% Mizar ND problem: t13_tops_2,tops_2,128,41 
fof(dh_c1_7__tops_2,definition,
    ( ( l1_struct_0(c1_7__tops_2)
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_7__tops_2))))
         => ( v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),A))
          <=> v1_finset_1(A) ) ) )
   => ! [B] : 
        ( l1_struct_0(B)
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
           => ( v1_finset_1(k7_setfam_1(u1_struct_0(B),C))
            <=> v1_finset_1(C) ) ) ) ),
    introduced(definition,[new_symbol(c1_7__tops_2),file(tops_2,c1_7__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c1_7__tops_2)]).

fof(dh_c2_7__tops_2,definition,
    ( ( m1_subset_1(c2_7__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_7__tops_2))))
     => ( v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
      <=> v1_finset_1(c2_7__tops_2) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_7__tops_2))))
       => ( v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),A))
        <=> v1_finset_1(A) ) ) ),
    introduced(definition,[new_symbol(c2_7__tops_2),file(tops_2,c2_7__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c2_7__tops_2)]).

fof(e1_7_1__tops_2,assumption,(
    v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    introduced(assumption,[file(tops_2,e1_7_1__tops_2)]),
    [interesting(0.65),axiom,file(tops_2,e1_7_1__tops_2)]).

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

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

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

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(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(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(involutiveness_k7_setfam_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k7_setfam_1(A,k7_setfam_1(A,B)) = B ) ),
    file(setfam_1,k7_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k7_setfam_1)]).

fof(dt_k7_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(setfam_1,k7_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k7_setfam_1)]).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_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_7__tops_2,assumption,(
    l1_struct_0(c1_7__tops_2) ),
    introduced(assumption,[file(tops_2,c1_7__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c1_7__tops_2)]).

fof(dh_c1_7_1__tops_2,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)
        & ! [B] : 
            ( r2_hidden(B,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
               => ( C = B
                 => k1_funct_1(A,B) = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) ) )
   => ( v1_relat_1(c1_7_1__tops_2)
      & v1_funct_1(c1_7_1__tops_2)
      & k1_relat_1(c1_7_1__tops_2) = k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)
      & ! [D] : 
          ( r2_hidden(D,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
         => ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( E = D
               => k1_funct_1(c1_7_1__tops_2,D) = k3_subset_1(u1_struct_0(c1_7__tops_2),E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_7_1__tops_2),file(tops_2,c1_7_1__tops_2)]),
    [interesting(0.65),axiom,file(tops_2,c1_7_1__tops_2)]).

fof(involutiveness_k3_subset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(subset_1,k3_subset_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

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),
    [interesting(0.9),axiom,file(subset_1,k3_subset_1)]).

fof(dt_c2_7__tops_2,assumption,(
    m1_subset_1(c2_7__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))) ),
    introduced(assumption,[file(tops_2,c2_7__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c2_7__tops_2)]).

fof(s2_funct_1__e4_7_1__tops_2,theorem,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
     => ( ( ! [C,D,E] : 
              ( ( r2_hidden(C,k7_setfam_1(u1_struct_0(A),B))
                & ! [F] : 
                    ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                   => ( F = C
                     => D = k3_subset_1(u1_struct_0(A),F) ) )
                & ! [G] : 
                    ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                   => ( G = C
                     => E = k3_subset_1(u1_struct_0(A),G) ) ) )
             => D = E )
          & ! [C] : 
              ~ ( r2_hidden(C,k7_setfam_1(u1_struct_0(A),B))
                & ! [D] : 
                    ~ ! [H] : 
                        ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                       => ( H = C
                         => D = k3_subset_1(u1_struct_0(A),H) ) ) ) )
       => ? [C] : 
            ( v1_relat_1(C)
            & v1_funct_1(C)
            & k1_relat_1(C) = k7_setfam_1(u1_struct_0(A),B)
            & ! [D] : 
                ( r2_hidden(D,k7_setfam_1(u1_struct_0(A),B))
               => ! [I] : 
                    ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                   => ( I = D
                     => k1_funct_1(C,D) = k3_subset_1(u1_struct_0(A),I) ) ) ) ) ) ) ),
    file(tops_2,s2_funct_1__e4_7_1__tops_2),
    [interesting(0.9),axiom,file(tops_2,s2_funct_1__e4_7_1__tops_2)]).

