% Mizar problem: e9_38,heyting1,1062,52 
include('Axioms/SET010^2.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_38_type,type,( c1_38__heyting1: $i )).
thf(c2_38_type,type,( c2_38__heyting1: $i )).
thf(c3_38_type,type,( c3_38__heyting1: $i )).
thf(g3_lattices_type,type,( g3_lattices: $i > $i > $i > $i )).
thf(k12_normform_type,type,( k12_normform: $i > $i )).
thf(k1_normform_type,type,( k1_normform: $i > $i > $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_heyting1_type,type,( k2_heyting1: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k5_finsub_1_type,type,( k5_finsub_1: $i > $i )).
thf(k7_normform_type,type,( k7_normform: $i > $i )).
thf(k8_normform_type,type,( k8_normform: $i > $i )).
thf(u1_lattices_type,type,( u1_lattices: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_lattices_type,type,( u2_lattices: $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(m2_subset_1_type,type,( m2_subset_1: $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(v18_lattices_type,type,( v18_lattices: $i > $i > $o )).
thf(v19_lattices_type,type,( v19_lattices: $i > $i > $o )).
thf(v1_binop_1_type,type,( v1_binop_1: $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_finsub_1_type,type,( v1_finsub_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_setwiseo_type,type,( v1_setwiseo: $i > $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_binop_1_type,type,( v2_binop_1: $i > $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v3_binop_1_type,type,( v3_binop_1: $i > $i > $o )).
thf(v3_filter_0_type,type,( v3_filter_0: $i > $o )).
thf(v3_finsub_1_type,type,( v3_finsub_1: $i > $o )).
thf(v3_lattices_type,type,( v3_lattices: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v4_finsub_1_type,type,( v4_finsub_1: $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_finset_1_type,type,( v5_finset_1: $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(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(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(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(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(cc3_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( v1_finset_1 @ C ) ) ) ) ) ),file(finset_1,cc3_finset_1)).
thf(cc3_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_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_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(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(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(fc10_lattice2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v14_lattices @ A ) & ( l3_lattices @ A ) ) => ( ( v1_funct_1 @ ( u1_lattices @ A ) ) & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v1_setwiseo @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(lattice2,fc10_lattice2)).
thf(fc3_lattices,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( 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 ) ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ) => ( ~ ( v2_struct_0 @ ( g3_lattices @ A @ B @ C ) ) & ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ) ),file(lattices,fc3_lattices)).
thf(rc10_lattices,axiom,( ? [A: $i] : ( ( l3_lattices @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_lattices @ A ) & ( v4_lattices @ A ) & ( v5_lattices @ A ) & ( v6_lattices @ A ) & ( v7_lattices @ A ) & ( v8_lattices @ A ) & ( v9_lattices @ A ) & ( v10_lattices @ A ) & ( v11_lattices @ A ) & ( v12_lattices @ A ) & ( v13_lattices @ A ) & ( v14_lattices @ A ) ) ),file(lattices,rc10_lattices)).
thf(rc11_lattices,axiom,( ? [A: $i] : ( ( l3_lattices @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_lattices @ A ) & ( v4_lattices @ A ) & ( v5_lattices @ A ) & ( v6_lattices @ A ) & ( v7_lattices @ A ) & ( v8_lattices @ A ) & ( v9_lattices @ A ) & ( v10_lattices @ A ) & ( v15_lattices @ A ) ) ),file(lattices,rc11_lattices)).
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_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(rc2_lattice2,axiom,( ? [A: $i] : ( ( l3_lattices @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_lattices @ 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,rc2_lattice2)).
thf(rc3_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc3_finset_1)).
thf(rc5_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ),file(finset_1,rc5_finset_1)).
thf(rc6_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ) ),file(finset_1,rc6_finset_1)).
thf(rc6_lattices,axiom,( ? [A: $i] : ( ( l3_lattices @ A ) & ( v13_struct_0 @ A @ np__1 ) & ( v3_lattices @ A ) ) ),file(lattices,rc6_lattices)).
