% Mizar problem: t27_lattice3,lattice3,1136,31 
fof(t27_lattice3,conjecture,(
    ! [A] : v6_lattice3(k1_lattice3(A)) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_lattices,antisymmetry_r2_hidden,cc1_lattices,cc1_relset_1,cc2_lattices,cc3_lattices,cc4_lattices,cc5_lattices,cc6_lattices,cc7_lattices,commutativity_k2_tarski,commutativity_k3_lattices,commutativity_k4_lattices,d10_xboole_0,d19_lattice3,d1_binop_1,d1_lattices,d20_lattice3,d2_lattices,d3_tarski,d5_tarski,dt_g3_lattices,dt_k1_binop_1,dt_k1_funct_1,dt_k1_lattice3,dt_k1_lattices,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_lattices,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_lattices,dt_k4_lattices,dt_k4_tarski,dt_k7_lattices,dt_l1_lattices,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_lattices,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_lattice3,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_lattice2,fc2_lattice3,fc2_subset_1,fc3_lattice2,fc3_lattice3,fc3_lattices,fc3_subset_1,fc4_lattice2,fc4_subset_1,fc5_lattice2,fraenkel_a_2_0_lattice3,fraenkel_a_2_1_lattice3,fraenkel_a_3_1_lattice3,fraenkel_a_3_2_lattice3,fraenkel_a_3_5_lattice3,fraenkel_a_3_6_lattice3,fraenkel_a_3_7_lattice3,fraenkel_a_3_8_lattice3,free_g3_lattices,rc10_lattices,rc11_lattices,rc12_lattices,rc13_lattices,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_lattices,rc3_struct_0,rc5_struct_0,rc6_lattices,rc9_lattices,redefinition_k2_binop_1,redefinition_k3_lattices,redefinition_k4_lattices,redefinition_m2_relset_1,redefinition_r3_lattices,reflexivity_r1_tarski,reflexivity_r3_lattices,t1_subset,t24_lattice3,t26_lattice3,t2_subset,t2_tarski,t3_subset,t49_lattices,t4_subset,t50_lattices,t51_lattices,t53_lattices,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(lattice3,t27_lattice3)]).

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

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_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_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_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_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_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v17_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) ) ) ) ),
    file(lattices,cc5_lattices),
    []).

fof(cc6_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v17_lattices(A) ) ) ) ),
    file(lattices,cc6_lattices),
    []).

fof(cc7_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v12_lattices(A) ) ) ) ),
    file(lattices,cc7_lattices),
    []).

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

fof(commutativity_k3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_lattices(A,B,C) = k3_lattices(A,C,B) ) ),
    file(lattices,k3_lattices),
    []).

fof(commutativity_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_lattices(A,B,C) = k4_lattices(A,C,B) ) ),
    file(lattices,k4_lattices),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d19_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v5_lattice3(A)
      <=> ! [B,C] : 
            ( m1_subset_1(C,u1_struct_0(A))
           => ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ! [E] : 
                    ( m1_subset_1(E,u1_struct_0(A))
                   => ( ( r4_lattice3(A,C,B)
                        & ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r4_lattice3(A,F,B)
                             => r1_lattices(A,C,F) ) )
                        & r4_lattice3(A,E,a_3_1_lattice3(A,B,D))
                        & ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r4_lattice3(A,F,a_3_1_lattice3(A,B,D))
                             => r1_lattices(A,E,F) ) ) )
                     => r1_lattices(A,k2_lattices(A,D,C),E) ) ) ) ) ) ) ),
    file(lattice3,d19_lattice3),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d1_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) ) ) ) ),
    file(lattices,d1_lattices),
    []).

fof(d20_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v6_lattice3(A)
      <=> ! [B,C] : 
            ( m1_subset_1(C,u1_struct_0(A))
           => ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ! [E] : 
                    ( m1_subset_1(E,u1_struct_0(A))
                   => ( ( r3_lattice3(A,C,B)
                        & ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r3_lattice3(A,F,B)
                             => r1_lattices(A,F,C) ) )
                        & r3_lattice3(A,E,a_3_2_lattice3(A,B,D))
                        & ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r3_lattice3(A,F,a_3_2_lattice3(A,B,D))
                             => r1_lattices(A,F,E) ) ) )
                     => r1_lattices(A,E,k1_lattices(A,D,C)) ) ) ) ) ) ) ),
    file(lattice3,d20_lattice3),
    []).

fof(d2_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) ) ) ) ),
    file(lattices,d2_lattices),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

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

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_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

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

fof(dt_k1_lattice3,axiom,(
    ! [A] : 
      ( v3_lattices(k1_lattice3(A))
      & l3_lattices(k1_lattice3(A)) ) ),
    file(lattice3,k1_lattice3),
    []).

fof(dt_k1_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k1_lattices),
    []).

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_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,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),
    []).

fof(dt_k2_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k2_lattices),
    []).

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_k3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k3_lattices),
    []).

fof(dt_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k4_lattices),
    []).

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

fof(dt_k7_lattices,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k7_lattices(A,B),u1_struct_0(A)) ) ),
    file(lattices,k7_lattices),
    []).

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_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_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_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(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_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_lattice3,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k1_lattice3(A))
      & v3_lattices(k1_lattice3(A)) ) ),
    file(lattice3,fc1_lattice3),
    []).

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_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_lattice3,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k1_lattice3(A))
      & v3_lattices(k1_lattice3(A))
      & v4_lattices(k1_lattice3(A))
      & v5_lattices(k1_lattice3(A))
      & v6_lattices(k1_lattice3(A))
      & v7_lattices(k1_lattice3(A))
      & v8_lattices(k1_lattice3(A))
      & v9_lattices(k1_lattice3(A))
      & v10_lattices(k1_lattice3(A)) ) ),
    file(lattice3,fc2_lattice3),
    []).

