% Mizar problem: e5_53,waybel19,1850,59 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_53_type,type,( c1_53__waybel19: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_struct_0_type,type,( k2_struct_0: $i > $i )).
thf(k3_tarski_type,type,( k3_tarski: $i > $i )).
thf(k3_xboole_0_type,type,( k3_xboole_0: $i > $i > $i )).
thf(k5_setfam_1_type,type,( k5_setfam_1: $i > $i > $i )).
thf(k9_subset_1_type,type,( k9_subset_1: $i > $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_orders_2_type,type,( l1_orders_2: $i > $o )).
thf(l1_pre_topc_type,type,( l1_pre_topc: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l1_waybel_9_type,type,( l1_waybel_9: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(v12_waybel_0_type,type,( v12_waybel_0: $i > $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v13_waybel_0_type,type,( v13_waybel_0: $i > $i > $o )).
thf(v16_waybel_0_type,type,( v16_waybel_0: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_lattice3_type,type,( v1_lattice3: $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $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_waybel11_type,type,( v1_waybel11: $i > $i > $o )).
thf(v1_waybel19_type,type,( v1_waybel19: $i > $o )).
thf(v1_waybel_0_type,type,( v1_waybel_0: $i > $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_yellow_0_type,type,( v1_yellow_0: $i > $o )).
thf(v1_yellow_3_type,type,( v1_yellow_3: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v24_waybel_0_type,type,( v24_waybel_0: $i > $o )).
thf(v25_waybel_0_type,type,( v25_waybel_0: $i > $o )).
thf(v2_cantor_1_type,type,( v2_cantor_1: $i > $i > $o )).
thf(v2_lattice3_type,type,( v2_lattice3: $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_waybel11_type,type,( v2_waybel11: $i > $i > $o )).
thf(v2_waybel_0_type,type,( v2_waybel_0: $i > $i > $o )).
thf(v2_waybel_3_type,type,( v2_waybel_3: $i > $o )).
thf(v2_yellow_0_type,type,( v2_yellow_0: $i > $o )).
thf(v3_lattice3_type,type,( v3_lattice3: $i > $o )).
thf(v3_orders_2_type,type,( v3_orders_2: $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(v3_waybel11_type,type,( v3_waybel11: $i > $i > $o )).
thf(v3_waybel_3_type,type,( v3_waybel_3: $i > $o )).
thf(v3_yellow_0_type,type,( v3_yellow_0: $i > $o )).
thf(v4_orders_2_type,type,( v4_orders_2: $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_orders_2_type,type,( v5_orders_2: $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(cc4_waybel_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v3_waybel_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v24_waybel_0 @ A ) & ( v2_waybel_3 @ A ) ) ) ) ),file(waybel_3,cc4_waybel_3)).
thf(cc13_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_lattice3 @ A ) & ( v1_yellow_0 @ A ) & ( v24_waybel_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v3_lattice3 @ A ) ) ) ) ),file(waybel_0,cc13_waybel_0)).
thf(cc2_waybel_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_yellow_0 @ A ) & ( v16_waybel_0 @ A ) & ( v24_waybel_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v3_lattice3 @ A ) & ( v16_waybel_0 @ A ) ) ) ) ),file(waybel_3,cc2_waybel_3)).
thf(cc5_waybel_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_yellow_0 @ A ) & ( v1_lattice3 @ A ) & ( v24_waybel_0 @ A ) & ( v2_waybel_3 @ A ) ) => ( ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_yellow_0 @ A ) & ( v1_lattice3 @ A ) & ( v3_waybel_3 @ A ) ) ) ) ),file(waybel_3,cc5_waybel_3)).
thf(cc5_yellow_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ( v1_yellow_0 @ A ) & ( v2_yellow_0 @ A ) ) => ( v3_yellow_0 @ A ) ) ) ),file(yellow_0,cc5_yellow_0)).
thf(fc4_waybel_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v1_yellow_0 @ A ) & ( l1_orders_2 @ A ) ) => ( v2_waybel_0 @ ( k2_struct_0 @ A ) @ A ) ) ),file(waybel_0,fc4_waybel_0)).
