% Mizar problem: t51_tdlat_3,tdlat_3,1605,64 
fof(t51_tdlat_3,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ( ~ v3_struct_0(k4_tdlat_1(A))
          & v10_lattices(k4_tdlat_1(A))
          & v12_lattices(k4_tdlat_1(A))
          & l3_lattices(k4_tdlat_1(A)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_lattices,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_lattices,cc1_membered,cc1_relset_1,cc1_tops_1,cc20_membered,cc2_lattices,cc2_membered,cc2_tops_1,cc3_lattices,cc3_membered,cc3_tops_1,cc4_lattices,cc4_membered,cc4_tops_1,cc5_lattices,cc5_tops_1,cc6_lattices,cc6_tops_1,cc7_lattices,commutativity_k2_xboole_0,commutativity_k3_lattices,commutativity_k3_xboole_0,commutativity_k4_lattices,commutativity_k4_subset_1,commutativity_k5_subset_1,d12_lattices,d1_tdlat_1,d4_tdlat_1,d6_tops_1,d7_tops_1,d7_xboole_0,d8_tops_1,dt_g3_lattices,dt_k12_tdlat_1,dt_k1_lattices,dt_k1_pre_topc,dt_k1_tdlat_1,dt_k1_tops_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_lattices,dt_k2_pre_topc,dt_k2_tdlat_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_lattices,dt_k3_subset_1,dt_k3_tdlat_1,dt_k3_xboole_0,dt_k4_lattices,dt_k4_subset_1,dt_k4_tdlat_1,dt_k5_subset_1,dt_k6_pre_topc,dt_l1_lattices,dt_l1_pre_topc,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_lattices,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_pre_topc,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_tops_1,fc11_tops_1,fc1_pre_topc,fc1_struct_0,fc1_subset_1,fc1_tops_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc2_pre_topc,fc2_tops_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_lattices,fc3_tops_1,fc4_subset_1,fc4_tops_1,fc5_pre_topc,fc5_tops_1,fc6_membered,fc6_tops_1,fc7_tops_1,fc8_tops_1,fc9_tops_1,fraenkel_a_1_0_tdlat_1,fraenkel_a_1_3_tdlat_3,free_g3_lattices,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,involutiveness_k3_subset_1,rc10_lattices,rc11_lattices,rc12_lattices,rc13_lattices,rc1_membered,rc1_subset_1,rc1_tops_1,rc2_subset_1,rc2_tops_1,rc3_lattices,rc3_struct_0,rc3_tops_1,rc4_tops_1,rc5_struct_0,rc5_tops_1,rc6_lattices,rc6_pre_topc,rc7_pre_topc,rc9_lattices,redefinition_k3_lattices,redefinition_k4_lattices,redefinition_k4_subset_1,redefinition_k5_subset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r3_lattices,reflexivity_r1_tarski,reflexivity_r3_lattices,symmetry_r1_xboole_0,t101_tops_1,t106_tops_1,t107_tops_1,t15_pre_topc,t18_pre_topc,t1_boole,t1_subset,t1_xboole_1,t22_tdlat_1,t23_tdlat_1,t26_subset_1,t27_tops_1,t2_boole,t2_subset,t2_tarski,t2_tops_1,t36_tdlat_3,t3_subset,t3_tdlat_3,t43_tops_1,t46_tdlat_3,t4_subset,t4_tdlat_3,t50_pre_topc,t5_subset,t6_boole,t6_tdlat_1,t7_boole,t87_tdlat_2,t89_tdlat_2,t8_boole]),
    [file(tdlat_3,t51_tdlat_3)]).

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(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

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_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

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(cc1_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => ( v3_pre_topc(B,A)
              & v4_pre_topc(B,A) ) ) ) ) ),
    file(tops_1,cc1_tops_1),
    []).

fof(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

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(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc2_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v2_tops_1(B,A) ) ) ) ),
    file(tops_1,cc2_tops_1),
    []).

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(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc3_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v3_tops_1(B,A) ) ) ) ),
    file(tops_1,cc3_tops_1),
    []).