thf(rc9_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) ),file(finset_1,rc9_finset_1)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(free_g3_lattices,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $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 ) ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ) => ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( = @ ( g3_lattices @ A @ B @ C ) @ ( g3_lattices @ D @ E @ F ) ) => ( ( = @ A @ D ) & ( = @ B @ E ) & ( = @ C @ F ) ) ) ) ),file(lattices,g3_lattices)).
thf(dt_g3_lattices,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $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 ) ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ) => ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) & ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ) ),file(lattices,g3_lattices)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_l1_lattices,axiom,( ! [A: $i] : ( ( l1_lattices @ A ) => ( l1_struct_0 @ A ) ) ),file(lattices,l1_lattices)).
thf(dt_l2_lattices,axiom,( ! [A: $i] : ( ( l2_lattices @ A ) => ( l1_struct_0 @ A ) ) ),file(lattices,l2_lattices)).
thf(dt_u1_lattices,axiom,( ! [A: $i] : ( ( l1_lattices @ A ) => ( ( v1_funct_1 @ ( u1_lattices @ A ) ) & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u1_lattices @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(lattices,u1_lattices)).
thf(dt_u2_lattices,axiom,( ! [A: $i] : ( ( l2_lattices @ A ) => ( ( v1_funct_1 @ ( u2_lattices @ A ) ) & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u2_lattices @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(lattices,u2_lattices)).
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_finsub_1,axiom,( ! [A: $i] : ( ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) => ( v4_finsub_1 @ A ) ) ),file(finsub_1,cc2_finsub_1)).
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(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(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
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_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(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(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_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(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_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(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(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(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_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(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(fc2_lattice2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ( ( v1_funct_1 @ ( u2_lattices @ A ) ) & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v3_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(lattice2,fc2_lattice2)).
thf(fc3_lattice2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v4_lattices @ A ) & ( l2_lattices @ A ) ) => ( ( v1_funct_1 @ ( u2_lattices @ A ) ) & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(lattice2,fc3_lattice2)).
thf(fc4_lattice2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v5_lattices @ A ) & ( l2_lattices @ A ) ) => ( ( v1_funct_1 @ ( u2_lattices @ A ) ) & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(lattice2,fc4_lattice2)).
thf(fc5_lattice2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ( ( v1_funct_1 @ ( u1_lattices @ A ) ) & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v3_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(lattice2,fc5_lattice2)).
thf(fc6_lattice2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v6_lattices @ A ) & ( l1_lattices @ A ) ) => ( ( v1_funct_1 @ ( u1_lattices @ A ) ) & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(lattice2,fc6_lattice2)).
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_lattice2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v7_lattices @ A ) & ( l1_lattices @ A ) ) => ( ( v1_funct_1 @ ( u1_lattices @ A ) ) & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(lattice2,fc7_lattice2)).
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_lattice2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( v13_lattices @ A ) & ( l3_lattices @ A ) ) => ( ( v1_funct_1 @ ( u2_lattices @ A ) ) & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v1_setwiseo @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(lattice2,fc9_lattice2)).
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(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(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(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_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(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_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc5_subset_1)).
thf(rc6_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc6_subset_1)).
thf(rc7_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc7_finset_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(abstractness_v3_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( v3_lattices @ A ) => ( = @ A @ ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ) ),file(lattices,v3_lattices)).
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_k8_normform,axiom,( ! [A: $i] : ( m1_subset_1 @ ( k8_normform @ A ) @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ ( k7_normform @ A ) ) ) ) ),file(normform,k8_normform)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l3_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( l1_lattices @ A ) & ( l2_lattices @ A ) ) ) ),file(lattices,l3_lattices)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_finsub_1,axiom,( ! [A: $i] : ( ( v4_finsub_1 @ A ) => ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) ) ),file(finsub_1,cc1_finsub_1)).
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_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_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(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_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_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_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_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(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_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(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
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_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(cc9_finset_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) ) ),file(finset_1,cc9_finset_1)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc14_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(finset_1,fc14_finset_1)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(fc1_finset_1,axiom,( ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ) ),file(finset_1,fc1_finset_1)).
thf(fc1_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),file(finsub_1,fc1_finsub_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(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_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(fc2_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
thf(fc30_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_tarski @ A ) ) ) ),file(finset_1,fc30_finset_1)).
thf(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(fc3_normform,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k8_normform @ A ) ) ),file(normform,fc3_normform)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_heyting1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k8_normform @ A ) ) & ~ ( v1_xboole_0 @ B ) ) ),file(heyting1,rc1_heyting1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_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_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc2_finset_1)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc3_lattices,axiom,( ? [A: $i] : ( ( l3_lattices @ A ) & ( v3_lattices @ A ) ) ),file(lattices,rc3_lattices)).
