% Mizar ND problem: t6_tops_2,tops_2,80,32 
fof(dh_c1_3__tops_2,definition,
    ( ( l1_struct_0(c1_3__tops_2)
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
             => r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),A),k5_setfam_1(u1_struct_0(c1_3__tops_2),B)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),A,B))) ) ) )
   => ! [C] : 
        ( l1_struct_0(C)
       => ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C))))
           => ! [E] : 
                ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C))))
               => r1_tarski(k6_subset_1(u1_struct_0(C),k5_setfam_1(u1_struct_0(C),D),k5_setfam_1(u1_struct_0(C),E)),k5_setfam_1(u1_struct_0(C),k6_subset_1(k1_zfmisc_1(u1_struct_0(C)),D,E))) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__tops_2),file(tops_2,c1_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c1_3__tops_2)]).

fof(dh_c2_3__tops_2,definition,
    ( ( m1_subset_1(c2_3__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
         => r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),A)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,A))) ) )
   => ! [B] : 
        ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
           => r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),B),k5_setfam_1(u1_struct_0(c1_3__tops_2),C)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),B,C))) ) ) ),
    introduced(definition,[new_symbol(c2_3__tops_2),file(tops_2,c2_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c2_3__tops_2)]).

fof(dh_c3_3__tops_2,definition,
    ( ( m1_subset_1(c3_3__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
     => r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
       => r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),A)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,A))) ) ),
    introduced(definition,[new_symbol(c3_3__tops_2),file(tops_2,c3_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c3_3__tops_2)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(fc37_membered,theorem,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k4_xboole_0(A,B)) ) ),
    file(membered,fc37_membered),
    [interesting(0.9),axiom,file(membered,fc37_membered)]).

fof(fc38_membered,theorem,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc38_membered),
    [interesting(0.9),axiom,file(membered,fc38_membered)]).

fof(fc39_membered,theorem,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc39_membered),
    [interesting(0.9),axiom,file(membered,fc39_membered)]).

fof(fc40_membered,theorem,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc40_membered),
    [interesting(0.9),axiom,file(membered,fc40_membered)]).

fof(fc41_membered,theorem,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B))
        & v5_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc41_membered),
    [interesting(0.9),axiom,file(membered,fc41_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(redefinition_k5_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(redefinition_k6_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    [interesting(0.9),axiom,file(subset_1,k6_subset_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(dt_k6_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(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    [interesting(0.9),axiom,file(subset_1,k6_subset_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_3__tops_2,assumption,(
    l1_struct_0(c1_3__tops_2) ),
    introduced(assumption,[file(tops_2,c1_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c1_3__tops_2)]).

fof(dt_c2_3__tops_2,assumption,(
    m1_subset_1(c2_3__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)))) ),
    introduced(assumption,[file(tops_2,c2_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c2_3__tops_2)]).

fof(dt_c3_3__tops_2,assumption,(
    m1_subset_1(c3_3__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)))) ),
    introduced(assumption,[file(tops_2,c3_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c3_3__tops_2)]).

fof(dt_c4_3__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c4_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c4_3__tops_2)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c4_3__tops_2,definition,
    ( ~ ( r2_hidden(c4_3__tops_2,k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2)))
        & ~ r2_hidden(c4_3__tops_2,k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2)))
          & ~ r2_hidden(A,k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) ) ),
    introduced(definition,[new_symbol(c4_3__tops_2),file(tops_2,c4_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c4_3__tops_2)]).

fof(e1_3__tops_2,assumption,(
    r2_hidden(c4_3__tops_2,k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2))) ),
    introduced(assumption,[file(tops_2,e1_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,e1_3__tops_2)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc6_membered,theorem,
    ( 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),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_boole)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(dh_c5_3__tops_2,definition,
    ( ? [A] : 
        ( r2_hidden(c4_3__tops_2,A)
        & r2_hidden(A,c2_3__tops_2) )
   => ( r2_hidden(c4_3__tops_2,c5_3__tops_2)
      & r2_hidden(c5_3__tops_2,c2_3__tops_2) ) ),
    introduced(definition,[new_symbol(c5_3__tops_2),file(tops_2,c5_3__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c5_3__tops_2)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(d4_xboole_0,definition,(
    ! [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),
    [interesting(0.9),axiom,file(xboole_0,d4_xboole_0)]).