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(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc4_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tops_1(B,A)
           => v2_tops_1(B,A) ) ) ) ),
    file(tops_1,cc4_tops_1),
    []).

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(cc5_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v4_pre_topc(B,A)
              & v2_tops_1(B,A) )
           => ( v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) ),
    file(tops_1,cc5_tops_1),
    []).

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(cc6_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v3_tops_1(B,A) )
           => ( v1_xboole_0(B)
              & v3_pre_topc(B,A)
              & v4_pre_topc(B,A)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) ),
    file(tops_1,cc6_tops_1),
    []).

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_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

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_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

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(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( 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),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(d12_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v12_lattices(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_lattices(A,B,D)
                     => k1_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k1_lattices(A,B,C),D) ) ) ) ) ) ) ),
    file(lattices,d12_lattices),
    []).

fof(d1_tdlat_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => k1_tdlat_1(A) = a_1_0_tdlat_1(A) ) ),
    file(tdlat_1,d1_tdlat_1),
    []).

fof(d4_tdlat_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k4_tdlat_1(A) = g3_lattices(k1_tdlat_1(A),k2_tdlat_1(A),k3_tdlat_1(A)) ) ),
    file(tdlat_1,d4_tdlat_1),
    []).

fof(d6_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)
              & r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ) ),
    file(tops_1,d6_tops_1),
    []).

fof(d7_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
          <=> B = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ),
    file(tops_1,d7_tops_1),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

fof(d8_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
          <=> B = k1_tops_1(A,k6_pre_topc(A,B)) ) ) ) ),
    file(tops_1,d8_tops_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_k12_tdlat_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k12_tdlat_1(A))
        & v10_lattices(k12_tdlat_1(A))
        & v17_lattices(k12_tdlat_1(A))
        & l3_lattices(k12_tdlat_1(A)) ) ) ),
    file(tdlat_1,k12_tdlat_1),
    []).

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_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k1_pre_topc),
    []).

fof(dt_k1_tdlat_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(k1_tdlat_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(tdlat_1,k1_tdlat_1),
    []).

fof(dt_k1_tops_1,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(tops_1,k1_tops_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_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_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    []).

fof(dt_k2_tdlat_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k2_tdlat_1(A))
        & v1_funct_2(k2_tdlat_1(A),k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A))
        & m2_relset_1(k2_tdlat_1(A),k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A)) ) ) ),
    file(tdlat_1,k2_tdlat_1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ),
    file(subset_1,k3_subset_1),
    []).

fof(dt_k3_tdlat_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k3_tdlat_1(A))
        & v1_funct_2(k3_tdlat_1(A),k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A))
        & m2_relset_1(k3_tdlat_1(A),k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A)) ) ) ),
    file(tdlat_1,k3_tdlat_1),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( 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),
    []).

fof(dt_k4_tdlat_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k4_tdlat_1(A))
        & v10_lattices(k4_tdlat_1(A))
        & v15_lattices(k4_tdlat_1(A))
        & v16_lattices(k4_tdlat_1(A))
        & l3_lattices(k4_tdlat_1(A)) ) ) ),
    file(tdlat_1,k4_tdlat_1),
    []).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_k6_pre_topc,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k6_pre_topc),
    []).

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

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

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_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_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_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

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(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc10_tops_1,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & v2_tops_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k1_tops_1(A,B))
        & v1_membered(k1_tops_1(A,B))
        & v2_membered(k1_tops_1(A,B))
        & v3_membered(k1_tops_1(A,B))
        & v4_membered(k1_tops_1(A,B))
        & v5_membered(k1_tops_1(A,B))
        & v2_tops_1(k1_tops_1(A,B),A) ) ) ),
    file(tops_1,fc10_tops_1),
    []).

fof(fc11_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v3_tops_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ),
    file(tops_1,fc11_tops_1),
    []).

fof(fc1_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v1_xboole_0(k1_pre_topc(A))
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A)) ) ) ),
    file(pre_topc,fc1_pre_topc),
    []).

