% Mizar problem: e1_48_1_2,lattice4,992,35 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_48_type,type,( c1_48__lattice4: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $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_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k7_lattices_type,type,( k7_lattices: $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_lattices_type,type,( l1_lattices: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_lattices_type,type,( l2_lattices: $i > $o )).
thf(l3_lattices_type,type,( l3_lattices: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r2_funct_2_type,type,( r2_funct_2: $i > $i > $i > $i > $o )).
thf(v10_lattices_type,type,( v10_lattices: $i > $o )).
thf(v11_lattices_type,type,( v11_lattices: $i > $o )).
thf(v12_lattices_type,type,( v12_lattices: $i > $o )).
thf(v13_lattices_type,type,( v13_lattices: $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v14_lattices_type,type,( v14_lattices: $i > $o )).
thf(v15_lattices_type,type,( v15_lattices: $i > $o )).
thf(v16_lattices_type,type,( v16_lattices: $i > $o )).
thf(v17_lattices_type,type,( v17_lattices: $i > $o )).
thf(v18_lattices_type,type,( v18_lattices: $i > $i > $o )).
thf(v19_lattices_type,type,( v19_lattices: $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_lattice2_type,type,( v1_lattice2: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $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(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v20_lattices_type,type,( v20_lattices: $i > $i > $o )).
thf(v21_lattices_type,type,( v21_lattices: $i > $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v3_filter_0_type,type,( v3_filter_0: $i > $o )).
thf(v4_lattices_type,type,( v4_lattices: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_lattices_type,type,( v5_lattices: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_lattices_type,type,( v6_lattices: $i > $o )).
thf(v7_lattices_type,type,( v7_lattices: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_lattices_type,type,( v8_lattices: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(v9_lattices_type,type,( v9_lattices: $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(cc1_lattice2,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v1_lattice2 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v13_lattices @ A ) & ( v3_filter_0 @ A ) ) ) ) ),file(lattice2,cc1_lattice2)).
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(rc1_lattice2,axiom,( ? [A: $i] : ( ( l3_lattices @ A ) & ~ ( v2_struct_0 @ A ) & ( v4_lattices @ A ) & ( v5_lattices @ A ) & ( v6_lattices @ A ) & ( v7_lattices @ A ) & ( v8_lattices @ A ) & ( v9_lattices @ A ) & ( v10_lattices @ A ) & ( v1_lattice2 @ A ) ) ),file(lattice2,rc1_lattice2)).
thf(rc1_lattice4,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v20_lattices @ B @ A ) & ( v21_lattices @ B @ A ) ) ) ),file(lattice4,rc1_lattice4)).
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_lattices,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v19_lattices @ B @ A ) => ( v21_lattices @ B @ A ) ) ) ) ),file(lattices,cc10_lattices)).
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_lattice2,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v13_lattices @ A ) & ( v3_filter_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v1_lattice2 @ A ) ) ) ) ),file(lattice2,cc2_lattice2)).
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(cc3_lattice2,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v10_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v13_lattices @ A ) ) ) ) ),file(lattice2,cc3_lattice2)).
thf(cc3_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v13_lattices @ A ) & ( v14_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v15_lattices @ A ) ) ) ) ),file(lattices,cc3_lattices)).
thf(cc4_lattice2,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v10_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v14_lattices @ A ) ) ) ) ),file(lattice2,cc4_lattice2)).
thf(cc5_lattice2,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v10_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v15_lattices @ A ) ) ) ) ),file(lattice2,cc5_lattice2)).
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_lattice2,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v10_lattices @ A ) & ( v11_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v1_lattice2 @ A ) ) ) ) ),file(lattice2,cc6_lattice2)).
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_lattices,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v18_lattices @ B @ A ) => ( v20_lattices @ B @ A ) ) ) ) ),file(lattices,cc9_lattices)).
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(rc14_lattices,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v18_lattices @ B @ A ) & ( v19_lattices @ B @ A ) ) ) ),file(lattices,rc14_lattices)).
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(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_l1_lattices,axiom,( ! [A: $i] : ( ( l1_lattices @ A ) => ( l1_struct_0 @ A ) ) ),file(lattices,l1_lattices)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l2_lattices,axiom,( ! [A: $i] : ( ( l2_lattices @ A ) => ( l1_struct_0 @ A ) ) ),file(lattices,l2_lattices)).
thf(cc1_filter_0,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v3_filter_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v14_lattices @ A ) & ( v3_filter_0 @ A ) ) ) ) ),file(filter_0,cc1_filter_0)).
thf(cc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
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(cc2_filter_0,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v3_filter_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v11_lattices @ A ) & ( v3_filter_0 @ A ) ) ) ) ),file(filter_0,cc2_filter_0)).
thf(cc2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc2_funct_2)).
thf(cc2_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_lattices @ A ) & ( v5_lattices @ A ) & ( v6_lattices @ A ) & ( v7_lattices @ A ) & ( v8_lattices @ A ) & ( v9_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) ) ) ) ),file(lattices,cc2_lattices)).
thf(cc3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc3_funct_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(cc4_filter_0,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v3_filter_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v11_lattices @ A ) ) ) ) ),file(filter_0,cc4_filter_0)).
thf(cc4_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v15_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v13_lattices @ A ) & ( v14_lattices @ A ) ) ) ) ),file(lattices,cc4_lattices)).
