% Mizar problem: e4_33,tsp_2,1284,46 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_33_type,type,( c1_33__tsp_2: $i )).
thf(c2_33_type,type,( c2_33__tsp_2: $i )).
thf(c3_33_type,type,( c3_33__tsp_2: $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_tex_4_type,type,( k2_tex_4: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_xboole_0_type,type,( k3_xboole_0: $i > $i > $i )).
thf(k4_tex_4_type,type,( k4_tex_4: $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_pre_topc_type,type,( l1_pre_topc: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(m1_pre_topc_type,type,( m1_pre_topc: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_borsuk_1_type,type,( v1_borsuk_1: $i > $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_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_tdlat_3_type,type,( v1_tdlat_3: $i > $o )).
thf(v1_tex_2_type,type,( v1_tex_2: $i > $i > $o )).
thf(v1_tex_3_type,type,( v1_tex_3: $i > $i > $o )).
thf(v1_tsep_1_type,type,( v1_tsep_1: $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_pre_topc_type,type,( v2_pre_topc: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_tdlat_3_type,type,( v2_tdlat_3: $i > $o )).
thf(v2_tops_1_type,type,( v2_tops_1: $i > $i > $o )).
thf(v2_tsp_2_type,type,( v2_tsp_2: $i > $i > $o )).
thf(v3_pre_topc_type,type,( v3_pre_topc: $i > $i > $o )).
thf(v3_tdlat_3_type,type,( v3_tdlat_3: $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(v4_relat_1_type,type,( v4_relat_1: $i > $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(cc4_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ~ ( v7_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v2_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v6_pre_topc @ A ) ) ) ) ),file(tsp_1,cc4_tsp_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(cc5_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v6_pre_topc @ A ) & ( v2_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) & ( v2_pre_topc @ A ) ) ) ) ),file(tsp_1,cc5_tsp_1)).
thf(cc5_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ( v1_tsep_1 @ B @ A ) & ( v2_tsp_2 @ B @ A ) ) => ~ ( v1_tex_2 @ B @ A ) ) ) ) ),file(tsp_2,cc5_tsp_2)).
thf(cc6_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ( v1_tsep_1 @ B @ A ) & ( v1_tex_2 @ B @ A ) ) => ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),file(tsp_2,cc6_tsp_2)).
thf(cc7_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v6_pre_topc @ A ) & ( v3_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_tdlat_3 @ A ) ) ) ) ),file(tsp_1,cc7_tsp_1)).
thf(cc8_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v1_tdlat_3 @ A ) & ( v3_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v6_pre_topc @ A ) ) ) ) ),file(tsp_1,cc8_tsp_1)).
thf(cc8_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ( v1_borsuk_1 @ B @ A ) & ( v2_tsp_2 @ B @ A ) ) => ~ ( v1_tex_2 @ B @ A ) ) ) ) ),file(tsp_2,cc8_tsp_2)).
thf(cc9_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ( v1_borsuk_1 @ B @ A ) & ( v1_tex_2 @ B @ A ) ) => ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),file(tsp_2,cc9_tsp_2)).
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(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(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(cc10_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ( v1_tex_2 @ B @ A ) & ( v2_tsp_2 @ B @ A ) ) => ~ ( v1_borsuk_1 @ B @ A ) ) ) ) ),file(tsp_2,cc10_tsp_2)).
thf(cc11_tsp_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v6_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ~ ( v2_struct_0 @ B ) & ~ ( v1_tex_2 @ B @ A ) ) => ( ~ ( v2_struct_0 @ B ) & ~ ( v6_pre_topc @ B ) ) ) ) ) ),file(tsp_1,cc11_tsp_1)).
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_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v6_pre_topc @ A ) ) ) ) ),file(tsp_1,cc1_tsp_1)).
thf(cc2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc2_struct_0)).
thf(cc2_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ~ ( v1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(subset_1,cc2_subset_1)).
thf(cc2_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v6_pre_topc @ A ) ) ) ) ),file(tsp_1,cc2_tsp_1)).
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_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_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_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_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(cc6_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ~ ( v7_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v6_pre_topc @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v2_tdlat_3 @ A ) ) ) ) ),file(tsp_1,cc6_tsp_1)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc7_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ( v1_tex_2 @ B @ A ) & ( v2_tsp_2 @ B @ A ) ) => ~ ( v1_tsep_1 @ B @ A ) ) ) ) ),file(tsp_2,cc7_tsp_2)).