fof(dh_c1_7_1_1__tops_2,definition,
    ( ! [A,B] : 
        ( ( r2_hidden(c1_7_1_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = c1_7_1_1__tops_2
               => A = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) )
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = c1_7_1_1__tops_2
               => B = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) )
       => A = B )
   => ! [D,E,F] : 
        ( ( r2_hidden(D,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
          & ! [G] : 
              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( G = D
               => E = k3_subset_1(u1_struct_0(c1_7__tops_2),G) ) )
          & ! [G] : 
              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( G = D
               => F = k3_subset_1(u1_struct_0(c1_7__tops_2),G) ) ) )
       => E = F ) ),
    introduced(definition,[new_symbol(c1_7_1_1__tops_2),file(tops_2,c1_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_1_1__tops_2)]).

fof(dh_c2_7_1_1__tops_2,definition,
    ( ! [A] : 
        ( ( r2_hidden(c1_7_1_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
          & ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( B = c1_7_1_1__tops_2
               => c2_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) )
          & ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( B = c1_7_1_1__tops_2
               => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) )
       => c2_7_1_1__tops_2 = A )
   => ! [C,D] : 
        ( ( r2_hidden(c1_7_1_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
          & ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( E = c1_7_1_1__tops_2
               => C = k3_subset_1(u1_struct_0(c1_7__tops_2),E) ) )
          & ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( E = c1_7_1_1__tops_2
               => D = k3_subset_1(u1_struct_0(c1_7__tops_2),E) ) ) )
       => C = D ) ),
    introduced(definition,[new_symbol(c2_7_1_1__tops_2),file(tops_2,c2_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c2_7_1_1__tops_2)]).

fof(dh_c3_7_1_1__tops_2,definition,
    ( ( ( r2_hidden(c1_7_1_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
        & ! [A] : 
            ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
           => ( A = c1_7_1_1__tops_2
             => c2_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) )
        & ! [A] : 
            ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
           => ( A = c1_7_1_1__tops_2
             => c3_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) )
     => c2_7_1_1__tops_2 = c3_7_1_1__tops_2 )
   => ! [B] : 
        ( ( r2_hidden(c1_7_1_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = c1_7_1_1__tops_2
               => c2_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) )
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = c1_7_1_1__tops_2
               => B = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) )
       => c2_7_1_1__tops_2 = B ) ),
    introduced(definition,[new_symbol(c3_7_1_1__tops_2),file(tops_2,c3_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c3_7_1_1__tops_2)]).

fof(e1_7_1_1__tops_2,assumption,(
    r2_hidden(c1_7_1_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    introduced(assumption,[file(tops_2,e1_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e1_7_1_1__tops_2)]).

fof(e2_7_1_1__tops_2,assumption,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( A = c1_7_1_1__tops_2
       => c2_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) ),
    introduced(assumption,[file(tops_2,e2_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e2_7_1_1__tops_2)]).

fof(e3_7_1_1__tops_2,assumption,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( A = c1_7_1_1__tops_2
       => c3_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) ),
    introduced(assumption,[file(tops_2,e3_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e3_7_1_1__tops_2)]).

fof(dt_c1_7_1_1__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c1_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_1_1__tops_2)]).

fof(dt_c2_7_1_1__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c2_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c2_7_1_1__tops_2)]).

fof(dt_c3_7_1_1__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c3_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c3_7_1_1__tops_2)]).

fof(de_c4_7_1_1__tops_2,definition,(
    c4_7_1_1__tops_2 = c1_7_1_1__tops_2 ),
    introduced(definition,[new_symbol(c4_7_1_1__tops_2),file(tops_2,c4_7_1_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c4_7_1_1__tops_2)]).

