% Mizar problem: t15_conlat_2,conlat_2,2458,22 
fof(t15_conlat_2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => r1_filter_1(k11_conlat_1(k6_conlat_2(A)),A) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_lattices,abstractness_v4_conlat_1,antisymmetry_r2_hidden,cc1_funct_2,cc1_lattices,cc1_partfun1,cc1_relset_1,cc2_funct_2,cc2_lattices,cc3_funct_2,cc3_lattices,cc4_funct_2,cc4_lattices,cc5_funct_2,cc6_funct_2,commutativity_k2_tarski,d13_lattice6,d14_lattice6,d22_lattice3,d5_conlat_1,d5_tarski,d6_conlat_2,dt_g2_conlat_1,dt_g3_lattices,dt_k11_conlat_1,dt_k15_lattice3,dt_k16_lattice3,dt_k1_domain_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_lattice3,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_k5_relset_1,dt_k6_conlat_2,dt_k6_partfun1,dt_k6_relat_1,dt_k8_funct_2,dt_k9_filter_1,dt_l1_conlat_1,dt_l1_lattices,dt_l1_struct_0,dt_l2_conlat_1,dt_l2_lattices,dt_l3_lattices,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_conlat_1,dt_u1_lattices,dt_u1_struct_0,dt_u2_conlat_1,dt_u2_lattices,dt_u3_conlat_1,existence_l1_conlat_1,existence_l1_lattices,existence_l1_struct_0,existence_l2_conlat_1,existence_l2_lattices,existence_l3_lattices,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_conlat_1,fc1_conlat_2,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_conlat_1,fc2_lattice2,fc2_partfun1,fc2_subset_1,fc3_lattice2,fc3_lattices,fc3_subset_1,fc4_conlat_1,fc4_lattice2,fc4_subset_1,fc5_conlat_1,fc5_lattice2,fraenkel_a_2_2_lattice3,free_g2_conlat_1,free_g3_lattices,rc11_lattices,rc1_funct_2,rc1_partfun1,rc1_subset_1,rc1_xboole_0,rc2_funct_2,rc2_partfun1,rc2_subset_1,rc2_xboole_0,rc3_lattices,rc3_partfun1,rc3_struct_0,rc5_conlat_1,rc5_struct_0,rc6_lattices,rc7_conlat_1,rc8_conlat_1,rc9_conlat_1,rc9_lattices,redefinition_k1_domain_1,redefinition_k1_struct_0,redefinition_k2_lattice3,redefinition_k5_relset_1,redefinition_k6_partfun1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_r3_lattices,reflexivity_r1_filter_1,reflexivity_r1_tarski,reflexivity_r3_lattices,symmetry_r1_filter_1,t14_conlat_2,t1_subset,t2_subset,t2_tarski,t32_filter_1,t34_funct_1,t3_subset,t43_lattice3,t4_subset,t5_subset,t6_boole,t71_relat_1,t7_boole,t8_boole]),
    [file(conlat_2,t15_conlat_2)]).

fof(abstractness_v3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( v3_lattices(A)
       => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ),
    file(lattices,v3_lattices),
    []).

fof(abstractness_v4_conlat_1,axiom,(
    ! [A] : 
      ( l2_conlat_1(A)
     => ( v4_conlat_1(A)
       => A = g2_conlat_1(u1_conlat_1(A),u2_conlat_1(A),u3_conlat_1(A)) ) ) ),
    file(conlat_1,v4_conlat_1),
    []).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A) )
       => ( ~ v3_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),
    []).

fof(cc1_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc2_funct_2),
    []).

fof(cc2_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v10_lattices(A) ) ) ) ),
    file(lattices,cc2_lattices),
    []).

fof(cc3_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc3_funct_2),
    []).

fof(cc3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v15_lattices(A) ) ) ) ),
    file(lattices,cc3_lattices),
    []).

fof(cc4_funct_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( ( v1_funct_1(B)
          & v1_partfun1(B,A,A)
          & v1_relat_2(B)
          & v1_funct_2(B,A,A) )
       => ( v1_funct_1(B)
          & v2_funct_1(B)
          & v1_funct_2(B,A,A)
          & v2_funct_2(B,A,A)
          & v3_funct_2(B,A,A) ) ) ) ),
    file(funct_2,cc4_funct_2),
    []).