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_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_xboole_0(k1_pre_topc(A))
        & v4_pre_topc(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A)) ) ) ),
    file(tops_1,fc1_tops_1),
    []).

fof(fc22_membered,axiom,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    []).

fof(fc23_membered,axiom,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    []).

fof(fc24_membered,axiom,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    []).

fof(fc25_membered,axiom,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    []).

fof(fc26_membered,axiom,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    []).

fof(fc27_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(A,B)) ) ),
    file(membered,fc27_membered),
    []).

fof(fc28_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(B,A)) ) ),
    file(membered,fc28_membered),
    []).

fof(fc29_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc29_membered),
    []).

fof(fc2_pre_topc,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(k2_pre_topc(A)) ) ),
    file(pre_topc,fc2_pre_topc),
    []).

fof(fc2_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k6_pre_topc(A,B),A) ) ),
    file(tops_1,fc2_tops_1),
    []).

fof(fc30_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc30_membered),
    []).

fof(fc31_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc31_membered),
    []).

fof(fc32_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc32_membered),
    []).

fof(fc33_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc33_membered),
    []).

fof(fc34_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc34_membered),
    []).

fof(fc35_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B))
        & v5_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc35_membered),
    []).

fof(fc36_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A))
        & v5_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc36_membered),
    []).

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_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v4_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ),
    file(tops_1,fc3_tops_1),
    []).

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(fc4_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v3_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ),
    file(tops_1,fc4_tops_1),
    []).

fof(fc5_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_pre_topc(k2_pre_topc(A),A) ) ),
    file(pre_topc,fc5_pre_topc),
    []).

fof(fc5_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_xboole_0(k1_tops_1(A,k1_pre_topc(A)))
        & v1_membered(k1_tops_1(A,k1_pre_topc(A)))
        & v2_membered(k1_tops_1(A,k1_pre_topc(A)))
        & v3_membered(k1_tops_1(A,k1_pre_topc(A)))
        & v4_membered(k1_tops_1(A,k1_pre_topc(A)))
        & v5_membered(k1_tops_1(A,k1_pre_topc(A))) ) ) ),
    file(tops_1,fc5_tops_1),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(fc6_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_pre_topc(k1_tops_1(A,B),A) ) ),
    file(tops_1,fc6_tops_1),
    []).

fof(fc7_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_xboole_0(k1_pre_topc(A))
        & v3_pre_topc(k1_pre_topc(A),A)
        & v4_pre_topc(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A)) ) ) ),
    file(tops_1,fc7_tops_1),
    []).

fof(fc8_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_pre_topc(k2_pre_topc(A),A)
        & v4_pre_topc(k2_pre_topc(A),A) ) ) ),
    file(tops_1,fc8_tops_1),
    []).

fof(fc9_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => v1_tops_1(k2_pre_topc(A),A) ) ),
    file(tops_1,fc9_tops_1),
    []).

fof(fraenkel_a_1_0_tdlat_1,axiom,(
    ! [A,B] : 
      ( l1_pre_topc(B)
     => ( r2_hidden(A,a_1_0_tdlat_1(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & v4_tops_1(C,B) ) ) ) ),
    file(tdlat_1,a_1_0_tdlat_1),
    []).

fof(fraenkel_a_1_3_tdlat_3,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( r2_hidden(A,a_1_3_tdlat_3(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & v4_tops_1(C,B) ) ) ) ),
    file(tdlat_3,a_1_3_tdlat_3),
    []).

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

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( 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),
    []).

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

fof(involutiveness_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,k3_subset_1(A,B)) = B ) ),
    file(subset_1,k3_subset_1),
    []).

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_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

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_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A) ) ) ),
    file(tops_1,rc1_tops_1),
    []).

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_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc2_tops_1),
    []).

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(rc3_tops_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc3_tops_1),
    []).

fof(rc4_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A) ) ) ),
    file(tops_1,rc4_tops_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(rc5_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A)
          & v3_tops_1(B,A) ) ) ),
    file(tops_1,rc5_tops_1),
    []).

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

fof(rc6_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc6_pre_topc),
    []).

fof(rc7_pre_topc,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc7_pre_topc),
    []).