fof(e4_7_1_1__tops_2,plain,(
    m1_subset_1(c1_7_1_1__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7__tops_2,e1_7_1_1__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e1_7_1_1__tops_2]),
    [interesting(0.5),file(tops_2,e4_7_1_1__tops_2),[file(tops_2,e4_7_1_1__tops_2)]]).

fof(dt_c4_7_1_1__tops_2,plain,(
    m1_subset_1(c4_7_1_1__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7__tops_2,e1_7_1_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,fc1_subset_1,t3_subset,de_c4_7_1_1__tops_2,e4_7_1_1__tops_2]),
    [interesting(0.5),file(tops_2,c4_7_1_1__tops_2),[file(tops_2,c4_7_1_1__tops_2)]]).

fof(e5_7_1_1__tops_2,plain,(
    c2_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),c4_7_1_1__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7_1_1__tops_2,dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7__tops_2,e1_7_1_1__tops_2,e2_7_1_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7_1_1__tops_2,dt_c4_7_1_1__tops_2,de_c4_7_1_1__tops_2,fc1_subset_1,t3_subset,e2_7_1_1__tops_2]),
    [interesting(0.5),file(tops_2,e5_7_1_1__tops_2),[file(tops_2,e5_7_1_1__tops_2)]]).

fof(e6_7_1_1__tops_2,plain,(
    c2_7_1_1__tops_2 = c3_7_1_1__tops_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_7_1_1__tops_2,dt_c2_7_1_1__tops_2,dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7__tops_2,e1_7_1_1__tops_2,e2_7_1_1__tops_2,e3_7_1_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7_1_1__tops_2,dt_c3_7_1_1__tops_2,dt_c4_7_1_1__tops_2,de_c4_7_1_1__tops_2,fc1_subset_1,t3_subset,e5_7_1_1__tops_2,e3_7_1_1__tops_2]),
    [interesting(0.5),file(tops_2,e6_7_1_1__tops_2),[file(tops_2,e6_7_1_1__tops_2)]]).

fof(i3_7_1_1__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i3_7_1_1__tops_2)]),
    [interesting(0.5),trivial,file(tops_2,i3_7_1_1__tops_2)]).

fof(i2_7_1_1__tops_2,plain,(
    c2_7_1_1__tops_2 = c3_7_1_1__tops_2 ),
    inference(conclusion,[status(thm),assumptions([dt_c3_7_1_1__tops_2,dt_c2_7_1_1__tops_2,dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7__tops_2,e1_7_1_1__tops_2,e2_7_1_1__tops_2,e3_7_1_1__tops_2])],[e6_7_1_1__tops_2,i3_7_1_1__tops_2]),
    [interesting(0.5),file(tops_2,i2_7_1_1__tops_2),[file(tops_2,i2_7_1_1__tops_2)]]).

fof(i1_7_1_1__tops_2,plain,
    ( ( r2_hidden(c1_7_1_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( A = c1_7_1_1__tops_2
           => c2_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) )
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( A = c1_7_1_1__tops_2
           => c3_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) )
   => c2_7_1_1__tops_2 = c3_7_1_1__tops_2 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_7_1_1__tops_2,dt_c2_7_1_1__tops_2,dt_c1_7__tops_2,dt_c1_7_1_1__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[e1_7_1_1__tops_2,e2_7_1_1__tops_2,e3_7_1_1__tops_2])],[e1_7_1_1__tops_2,e2_7_1_1__tops_2,e3_7_1_1__tops_2,i2_7_1_1__tops_2]),
    [interesting(0.5),file(tops_2,i1_7_1_1__tops_2),[file(tops_2,i1_7_1_1__tops_2)]]).

fof(i1_7_1_1_tmp__tops_2,plain,
    ( ( r2_hidden(c1_7_1_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( A = c1_7_1_1__tops_2
           => c2_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) )
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( A = c1_7_1_1__tops_2
           => c3_7_1_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) )
   => c2_7_1_1__tops_2 = c3_7_1_1__tops_2 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[dt_c1_7_1_1__tops_2,dt_c2_7_1_1__tops_2,dt_c3_7_1_1__tops_2])],[dt_c1_7_1_1__tops_2,dt_c2_7_1_1__tops_2,dt_c3_7_1_1__tops_2,i1_7_1_1__tops_2]),
    [interesting(0.65),e2_7_1__tops_2]).