fof(e2_3__tops_2,plain,
    ( r2_hidden(c4_3__tops_2,k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2))
    & ~ r2_hidden(c4_3__tops_2,k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,e1_3__tops_2])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,rc1_membered,t3_boole,t4_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_tarski,dt_l1_struct_0,dt_m1_subset_1,cc15_membered,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_setfam_1,redefinition_k6_subset_1,dt_k4_xboole_0,dt_k5_setfam_1,dt_k6_subset_1,dt_u1_struct_0,dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,t1_subset,t7_boole,e1_3__tops_2,d4_xboole_0]),
    [interesting(0.8),file(tops_2,e2_3__tops_2),[file(tops_2,e2_3__tops_2)]]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.9),axiom,file(tarski,d4_tarski)]).

fof(e3_3__tops_2,plain,(
    ? [A] : 
      ( r2_hidden(c4_3__tops_2,A)
      & r2_hidden(A,c2_3__tops_2) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,e1_3__tops_2])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,cc15_membered,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_setfam_1,dt_k3_tarski,dt_k5_setfam_1,dt_u1_struct_0,dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,t1_subset,t7_boole,e2_3__tops_2,d4_tarski]),
    [interesting(0.8),file(tops_2,e3_3__tops_2),[file(tops_2,e3_3__tops_2)]]).

fof(dt_c5_3__tops_2,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,e1_3__tops_2])],[dh_c5_3__tops_2,e3_3__tops_2]),
    [interesting(0.8),file(tops_2,c5_3__tops_2),[file(tops_2,c5_3__tops_2)]]).

fof(e4_3__tops_2,plain,
    ( r2_hidden(c4_3__tops_2,c5_3__tops_2)
    & r2_hidden(c5_3__tops_2,c2_3__tops_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,e1_3__tops_2])],[dh_c5_3__tops_2,e3_3__tops_2]),
    [interesting(0.8),file(tops_2,e4_3__tops_2),[file(tops_2,e4_3__tops_2)]]).

fof(e5_3__tops_2,plain,(
    ~ r2_hidden(c5_3__tops_2,c3_3__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,e1_3__tops_2])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,cc15_membered,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_setfam_1,dt_k3_tarski,dt_k5_setfam_1,dt_u1_struct_0,dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,dt_c5_3__tops_2,t1_subset,t7_boole,e2_3__tops_2,e4_3__tops_2,d4_tarski]),
    [interesting(0.8),file(tops_2,e5_3__tops_2),[file(tops_2,e5_3__tops_2)]]).

fof(e6_3__tops_2,plain,
    ( r2_hidden(c4_3__tops_2,c5_3__tops_2)
    & r2_hidden(c5_3__tops_2,k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,e1_3__tops_2])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,rc1_membered,t3_boole,t4_boole,existence_l1_struct_0,existence_m1_subset_1,dt_l1_struct_0,dt_m1_subset_1,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k6_subset_1,dt_k1_zfmisc_1,dt_k4_xboole_0,dt_k6_subset_1,dt_u1_struct_0,dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,dt_c5_3__tops_2,fc1_subset_1,t1_subset,t7_boole,e5_3__tops_2,e4_3__tops_2,d4_xboole_0]),
    [interesting(0.8),file(tops_2,e6_3__tops_2),[file(tops_2,e6_3__tops_2)]]).

fof(e7_3__tops_2,plain,(
    r2_hidden(c4_3__tops_2,k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,e1_3__tops_2])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,rc1_membered,t3_boole,t4_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k4_xboole_0,dt_l1_struct_0,dt_m1_subset_1,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_setfam_1,redefinition_k6_subset_1,dt_k1_zfmisc_1,dt_k3_tarski,dt_k5_setfam_1,dt_k6_subset_1,dt_u1_struct_0,dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,dt_c5_3__tops_2,fc1_subset_1,t1_subset,t7_boole,e6_3__tops_2,d4_tarski]),
    [interesting(0.8),file(tops_2,e7_3__tops_2),[file(tops_2,e7_3__tops_2)]]).

