% Mizar problem: t5_lattice4,lattice4,74,31 
fof(t5_lattice4,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_filter_0(B,A)
         => ! [C] : 
              ( m1_filter_0(C,A)
             => ( r1_tarski(B,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C)))
                & r1_tarski(C,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finsub_1,cc1_lattices,cc2_finsub_1,cc2_lattices,commutativity_k1_finsub_1,commutativity_k2_xboole_0,d5_filter_0,dt_k1_finsub_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_xboole_0,dt_k3_filter_0,dt_l1_lattices,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_filter_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_lattices,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_filter_0,existence_m1_subset_1,fc1_finsub_1,fc1_struct_0,fc1_xboole_0,fc2_xboole_0,fc3_xboole_0,idempotence_k1_finsub_1,idempotence_k2_xboole_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,redefinition_k1_finsub_1,reflexivity_r1_tarski,t1_boole,t1_subset,t1_xboole_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t7_xboole_1,t8_boole]),
    [file(lattice4,t5_lattice4)]).

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

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    []).

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(cc2_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_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(commutativity_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,C) = k1_finsub_1(A,C,B) ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d5_filter_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_filter_0(C,A)
             => ( C = k3_filter_0(A,B)
              <=> ( r1_tarski(B,C)
                  & ! [D] : 
                      ( m1_filter_0(D,A)
                     => ( r1_tarski(B,D)
                       => r1_tarski(C,D) ) ) ) ) ) ) ) ),
    file(filter_0,d5_filter_0),
    []).

fof(dt_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k1_finsub_1(A,B,C),A) ) ),
    file(finsub_1,k1_finsub_1),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k3_filter_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_filter_0(k3_filter_0(A,B),A) ) ),
    file(filter_0,k3_filter_0),
    []).

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_filter_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_filter_0(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ),
    file(filter_0,m1_filter_0),
    []).

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

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

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_filter_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ? [B] : m1_filter_0(B,A) ) ),
    file(filter_0,m1_filter_0),
    []).

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

fof(fc1_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    []).

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_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(idempotence_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,B) = B ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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

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

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(redefinition_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(finsub_1,k1_finsub_1),
    []).

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

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

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

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

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

fof(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

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