fof(e2_7_1__tops_2,plain,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
        & ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
           => ( D = A
             => B = k3_subset_1(u1_struct_0(c1_7__tops_2),D) ) )
        & ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
           => ( D = A
             => C = k3_subset_1(u1_struct_0(c1_7__tops_2),D) ) ) )
     => B = C ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[i1_7_1_1_tmp__tops_2,dh_c1_7_1_1__tops_2,dh_c2_7_1_1__tops_2,dh_c3_7_1_1__tops_2]),
    [interesting(0.65),file(tops_2,e2_7_1__tops_2),[file(tops_2,e2_7_1__tops_2)]]).

fof(dh_c1_7_1_2__tops_2,definition,
    ( ~ ( r2_hidden(c1_7_1_2__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
        & ! [A] : 
            ~ ! [B] : 
                ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
               => ( B = c1_7_1_2__tops_2
                 => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) )
   => ! [C] : 
        ~ ( r2_hidden(C,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
          & ! [D] : 
              ~ ! [E] : 
                  ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
                 => ( E = C
                   => D = k3_subset_1(u1_struct_0(c1_7__tops_2),E) ) ) ) ),
    introduced(definition,[new_symbol(c1_7_1_2__tops_2),file(tops_2,c1_7_1_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_1_2__tops_2)]).

fof(e1_7_1_2__tops_2,assumption,(
    r2_hidden(c1_7_1_2__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    introduced(assumption,[file(tops_2,e1_7_1_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e1_7_1_2__tops_2)]).

fof(dt_c1_7_1_2__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c1_7_1_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_1_2__tops_2)]).

fof(de_c2_7_1_2__tops_2,definition,(
    c2_7_1_2__tops_2 = c1_7_1_2__tops_2 ),
    introduced(definition,[new_symbol(c2_7_1_2__tops_2),file(tops_2,c2_7_1_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c2_7_1_2__tops_2)]).

fof(e2_7_1_2__tops_2,plain,(
    m1_subset_1(c1_7_1_2__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2,e1_7_1_2__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e1_7_1_2__tops_2]),
    [interesting(0.5),file(tops_2,e2_7_1_2__tops_2),[file(tops_2,e2_7_1_2__tops_2)]]).

fof(dt_c2_7_1_2__tops_2,plain,(
    m1_subset_1(c2_7_1_2__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2,e1_7_1_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,fc1_subset_1,t3_subset,de_c2_7_1_2__tops_2,e2_7_1_2__tops_2]),
    [interesting(0.5),file(tops_2,c2_7_1_2__tops_2),[file(tops_2,c2_7_1_2__tops_2)]]).

fof(de_c3_7_1_2__tops_2,definition,(
    c3_7_1_2__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_1_2__tops_2) ),
    introduced(definition,[new_symbol(c3_7_1_2__tops_2),file(tops_2,c3_7_1_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c3_7_1_2__tops_2)]).

fof(e3_7_1_2__tops_2,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2,e1_7_1_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,dt_c1_7_1_2__tops_2,fc1_subset_1,t3_subset,involutiveness_k3_subset_1,dt_k3_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c2_7_1_2__tops_2,de_c2_7_1_2__tops_2]),
    [interesting(0.5),file(tops_2,e3_7_1_2__tops_2),[file(tops_2,e3_7_1_2__tops_2)]]).

fof(dt_c3_7_1_2__tops_2,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2,e1_7_1_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,dt_c1_7_1_2__tops_2,fc1_subset_1,t3_subset,involutiveness_k3_subset_1,dt_k3_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c2_7_1_2__tops_2,de_c2_7_1_2__tops_2,de_c3_7_1_2__tops_2,e3_7_1_2__tops_2]),
    [interesting(0.5),file(tops_2,c3_7_1_2__tops_2),[file(tops_2,c3_7_1_2__tops_2)]]).