thf(cc12_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v25_waybel_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v1_yellow_0 @ A ) ) ) ) ),file(waybel_0,cc12_waybel_0)).
thf(cc14_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v25_waybel_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v2_lattice3 @ A ) ) ) ) ),file(waybel_0,cc14_waybel_0)).
thf(cc15_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v2_yellow_0 @ A ) & ( v25_waybel_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_lattice3 @ A ) & ( v2_yellow_0 @ A ) ) ) ) ),file(waybel_0,cc15_waybel_0)).
thf(cc4_yellow_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v3_yellow_0 @ A ) => ( ( v1_yellow_0 @ A ) & ( v2_yellow_0 @ A ) ) ) ) ),file(yellow_0,cc4_yellow_0)).
thf(cc11_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v3_lattice3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v24_waybel_0 @ A ) & ( v25_waybel_0 @ A ) ) ) ) ),file(waybel_0,cc11_waybel_0)).
thf(cc1_yellow_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_lattice3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_lattice3 @ A ) & ( v2_lattice3 @ A ) ) ) ) ),file(yellow_0,cc1_yellow_0)).
thf(cc3_yellow_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_lattice3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_yellow_0 @ A ) ) ) ) ),file(yellow_0,cc3_yellow_0)).
thf(cc6_waybel11,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_lattice3 @ A ) & ( v2_lattice3 @ A ) & ( v3_lattice3 @ A ) & ( l1_waybel_9 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v12_waybel_0 @ B @ A ) => ( v3_waybel11 @ B @ A ) ) ) ) ),file(waybel11,cc6_waybel11)).
thf(cc6_waybel_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v3_lattice3 @ A ) & ( v16_waybel_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v16_waybel_0 @ A ) & ( v2_waybel_3 @ A ) ) ) ) ),file(waybel_3,cc6_waybel_3)).
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(cc1_waybel19,axiom,( ! [A: $i] : ( ( l1_waybel_9 @ A ) => ( ( ( v13_struct_0 @ A @ np__1 ) & ( v2_pre_topc @ A ) & ( v3_orders_2 @ A ) ) => ( ( v13_struct_0 @ A @ np__1 ) & ( v2_pre_topc @ A ) & ( v3_orders_2 @ A ) & ( v1_waybel19 @ A ) ) ) ) ),file(waybel19,cc1_waybel19)).
thf(cc1_waybel_3,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v16_waybel_0 @ A ) & ( l1_orders_2 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_waybel_0 @ B @ A ) & ( v2_waybel_0 @ B @ A ) ) ) ) ),file(waybel_3,cc1_waybel_3)).
thf(cc2_yellow_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ( v13_struct_0 @ A @ np__1 ) & ( v3_orders_2 @ A ) ) => ( ( v13_struct_0 @ A @ np__1 ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v3_lattice3 @ A ) ) ) ) ),file(yellow_0,cc2_yellow_0)).
thf(cc3_waybel11,axiom,( ! [A: $i] : ( ( ( v13_struct_0 @ A @ np__1 ) & ( l1_orders_2 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( v13_waybel_0 @ B @ A ) ) ) ),file(waybel11,cc3_waybel11)).
thf(cc3_waybel_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ( v13_struct_0 @ A @ np__1 ) & ( v3_orders_2 @ A ) ) => ( ( v13_struct_0 @ A @ np__1 ) & ( v3_orders_2 @ A ) & ( v2_waybel_3 @ A ) ) ) ) ),file(waybel_3,cc3_waybel_3)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
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(cc1_waybel11,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( v1_finset_1 @ B ) ) ) ),file(waybel11,cc1_waybel11)).
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_yellow_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ~ ( v1_yellow_3 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(yellow_3,cc2_yellow_3)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_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(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_waybel11,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_lattice3 @ A ) & ( l1_orders_2 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( v1_waybel11 @ B @ A ) ) ) ),file(waybel11,cc5_waybel11)).