fof(cc4_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v15_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) ) ) ) ),
    file(lattices,cc4_lattices),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d13_lattice6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v8_lattice6(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(B))
                    & C = k15_lattice3(A,D) ) ) ) ) ) ),
    file(lattice6,d13_lattice6),
    []).

fof(d14_lattice6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v9_lattice6(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(B))
                    & C = k16_lattice3(A,D) ) ) ) ) ) ),
    file(lattice6,d14_lattice6),
    []).

fof(d22_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] : k16_lattice3(A,B) = k15_lattice3(A,a_2_2_lattice3(A,B)) ) ),
    file(lattice3,d22_lattice3),
    []).

fof(d5_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_conlat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_conlat_1(A))
             => ( r1_conlat_1(A,B,C)
              <=> r2_hidden(k4_tarski(B,C),u3_conlat_1(A)) ) ) ) ) ),
    file(conlat_1,d5_conlat_1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d6_conlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k6_conlat_2(A) = g2_conlat_1(u1_struct_0(A),u1_struct_0(A),k2_lattice3(A)) ) ),
    file(conlat_2,d6_conlat_2),
    []).

fof(dt_g2_conlat_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( v4_conlat_1(g2_conlat_1(A,B,C))
        & l2_conlat_1(g2_conlat_1(A,B,C)) ) ) ),
    file(conlat_1,g2_conlat_1),
    []).

fof(dt_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( v3_lattices(g3_lattices(A,B,C))
        & l3_lattices(g3_lattices(A,B,C)) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(dt_k11_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( ~ v3_struct_0(k11_conlat_1(A))
        & v3_lattices(k11_conlat_1(A))
        & l3_lattices(k11_conlat_1(A)) ) ) ),
    file(conlat_1,k11_conlat_1),
    []).

fof(dt_k15_lattice3,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => m1_subset_1(k15_lattice3(A,B),u1_struct_0(A)) ) ),
    file(lattice3,k15_lattice3),
    []).

fof(dt_k16_lattice3,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)) ) ),
    file(lattice3,k16_lattice3),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_relat_2(k2_lattice3(A))
        & v4_relat_2(k2_lattice3(A))
        & v8_relat_2(k2_lattice3(A))
        & v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(lattice3,k2_lattice3),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(dt_k6_conlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_conlat_1(k6_conlat_2(A))
        & v4_conlat_1(k6_conlat_2(A))
        & l2_conlat_1(k6_conlat_2(A)) ) ) ),
    file(conlat_2,k6_conlat_2),
    []).

fof(dt_k6_partfun1,axiom,(
    ! [A] : 
      ( v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) ),
    file(partfun1,k6_partfun1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_k9_filter_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => v1_relat_1(k9_filter_1(A)) ) ),
    file(filter_1,k9_filter_1),
    []).

fof(dt_l1_conlat_1,axiom,(
    $true ),
    file(conlat_1,l1_conlat_1),
    []).

fof(dt_l1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l1_lattices),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_conlat_1,axiom,(
    ! [A] : 
      ( l2_conlat_1(A)
     => l1_conlat_1(A) ) ),
    file(conlat_1,l2_conlat_1),
    []).

fof(dt_l2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l2_lattices),
    []).

fof(dt_l3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) ),
    file(lattices,l3_lattices),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_conlat_1,axiom,(
    $true ),
    file(conlat_1,u1_conlat_1),
    []).

fof(dt_u1_lattices,axiom,(
    ! [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))
        & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u1_lattices),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_conlat_1,axiom,(
    $true ),
    file(conlat_1,u2_conlat_1),
    []).

fof(dt_u2_lattices,axiom,(
    ! [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))
        & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u2_lattices),
    []).

fof(dt_u3_conlat_1,axiom,(
    ! [A] : 
      ( l2_conlat_1(A)
     => m2_relset_1(u3_conlat_1(A),u1_conlat_1(A),u2_conlat_1(A)) ) ),
    file(conlat_1,u3_conlat_1),
    []).

fof(existence_l1_conlat_1,axiom,(
    ? [A] : l1_conlat_1(A) ),
    file(conlat_1,l1_conlat_1),
    []).