fof(e4_7_1_2__tops_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( A = c1_7_1_2__tops_2
       => c3_7_1_2__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2,e1_7_1_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,dt_c2_7_1_2__tops_2,de_c2_7_1_2__tops_2,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c3_7_1_2__tops_2,de_c3_7_1_2__tops_2,fc1_subset_1,t3_subset]),
    [interesting(0.5),file(tops_2,e4_7_1_2__tops_2),[file(tops_2,e4_7_1_2__tops_2)]]).

fof(i4_7_1_2__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i4_7_1_2__tops_2)]),
    [interesting(0.5),trivial,file(tops_2,i4_7_1_2__tops_2)]).

fof(i3_7_1_2__tops_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( A = c1_7_1_2__tops_2
       => c3_7_1_2__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2,e1_7_1_2__tops_2])],[e4_7_1_2__tops_2,i4_7_1_2__tops_2]),
    [interesting(0.5),file(tops_2,i3_7_1_2__tops_2),[file(tops_2,i3_7_1_2__tops_2)]]).

fof(i2_7_1_2__tops_2,plain,(
    ? [A] : 
    ! [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( B = c1_7_1_2__tops_2
       => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) ),
    inference(take,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2,e1_7_1_2__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,rc1_membered,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,involutiveness_k3_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c3_7_1_2__tops_2,fc1_subset_1,i3_7_1_2__tops_2]),
    [interesting(0.5),file(tops_2,i2_7_1_2__tops_2),[file(tops_2,i2_7_1_2__tops_2)]]).

fof(i1_7_1_2__tops_2,plain,(
    ~ ( r2_hidden(c1_7_1_2__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
      & ! [A] : 
          ~ ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( B = c1_7_1_2__tops_2
               => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_2__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[e1_7_1_2__tops_2])],[e1_7_1_2__tops_2,i2_7_1_2__tops_2]),
    [interesting(0.5),file(tops_2,i1_7_1_2__tops_2),[file(tops_2,i1_7_1_2__tops_2)]]).

fof(i1_7_1_2_tmp__tops_2,plain,(
    ~ ( r2_hidden(c1_7_1_2__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
      & ! [A] : 
          ~ ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( B = c1_7_1_2__tops_2
               => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[dt_c1_7_1_2__tops_2])],[dt_c1_7_1_2__tops_2,i1_7_1_2__tops_2]),
    [interesting(0.65),e3_7_1__tops_2]).

fof(e3_7_1__tops_2,plain,(
    ! [A] : 
      ~ ( r2_hidden(A,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
        & ! [B] : 
            ~ ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
               => ( C = A
                 => B = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[i1_7_1_2_tmp__tops_2,dh_c1_7_1_2__tops_2]),
    [interesting(0.65),file(tops_2,e3_7_1__tops_2),[file(tops_2,e3_7_1__tops_2)]]).

fof(e4_7_1__tops_2,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)
      & ! [B] : 
          ( r2_hidden(B,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = B
               => k1_funct_1(A,B) = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__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,rc1_membered,cc15_membered,rc1_subset_1,rc2_subset_1,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c2_7__tops_2,fc1_subset_1,s2_funct_1__e4_7_1__tops_2,e2_7_1__tops_2,e3_7_1__tops_2]),
    [interesting(0.65),file(tops_2,e4_7_1__tops_2),[file(tops_2,e4_7_1__tops_2)]]).

fof(dt_c1_7_1__tops_2,plain,
    ( v1_relat_1(c1_7_1__tops_2)
    & v1_funct_1(c1_7_1__tops_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[dh_c1_7_1__tops_2,e4_7_1__tops_2]),
    [interesting(0.65),file(tops_2,c1_7_1__tops_2),[file(tops_2,c1_7_1__tops_2)]]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dh_c1_7_1_3__tops_2,definition,
    ( ( r2_hidden(c1_7_1_3__tops_2,k2_relat_1(c1_7_1__tops_2))
    <=> r2_hidden(c1_7_1_3__tops_2,c2_7__tops_2) )
   => ! [A] : 
        ( r2_hidden(A,k2_relat_1(c1_7_1__tops_2))
      <=> r2_hidden(A,c2_7__tops_2) ) ),
    introduced(definition,[new_symbol(c1_7_1_3__tops_2),file(tops_2,c1_7_1_3__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_1_3__tops_2)]).

