% Mizar problem: e8_25,yellow17,767,49 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_25_type,type,( c1_25__yellow17: $i )).
thf(c2_25_type,type,( c2_25__yellow17: $i )).
thf(c3_25_type,type,( c3_25__yellow17: $i )).
thf(c4_25_type,type,( c4_25__yellow17: $i )).
thf(g1_pre_topc_type,type,( g1_pre_topc: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_tarski_type,type,( k3_tarski: $i > $i )).
thf(k3_waybel18_type,type,( k3_waybel18: $i > $i > $i )).
thf(k4_waybel18_type,type,( k4_waybel18: $i > $i > $i > $i )).
thf(k5_waybel18_type,type,( k5_waybel18: $i > $i > $i > $i > $i )).
thf(k6_waybel18_type,type,( k6_waybel18: $i > $i > $i > $i )).
thf(k8_relat_1_type,type,( k8_relat_1: $i > $i > $i )).
thf(k8_relset_1_type,type,( k8_relset_1: $i > $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_subset_1_type,type,( m1_subset_1: $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_3_type,type,( v1_card_3: $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_monoid_0_type,type,( v1_monoid_0: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_pre_topc_type,type,( v1_pre_topc: $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_tops_2_type,type,( v1_tops_2: $i > $i > $o )).
thf(v1_waybel18_type,type,( v1_waybel18: $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_cantor_1_type,type,( v2_cantor_1: $i > $i > $o )).
thf(v2_card_3_type,type,( v2_card_3: $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_pralg_1_type,type,( v2_pralg_1: $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(v4_card_3_type,type,( v4_card_3: $i > $o )).
thf(v4_pre_topc_type,type,( v4_pre_topc: $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_waybel_3_type,type,( v4_waybel_3: $i > $o )).
thf(v5_card_3_type,type,( v5_card_3: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_pre_topc_type,type,( v6_pre_topc: $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(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(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
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(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_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
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_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(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(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(cc4_card_3,axiom,( ! [A: $i] : ( ( v5_card_3 @ A ) => ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) ) ),file(card_3,cc4_card_3)).
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(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(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(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(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_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_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_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(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_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(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(rc5_card_3,axiom,( ? [A: $i] : ( v5_card_3 @ A ) ),file(card_3,rc5_card_3)).
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(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_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(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(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(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k8_relat_1,axiom,( $true ),file(relat_1,k8_relat_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_c3_25__yellow17,axiom,( ( v1_tops_2 @ c3_25__yellow17 @ ( k3_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 ) ) & ( v2_cantor_1 @ c3_25__yellow17 @ ( k3_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 ) ) & ( m1_subset_1 @ c3_25__yellow17 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 ) ) ) ) ) ),file(yellow17,c3_25__yellow17)).
thf(cc1_monoid_0,axiom,( ! [A: $i] : ( ( ( v1_monoid_0 @ A ) & ( l1_struct_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(monoid_0,cc1_monoid_0)).
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(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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc2_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ~ ( v1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(subset_1,cc2_subset_1)).
thf(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_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(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_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(cc5_card_3,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) => ( v5_card_3 @ A ) ) ),file(card_3,cc5_card_3)).
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(cc7_card_3,axiom,( ! [A: $i] : ( ( v4_card_3 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_card_3 @ B ) ) ) ),file(card_3,cc7_card_3)).
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(cc8_card_3,axiom,( ! [A: $i] : ( ( v2_card_3 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_card_3 @ B ) ) ) ),file(card_3,cc8_card_3)).
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_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_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v2_struct_0 @ A ) => ( v6_pre_topc @ A ) ) ) ),file(pre_topc,cc9_pre_topc)).
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(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(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(fc23_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k8_relat_1 @ A @ B ) ) ) ),file(finset_1,fc23_finset_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(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(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(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_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ),file(card_3,rc1_card_3)).
thf(rc1_monoid_0,axiom,( ? [A: $i] : ( ( l1_struct_0 @ A ) & ( v1_monoid_0 @ A ) ) ),file(monoid_0,rc1_monoid_0)).
thf(rc1_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ( v1_pre_topc @ A ) ) ),file(pre_topc,rc1_pre_topc)).
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_yellow_6,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_pralg_1 @ B ) & ( v4_waybel_3 @ B ) ) ),file(yellow_6,rc2_yellow_6)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_1)).
thf(rc4_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_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(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(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(redefinition_k4_waybel18,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) & ( m1_subset_1 @ C @ A ) ) => ( = @ ( k4_waybel18 @ A @ B @ C ) @ ( k1_funct_1 @ B @ C ) ) ) ),file(waybel18,k4_waybel18)).
thf(redefinition_k5_waybel18,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_waybel18 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k5_waybel18 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(waybel18,k5_waybel18)).
thf(redefinition_k8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( = @ ( k8_relset_1 @ A @ B @ C @ D ) @ ( k8_relat_1 @ C @ D ) ) ) ),file(relset_1,k8_relset_1)).
thf(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k3_tarski,axiom,( $true ),file(tarski,k3_tarski)).
thf(dt_k3_waybel18,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) ) => ( ( v1_pre_topc @ ( k3_waybel18 @ A @ B ) ) & ( v2_pre_topc @ ( k3_waybel18 @ A @ B ) ) & ( l1_pre_topc @ ( k3_waybel18 @ A @ B ) ) ) ) ),file(waybel18,k3_waybel18)).
