% Mizar problem: e2_69_1_1,conlat_1,2324,50 
include('Axioms/SET010^0.ax').
thf(c1_69_type,type,( c1_69__conlat_1: $i )).
thf(g2_conlat_1_type,type,( g2_conlat_1: $i > $i > $i > $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_conlat_1_type,type,( k1_conlat_1: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_binop_1_type,type,( k2_binop_1: $i > $i > $i > $i > $i > $i > $i )).
thf(k2_conlat_1_type,type,( k2_conlat_1: $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(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_xboole_0_type,type,( k3_xboole_0: $i > $i > $i )).
thf(k4_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(k7_conlat_1_type,type,( k7_conlat_1: $i > $i )).
thf(k8_conlat_1_type,type,( k8_conlat_1: $i > $i )).
thf(k9_setfam_1_type,type,( k9_setfam_1: $i > $i )).
thf(k9_subset_1_type,type,( k9_subset_1: $i > $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_conlat_1_type,type,( u2_conlat_1: $i > $i > $i )).
thf(u3_conlat_1_type,type,( u3_conlat_1: $i > $i > $i )).
thf(u4_struct_0_type,type,( u4_struct_0: $i > $i )).
thf(l1_conlat_1_type,type,( l1_conlat_1: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_conlat_1_type,type,( l2_conlat_1: $i > $i > $o )).
thf(l5_struct_0_type,type,( l5_struct_0: $i > $o )).
thf(m1_conlat_1_type,type,( m1_conlat_1: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_conlat_1_type,type,( m2_conlat_1: $i > $i > $i > $o )).
thf(v1_conlat_1_type,type,( v1_conlat_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_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(v4_conlat_1_type,type,( v4_conlat_1: $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_conlat_1_type,type,( v5_conlat_1: $i > $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_conlat_1_type,type,( v6_conlat_1: $i > $i > $o )).
thf(v7_conlat_1_type,type,( v7_conlat_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(rc11_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l5_struct_0 @ A ) ) => ? [B: $i] : ( ( l2_conlat_1 @ B @ A ) & ( v4_conlat_1 @ B @ A ) & ( v6_conlat_1 @ B @ A ) ) ) ),file(conlat_1,rc11_conlat_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(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_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ A ) ) ),file(xboole_0,k3_xboole_0)).
thf(idempotence_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k3_xboole_0)).
thf(abstractness_v4_conlat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l5_struct_0 @ A ) & ( l2_conlat_1 @ B @ A ) ) => ( ( v4_conlat_1 @ B @ A ) => ( = @ B @ ( g2_conlat_1 @ A @ ( u2_conlat_1 @ A @ B ) @ ( u3_conlat_1 @ A @ B ) ) ) ) ) ),file(conlat_1,v4_conlat_1)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k3_xboole_0,axiom,( $true ),file(xboole_0,k3_xboole_0)).
thf(dt_k7_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ) ),file(conlat_1,k7_conlat_1)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l2_conlat_1,axiom,( $true ),file(conlat_1,l2_conlat_1)).
thf(dt_l5_struct_0,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l5_struct_0)).
thf(dt_m1_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ! [B: $i] : ( ( m1_conlat_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ),file(conlat_1,m1_conlat_1)).
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_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_conlat_1,axiom,( ! [A: $i] : ( ( ( v1_conlat_1 @ A ) & ( l5_struct_0 @ A ) ) => ! [B: $i] : ( ( l2_conlat_1 @ B @ A ) => ( v6_conlat_1 @ B @ A ) ) ) ),file(conlat_1,cc2_conlat_1)).
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_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_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(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_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_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l5_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u4_struct_0 @ A ) ) ) ),file(conlat_1,fc1_conlat_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(fc2_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l5_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(conlat_1,fc2_conlat_1)).
thf(fc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( v4_relat_1 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc2_relset_1)).
thf(fc3_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ) ),file(conlat_1,fc3_conlat_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(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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( v5_relat_1 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc5_relset_1)).
thf(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(rc10_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l5_struct_0 @ A ) ) => ? [B: $i] : ( ( l2_conlat_1 @ B @ A ) & ( v4_conlat_1 @ B @ A ) & ~ ( v5_conlat_1 @ B @ A ) ) ) ),file(conlat_1,rc10_conlat_1)).
thf(rc12_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ? [B: $i] : ( ( l2_conlat_1 @ B @ A ) & ~ ( v5_conlat_1 @ B @ A ) & ( v7_conlat_1 @ B @ A ) ) ) ),file(conlat_1,rc12_conlat_1)).
thf(rc13_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ? [B: $i] : ( ( l2_conlat_1 @ B @ A ) & ( v4_conlat_1 @ B @ A ) & ~ ( v5_conlat_1 @ B @ A ) & ( v7_conlat_1 @ B @ A ) ) ) ),file(conlat_1,rc13_conlat_1)).