fof(existence_l1_lattices,axiom,(
    ? [A] : l1_lattices(A) ),
    file(lattices,l1_lattices),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_conlat_1,axiom,(
    ? [A] : l2_conlat_1(A) ),
    file(conlat_1,l2_conlat_1),
    []).

fof(existence_l2_lattices,axiom,(
    ? [A] : l2_lattices(A) ),
    file(lattices,l2_lattices),
    []).

fof(existence_l3_lattices,axiom,(
    ? [A] : l3_lattices(A) ),
    file(lattices,l3_lattices),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc1_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ~ v1_xboole_0(u2_conlat_1(A)) ) ),
    file(conlat_1,fc1_conlat_1),
    []).

fof(fc1_conlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( ~ v3_struct_0(k11_conlat_1(A))
        & v3_lattices(k11_conlat_1(A))
        & v4_lattices(k11_conlat_1(A))
        & v5_lattices(k11_conlat_1(A))
        & v6_lattices(k11_conlat_1(A))
        & v7_lattices(k11_conlat_1(A))
        & v8_lattices(k11_conlat_1(A))
        & v9_lattices(k11_conlat_1(A))
        & v10_lattices(k11_conlat_1(A))
        & v13_lattices(k11_conlat_1(A))
        & v14_lattices(k11_conlat_1(A))
        & v15_lattices(k11_conlat_1(A))
        & v4_lattice3(k11_conlat_1(A)) ) ) ),
    file(conlat_2,fc1_conlat_2),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ~ v1_xboole_0(u1_conlat_1(A)) ) ),
    file(conlat_1,fc2_conlat_1),
    []).

fof(fc2_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A) )
     => ( v1_relat_1(u2_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))
        & v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattice2,fc2_lattice2),
    []).

fof(fc2_partfun1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A))
      & v1_relat_2(k6_relat_1(A))
      & v3_relat_2(k6_relat_1(A))
      & v4_relat_2(k6_relat_1(A))
      & v8_relat_2(k6_relat_1(A)) ) ),
    file(partfun1,fc2_partfun1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & l2_lattices(A) )
     => ( v1_relat_1(u2_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))
        & v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattice2,fc3_lattice2),
    []).

fof(fc3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g3_lattices(A,B,C))
        & v3_lattices(g3_lattices(A,B,C)) ) ) ),
    file(lattices,fc3_lattices),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( ~ v3_struct_0(k11_conlat_1(A))
        & v3_lattices(k11_conlat_1(A))
        & v4_lattices(k11_conlat_1(A))
        & v5_lattices(k11_conlat_1(A))
        & v6_lattices(k11_conlat_1(A))
        & v7_lattices(k11_conlat_1(A))
        & v8_lattices(k11_conlat_1(A))
        & v9_lattices(k11_conlat_1(A))
        & v10_lattices(k11_conlat_1(A)) ) ) ),
    file(conlat_1,fc4_conlat_1),
    []).

fof(fc4_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A) )
     => ( v1_relat_1(u1_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))
        & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattice2,fc4_lattice2),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( ~ v3_struct_0(k11_conlat_1(A))
        & v3_lattices(k11_conlat_1(A))
        & v4_lattices(k11_conlat_1(A))
        & v5_lattices(k11_conlat_1(A))
        & v6_lattices(k11_conlat_1(A))
        & v7_lattices(k11_conlat_1(A))
        & v8_lattices(k11_conlat_1(A))
        & v9_lattices(k11_conlat_1(A))
        & v10_lattices(k11_conlat_1(A))
        & v4_lattice3(k11_conlat_1(A)) ) ) ),
    file(conlat_1,fc5_conlat_1),
    []).

fof(fc5_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v7_lattices(A)
        & l1_lattices(A) )
     => ( v1_relat_1(u1_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))
        & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattice2,fc5_lattice2),
    []).

fof(fraenkel_a_2_2_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & l3_lattices(B) )
     => ( r2_hidden(A,a_2_2_lattice3(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r3_lattice3(B,D,C) ) ) ) ),
    file(lattice3,a_2_2_lattice3),
    []).

fof(free_g2_conlat_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ! [D,E,F] : 
          ( g2_conlat_1(A,B,C) = g2_conlat_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(conlat_1,g2_conlat_1),
    []).