thf(dt_k4_waybel18,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) & ( m1_subset_1 @ C @ A ) ) => ( ~ ( v2_struct_0 @ ( k4_waybel18 @ A @ B @ C ) ) & ( l1_pre_topc @ ( k4_waybel18 @ A @ B @ C ) ) ) ) ),file(waybel18,k4_waybel18)).
thf(dt_k5_waybel18,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_waybel18 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k5_waybel18 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k4_waybel18 @ A @ B @ D ) ) ) ) ),file(waybel18,k5_waybel18)).
thf(dt_k6_waybel18,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) & ( m1_subset_1 @ C @ A ) ) => ( ( v1_funct_1 @ ( k6_waybel18 @ A @ B @ C ) ) & ( v1_funct_2 @ ( k6_waybel18 @ A @ B @ C ) @ ( u1_struct_0 @ ( k3_waybel18 @ A @ B ) ) @ ( u1_struct_0 @ ( k4_waybel18 @ A @ B @ C ) ) ) & ( m1_subset_1 @ ( k6_waybel18 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ ( k3_waybel18 @ A @ B ) ) @ ( u1_struct_0 @ ( k4_waybel18 @ A @ B @ C ) ) ) ) ) ) ) ),file(waybel18,k6_waybel18)).
thf(dt_k8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( m1_subset_1 @ ( k8_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k8_relset_1)).
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_25__yellow17,axiom,( ~ ( v1_xboole_0 @ c1_25__yellow17 ) ),file(yellow17,c1_25__yellow17)).
thf(dt_c2_25__yellow17,axiom,( ( v1_relat_1 @ c2_25__yellow17 ) & ( v4_relat_1 @ c2_25__yellow17 @ c1_25__yellow17 ) & ( v1_funct_1 @ c2_25__yellow17 ) & ( v1_partfun1 @ c2_25__yellow17 @ c1_25__yellow17 ) & ( v4_waybel_3 @ c2_25__yellow17 ) & ( v1_waybel18 @ c2_25__yellow17 ) ),file(yellow17,c2_25__yellow17)).
thf(dt_c4_25__yellow17,axiom,( m1_subset_1 @ c4_25__yellow17 @ ( k1_zfmisc_1 @ c3_25__yellow17 ) ),file(yellow17,c4_25__yellow17)).
thf(cc1_card_3,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ) ),file(card_3,cc1_card_3)).
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_waybel18,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_waybel18 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_pralg_1 @ A ) ) ) ),file(waybel18,cc1_waybel18)).
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(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(cc4_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_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc6_card_3,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v4_card_3 @ A ) ) ),file(card_3,cc6_card_3)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_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(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_finset_1,axiom,( ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ) ),file(finset_1,fc1_finset_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc1_waybel18,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) ) => ( ~ ( v2_struct_0 @ ( k3_waybel18 @ A @ B ) ) & ( v1_pre_topc @ ( k3_waybel18 @ A @ B ) ) & ( v2_pre_topc @ ( k3_waybel18 @ A @ B ) ) ) ) ),file(waybel18,fc1_waybel18)).
thf(fc2_waybel18,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) ) => ( ( v1_pre_topc @ ( k3_waybel18 @ A @ B ) ) & ( v2_pre_topc @ ( k3_waybel18 @ A @ B ) ) & ( v1_monoid_0 @ ( k3_waybel18 @ A @ B ) ) ) ) ),file(waybel18,fc2_waybel18)).
thf(fc30_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_tarski @ A ) ) ) ),file(finset_1,fc30_finset_1)).
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(fc7_card_3,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v2_card_3 @ ( k1_tarski @ A ) ) ) ),file(card_3,fc7_card_3)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_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_waybel18,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_waybel18 @ B ) ) ),file(waybel18,rc1_waybel18)).
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(rc2_waybel18,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) ) ),file(waybel18,rc2_waybel18)).
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(rc6_card_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v1_finset_1 @ A ) ) ),file(card_3,rc6_card_3)).
thf(e7_25__yellow17,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ c1_25__yellow17 ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k4_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 @ A ) ) ) & ! [C: $i] : ( ( ( v1_finset_1 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ c4_25__yellow17 ) ) ) => ~ ( r1_tarski @ ( k8_relset_1 @ ( u1_struct_0 @ ( k3_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 ) ) @ ( u1_struct_0 @ ( k4_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 @ A ) ) @ ( k6_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 @ A ) @ ( k1_tarski @ B ) ) @ ( k3_tarski @ C ) ) ) ) ) ),file(yellow17,e7_25__yellow17)).
thf(s1_yellow17,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ C ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ C ) & ( v4_waybel_3 @ B ) & ( v1_waybel18 @ B ) ) => ( ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k4_waybel18 @ C @ B @ D ) ) ) & ( A @ E @ D ) ) ) => ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k3_waybel18 @ C @ B ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ C ) => ( A @ ( k5_waybel18 @ C @ B @ D @ E ) @ E ) ) ) ) ) ),file(yellow17,s1_yellow17)).
thf(e8_25__yellow17,conjecture,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ ( k3_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ c1_25__yellow17 ) => ! [C: $i] : ( ( ( v1_finset_1 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ c4_25__yellow17 ) ) ) => ~ ( r1_tarski @ ( k8_relset_1 @ ( u1_struct_0 @ ( k3_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 ) ) @ ( u1_struct_0 @ ( k4_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 @ B ) ) @ ( k6_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 @ B ) @ ( k1_tarski @ ( k5_waybel18 @ c1_25__yellow17 @ c2_25__yellow17 @ A @ B ) ) ) @ ( k3_tarski @ C ) ) ) ) ) ),file(yellow17,e8_25__yellow17)).
