% Mizar problem: e4_30,lattice4,627,67 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_30_type,type,( c1_30__lattice4: $i )).
thf(c2_30_type,type,( c2_30__lattice4: $i )).
thf(k1_setwiseo_type,type,( k1_setwiseo: $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_lattice4_type,type,( k2_lattice4: $i > $i > $i )).
thf(k2_setwiseo_type,type,( k2_setwiseo: $i > $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k5_finsub_1_type,type,( k5_finsub_1: $i > $i )).
thf(k5_setwiseo_type,type,( k5_setwiseo: $i > $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(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v10_lattices_type,type,( v10_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_finset_1_type,type,( v1_finset_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(v4_finsub_1_type,type,( v4_finsub_1: $i > $o )).
thf(v4_lattices_type,type,( v4_lattices: $i > $o )).
thf(v5_lattices_type,type,( v5_lattices: $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(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_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(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(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_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_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_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_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_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_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_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_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(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(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(fc4_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(xboole_0,fc4_xboole_0)).
thf(fc5_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ) ),file(xboole_0,fc5_xboole_0)).
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(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_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(commutativity_k5_setwiseo,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) => ( = @ ( k5_setwiseo @ A @ B @ C ) @ ( k5_setwiseo @ A @ C @ B ) ) ) ),file(setwiseo,k5_setwiseo)).
thf(idempotence_k5_setwiseo,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) => ( = @ ( k5_setwiseo @ A @ B @ B ) @ B ) ) ),file(setwiseo,k5_setwiseo)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k2_setwiseo,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( = @ ( k2_setwiseo @ A @ B ) @ ( k1_tarski @ B ) ) ) ),file(setwiseo,k2_setwiseo)).
thf(redefinition_k5_setwiseo,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) => ( = @ ( k5_setwiseo @ A @ B @ C ) @ ( k2_xboole_0 @ B @ C ) ) ) ),file(setwiseo,k5_setwiseo)).
thf(dt_k1_setwiseo,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ ( k1_setwiseo @ A ) ) & ( m1_subset_1 @ ( k1_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ) ) ),file(setwiseo,k1_setwiseo)).
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_lattice4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) & ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) ) => ( m1_subset_1 @ ( k2_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),file(lattice4,k2_lattice4)).
thf(dt_k2_setwiseo,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( m1_subset_1 @ ( k2_setwiseo @ A @ B ) @ ( k5_finsub_1 @ A ) ) ) ),file(setwiseo,k2_setwiseo)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k5_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ) ),file(finsub_1,k5_finsub_1)).
thf(dt_k5_setwiseo,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) => ( m1_subset_1 @ ( k5_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ) ),file(setwiseo,k5_setwiseo)).
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_30__lattice4,axiom,( ~ ( v2_struct_0 @ c1_30__lattice4 ) & ( v10_lattices @ c1_30__lattice4 ) & ( v14_lattices @ c1_30__lattice4 ) & ( l3_lattices @ c1_30__lattice4 ) ),file(lattice4,c1_30__lattice4)).
thf(dt_c2_30__lattice4,axiom,( ( v20_lattices @ c2_30__lattice4 @ c1_30__lattice4 ) & ( v21_lattices @ c2_30__lattice4 @ c1_30__lattice4 ) & ( m1_subset_1 @ c2_30__lattice4 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_30__lattice4 ) ) ) ),file(lattice4,c2_30__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(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_30__lattice4,axiom,( ( r1_tarski @ ( k1_setwiseo @ ( u1_struct_0 @ c1_30__lattice4 ) ) @ c2_30__lattice4 ) => ( r2_hidden @ ( k2_lattice4 @ c1_30__lattice4 @ ( k1_setwiseo @ ( u1_struct_0 @ c1_30__lattice4 ) ) ) @ c2_30__lattice4 ) ),file(lattice4,e3_30__lattice4)).
thf(e1_30__lattice4,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k5_finsub_1 @ ( u1_struct_0 @ c1_30__lattice4 ) ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ c1_30__lattice4 ) ) => ( ( ( r1_tarski @ A @ c2_30__lattice4 ) => ( r2_hidden @ ( k2_lattice4 @ c1_30__lattice4 @ A ) @ c2_30__lattice4 ) ) => ( ( r1_tarski @ ( k5_setwiseo @ ( u1_struct_0 @ c1_30__lattice4 ) @ A @ ( k2_setwiseo @ ( u1_struct_0 @ c1_30__lattice4 ) @ B ) ) @ c2_30__lattice4 ) => ( r2_hidden @ ( k2_lattice4 @ c1_30__lattice4 @ ( k5_setwiseo @ ( u1_struct_0 @ c1_30__lattice4 ) @ A @ ( k2_setwiseo @ ( u1_struct_0 @ c1_30__lattice4 ) @ B ) ) ) @ c2_30__lattice4 ) ) ) ) ) ),file(lattice4,e1_30__lattice4)).
thf(s4_setwiseo,axiom,( ! [A: $i > $o] : ! [B: $i] : ( ( ( A @ ( k1_setwiseo @ B ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ B ) => ( ( A @ C ) => ( A @ ( k2_xboole_0 @ C @ ( k1_tarski @ D ) ) ) ) ) ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) ) => ( A @ C ) ) ) ),file(setwiseo,s4_setwiseo)).
thf(e4_30__lattice4,conjecture,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k5_finsub_1 @ ( u1_struct_0 @ c1_30__lattice4 ) ) ) => ( ( r1_tarski @ A @ c2_30__lattice4 ) => ( r2_hidden @ ( k2_lattice4 @ c1_30__lattice4 @ A ) @ c2_30__lattice4 ) ) ) ),file(lattice4,e4_30__lattice4)).