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(rc7_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l5_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(conlat_1,rc7_conlat_1)).
thf(rc8_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l5_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u4_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(conlat_1,rc8_conlat_1)).
thf(rc9_conlat_1,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ? [B: $i] : ( ( l2_conlat_1 @ B @ A ) & ( v4_conlat_1 @ B @ A ) ) ) ),file(conlat_1,rc9_conlat_1)).
thf(free_g2_conlat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( l5_struct_0 @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u4_struct_0 @ A ) ) ) ) => ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( = @ ( g2_conlat_1 @ A @ B @ C ) @ ( g2_conlat_1 @ D @ E @ F ) ) => ( ( = @ A @ D ) & ( = @ B @ E ) & ( = @ C @ F ) ) ) ) ),file(conlat_1,g2_conlat_1)).
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(commutativity_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ C ) @ ( k9_subset_1 @ A @ C @ B ) ) ) ),file(subset_1,k9_subset_1)).
thf(idempotence_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ B ) @ B ) ) ),file(subset_1,k9_subset_1)).
thf(redefinition_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( 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 ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( = @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_binop_1 @ D @ E @ F ) ) ) ),file(binop_1,k2_binop_1)).
thf(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_k4_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_k8_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ( = @ ( k8_conlat_1 @ A ) @ ( k7_conlat_1 @ A ) ) ) ),file(conlat_1,k8_conlat_1)).
thf(redefinition_k9_setfam_1,axiom,( ! [A: $i] : ( = @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),file(setfam_1,k9_setfam_1)).
thf(redefinition_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ C ) @ ( k3_xboole_0 @ B @ C ) ) ) ),file(subset_1,k9_subset_1)).
thf(redefinition_m2_conlat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) & ( m1_conlat_1 @ B @ A ) ) => ! [C: $i] : ( ( m2_conlat_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(conlat_1,m2_conlat_1)).
thf(dt_g2_conlat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( l5_struct_0 @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u4_struct_0 @ A ) ) ) ) => ( ( v4_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) @ A ) & ( l2_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) @ A ) ) ) ),file(conlat_1,g2_conlat_1)).
thf(dt_k1_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ( ( v1_funct_1 @ ( k1_conlat_1 @ A ) ) & ( v1_funct_2 @ ( k1_conlat_1 @ A ) @ ( k9_setfam_1 @ ( u1_struct_0 @ A ) ) @ ( k9_setfam_1 @ ( u4_struct_0 @ A ) ) ) & ( m1_subset_1 @ ( k1_conlat_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k9_setfam_1 @ ( u1_struct_0 @ A ) ) @ ( k9_setfam_1 @ ( u4_struct_0 @ A ) ) ) ) ) ) ) ),file(conlat_1,k1_conlat_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( 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 ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ) ),file(binop_1,k2_binop_1)).
thf(dt_k2_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ( ( v1_funct_1 @ ( k2_conlat_1 @ A ) ) & ( v1_funct_2 @ ( k2_conlat_1 @ A ) @ ( k9_setfam_1 @ ( u4_struct_0 @ A ) ) @ ( k9_setfam_1 @ ( u1_struct_0 @ A ) ) ) & ( m1_subset_1 @ ( k2_conlat_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k9_setfam_1 @ ( u4_struct_0 @ A ) ) @ ( k9_setfam_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),file(conlat_1,k2_conlat_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k4_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_k8_conlat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) ) => ( m1_conlat_1 @ ( k8_conlat_1 @ A ) @ A ) ) ),file(conlat_1,k8_conlat_1)).
thf(dt_k9_setfam_1,axiom,( ! [A: $i] : ( m1_subset_1 @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(setfam_1,k9_setfam_1)).
thf(dt_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( m1_subset_1 @ ( k9_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(subset_1,k9_subset_1)).
thf(dt_l1_conlat_1,axiom,( ! [A: $i] : ( ( l1_conlat_1 @ A ) => ( l5_struct_0 @ A ) ) ),file(conlat_1,l1_conlat_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_conlat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_conlat_1 @ A ) & ( l1_conlat_1 @ A ) & ( m1_conlat_1 @ B @ A ) ) => ! [C: $i] : ( ( m2_conlat_1 @ C @ A @ B ) => ( ~ ( v5_conlat_1 @ C @ A ) & ( v7_conlat_1 @ C @ A ) & ( l2_conlat_1 @ C @ A ) ) ) ) ),file(conlat_1,m2_conlat_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_u2_conlat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l5_struct_0 @ A ) & ( l2_conlat_1 @ B @ A ) ) => ( m1_subset_1 @ ( u2_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),file(conlat_1,u2_conlat_1)).
thf(dt_u3_conlat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l5_struct_0 @ A ) & ( l2_conlat_1 @ B @ A ) ) => ( m1_subset_1 @ ( u3_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u4_struct_0 @ A ) ) ) ) ),file(conlat_1,u3_conlat_1)).