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(rc9_lattices,axiom,( ? [A: $i] : ( ( l3_lattices @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_lattices @ A ) & ( v10_lattices @ A ) ) ),file(lattices,rc9_lattices)).
thf(commutativity_k1_normform,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_finsub_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v4_finsub_1 @ B ) & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( = @ ( k1_normform @ A @ B @ C @ D ) @ ( k1_normform @ A @ B @ D @ C ) ) ) ),file(normform,k1_normform)).
thf(idempotence_k1_normform,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_finsub_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v4_finsub_1 @ B ) & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( = @ ( k1_normform @ A @ B @ C @ C ) @ C ) ) ),file(normform,k1_normform)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k2_heyting1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k7_normform @ A ) ) => ( = @ ( k2_heyting1 @ A @ B ) @ ( k1_tarski @ B ) ) ) ),file(heyting1,k2_heyting1)).
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(dt_k12_normform,axiom,( ! [A: $i] : ( ( v3_lattices @ ( k12_normform @ A ) ) & ( l3_lattices @ ( k12_normform @ A ) ) ) ),file(normform,k12_normform)).
thf(dt_k1_normform,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_finsub_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v4_finsub_1 @ B ) & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( m1_subset_1 @ ( k1_normform @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(normform,k1_normform)).
thf(dt_k2_heyting1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k7_normform @ A ) ) => ( m2_subset_1 @ ( k2_heyting1 @ A @ B ) @ ( k5_finsub_1 @ ( k7_normform @ A ) ) @ ( k8_normform @ A ) ) ) ),file(heyting1,k2_heyting1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k5_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ) ),file(finsub_1,k5_finsub_1)).
thf(dt_k7_normform,axiom,( ! [A: $i] : ( m1_subset_1 @ ( k7_normform @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) ) ) ),file(normform,k7_normform)).
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_38__heyting1,axiom,( $true ),file(heyting1,c1_38__heyting1)).
thf(dt_c2_38__heyting1,axiom,( m2_subset_1 @ c2_38__heyting1 @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ),file(heyting1,c2_38__heyting1)).
thf(dt_c3_38__heyting1,axiom,( m1_subset_1 @ c3_38__heyting1 @ ( u1_struct_0 @ ( k12_normform @ c1_38__heyting1 ) ) ),file(heyting1,c3_38__heyting1)).
thf(cc3_finsub_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) => ( v1_finset_1 @ B ) ) ),file(finsub_1,cc3_finsub_1)).
thf(fc2_finsub_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ ( k5_finsub_1 @ A ) ) & ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ) ) ),file(finsub_1,fc2_finsub_1)).
thf(fc2_normform,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k7_normform @ A ) ) ),file(normform,fc2_normform)).
thf(fc4_normform,axiom,( ! [A: $i] : ( ~ ( v2_struct_0 @ ( k12_normform @ A ) ) & ( v3_lattices @ ( k12_normform @ A ) ) ) ),file(normform,fc4_normform)).
thf(fc5_normform,axiom,( ! [A: $i] : ( ( v3_lattices @ ( k12_normform @ A ) ) & ( v10_lattices @ ( k12_normform @ A ) ) ) ),file(normform,fc5_normform)).