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_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) & ( v3_orders_2 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v16_waybel_0 @ A ) ) ) ) ),file(waybel_0,cc6_waybel_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_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_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(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(rc3_waybel11,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v2_waybel11 @ B @ A ) & ( v3_waybel11 @ B @ A ) ) ) ),file(waybel11,rc3_waybel11)).
thf(rc5_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc5_subset_1)).
thf(rc5_waybel11,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v12_waybel_0 @ B @ A ) & ( v13_waybel_0 @ B @ A ) & ( v1_waybel11 @ B @ A ) & ( v2_waybel11 @ B @ A ) ) ) ),file(waybel11,rc5_waybel11)).
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(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_yellow_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v2_struct_0 @ A ) => ( v1_yellow_3 @ A ) ) ) ),file(yellow_3,cc1_yellow_3)).
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_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_waybel19,axiom,( ! [A: $i] : ( ( l1_waybel_9 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_waybel19 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v6_pre_topc @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) ) ) ) ),file(waybel19,cc2_waybel19)).
thf(cc3_yellow_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) ) => ~ ( v1_yellow_3 @ A ) ) ) ),file(yellow_3,cc3_yellow_3)).
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(cc4_waybel11,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( ( v2_waybel11 @ B @ A ) & ( v3_waybel11 @ B @ A ) ) ) ) ) ),file(waybel11,cc4_waybel11)).
thf(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
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_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_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_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_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(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(fc14_tops_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ~ ( v2_tops_1 @ ( k2_struct_0 @ A ) @ A ) ) ),file(tops_1,fc14_tops_1)).
thf(fc14_waybel_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_orders_2 @ A ) ) => ( ( v12_waybel_0 @ ( k2_struct_0 @ A ) @ A ) & ( v13_waybel_0 @ ( k2_struct_0 @ A ) @ A ) ) ) ),file(waybel_0,fc14_waybel_0)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(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_waybel11,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ( ( v1_waybel11 @ ( k2_struct_0 @ A ) @ A ) & ( v2_waybel11 @ ( k2_struct_0 @ A ) @ A ) ) ) ),file(waybel11,fc2_waybel11)).
thf(fc2_waybel_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_yellow_0 @ A ) & ( l1_orders_2 @ A ) ) => ( v1_waybel_0 @ ( k2_struct_0 @ A ) @ A ) ) ),file(waybel_0,fc2_waybel_0)).
thf(fc2_yellow_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_orders_2 @ A ) ) => ~ ( v1_xboole_0 @ ( k2_struct_0 @ A ) ) ) ),file(yellow_0,fc2_yellow_0)).
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(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(fc4_struct_0,axiom,( ! [A: $i] : ( ( ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_xboole_0 @ ( k2_struct_0 @ A ) ) ) ),file(struct_0,fc4_struct_0)).
thf(fc4_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 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(tops_1,fc4_tops_1)).
thf(fc5_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( k2_struct_0 @ A ) ) ) ),file(struct_0,fc5_struct_0)).
thf(rc10_waybel_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v2_waybel_0 @ B @ A ) & ( v13_waybel_0 @ B @ A ) ) ) ),file(waybel_0,rc10_waybel_0)).
thf(rc11_waybel_0,axiom,( ! [A: $i] : ( ( ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( v1_lattice3 @ A ) & ( v2_lattice3 @ A ) & ( l1_orders_2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_waybel_0 @ B @ A ) & ( v2_waybel_0 @ B @ A ) & ( v12_waybel_0 @ B @ A ) & ( v13_waybel_0 @ B @ A ) ) ) ),file(waybel_0,rc11_waybel_0)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_waybel11,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) & ( v1_waybel_0 @ B @ A ) ) ) ),file(waybel11,rc1_waybel11)).
thf(rc1_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v1_waybel_0 @ B @ A ) & ( v2_waybel_0 @ B @ A ) ) ) ),file(waybel_0,rc1_waybel_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_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(rc2_waybel_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) & ( v1_waybel_0 @ B @ A ) & ( v2_waybel_0 @ B @ A ) ) ) ),file(waybel_0,rc2_waybel_0)).