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(cc9_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v6_pre_topc @ A ) & ~ ( v1_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v3_tdlat_3 @ A ) ) ) ) ),file(tsp_1,cc9_tsp_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_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(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(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(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(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_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(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_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_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_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(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_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k2_tex_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k2_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),file(tex_4,k2_tex_4)).
thf(dt_k3_xboole_0,axiom,( $true ),file(xboole_0,k3_xboole_0)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(cc10_tsp_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v6_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ~ ( v2_struct_0 @ B ) => ( ~ ( v2_struct_0 @ B ) & ( v6_pre_topc @ B ) ) ) ) ) ),file(tsp_1,cc10_tsp_1)).
thf(cc12_tsp_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v6_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ~ ( v2_struct_0 @ B ) & ( v6_pre_topc @ B ) ) => ( ~ ( v2_struct_0 @ B ) & ( v1_tex_2 @ B @ A ) ) ) ) ) ),file(tsp_1,cc12_tsp_1)).
thf(cc1_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
thf(cc1_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc1_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_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_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ~ ( v2_struct_0 @ B ) & ~ ( v6_pre_topc @ B ) ) => ( ~ ( v2_struct_0 @ B ) & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ) ),file(tsp_2,cc2_tsp_2)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(cc3_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(cc3_tsp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v6_pre_topc @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v1_tdlat_3 @ A ) ) ) ) ),file(tsp_1,cc3_tsp_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(cc4_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ~ ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,cc4_subset_1)).
thf(cc4_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ~ ( v1_tex_3 @ B @ A ) => ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),file(tsp_2,cc4_tsp_2)).
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(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(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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( v4_relat_1 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc2_relset_1)).
thf(fc2_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc2_struct_0)).
thf(fc5_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( v5_relat_1 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc5_relset_1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc1_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(subset_1,rc1_subset_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(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(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(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(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_k4_tex_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( = @ ( k4_tex_4 @ A @ B ) @ ( k2_tex_4 @ A @ B ) ) ) ),file(tex_4,k4_tex_4)).
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_tarski,axiom,( $true ),file(tarski,k1_tarski)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k4_tex_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( ~ ( v1_xboole_0 @ ( k4_tex_4 @ A @ B ) ) & ( m1_subset_1 @ ( k4_tex_4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),file(tex_4,k4_tex_4)).
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_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( l1_struct_0 @ A ) ) ),file(pre_topc,l1_pre_topc)).
thf(dt_m1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( l1_pre_topc @ B ) ) ) ),file(pre_topc,m1_pre_topc)).
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_33__tsp_2,axiom,( ~ ( v2_struct_0 @ c1_33__tsp_2 ) & ( v2_pre_topc @ c1_33__tsp_2 ) & ( l1_pre_topc @ c1_33__tsp_2 ) ),file(tsp_2,c1_33__tsp_2)).
thf(dt_c2_33__tsp_2,axiom,( ~ ( v2_struct_0 @ c2_33__tsp_2 ) & ( v2_tsp_2 @ c2_33__tsp_2 @ c1_33__tsp_2 ) & ( m1_pre_topc @ c2_33__tsp_2 @ c1_33__tsp_2 ) ),file(tsp_2,c2_33__tsp_2)).
thf(dt_c3_33__tsp_2,axiom,( m1_subset_1 @ c3_33__tsp_2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_33__tsp_2 ) ) ),file(tsp_2,c3_33__tsp_2)).
thf(cc1_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( v2_pre_topc @ B ) ) ) ),file(pre_topc,cc1_pre_topc)).
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_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( ~ ( v2_struct_0 @ B ) & ( v2_tsp_2 @ B @ A ) ) => ( ~ ( v2_struct_0 @ B ) & ( v6_pre_topc @ B ) ) ) ) ) ),file(tsp_2,cc1_tsp_2)).
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(cc3_tsp_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( ( v2_tsp_2 @ B @ A ) => ( v1_tex_3 @ B @ A ) ) ) ) ),file(tsp_2,cc3_tsp_2)).
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(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc2_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
thf(e3_33__tsp_2,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ c1_33__tsp_2 ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ c2_33__tsp_2 ) ) & ( = @ ( k9_subset_1 @ ( u1_struct_0 @ c1_33__tsp_2 ) @ c3_33__tsp_2 @ ( k4_tex_4 @ c1_33__tsp_2 @ A ) ) @ ( k1_tarski @ B ) ) ) ) ),file(tsp_2,e3_33__tsp_2)).
thf(s3_funct_2,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ? [E: $i] : ( ( m1_subset_1 @ E @ B ) & ( A @ D @ E ) ) ) => ? [D: $i] : ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ C @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ B ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ C ) => ( A @ E @ ( k3_funct_2 @ C @ B @ D @ E ) ) ) ) ) ),file(funct_2,s3_funct_2)).
thf(e4_33__tsp_2,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( u1_struct_0 @ c1_33__tsp_2 ) @ ( u1_struct_0 @ c2_33__tsp_2 ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_33__tsp_2 ) @ ( u1_struct_0 @ c2_33__tsp_2 ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ c1_33__tsp_2 ) ) => ( = @ ( k9_subset_1 @ ( u1_struct_0 @ c1_33__tsp_2 ) @ c3_33__tsp_2 @ ( k4_tex_4 @ c1_33__tsp_2 @ B ) ) @ ( k1_tarski @ ( k3_funct_2 @ ( u1_struct_0 @ c1_33__tsp_2 ) @ ( u1_struct_0 @ c2_33__tsp_2 ) @ A @ B ) ) ) ) ) ),file(tsp_2,e4_33__tsp_2)).