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_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_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( 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),
    []).

fof(redefinition_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

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_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_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(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t101_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
          <=> v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ),
    file(tops_1,t101_tops_1),
    []).

fof(t106_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( ( v4_pre_topc(D,B)
                        & v4_tops_1(D,B) )
                     => v5_tops_1(D,B) )
                    & ( v5_tops_1(C,A)
                     => ( v4_pre_topc(C,A)
                        & v4_tops_1(C,A) ) ) ) ) ) ) ) ),
    file(tops_1,t106_tops_1),
    []).

fof(t107_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( ( v3_pre_topc(D,B)
                        & v4_tops_1(D,B) )
                     => v6_tops_1(D,B) )
                    & ( v6_tops_1(C,A)
                     => ( v3_pre_topc(C,A)
                        & v4_tops_1(C,A) ) ) ) ) ) ) ) ),
    file(tops_1,t107_tops_1),
    []).

fof(t15_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = B ) ) ),
    file(pre_topc,t15_pre_topc),
    []).

fof(t18_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)) = k2_pre_topc(A) ) ) ),
    file(pre_topc,t18_pre_topc),
    []).

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(t22_tdlat_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v5_tops_1(k6_pre_topc(A,k1_tops_1(A,B)),A) ) ) ),
    file(tdlat_1,t22_tdlat_1),
    []).

fof(t23_tdlat_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v6_tops_1(k1_tops_1(A,k6_pre_topc(A,B)),A) ) ) ),
    file(tdlat_1,t23_tdlat_1),
    []).

fof(t26_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => r1_xboole_0(B,k3_subset_1(A,B)) ) ),
    file(subset_1,t26_subset_1),
    []).

fof(t27_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => k6_pre_topc(A,k2_pre_topc(A)) = k2_pre_topc(A) ) ),
    file(tops_1,t27_tops_1),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t2_tops_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = k2_pre_topc(A) ) ) ),
    file(tops_1,t2_tops_1),
    []).

fof(t36_tdlat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_tops_1(B,A)
             => k1_tops_1(A,k6_pre_topc(A,B)) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ) ),
    file(tdlat_3,t36_tdlat_3),
    []).

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

fof(t3_tdlat_3,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k1_tops_1(A,B)) ) ) ),
    file(tdlat_3,t3_tdlat_3),
    []).

fof(t43_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k1_tops_1(A,k2_pre_topc(A)) = k2_pre_topc(A) ) ),
    file(tops_1,t43_tops_1),
    []).

fof(t46_tdlat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => k4_tdlat_1(A) = k12_tdlat_1(A) ) ),
    file(tdlat_3,t46_tdlat_3),
    []).

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(t4_tdlat_3,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)) ) ) ),
    file(tdlat_3,t4_tdlat_3),
    []).

fof(t50_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ),
    file(pre_topc,t50_pre_topc),
    []).

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(t6_tdlat_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v4_pre_topc(B,A)
                  | v4_pre_topc(C,A) )
               => k4_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,C))) = k6_pre_topc(A,k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) ) ),
    file(tdlat_1,t6_tdlat_1),
    []).

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

fof(t87_tdlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A)))
             => ! [D] : 
                  ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
                 => ! [E] : 
                      ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
                     => ( ( B = D
                          & C = E )
                       => ( k1_lattices(k4_tdlat_1(A),B,C) = k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),D,E))),k4_subset_1(u1_struct_0(A),D,E))
                          & k2_lattices(k4_tdlat_1(A),B,C) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),D,E))),k5_subset_1(u1_struct_0(A),D,E)) ) ) ) ) ) ) ) ),
    file(tdlat_2,t87_tdlat_2),
    []).

fof(t89_tdlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A)))
             => ! [D] : 
                  ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
                 => ! [E] : 
                      ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
                     => ( ( B = D
                          & C = E )
                       => ( r1_lattices(k4_tdlat_1(A),B,C)
                        <=> r1_tarski(D,E) ) ) ) ) ) ) ) ),
    file(tdlat_2,t89_tdlat_2),
    []).

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