fof(i5_3__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i5_3__tops_2)]),
    [interesting(0.8),trivial,file(tops_2,i5_3__tops_2)]).

fof(i4_3__tops_2,plain,(
    r2_hidden(c4_3__tops_2,k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2,e1_3__tops_2])],[e7_3__tops_2,i5_3__tops_2]),
    [interesting(0.8),file(tops_2,i4_3__tops_2),[file(tops_2,i4_3__tops_2)]]).

fof(i3_3__tops_2,plain,(
    ~ ( r2_hidden(c4_3__tops_2,k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2)))
      & ~ r2_hidden(c4_3__tops_2,k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,dt_c4_3__tops_2]),discharge_asm(discharge,[e1_3__tops_2])],[e1_3__tops_2,i4_3__tops_2]),
    [interesting(0.8),file(tops_2,i3_3__tops_2),[file(tops_2,i3_3__tops_2)]]).

fof(i3_3_tmp__tops_2,plain,(
    ~ ( r2_hidden(c4_3__tops_2,k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2)))
      & ~ r2_hidden(c4_3__tops_2,k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2]),discharge_asm(discharge,[dt_c4_3__tops_2])],[dt_c4_3__tops_2,i3_3__tops_2]),
    [interesting(0.8),i2_3__tops_2]).

fof(i2_3__tops_2,plain,(
    r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) ),
    inference(let,[status(thm),assumptions([dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2])],[i3_3_tmp__tops_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,dt_k3_tarski,dt_k4_xboole_0,dt_l1_struct_0,dt_m1_subset_1,cc15_membered,rc1_subset_1,rc2_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_setfam_1,redefinition_k6_subset_1,dt_k1_zfmisc_1,dt_k5_setfam_1,dt_k6_subset_1,dt_u1_struct_0,dt_c1_3__tops_2,dt_c2_3__tops_2,dt_c3_3__tops_2,fc1_subset_1,d3_tarski,dh_c4_3__tops_2]),
    [interesting(0.8),file(tops_2,i2_3__tops_2),[file(tops_2,i2_3__tops_2)]]).

fof(i2_3_tmp__tops_2,plain,
    ( ( m1_subset_1(c2_3__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
      & m1_subset_1(c3_3__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)))) )
   => r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c2_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),c3_3__tops_2)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),c2_3__tops_2,c3_3__tops_2))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__tops_2]),discharge_asm(discharge,[dt_c2_3__tops_2,dt_c3_3__tops_2])],[dt_c2_3__tops_2,dt_c3_3__tops_2,i2_3__tops_2]),
    [interesting(0.8),i1_3__tops_2]).

fof(i1_3__tops_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
         => r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),A),k5_setfam_1(u1_struct_0(c1_3__tops_2),B)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),A,B))) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__tops_2])],[i2_3_tmp__tops_2,dh_c2_3__tops_2,dh_c3_3__tops_2]),
    [interesting(0.8),file(tops_2,i1_3__tops_2),[file(tops_2,i1_3__tops_2)]]).

fof(i1_3_tmp__tops_2,plain,
    ( l1_struct_0(c1_3__tops_2)
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2))))
           => r1_tarski(k6_subset_1(u1_struct_0(c1_3__tops_2),k5_setfam_1(u1_struct_0(c1_3__tops_2),A),k5_setfam_1(u1_struct_0(c1_3__tops_2),B)),k5_setfam_1(u1_struct_0(c1_3__tops_2),k6_subset_1(k1_zfmisc_1(u1_struct_0(c1_3__tops_2)),A,B))) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__tops_2])],[dt_c1_3__tops_2,i1_3__tops_2]),
    [interesting(1),t6_tops_2]).

fof(t6_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => r1_tarski(k6_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),C)),k5_setfam_1(u1_struct_0(A),k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__tops_2,dh_c1_3__tops_2]),
    [interesting(1),file(tops_2,t6_tops_2),[file(tops_2,t6_tops_2)]]).