% Mizar problem: t32_tex_1,tex_1,1226,37 
fof(t32_tex_1,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( k4_tex_1(A,B) = k2_tex_1(A)
          <=> A = k1_tarski(B) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc12_tdlat_3,cc13_tdlat_3,cc1_tdlat_3,cc1_tex_1,cc1_tops_1,cc2_tdlat_3,cc2_tex_1,cc2_tops_1,cc3_tdlat_3,cc3_tex_1,cc3_tops_1,cc4_tdlat_3,cc4_tex_1,cc4_tops_1,cc5_tops_1,cc6_tops_1,cc7_tdlat_3,cc8_tdlat_3,commutativity_k2_tarski,d10_xboole_0,d1_tarski,d2_tarski,d2_tex_1,d3_tex_1,d4_xboole_0,d5_tex_1,dt_g1_pre_topc,dt_k1_pcomps_1,dt_k1_tarski,dt_k1_tex_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_tex_1,dt_k3_tex_1,dt_k4_tex_1,dt_k4_xboole_0,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_complsp1,fc2_subset_1,fc2_tex_1,fc3_subset_1,fc3_tex_1,fc4_tex_1,fc6_tex_1,fc7_tex_1,fraenkel_a_2_1_tex_1,fraenkel_a_2_3_tex_1,free_g1_pre_topc,l38_tex_1,rc1_subset_1,rc1_tdlat_3,rc1_tops_1,rc1_xboole_0,rc2_subset_1,rc2_tdlat_3,rc2_tops_1,rc2_xboole_0,rc3_struct_0,rc3_tdlat_3,rc3_tex_1,rc3_tops_1,rc4_tex_1,rc4_tops_1,rc5_struct_0,rc5_tex_1,rc5_tops_1,rc6_tdlat_3,rc6_tex_1,rc7_tex_1,rc8_tdlat_3,rc8_tex_1,rc9_tdlat_3,rc9_tex_1,redefinition_k1_pcomps_1,redefinition_k3_tex_1,reflexivity_r1_tarski,t1_subset,t24_zfmisc_1,t2_subset,t2_tarski,t30_zfmisc_1,t37_xboole_1,t37_zfmisc_1,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,t64_zfmisc_1,t6_boole,t7_boole,t8_boole]),
    [file(tex_1,t32_tex_1)]).

fof(abstractness_v1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_pre_topc(A)
       => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ),
    file(pre_topc,v1_pre_topc),
    []).

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

fof(cc12_tdlat_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v5_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v4_tdlat_3(A) ) ) ) ),
    file(tdlat_3,cc12_tdlat_3),
    []).

fof(cc13_tdlat_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v5_tdlat_3(A) ) ) ) ),
    file(tdlat_3,cc13_tdlat_3),
    []).

fof(cc1_tdlat_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_tdlat_3(A)
       => v2_pre_topc(A) ) ) ),
    file(tdlat_3,cc1_tdlat_3),
    []).

fof(cc1_tex_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A)
          & v2_pre_topc(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v2_tdlat_3(A)
          & v3_tdlat_3(A)
          & v4_tdlat_3(A)
          & v5_tdlat_3(A) ) ) ) ),
    file(tex_1,cc1_tex_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(cc2_tdlat_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v2_tdlat_3(A)
       => v2_pre_topc(A) ) ) ),
    file(tdlat_3,cc2_tdlat_3),
    []).

fof(cc2_tex_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v2_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v3_realset2(A)
          & v2_pre_topc(A) ) ) ) ),
    file(tex_1,cc2_tex_1),
    []).

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_tdlat_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_tdlat_3(A)
       => v3_tdlat_3(A) ) ) ),
    file(tdlat_3,cc3_tdlat_3),
    []).

fof(cc3_tex_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A) ) ) ) ),
    file(tex_1,cc3_tex_1),
    []).

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_tdlat_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v2_tdlat_3(A)
       => v3_tdlat_3(A) ) ) ),
    file(tdlat_3,cc4_tdlat_3),
    []).

fof(cc4_tex_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v2_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A) ) ) ) ),
    file(tex_1,cc4_tex_1),
    []).

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_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_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_tdlat_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_tdlat_3(A) )
       => ( v2_pre_topc(A)
          & v3_tdlat_3(A) ) ) ) ),
    file(tdlat_3,cc7_tdlat_3),
    []).

fof(cc8_tdlat_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v2_tdlat_3(A) )
       => ( v2_pre_topc(A)
          & v3_tdlat_3(A) ) ) ) ),
    file(tdlat_3,cc8_tdlat_3),
    []).

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

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

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

fof(d2_tex_1,axiom,(
    ! [A] : k1_tex_1(A) = k2_tarski(k1_xboole_0,A) ),
    file(tex_1,d2_tex_1),
    []).

fof(d3_tex_1,axiom,(
    ! [A] : k2_tex_1(A) = g1_pre_topc(A,k1_tex_1(A)) ),
    file(tex_1,d3_tex_1),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_tex_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => k4_tex_1(A,B) = g1_pre_topc(A,k3_tex_1(A,k1_pcomps_1(A),a_2_1_tex_1(A,B))) ) ),
    file(tex_1,d5_tex_1),
    []).

fof(dt_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_pre_topc(g1_pre_topc(A,B))
        & l1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(dt_k1_pcomps_1,axiom,(
    ! [A] : m1_subset_1(k1_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) ),
    file(pcomps_1,k1_pcomps_1),
    []).