thf(fc6_normform,axiom,( ! [A: $i] : ( ( v3_lattices @ ( k12_normform @ A ) ) & ( v11_lattices @ ( k12_normform @ A ) ) & ( v13_lattices @ ( k12_normform @ A ) ) ) ),file(normform,fc6_normform)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(e8_38__heyting1,axiom,( ! [A: $i] : ( ( m2_subset_1 @ A @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) => ! [B: $i] : ( ( m2_subset_1 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) => ( ( ( r2_hidden @ A @ ( replSep1 @ ^ [C: $i] : ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) @ ^ [C: $i] : C @ ^ [C: $i] : ( ( r2_hidden @ C @ c3_38__heyting1 ) & ~ ( r2_hidden @ ( k1_normform @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) @ C @ c2_38__heyting1 ) @ ( k7_normform @ c1_38__heyting1 ) ) ) ) ) & ( r2_hidden @ B @ ( k2_heyting1 @ c1_38__heyting1 @ c2_38__heyting1 ) ) ) <=> ( ( = @ B @ c2_38__heyting1 ) & ( r2_hidden @ A @ ( replSep1 @ ^ [C: $i] : ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) @ ^ [C: $i] : C @ ^ [C: $i] : ( ( r2_hidden @ C @ c3_38__heyting1 ) & ~ ( r2_hidden @ ( k1_normform @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) @ C @ c2_38__heyting1 ) @ ( k7_normform @ c1_38__heyting1 ) ) ) ) ) ) ) ) ) ),file(heyting1,e8_38__heyting1)).
thf(s4_fraenkel,axiom,( ! [A: $i > $i > $i] : ! [B: $i > $i > $o] : ! [C: $i > $i > $o] : ! [D: $i] : ! [E: $i] : ( ! [F: $i] : ( ( m1_subset_1 @ F @ E ) => ! [G: $i] : ( ( m1_subset_1 @ G @ D ) => ( ( C @ F @ G ) <=> ( B @ F @ G ) ) ) ) => ( = @ ( replSep2 @ ^ [F: $i] : ( m1_subset_1 @ F @ E ) @ ^ [F: $i] : ^ [G: $i] : ( m1_subset_1 @ G @ D ) @ ^ [F: $i] : ^ [G: $i] : ( A @ F @ G ) @ ^ [F: $i] : ^ [G: $i] : ( C @ F @ G ) ) @ ( replSep2 @ ^ [F: $i] : ( m1_subset_1 @ F @ E ) @ ^ [F: $i] : ^ [G: $i] : ( m1_subset_1 @ G @ D ) @ ^ [F: $i] : ^ [G: $i] : ( A @ F @ G ) @ ^ [F: $i] : ^ [G: $i] : ( B @ F @ G ) ) ) ) ),file(fraenkel,s4_fraenkel)).
thf(e9_38__heyting1,conjecture,( = @ ( replSep2 @ ^ [A: $i] : ( m2_subset_1 @ A @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) @ ^ [A: $i] : ^ [B: $i] : ( m2_subset_1 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) @ ^ [A: $i] : ^ [B: $i] : ( k1_normform @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) @ A @ B ) @ ^ [A: $i] : ^ [B: $i] : ( ( r2_hidden @ A @ ( replSep1 @ ^ [C: $i] : ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) @ ^ [C: $i] : C @ ^ [C: $i] : ( ( r2_hidden @ C @ c3_38__heyting1 ) & ~ ( r2_hidden @ ( k1_normform @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) @ C @ c2_38__heyting1 ) @ ( k7_normform @ c1_38__heyting1 ) ) ) ) ) & ( r2_hidden @ B @ ( k2_heyting1 @ c1_38__heyting1 @ c2_38__heyting1 ) ) ) ) @ ( replSep2 @ ^ [A: $i] : ( m2_subset_1 @ A @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) @ ^ [A: $i] : ^ [B: $i] : ( m2_subset_1 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) @ ^ [A: $i] : ^ [B: $i] : ( k1_normform @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) @ A @ B ) @ ^ [A: $i] : ^ [B: $i] : ( ( = @ B @ c2_38__heyting1 ) & ( r2_hidden @ A @ ( replSep1 @ ^ [C: $i] : ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) ) @ ( k7_normform @ c1_38__heyting1 ) ) @ ^ [C: $i] : C @ ^ [C: $i] : ( ( r2_hidden @ C @ c3_38__heyting1 ) & ~ ( r2_hidden @ ( k1_normform @ ( k5_finsub_1 @ c1_38__heyting1 ) @ ( k5_finsub_1 @ c1_38__heyting1 ) @ C @ c2_38__heyting1 ) @ ( k7_normform @ c1_38__heyting1 ) ) ) ) ) ) ) ),file(heyting1,e9_38__heyting1)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