fof(e1_7_1_3_1__tops_2,assumption,(
    r2_hidden(c1_7_1_3__tops_2,k2_relat_1(c1_7_1__tops_2)) ),
    introduced(assumption,[file(tops_2,e1_7_1_3_1__tops_2)]),
    [interesting(0.35),axiom,file(tops_2,e1_7_1_3_1__tops_2)]).

fof(dt_c1_7_1_3__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c1_7_1_3__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_1_3__tops_2)]).

fof(dh_c1_7_1_3_1__tops_2,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_7_1__tops_2))
        & c1_7_1_3__tops_2 = k1_funct_1(c1_7_1__tops_2,A) )
   => ( r2_hidden(c1_7_1_3_1__tops_2,k1_relat_1(c1_7_1__tops_2))
      & c1_7_1_3__tops_2 = k1_funct_1(c1_7_1__tops_2,c1_7_1_3_1__tops_2) ) ),
    introduced(definition,[new_symbol(c1_7_1_3_1__tops_2),file(tops_2,c1_7_1_3_1__tops_2)]),
    [interesting(0.35),axiom,file(tops_2,c1_7_1_3_1__tops_2)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e2_7_1_3_1__tops_2,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_7_1__tops_2))
      & c1_7_1_3__tops_2 = k1_funct_1(c1_7_1__tops_2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_7_1__tops_2,dt_c1_7_1_3__tops_2,t1_subset,t7_boole,e1_7_1_3_1__tops_2,d5_funct_1]),
    [interesting(0.35),file(tops_2,e2_7_1_3_1__tops_2),[file(tops_2,e2_7_1_3_1__tops_2)]]).

fof(dt_c1_7_1_3_1__tops_2,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[dh_c1_7_1_3_1__tops_2,e2_7_1_3_1__tops_2]),
    [interesting(0.35),file(tops_2,c1_7_1_3_1__tops_2),[file(tops_2,c1_7_1_3_1__tops_2)]]).

fof(de_c2_7_1_3_1__tops_2,definition,(
    c2_7_1_3_1__tops_2 = c1_7_1_3_1__tops_2 ),
    introduced(definition,[new_symbol(c2_7_1_3_1__tops_2),file(tops_2,c2_7_1_3_1__tops_2)]),
    [interesting(0.35),axiom,file(tops_2,c2_7_1_3_1__tops_2)]).

fof(e5_7_1__tops_2,plain,(
    k1_relat_1(c1_7_1__tops_2) = k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[dh_c1_7_1__tops_2,e4_7_1__tops_2]),
    [interesting(0.65),file(tops_2,e5_7_1__tops_2),[file(tops_2,e5_7_1__tops_2)]]).

fof(e3_7_1_3_1__tops_2,plain,(
    r2_hidden(c1_7_1_3_1__tops_2,k1_relat_1(c1_7_1__tops_2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[dh_c1_7_1_3_1__tops_2,e2_7_1_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e3_7_1_3_1__tops_2),[file(tops_2,e3_7_1_3_1__tops_2)]]).

fof(e5_7_1_3_1__tops_2,plain,(
    m1_subset_1(c1_7_1_3_1__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1__tops_2,dt_c1_7_1_3_1__tops_2,dt_c2_7__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e5_7_1__tops_2,e3_7_1_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e5_7_1_3_1__tops_2),[file(tops_2,e5_7_1_3_1__tops_2)]]).

fof(dt_c2_7_1_3_1__tops_2,plain,(
    m1_subset_1(c2_7_1_3_1__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_3_1__tops_2,fc1_subset_1,t3_subset,de_c2_7_1_3_1__tops_2,e5_7_1_3_1__tops_2]),
    [interesting(0.35),file(tops_2,c2_7_1_3_1__tops_2),[file(tops_2,c2_7_1_3_1__tops_2)]]).