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

fof(dt_k1_tex_1,axiom,(
    ! [A] : m1_subset_1(k1_tex_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) ),
    file(tex_1,k1_tex_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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_tex_1,axiom,(
    ! [A] : l1_pre_topc(k2_tex_1(A)) ),
    file(tex_1,k2_tex_1),
    []).

fof(dt_k3_tex_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k3_tex_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(tex_1,k3_tex_1),
    []).

fof(dt_k4_tex_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => l1_pre_topc(k4_tex_1(A,B)) ) ),
    file(tex_1,k4_tex_1),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_u1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pre_topc,u1_pre_topc),
    []).

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

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_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_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_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_complsp1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( ~ v3_struct_0(g1_pre_topc(A,B))
        & v1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(complsp1,fc2_complsp1),
    []).

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

fof(fc2_tex_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tex_1(A)) ),
    file(tex_1,fc2_tex_1),
    []).

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

fof(fc3_tex_1,axiom,(
    ! [A] : 
      ( v1_pre_topc(k2_tex_1(A))
      & v2_pre_topc(k2_tex_1(A))
      & v2_tdlat_3(k2_tex_1(A))
      & v3_tdlat_3(k2_tex_1(A)) ) ),
    file(tex_1,fc3_tex_1),
    []).

fof(fc4_tex_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k2_tex_1(A))
        & v1_pre_topc(k2_tex_1(A))
        & v2_pre_topc(k2_tex_1(A))
        & v2_tdlat_3(k2_tex_1(A))
        & v3_tdlat_3(k2_tex_1(A))
        & v4_tdlat_3(k2_tex_1(A))
        & v5_tdlat_3(k2_tex_1(A)) ) ) ),
    file(tex_1,fc4_tex_1),
    []).

fof(fc6_tex_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ( v1_pre_topc(k4_tex_1(A,B))
        & v2_pre_topc(k4_tex_1(A,B)) ) ) ),
    file(tex_1,fc6_tex_1),
    []).

fof(fc7_tex_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => ( ~ v3_struct_0(k4_tex_1(A,B))
        & v1_pre_topc(k4_tex_1(A,B))
        & v2_pre_topc(k4_tex_1(A,B)) ) ) ),
    file(tex_1,fc7_tex_1),
    []).

fof(fraenkel_a_2_1_tex_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,B)
     => ( r2_hidden(A,a_2_1_tex_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(B))
            & A = D
            & r2_hidden(C,D)
            & D != B ) ) ) ),
    file(tex_1,a_2_1_tex_1),
    []).

fof(fraenkel_a_2_3_tex_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(C,B) )
     => ( r2_hidden(A,a_2_3_tex_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(B))
            & A = D
            & r2_hidden(C,D)
            & D != B ) ) ) ),
    file(tex_1,a_2_3_tex_1),
    []).

fof(free_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C,D] : 
          ( g1_pre_topc(A,B) = g1_pre_topc(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(l38_tex_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( ( C = a_2_3_tex_1(A,B)
                & A = k1_tarski(B) )
             => C = k1_xboole_0 ) ) ) ),
    file(tex_1,l38_tex_1),
    []).

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_tdlat_3,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v1_tdlat_3(A)
      & v2_tdlat_3(A) ) ),
    file(tdlat_3,rc1_tdlat_3),
    []).

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(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_tdlat_3,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A)
      & v3_tdlat_3(A) ) ),
    file(tdlat_3,rc2_tdlat_3),
    []).

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(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(rc3_tdlat_3,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_tdlat_3(A)
      & v2_tdlat_3(A)
      & v3_tdlat_3(A) ) ),
    file(tdlat_3,rc3_tdlat_3),
    []).

fof(rc3_tex_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v1_pre_topc(A) ) ),
    file(tex_1,rc3_tex_1),
    []).

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_tex_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A) ) ),
    file(tex_1,rc4_tex_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_tex_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(tex_1,rc5_tex_1),
    []).

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_tdlat_3,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v3_tdlat_3(A) ) ),
    file(tdlat_3,rc6_tdlat_3),
    []).

fof(rc6_tex_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(tex_1,rc6_tex_1),
    []).

fof(rc7_tex_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_tdlat_3(A)
      & ~ v2_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A) ) ),
    file(tex_1,rc7_tex_1),
    []).

fof(rc8_tdlat_3,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v4_tdlat_3(A) ) ),
    file(tdlat_3,rc8_tdlat_3),
    []).

fof(rc8_tex_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v1_tdlat_3(A)
      & v2_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A) ) ),
    file(tex_1,rc8_tex_1),
    []).

fof(rc9_tdlat_3,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v5_tdlat_3(A) ) ),
    file(tdlat_3,rc9_tdlat_3),
    []).

fof(rc9_tex_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v1_tdlat_3(A)
      & ~ v2_tdlat_3(A) ) ),
    file(tex_1,rc9_tex_1),
    []).

fof(redefinition_k1_pcomps_1,axiom,(
    ! [A] : k1_pcomps_1(A) = k1_zfmisc_1(A) ),
    file(pcomps_1,k1_pcomps_1),
    []).

fof(redefinition_k3_tex_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k3_tex_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(tex_1,k3_tex_1),
    []).

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

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

fof(t24_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) ),
    file(zfmisc_1,t24_zfmisc_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(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t30_zfmisc_1,axiom,(
    ! [A] : k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A)) ),
    file(zfmisc_1,t30_zfmisc_1),
    []).

fof(t37_xboole_1,axiom,(
    ! [A,B] : 
      ( k4_xboole_0(A,B) = k1_xboole_0
    <=> r1_tarski(A,B) ) ),
    file(xboole_1,t37_xboole_1),
    []).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t64_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        & A != C ) ) ),
    file(zfmisc_1,t64_zfmisc_1),
    []).

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),
    []).