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(cc6_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v11_lattices @ A ) & ( v15_lattices @ A ) & ( v16_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v17_lattices @ A ) ) ) ) ),file(lattices,cc6_lattices)).
thf(cc7_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v11_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v12_lattices @ A ) ) ) ) ),file(lattices,cc7_lattices)).
thf(cc8_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ! [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_xboole_0 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ),file(funct_2,cc8_funct_2)).
thf(cc8_lattices,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( ( v18_lattices @ B @ A ) & ( v19_lattices @ B @ A ) ) ) ) ) ),file(lattices,cc8_lattices)).
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_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(rc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ),file(funct_2,rc1_funct_2)).
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(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(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_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(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_k7_lattices,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l3_lattices @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),file(lattices,k7_lattices)).
thf(dt_l3_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( l1_lattices @ A ) & ( l2_lattices @ A ) ) ) ),file(lattices,l3_lattices)).
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_48__lattice4,axiom,( ~ ( v2_struct_0 @ c1_48__lattice4 ) & ( v10_lattices @ c1_48__lattice4 ) & ( v17_lattices @ c1_48__lattice4 ) & ( l3_lattices @ c1_48__lattice4 ) ),file(lattice4,c1_48__lattice4)).
thf(cc1_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v4_lattices @ A ) & ( v5_lattices @ A ) & ( v6_lattices @ A ) & ( v7_lattices @ A ) & ( v8_lattices @ A ) & ( v9_lattices @ A ) ) ) ) ),file(lattices,cc1_lattices)).
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(cc3_filter_0,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v17_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v17_lattices @ A ) & ( v3_filter_0 @ A ) ) ) ) ),file(filter_0,cc3_filter_0)).
thf(cc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_funct_2 @ B @ A @ A ) => ( v1_partfun1 @ B @ A ) ) ) ),file(funct_2,cc4_funct_2)).
thf(cc5_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v17_lattices @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v11_lattices @ A ) & ( v15_lattices @ A ) & ( v16_lattices @ A ) ) ) ) ),file(lattices,cc5_lattices)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(rd7_lattices,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v17_lattices @ A ) & ( l3_lattices @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( = @ ( k7_lattices @ A @ ( k7_lattices @ A @ B ) ) @ B ) ) ),file(lattices,rd7_lattices)).
thf(s1_binop_2,axiom,( ! [A: $i > $i] : ! [B: $i] : ! [C: $i] : ! [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] : ( ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ C @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ B ) ) ) ) => ( ( ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ( = @ ( k3_funct_2 @ C @ B @ D @ F ) @ ( A @ F ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ( = @ ( k3_funct_2 @ C @ B @ E @ F ) @ ( A @ F ) ) ) ) => ( r2_funct_2 @ C @ B @ D @ E ) ) ) ) ),file(binop_2,s1_binop_2)).
thf(e1_48_1_2__lattice4,conjecture,( ! [A: $i] : ( ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( u1_struct_0 @ c1_48__lattice4 ) @ ( u1_struct_0 @ c1_48__lattice4 ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_48__lattice4 ) @ ( u1_struct_0 @ c1_48__lattice4 ) ) ) ) ) => ! [B: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( u1_struct_0 @ c1_48__lattice4 ) @ ( u1_struct_0 @ c1_48__lattice4 ) ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_48__lattice4 ) @ ( u1_struct_0 @ c1_48__lattice4 ) ) ) ) ) => ( ( ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ c1_48__lattice4 ) ) => ( = @ ( k3_funct_2 @ ( u1_struct_0 @ c1_48__lattice4 ) @ ( u1_struct_0 @ c1_48__lattice4 ) @ A @ C ) @ ( k7_lattices @ c1_48__lattice4 @ C ) ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ c1_48__lattice4 ) ) => ( = @ ( k3_funct_2 @ ( u1_struct_0 @ c1_48__lattice4 ) @ ( u1_struct_0 @ c1_48__lattice4 ) @ B @ C ) @ ( k7_lattices @ c1_48__lattice4 @ C ) ) ) ) => ( r2_funct_2 @ ( u1_struct_0 @ c1_48__lattice4 ) @ ( u1_struct_0 @ c1_48__lattice4 ) @ A @ B ) ) ) ) ),file(lattice4,e1_48_1_2__lattice4)).