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_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_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(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_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(rc7_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v12_waybel_0 @ B @ A ) & ( v13_waybel_0 @ B @ A ) ) ) ),file(waybel_0,rc7_waybel_0)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(rc8_waybel_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_orders_2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v12_waybel_0 @ B @ A ) & ( v13_waybel_0 @ B @ A ) ) ) ),file(waybel_0,rc8_waybel_0)).
thf(rc9_waybel_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_waybel_0 @ B @ A ) & ( v12_waybel_0 @ B @ A ) ) ) ),file(waybel_0,rc9_waybel_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(idempotence_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k3_xboole_0)).
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_l1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( l1_struct_0 @ A ) ) ),file(orders_2,l1_orders_2)).
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(cc10_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( ( v3_orders_2 @ A ) & ( v1_lattice3 @ A ) & ( v24_waybel_0 @ A ) ) => ( ( v3_orders_2 @ A ) & ( v1_lattice3 @ A ) & ( v2_yellow_0 @ A ) ) ) ) ),file(waybel_0,cc10_waybel_0)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_lattice3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v1_lattice3 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(lattice3,cc1_lattice3)).
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(cc1_waybel_0,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( ( v1_waybel_0 @ B @ A ) & ( v2_waybel_0 @ B @ A ) ) ) ) ) ),file(waybel_0,cc1_waybel_0)).
thf(cc2_lattice3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v2_lattice3 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(lattice3,cc2_lattice3)).
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(cc2_waybel11,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( ( v12_waybel_0 @ B @ A ) & ( v13_waybel_0 @ B @ A ) ) ) ) ) ),file(waybel11,cc2_waybel11)).
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_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(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(fc10_tops_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ( v3_pre_topc @ ( k2_struct_0 @ A ) @ A ) ) ),file(tops_1,fc10_tops_1)).
thf(fc12_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ~ ( v1_subset_1 @ ( k2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc12_struct_0)).
thf(fc12_tops_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( v1_tops_1 @ ( k2_struct_0 @ A ) @ A ) ) ),file(tops_1,fc12_tops_1)).
thf(fc1_waybel_0,axiom,( ! [A: $i] : ( ( ( v1_lattice3 @ A ) & ( l1_orders_2 @ A ) ) => ( v1_waybel_0 @ ( k2_struct_0 @ A ) @ A ) ) ),file(waybel_0,fc1_waybel_0)).
thf(fc1_yellow12,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k3_tarski @ A ) ) ) ),file(yellow12,fc1_yellow12)).
thf(fc3_waybel_0,axiom,( ! [A: $i] : ( ( ( v2_lattice3 @ A ) & ( l1_orders_2 @ A ) ) => ( v2_waybel_0 @ ( k2_struct_0 @ A ) @ A ) ) ),file(waybel_0,fc3_waybel_0)).
thf(fc4_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ( v4_pre_topc @ ( k2_struct_0 @ A ) @ A ) ) ),file(pre_topc,fc4_pre_topc)).
thf(fc6_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 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(tops_1,fc6_tops_1)).
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(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_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(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(commutativity_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ C ) @ ( k9_subset_1 @ A @ C @ B ) ) ) ),file(subset_1,k9_subset_1)).
thf(idempotence_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ B ) @ B ) ) ),file(subset_1,k9_subset_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k5_setfam_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ( = @ ( k5_setfam_1 @ A @ B ) @ ( k3_tarski @ B ) ) ) ),file(setfam_1,k5_setfam_1)).
thf(redefinition_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ C ) @ ( k3_xboole_0 @ B @ C ) ) ) ),file(subset_1,k9_subset_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( m1_subset_1 @ ( k2_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),file(struct_0,k2_struct_0)).
thf(dt_k5_setfam_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(setfam_1,k5_setfam_1)).
thf(dt_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( m1_subset_1 @ ( k9_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(subset_1,k9_subset_1)).
thf(dt_l1_waybel_9,axiom,( ! [A: $i] : ( ( l1_waybel_9 @ A ) => ( ( l1_pre_topc @ A ) & ( l1_orders_2 @ A ) ) ) ),file(waybel_9,l1_waybel_9)).
