v1_xboole_0 @ B ) ) ) ) ),file(tops_1,cc6_tops_1)).
thf(cc7_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_1)).
thf(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(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_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v2_struct_0 @ A ) => ( v6_pre_topc @ A ) ) ) ),file(pre_topc,cc9_pre_topc)).
thf(fc15_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( v3_tops_1 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ),file(tops_1,fc15_tops_1)).
thf(fc1_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ~ ( v1_xboole_0 @ ( u1_pre_topc @ A ) ) ) ),file(pre_topc,fc1_pre_topc)).
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(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_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( v4_pre_topc @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ),file(tops_1,fc2_tops_1)).
thf(fc33_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_finset_1 @ A ) & ( v5_finset_1 @ B ) ) => ( v5_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc33_finset_1)).
thf(fc3_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( v3_pre_topc @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ),file(tops_1,fc3_tops_1)).
thf(fc5_compts_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( v1_tops_2 @ ( u1_pre_topc @ A ) @ A ) ) ),file(compts_1,fc5_compts_1)).
thf(fc5_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( v4_pre_topc @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v4_pre_topc @ C @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( v4_pre_topc @ ( k2_xboole_0 @ B @ C ) @ A ) ) ),file(tops_1,fc5_tops_1)).
thf(fc6_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ( ( v1_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) & ( v2_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ),file(pre_topc,fc6_pre_topc)).
thf(fc7_pre_topc,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) ) => ( ~ ( v2_struct_0 @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) & ( v1_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ),file(pre_topc,fc7_pre_topc)).
thf(fc7_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( v3_pre_topc @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v3_pre_topc @ C @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( v3_pre_topc @ ( k2_xboole_0 @ B @ C ) @ A ) ) ),file(tops_1,fc7_tops_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_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) => ( ~ ( v2_struct_0 @ ( g1_pre_topc @ A @ B ) ) & ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ) ),file(pre_topc,fc9_pre_topc)).
thf(rc10_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v3_pre_topc @ B @ A ) ) ) ),file(pre_topc,rc10_pre_topc)).
thf(rc11_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) ) ),file(pre_topc,rc11_pre_topc)).
thf(rc12_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) & ( v2_pre_topc @ A ) ) ),file(pre_topc,rc12_pre_topc)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v3_pre_topc @ B @ A ) ) ) ),file(tops_1,rc1_tops_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(rc2_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) & ( v2_pre_topc @ A ) ) ),file(pre_topc,rc2_pre_topc)).
thf(rc2_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v3_pre_topc @ B @ A ) & ( v4_pre_topc @ B @ A ) ) ) ),file(tops_1,rc2_tops_1)).
thf(rc3_compts_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v2_compts_1 @ B @ A ) ) ) ),file(compts_1,rc3_compts_1)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_1)).
thf(rc3_tops_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v3_pre_topc @ B @ A ) & ( v4_pre_topc @ B @ A ) ) ) ),file(tops_1,rc3_tops_1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
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_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc5_tops_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v2_tops_1 @ B @ A ) ) ) ),file(tops_1,rc5_tops_1)).
thf(rc6_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v4_pre_topc @ B @ A ) ) ) ),file(pre_topc,rc6_pre_topc)).
thf(rc6_tops_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ~ ( v2_tops_1 @ B @ A ) ) ) ),file(tops_1,rc6_tops_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_pre_topc,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v4_pre_topc @ B @ A ) ) ) ),file(pre_topc,rc7_pre_topc)).
thf(rc7_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v3_tops_1 @ B @ A ) ) ) ),file(tops_1,rc7_tops_1)).
thf(t1_boole,axiom,( ! [A: $i] : ( = @ ( k2_xboole_0 @ A @ k1_xboole_0 ) @ A ) ),file(boole,t1_boole)).
thf(t3_boole,axiom,( ! [A: $i] : ( = @ ( k4_xboole_0 @ A @ k1_xboole_0 ) @ A ) ),file(boole,t3_boole)).
thf(t4_boole,axiom,( ! [A: $i] : ( = @ ( k4_xboole_0 @ k1_xboole_0 @ A ) @ k1_xboole_0 ) ),file(boole,t4_boole)).
thf(d2_xboole_0,axiom,( = @ k1_xboole_0 @ ( eps @ ^ [A: $i] : ( v1_xboole_0 @ A ) ) ),file(xboole_0,d2_xboole_0)).