fof(d8_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k7_setfam_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> r2_hidden(k3_subset_1(A,D),B) ) ) ) ) ) ),
    file(setfam_1,d8_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,d8_setfam_1)]).

fof(e6_7_1_3_1__tops_2,plain,(
    r2_hidden(k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_1_3_1__tops_2),c2_7__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1__tops_2,dt_c1_7_1_3_1__tops_2,dt_c2_7__tops_2,dt_c2_7_1_3_1__tops_2,de_c2_7_1_3_1__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e5_7_1__tops_2,e3_7_1_3_1__tops_2,d8_setfam_1]),
    [interesting(0.35),file(tops_2,e6_7_1_3_1__tops_2),[file(tops_2,e6_7_1_3_1__tops_2)]]).

fof(e6_7_1__tops_2,plain,(
    ! [A] : 
      ( r2_hidden(A,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( B = A
           => k1_funct_1(c1_7_1__tops_2,A) = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[dh_c1_7_1__tops_2,e4_7_1__tops_2]),
    [interesting(0.65),file(tops_2,e6_7_1__tops_2),[file(tops_2,e6_7_1__tops_2)]]).

fof(e4_7_1_3_1__tops_2,plain,(
    c1_7_1_3__tops_2 = k1_funct_1(c1_7_1__tops_2,c1_7_1_3_1__tops_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[dh_c1_7_1_3_1__tops_2,e2_7_1_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e4_7_1_3_1__tops_2),[file(tops_2,e4_7_1_3_1__tops_2)]]).

fof(e7_7_1_3_1__tops_2,plain,(
    r2_hidden(c1_7_1_3__tops_2,c2_7__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1__tops_2,dt_c1_7_1_3__tops_2,dt_c1_7_1_3_1__tops_2,dt_c2_7__tops_2,dt_c2_7_1_3_1__tops_2,de_c2_7_1_3_1__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e6_7_1_3_1__tops_2,e5_7_1__tops_2,e6_7_1__tops_2,e3_7_1_3_1__tops_2,e4_7_1_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e7_7_1_3_1__tops_2),[file(tops_2,e7_7_1_3_1__tops_2)]]).

fof(i2_7_1_3_1__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i2_7_1_3_1__tops_2)]),
    [interesting(0.35),trivial,file(tops_2,i2_7_1_3_1__tops_2)]).

fof(i1_7_1_3_1__tops_2,plain,(
    r2_hidden(c1_7_1_3__tops_2,c2_7__tops_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2,e1_7_1_3_1__tops_2])],[e7_7_1_3_1__tops_2,i2_7_1_3_1__tops_2]),
    [interesting(0.35),file(tops_2,i1_7_1_3_1__tops_2),[file(tops_2,i1_7_1_3_1__tops_2)]]).

fof(e1_7_1_3__tops_2,plain,
    ( r2_hidden(c1_7_1_3__tops_2,k2_relat_1(c1_7_1__tops_2))
   => r2_hidden(c1_7_1_3__tops_2,c2_7__tops_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_1_3__tops_2]),discharge_asm(discharge,[e1_7_1_3_1__tops_2])],[e1_7_1_3_1__tops_2,i1_7_1_3_1__tops_2]),
    [interesting(0.5),file(tops_2,e1_7_1_3__tops_2),[file(tops_2,e1_7_1_3__tops_2)]]).

fof(e2_7_1_3__tops_2,assumption,(
    r2_hidden(c1_7_1_3__tops_2,c2_7__tops_2) ),
    introduced(assumption,[file(tops_2,e2_7_1_3__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e2_7_1_3__tops_2)]).

fof(de_c2_7_1_3__tops_2,definition,(
    c2_7_1_3__tops_2 = c1_7_1_3__tops_2 ),
    introduced(definition,[new_symbol(c2_7_1_3__tops_2),file(tops_2,c2_7_1_3__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c2_7_1_3__tops_2)]).

fof(e3_7_1_3__tops_2,plain,(
    m1_subset_1(c1_7_1_3__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,e2_7_1_3__tops_2])],[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,t8_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e2_7_1_3__tops_2]),
    [interesting(0.5),file(tops_2,e3_7_1_3__tops_2),[file(tops_2,e3_7_1_3__tops_2)]]).

