% Mizar problem: e1_45_1_2,tdlat_1,1431,61 
include('Axioms/SET010^0.ax').
thf(c1_45_type,type,( c1_45__tdlat_1: $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_tops_1_type,type,( k1_tops_1: $i > $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_pre_topc_type,type,( k2_pre_topc: $i > $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k4_subset_1_type,type,( k4_subset_1: $i > $i > $i > $i )).
thf(k5_binop_1_type,type,( k5_binop_1: $i > $i > $i > $i > $i )).
thf(k9_tdlat_1_type,type,( k9_tdlat_1: $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(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(r2_funct_2_type,type,( r2_funct_2: $i > $i > $i > $i > $o )).
thf(r8_binop_1_type,type,( r8_binop_1: $i > $i > $i > $i > $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_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v2_pre_topc_type,type,( v2_pre_topc: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_tops_1_type,type,( v2_tops_1: $i > $i > $o )).
thf(v3_pre_topc_type,type,( v3_pre_topc: $i > $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $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(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(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_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(fc13_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_pre_topc @ A ) & ( v2_tops_1 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( v1_xboole_0 @ ( k1_tops_1 @ A @ B ) ) ) ),file(tops_1,fc13_tops_1)).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_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(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(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_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(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_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_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_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_relat_1 @ B ) ) ) ),file(relat_1,cc2_relat_1)).
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_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(cc3_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_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_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_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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v4_relat_1 @ C @ A ) ) ) ),file(relat_1,cc5_relat_1)).
thf(cc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v5_relat_1 @ C @ A ) ) ) ),file(relat_1,cc6_relat_1)).
thf(cc7_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc7_relat_1)).
thf(cc8_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc8_relat_1)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) ) => ( v4_relat_1 @ ( k2_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc1_relset_1)).
thf(fc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) ) => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc3_relat_1)).
thf(fc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) ) => ( v5_relat_1 @ ( k2_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc4_relset_1)).
thf(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(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(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_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_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_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_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_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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relat_1,rc3_relat_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(projectivity_k1_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( = @ ( k1_tops_1 @ A @ ( k1_tops_1 @ A @ B ) ) @ ( k1_tops_1 @ A @ B ) ) ) ),file(tops_1,k1_tops_1)).
thf(projectivity_k2_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( = @ ( k2_pre_topc @ A @ ( k2_pre_topc @ A @ B ) ) @ ( k2_pre_topc @ A @ B ) ) ) ),file(pre_topc,k2_pre_topc)).
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(symmetry_r2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_funct_2 @ A @ B @ C @ D ) => ( r2_funct_2 @ A @ B @ D @ C ) ) ) ),file(funct_2,r2_funct_2)).
thf(reflexivity_r2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( r2_funct_2 @ A @ B @ C @ C ) ) ),file(funct_2,r2_funct_2)).
thf(symmetry_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( ( r8_binop_1 @ A @ B @ C @ D @ E ) => ( r8_binop_1 @ A @ B @ C @ E @ D ) ) ) ),file(binop_1,r8_binop_1)).
thf(reflexivity_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( r8_binop_1 @ A @ B @ C @ D @ D ) ) ),file(binop_1,r8_binop_1)).
thf(redefinition_k4_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) => ( = @ ( k4_subset_1 @ A @ B @ C ) @ ( k2_xboole_0 @ B @ C ) ) ) ),file(subset_1,k4_subset_1)).
thf(redefinition_k5_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k5_binop_1 @ A @ B @ C @ D ) @ ( k1_binop_1 @ B @ C @ D ) ) ) ),file(binop_1,k5_binop_1)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(redefinition_r2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_funct_2 @ A @ B @ C @ D ) <=> ( = @ C @ D ) ) ) ),file(funct_2,r2_funct_2)).
thf(redefinition_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( ( r8_binop_1 @ A @ B @ C @ D @ E ) <=> ( = @ D @ E ) ) ) ),file(binop_1,r8_binop_1)).
thf(dt_k1_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( m1_subset_1 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),file(tops_1,k1_tops_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( m1_subset_1 @ ( k2_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),file(pre_topc,k2_pre_topc)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
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_k5_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k5_binop_1 @ A @ B @ C @ D ) @ A ) ) ),file(binop_1,k5_binop_1)).
thf(dt_k9_tdlat_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( m1_subset_1 @ ( k9_tdlat_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),file(tdlat_1,k9_tdlat_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_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_45__tdlat_1,axiom,( ( v2_pre_topc @ c1_45__tdlat_1 ) & ( l1_pre_topc @ c1_45__tdlat_1 ) ),file(tdlat_1,c1_45__tdlat_1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(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(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc1_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( v4_pre_topc @ ( k2_pre_topc @ A @ B ) @ A ) ) ),file(tops_1,fc1_tops_1)).
thf(fc3_tdlat_1,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ~ ( v1_xboole_0 @ ( k9_tdlat_1 @ A ) ) ) ),file(tdlat_1,fc3_tdlat_1)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(fc9_tops_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) => ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ) ),file(tops_1,fc9_tops_1)).
thf(s2_binop_2,axiom,( ! [A: $i > $i > $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ) => ! [D: $i] : ( ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ) => ( ( ! [E: $i] : ( ( m1_subset_1 @ E @ B ) => ! [F: $i] : ( ( m1_subset_1 @ F @ B ) => ( = @ ( k5_binop_1 @ B @ C @ E @ F ) @ ( A @ E @ F ) ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ B ) => ! [F: $i] : ( ( m1_subset_1 @ F @ B ) => ( = @ ( k5_binop_1 @ B @ D @ E @ F ) @ ( A @ E @ F ) ) ) ) ) => ( r8_binop_1 @ B @ B @ B @ C @ D ) ) ) ) ),file(binop_2,s2_binop_2)).
thf(e1_45_1_2__tdlat_1,conjecture,( ! [A: $i] : ( ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) ) ) ) => ! [B: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) ) ) ) => ( ( ! [C: $i] : ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) => ! [D: $i] : ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) => ( = @ ( k5_binop_1 @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) @ A @ C @ D ) @ ( k1_tops_1 @ c1_45__tdlat_1 @ ( k2_pre_topc @ c1_45__tdlat_1 @ ( k4_subset_1 @ ( u1_struct_0 @ c1_45__tdlat_1 ) @ C @ D ) ) ) ) ) ) & ! [C: $i] : ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) => ! [D: $i] : ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) => ( = @ ( k5_binop_1 @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) @ B @ C @ D ) @ ( k1_tops_1 @ c1_45__tdlat_1 @ ( k2_pre_topc @ c1_45__tdlat_1 @ ( k4_subset_1 @ ( u1_struct_0 @ c1_45__tdlat_1 ) @ C @ D ) ) ) ) ) ) ) => ( r2_funct_2 @ ( k2_zfmisc_1 @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) ) @ ( k9_tdlat_1 @ c1_45__tdlat_1 ) @ A @ B ) ) ) ) ),file(tdlat_1,e1_45_1_2__tdlat_1)).