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(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(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(abstractness_v1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v1_pre_topc @ A ) => ( = @ A @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ),file(pre_topc,v1_pre_topc)).
thf(existence_l1_pre_topc,axiom,( ? [A: $i] : ( l1_pre_topc @ A ) ),file(pre_topc,l1_pre_topc)).
thf(existence_l1_struct_0,axiom,( ? [A: $i] : ( l1_struct_0 @ A ) ),file(struct_0,l1_struct_0)).
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_k7_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k7_subset_1 @ A @ B @ C ) @ ( k4_xboole_0 @ B @ C ) ) ) ),file(subset_1,k7_subset_1)).
thf(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
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_xboole_0,axiom,( $true ),file(xboole_0,k4_xboole_0)).
thf(dt_k7_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(subset_1,k7_subset_1)).
thf(dt_l1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( l1_struct_0 @ A ) ) ),file(pre_topc,l1_pre_topc)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_c7_52__topgen_2,axiom,( m1_subset_1 @ c7_52__topgen_2 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k5_topgen_2 @ c1_52__topgen_2 @ c2_52__topgen_2 ) ) ) ) ),file(topgen_2,c7_52__topgen_2)).
thf(dt_c8_52__topgen_2,axiom,( m1_subset_1 @ c8_52__topgen_2 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k5_topgen_2 @ c1_52__topgen_2 @ c2_52__topgen_2 ) ) ) ) ),file(topgen_2,c8_52__topgen_2)).
thf(de_c7_52__topgen_2,axiom,( = @ c7_52__topgen_2 @ ( k10_eqrel_1 @ c1_52__topgen_2 ) ),file(topgen_2,c7_52__topgen_2)).
thf(de_c8_52__topgen_2,axiom,( = @ c8_52__topgen_2 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ c1_52__topgen_2 ) @ ^ [A: $i] : ( k3_subset_1 @ c1_52__topgen_2 @ ( k6_domain_1 @ c1_52__topgen_2 @ A ) ) @ ^ [A: $i] : $true ) ),file(topgen_2,c8_52__topgen_2)).
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(cc1_compts_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v2_compts_1 @ B @ A ) ) ) ) ),file(compts_1,cc1_compts_1)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc1_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v3_pre_topc @ B @ A ) ) ) ) ),file(tops_1,cc1_tops_1)).
thf(cc2_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_1)).
thf(cc2_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v4_pre_topc @ B @ A ) ) ) ) ),file(pre_topc,cc2_pre_topc)).
thf(cc2_tops_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v2_tops_1 @ B @ A ) ) ) ) ),file(tops_1,cc2_tops_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
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_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v3_tops_1 @ B @ A ) ) ) ) ),file(tops_1,cc3_tops_1)).
thf(cc4_compts_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_finset_1 @ B ) => ( v2_compts_1 @ B @ A ) ) ) ) ),file(compts_1,cc4_compts_1)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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_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_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
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(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc12_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc12_finset_1)).
thf(fc13_card_1,axiom,( ! [A: $i] : ( v3_card_1 @ ( k1_tarski @ A ) @ np__1 ) ),file(card_1,fc13_card_1)).
thf(fc1_finset_1,axiom,( ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ) ),file(finset_1,fc1_finset_1)).
thf(fc2_topgen_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ( ~ ( v2_struct_0 @ ( k5_topgen_2 @ A @ B ) ) & ( v1_pre_topc @ ( k5_topgen_2 @ A @ B ) ) ) ) ),file(topgen_2,fc2_topgen_2)).
thf(fc30_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_tarski @ A ) ) ) ),file(finset_1,fc30_finset_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ( v1_pre_topc @ A ) ) ),file(pre_topc,rc1_pre_topc)).