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_lattice3,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k1_lattice3(A))
      & v3_lattices(k1_lattice3(A))
      & v4_lattices(k1_lattice3(A))
      & v5_lattices(k1_lattice3(A))
      & v6_lattices(k1_lattice3(A))
      & v7_lattices(k1_lattice3(A))
      & v8_lattices(k1_lattice3(A))
      & v9_lattices(k1_lattice3(A))
      & v10_lattices(k1_lattice3(A))
      & v11_lattices(k1_lattice3(A))
      & v12_lattices(k1_lattice3(A))
      & v13_lattices(k1_lattice3(A))
      & v14_lattices(k1_lattice3(A))
      & v15_lattices(k1_lattice3(A))
      & v16_lattices(k1_lattice3(A))
      & v17_lattices(k1_lattice3(A)) ) ),
    file(lattice3,fc3_lattice3),
    []).

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_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_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_0_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(C)
        & v10_lattices(C)
        & v17_lattices(C)
        & l3_lattices(C) )
     => ( r2_hidden(A,a_2_0_lattice3(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k7_lattices(C,D)
            & r2_hidden(D,B) ) ) ) ),
    file(lattice3,a_2_0_lattice3),
    []).

fof(fraenkel_a_2_1_lattice3,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(A,a_2_1_lattice3(B,C))
    <=> ? [D] : 
          ( m1_subset_1(D,u1_struct_0(k1_lattice3(B)))
          & A = k7_lattices(k1_lattice3(B),D)
          & r2_hidden(D,C) ) ) ),
    file(lattice3,a_2_1_lattice3),
    []).

fof(fraenkel_a_3_1_lattice3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l3_lattices(B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_lattice3(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k2_lattices(B,D,E)
            & r2_hidden(E,C) ) ) ) ),
    file(lattice3,a_3_1_lattice3),
    []).

fof(fraenkel_a_3_2_lattice3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l3_lattices(B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_2_lattice3(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k1_lattices(B,D,E)
            & r2_hidden(E,C) ) ) ) ),
    file(lattice3,a_3_2_lattice3),
    []).

fof(fraenkel_a_3_5_lattice3,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,u1_struct_0(k1_lattice3(B)))
     => ( r2_hidden(A,a_3_5_lattice3(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(k1_lattice3(B)))
            & A = k1_lattices(k1_lattice3(B),D,E)
            & r2_hidden(E,C) ) ) ) ),
    file(lattice3,a_3_5_lattice3),
    []).

fof(fraenkel_a_3_6_lattice3,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,u1_struct_0(k1_lattice3(B)))
     => ( r2_hidden(A,a_3_6_lattice3(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(k1_lattice3(B)))
            & A = k3_lattices(k1_lattice3(B),D,E)
            & r2_hidden(E,C) ) ) ) ),
    file(lattice3,a_3_6_lattice3),
    []).

fof(fraenkel_a_3_7_lattice3,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,u1_struct_0(k1_lattice3(B)))
     => ( r2_hidden(A,a_3_7_lattice3(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(k1_lattice3(B)))
            & A = k7_lattices(k1_lattice3(B),E)
            & r2_hidden(E,a_3_6_lattice3(B,C,D)) ) ) ) ),
    file(lattice3,a_3_7_lattice3),
    []).

fof(fraenkel_a_3_8_lattice3,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,u1_struct_0(k1_lattice3(B)))
     => ( r2_hidden(A,a_3_8_lattice3(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(k1_lattice3(B)))
            & A = k4_lattices(k1_lattice3(B),k7_lattices(k1_lattice3(B),D),E)
            & r2_hidden(E,a_2_1_lattice3(B,C)) ) ) ) ),
    file(lattice3,a_3_8_lattice3),
    []).

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(rc10_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)
      & v11_lattices(A)
      & v12_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A) ) ),
    file(lattices,rc10_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(rc12_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)
      & v16_lattices(A) ) ),
    file(lattices,rc12_lattices),
    []).

fof(rc13_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)
      & v11_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A)
      & v15_lattices(A)
      & v16_lattices(A)
      & v17_lattices(A) ) ),
    file(lattices,rc13_lattices),
    []).

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_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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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(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_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,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),
    []).

fof(redefinition_k3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_lattices(A,B,C) = k1_lattices(A,B,C) ) ),
    file(lattices,k3_lattices),
    []).

fof(redefinition_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_lattices(A,B,C) = k2_lattices(A,B,C) ) ),
    file(lattices,k4_lattices),
    []).

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

fof(t24_lattice3,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v17_lattices(B)
        & l3_lattices(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r3_lattice3(B,C,A)
          <=> r4_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) ) ) ) ),
    file(lattice3,t24_lattice3),
    []).

fof(t26_lattice3,axiom,(
    ! [A] : v5_lattice3(k1_lattice3(A)) ),
    file(lattice3,t26_lattice3),
    []).

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

fof(t49_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_lattices(A,k7_lattices(A,B)) = B ) ) ),
    file(lattices,t49_lattices),
    []).

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(t50_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k7_lattices(A,k4_lattices(A,B,C)) = k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) ) ) ) ),
    file(lattices,t50_lattices),
    []).

fof(t51_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k7_lattices(A,k3_lattices(A,B,C)) = k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) ) ) ) ),
    file(lattices,t51_lattices),
    []).

fof(t53_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,B,C)
               => r3_lattices(A,k7_lattices(A,C),k7_lattices(A,B)) ) ) ) ) ),
    file(lattices,t53_lattices),
    []).

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(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),
    []).