fof(free_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ! [D,E,F] : 
          ( g3_lattices(A,B,C) = g3_lattices(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(rc11_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_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)
      & v13_lattices(A)
      & v14_lattices(A)
      & v15_lattices(A) ) ),
    file(lattices,rc11_lattices),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_funct_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) ),
    file(funct_2,rc2_funct_2),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & v3_lattices(A) ) ),
    file(lattices,rc3_lattices),
    []).

fof(rc3_partfun1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_relat_2(B)
      & v3_relat_2(B)
      & v4_relat_2(B)
      & v8_relat_2(B)
      & v1_partfun1(B,A,A) ) ),
    file(partfun1,rc3_partfun1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc5_conlat_1,axiom,(
    ? [A] : 
      ( l2_conlat_1(A)
      & v4_conlat_1(A) ) ),
    file(conlat_1,rc5_conlat_1),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc6_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A) ) ),
    file(lattices,rc6_lattices),
    []).

fof(rc7_conlat_1,axiom,(
    ? [A] : 
      ( l2_conlat_1(A)
      & ~ v3_conlat_1(A)
      & v4_conlat_1(A) ) ),
    file(conlat_1,rc7_conlat_1),
    []).

fof(rc8_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(conlat_1,rc8_conlat_1),
    []).

fof(rc9_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(conlat_1,rc9_conlat_1),
    []).

fof(rc9_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_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) ) ),
    file(lattices,rc9_lattices),
    []).

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(redefinition_k2_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k2_lattice3(A) = k9_filter_1(A) ) ),
    file(lattice3,k2_lattice3),
    []).

fof(redefinition_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(redefinition_k6_partfun1,axiom,(
    ! [A] : k6_partfun1(A) = k6_relat_1(A) ),
    file(partfun1,k6_partfun1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_r3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_lattices(A,B,C)
      <=> r1_lattices(A,B,C) ) ) ),
    file(lattices,r3_lattices),
    []).

fof(reflexivity_r1_filter_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => r1_filter_1(A,A) ) ),
    file(filter_1,r1_filter_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_lattices(A,B,B) ) ),
    file(lattices,r3_lattices),
    []).

fof(symmetry_r1_filter_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ( r1_filter_1(A,B)
       => r1_filter_1(B,A) ) ) ),
    file(filter_1,r1_filter_1),
    []).

fof(t14_conlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( ( ~ v3_conlat_1(B)
            & l2_conlat_1(B) )
         => ( r1_filter_1(k11_conlat_1(B),A)
          <=> ? [C] : 
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_conlat_1(B),u1_struct_0(A))
                & m2_relset_1(C,u1_conlat_1(B),u1_struct_0(A))
                & ? [D] : 
                    ( v1_funct_1(D)
                    & v1_funct_2(D,u2_conlat_1(B),u1_struct_0(A))
                    & m2_relset_1(D,u2_conlat_1(B),u1_struct_0(A))
                    & v8_lattice6(k5_relset_1(u1_conlat_1(B),u1_struct_0(A),C),A)
                    & v9_lattice6(k5_relset_1(u2_conlat_1(B),u1_struct_0(A),D),A)
                    & ! [E] : 
                        ( m1_subset_1(E,u1_conlat_1(B))
                       => ! [F] : 
                            ( m1_subset_1(F,u2_conlat_1(B))
                           => ( r1_conlat_1(B,E,F)
                            <=> r3_lattices(A,k8_funct_2(u1_conlat_1(B),u1_struct_0(A),C,E),k8_funct_2(u2_conlat_1(B),u1_struct_0(A),D,F)) ) ) ) ) ) ) ) ) ),
    file(conlat_2,t14_conlat_2),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t32_filter_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k9_filter_1(A))
              <=> r3_lattices(A,B,C) ) ) ) ) ),
    file(filter_1,t32_filter_1),
    []).

fof(t34_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k6_relat_1(A)
      <=> ( k1_relat_1(B) = A
          & ! [C] : 
              ( r2_hidden(C,A)
             => k1_funct_1(B,C) = C ) ) ) ) ),
    file(funct_1,t34_funct_1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t43_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k15_lattice3(A,k1_struct_0(A,B)) = B
            & k16_lattice3(A,k1_struct_0(A,B)) = B ) ) ) ),
    file(lattice3,t43_lattice3),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t71_relat_1,axiom,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).