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(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_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(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_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_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(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(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(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(involutiveness_k3_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) ) @ B ) ) ),file(subset_1,k3_subset_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_cantor_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ( m1_subset_1 @ ( k2_cantor_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),file(cantor_1,k2_cantor_1)).
thf(dt_k3_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(subset_1,k3_subset_1)).
thf(dt_k5_topgen_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_pre_topc @ ( k5_topgen_2 @ A @ B ) ) & ( l1_pre_topc @ ( k5_topgen_2 @ A @ B ) ) ) ),file(topgen_2,k5_topgen_2)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_52__topgen_2,axiom,( ~ ( v1_xboole_0 @ c1_52__topgen_2 ) ),file(topgen_2,c1_52__topgen_2)).
thf(dt_c1_52_3__topgen_2,axiom,( $true ),file(topgen_2,c1_52_3__topgen_2)).
thf(dt_c2_52__topgen_2,axiom,( $true ),file(topgen_2,c2_52__topgen_2)).
thf(dt_c9_52__topgen_2,axiom,( m1_subset_1 @ c9_52__topgen_2 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k5_topgen_2 @ c1_52__topgen_2 @ c2_52__topgen_2 ) ) ) ) ),file(topgen_2,c9_52__topgen_2)).
thf(de_c9_52__topgen_2,axiom,( = @ c9_52__topgen_2 @ ( k4_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k5_topgen_2 @ c1_52__topgen_2 @ c2_52__topgen_2 ) ) ) @ ( k7_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k5_topgen_2 @ c1_52__topgen_2 @ c2_52__topgen_2 ) ) ) @ c7_52__topgen_2 @ ( k1_tarski @ ( k1_tarski @ c2_52__topgen_2 ) ) ) @ c8_52__topgen_2 ) ),file(topgen_2,c9_52__topgen_2)).
thf(cc1_card_5,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(card_5,cc1_card_5)).
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(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
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(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc1_topgen_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_pre_topc @ ( k5_topgen_2 @ A @ B ) ) & ( v2_pre_topc @ ( k5_topgen_2 @ A @ B ) ) ) ),file(topgen_2,fc1_topgen_2)).
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(fc9_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(card_1,fc9_card_1)).
thf(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_1)).
thf(rc4_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_finset_1 @ B ) ) ) ),file(card_1,rc4_card_1)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_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_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) ) => ( m1_subset_1 @ A @ C ) ) ),file(subset,t4_subset)).
thf(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(d4_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k3_subset_1 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ) ) ),file(subset_1,d4_subset_1)).
thf(e3_52_3__topgen_2,axiom,( ( r2_hidden @ c1_52_3__topgen_2 @ c9_52__topgen_2 ) | ( r2_hidden @ c1_52_3__topgen_2 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ c1_52__topgen_2 ) ) @ ^ [A: $i] : ( k3_subset_1 @ c1_52__topgen_2 @ A ) @ ^ [A: $i] : ( v1_finset_1 @ A ) ) ) ),file(topgen_2,e3_52_3__topgen_2)).
thf(e9_52__topgen_2,axiom,( r1_tarski @ c9_52__topgen_2 @ ( k2_cantor_1 @ ( u1_struct_0 @ ( k5_topgen_2 @ c1_52__topgen_2 @ c2_52__topgen_2 ) ) @ c9_52__topgen_2 ) ),file(topgen_2,e9_52__topgen_2)).
thf(e8_52__topgen_2,axiom,( r1_tarski @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ c1_52__topgen_2 ) ) @ ^ [A: $i] : ( k3_subset_1 @ c1_52__topgen_2 @ A ) @ ^ [A: $i] : ( v1_finset_1 @ A ) ) @ ( k2_cantor_1 @ ( u1_struct_0 @ ( k5_topgen_2 @ c1_52__topgen_2 @ c2_52__topgen_2 ) ) @ c9_52__topgen_2 ) ),file(topgen_2,e8_52__topgen_2)).
thf(e4_52_3__topgen_2,conjecture,( r2_hidden @ c1_52_3__topgen_2 @ ( k2_cantor_1 @ ( u1_struct_0 @ ( k5_topgen_2 @ c1_52__topgen_2 @ c2_52__topgen_2 ) ) @ c9_52__topgen_2 ) ),file(topgen_2,e4_52_3__topgen_2)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