thf(dt_u4_struct_0,axiom,( $true ),file(struct_0,u4_struct_0)).
thf(dt_c1_69__conlat_1,axiom,( ~ ( v1_conlat_1 @ c1_69__conlat_1 ) & ( l1_conlat_1 @ c1_69__conlat_1 ) ),file(conlat_1,c1_69__conlat_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(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(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(e1_69_1_1__conlat_1,axiom,( ! [A: $i] : ( ( m2_conlat_1 @ A @ c1_69__conlat_1 @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) => ! [B: $i] : ( ( m2_conlat_1 @ B @ c1_69__conlat_1 @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) => ? [C: $i] : ( ( m2_conlat_1 @ C @ c1_69__conlat_1 @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_69__conlat_1 ) ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u4_struct_0 @ c1_69__conlat_1 ) ) ) & ( = @ C @ ( g2_conlat_1 @ c1_69__conlat_1 @ D @ E ) ) & ( = @ D @ ( k9_subset_1 @ ( u1_struct_0 @ c1_69__conlat_1 ) @ ( u2_conlat_1 @ c1_69__conlat_1 @ A ) @ ( u2_conlat_1 @ c1_69__conlat_1 @ B ) ) ) & ( = @ E @ ( k3_funct_2 @ ( k9_setfam_1 @ ( u1_struct_0 @ c1_69__conlat_1 ) ) @ ( k9_setfam_1 @ ( u4_struct_0 @ c1_69__conlat_1 ) ) @ ( k1_conlat_1 @ c1_69__conlat_1 ) @ ( k3_funct_2 @ ( k1_zfmisc_1 @ ( u4_struct_0 @ c1_69__conlat_1 ) ) @ ( k9_setfam_1 @ ( u1_struct_0 @ c1_69__conlat_1 ) ) @ ( k2_conlat_1 @ c1_69__conlat_1 ) @ ( k4_subset_1 @ ( u4_struct_0 @ c1_69__conlat_1 ) @ ( u3_conlat_1 @ c1_69__conlat_1 @ A ) @ ( u3_conlat_1 @ c1_69__conlat_1 @ B ) ) ) ) ) ) ) ) ) ) ),file(conlat_1,e1_69_1_1__conlat_1)).
thf(s3_binop_1,axiom,( ! [A: $i > $i > $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ? [G: $i] : ( ( m1_subset_1 @ G @ B ) & ( A @ E @ F @ G ) ) ) ) => ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ C ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ D @ C ) @ B ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ! [G: $i] : ( ( m1_subset_1 @ G @ C ) => ( A @ F @ G @ ( k2_binop_1 @ D @ C @ B @ E @ F @ G ) ) ) ) ) ) ),file(binop_1,s3_binop_1)).
thf(e2_69_1_1__conlat_1,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ c1_69__conlat_1 ) @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k8_conlat_1 @ c1_69__conlat_1 ) @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) ) ) & ! [B: $i] : ( ( m2_conlat_1 @ B @ c1_69__conlat_1 @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) => ! [C: $i] : ( ( m2_conlat_1 @ C @ c1_69__conlat_1 @ ( k8_conlat_1 @ c1_69__conlat_1 ) ) => ? [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_69__conlat_1 ) ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u4_struct_0 @ c1_69__conlat_1 ) ) ) & ( = @ ( k5_binop_1 @ ( k8_conlat_1 @ c1_69__conlat_1 ) @ A @ B @ C ) @ ( g2_conlat_1 @ c1_69__conlat_1 @ D @ E ) ) & ( = @ D @ ( k9_subset_1 @ ( u1_struct_0 @ c1_69__conlat_1 ) @ ( u2_conlat_1 @ c1_69__conlat_1 @ B ) @ ( u2_conlat_1 @ c1_69__conlat_1 @ C ) ) ) & ( = @ E @ ( k3_funct_2 @ ( k9_setfam_1 @ ( u1_struct_0 @ c1_69__conlat_1 ) ) @ ( k9_setfam_1 @ ( u4_struct_0 @ c1_69__conlat_1 ) ) @ ( k1_conlat_1 @ c1_69__conlat_1 ) @ ( k3_funct_2 @ ( k1_zfmisc_1 @ ( u4_struct_0 @ c1_69__conlat_1 ) ) @ ( k9_setfam_1 @ ( u1_struct_0 @ c1_69__conlat_1 ) ) @ ( k2_conlat_1 @ c1_69__conlat_1 ) @ ( k4_subset_1 @ ( u4_struct_0 @ c1_69__conlat_1 ) @ ( u3_conlat_1 @ c1_69__conlat_1 @ B ) @ ( u3_conlat_1 @ c1_69__conlat_1 @ C ) ) ) ) ) ) ) ) ) ) ),file(conlat_1,e2_69_1_1__conlat_1)).