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_53__waybel19,axiom,( ( v2_pre_topc @ c1_53__waybel19 ) & ( v3_orders_2 @ c1_53__waybel19 ) & ( v4_orders_2 @ c1_53__waybel19 ) & ( v5_orders_2 @ c1_53__waybel19 ) & ( v1_lattice3 @ c1_53__waybel19 ) & ( v2_lattice3 @ c1_53__waybel19 ) & ( v24_waybel_0 @ c1_53__waybel19 ) & ( v1_waybel19 @ c1_53__waybel19 ) & ( l1_waybel_9 @ c1_53__waybel19 ) ),file(waybel19,c1_53__waybel19)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(e1_53__waybel19,axiom,( ? [A: $i] : ( ( v1_tops_2 @ A @ c1_53__waybel19 ) & ( v2_cantor_1 @ A @ c1_53__waybel19 ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_53__waybel19 ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_53__waybel19 ) ) ) => ( ( r2_hidden @ B @ A ) => ( v3_waybel11 @ B @ c1_53__waybel19 ) ) ) ) ),file(waybel19,e1_53__waybel19)).
thf(e4_53__waybel19,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_53__waybel19 ) ) ) ) => ( ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_53__waybel19 ) ) ) => ( ( r2_hidden @ B @ A ) => ( v3_waybel11 @ B @ c1_53__waybel19 ) ) ) => ( v3_waybel11 @ ( k5_setfam_1 @ ( u1_struct_0 @ c1_53__waybel19 ) @ A ) @ c1_53__waybel19 ) ) ) ),file(waybel19,e4_53__waybel19)).
thf(e2_53__waybel19,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_53__waybel19 ) ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_53__waybel19 ) ) ) => ( ( ( v3_waybel11 @ A @ c1_53__waybel19 ) & ( v3_waybel11 @ B @ c1_53__waybel19 ) ) => ( v3_waybel11 @ ( k9_subset_1 @ ( u1_struct_0 @ c1_53__waybel19 ) @ A @ B ) @ c1_53__waybel19 ) ) ) ) ),file(waybel19,e2_53__waybel19)).
thf(e3_53__waybel19,axiom,( v3_waybel11 @ ( k2_struct_0 @ c1_53__waybel19 ) @ c1_53__waybel19 ),file(waybel19,e3_53__waybel19)).
thf(s1_waybel19,axiom,( ! [A: $i > $o] : ! [B: $i] : ( ( ( v2_pre_topc @ B ) & ( v3_orders_2 @ B ) & ( v4_orders_2 @ B ) & ( v5_orders_2 @ B ) & ( v1_lattice3 @ B ) & ( v2_lattice3 @ B ) & ( l1_waybel_9 @ B ) ) => ( ( ? [C: $i] : ( ( v1_tops_2 @ C @ B ) & ( v2_cantor_1 @ C @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) => ( ( r2_hidden @ D @ C ) => ( A @ D ) ) ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ) => ( ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) => ( ( r2_hidden @ D @ C ) => ( A @ D ) ) ) => ( A @ ( k5_setfam_1 @ ( u1_struct_0 @ B ) @ C ) ) ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) => ( ( ( A @ C ) & ( A @ D ) ) => ( A @ ( k9_subset_1 @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) ) & ( A @ ( k2_struct_0 @ B ) ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) => ( ( v3_pre_topc @ C @ B ) => ( A @ C ) ) ) ) ) ),file(waybel19,s1_waybel19)).
thf(e5_53__waybel19,conjecture,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_53__waybel19 ) ) ) => ( ( v3_pre_topc @ A @ c1_53__waybel19 ) => ( v3_waybel11 @ A @ c1_53__waybel19 ) ) ) ),file(waybel19,e5_53__waybel19)).