fof(dt_c2_7_1_3__tops_2,plain,(
    m1_subset_1(c2_7_1_3__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,e2_7_1_3__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,fc1_subset_1,t3_subset,de_c2_7_1_3__tops_2,e3_7_1_3__tops_2]),
    [interesting(0.5),file(tops_2,c2_7_1_3__tops_2),[file(tops_2,c2_7_1_3__tops_2)]]).

fof(e4_7_1_3__tops_2,plain,(
    k3_subset_1(u1_struct_0(c1_7__tops_2),k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_1_3__tops_2)) = c2_7_1_3__tops_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,e2_7_1_3__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,dt_c1_7_1_3__tops_2,fc1_subset_1,t3_subset,involutiveness_k3_subset_1,dt_k3_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c2_7_1_3__tops_2,de_c2_7_1_3__tops_2]),
    [interesting(0.5),file(tops_2,e4_7_1_3__tops_2),[file(tops_2,e4_7_1_3__tops_2)]]).

fof(e5_7_1_3__tops_2,plain,(
    r2_hidden(k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_1_3__tops_2),k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,e2_7_1_3__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,dt_c2_7_1_3__tops_2,de_c2_7_1_3__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e4_7_1_3__tops_2,e2_7_1_3__tops_2,d8_setfam_1]),
    [interesting(0.5),file(tops_2,e5_7_1_3__tops_2),[file(tops_2,e5_7_1_3__tops_2)]]).

fof(e7_7_1_3__tops_2,plain,(
    k1_funct_1(c1_7_1__tops_2,k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_1_3__tops_2)) = k3_subset_1(u1_struct_0(c1_7__tops_2),k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_1_3__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,e2_7_1_3__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,dt_c1_7_1_3__tops_2,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1__tops_2,dt_c2_7__tops_2,dt_c2_7_1_3__tops_2,de_c2_7_1_3__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e6_7_1__tops_2,e5_7_1_3__tops_2]),
    [interesting(0.5),file(tops_2,e7_7_1_3__tops_2),[file(tops_2,e7_7_1_3__tops_2)]]).

fof(e6_7_1_3__tops_2,plain,(
    r2_hidden(k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_1_3__tops_2),k1_relat_1(c1_7_1__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,e2_7_1_3__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,dt_c2_7_1_3__tops_2,de_c2_7_1_3__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e5_7_1__tops_2,e2_7_1_3__tops_2,e4_7_1_3__tops_2,d8_setfam_1]),
    [interesting(0.5),file(tops_2,e6_7_1_3__tops_2),[file(tops_2,e6_7_1_3__tops_2)]]).

fof(e8_7_1_3__tops_2,plain,(
    r2_hidden(c1_7_1_3__tops_2,k2_relat_1(c1_7_1__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,e2_7_1_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,involutiveness_k3_subset_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7_1_3__tops_2,de_c2_7_1_3__tops_2,t1_subset,t7_boole,e7_7_1_3__tops_2,e6_7_1_3__tops_2,d5_funct_1]),
    [interesting(0.5),file(tops_2,e8_7_1_3__tops_2),[file(tops_2,e8_7_1_3__tops_2)]]).

fof(i4_7_1_3__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i4_7_1_3__tops_2)]),
    [interesting(0.5),trivial,file(tops_2,i4_7_1_3__tops_2)]).

fof(i3_7_1_3__tops_2,plain,(
    r2_hidden(c1_7_1_3__tops_2,k2_relat_1(c1_7_1__tops_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2,e2_7_1_3__tops_2])],[e8_7_1_3__tops_2,i4_7_1_3__tops_2]),
    [interesting(0.5),file(tops_2,i3_7_1_3__tops_2),[file(tops_2,i3_7_1_3__tops_2)]]).

fof(i2_7_1_3__tops_2,plain,
    ( r2_hidden(c1_7_1_3__tops_2,c2_7__tops_2)
   => r2_hidden(c1_7_1_3__tops_2,k2_relat_1(c1_7_1__tops_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[e2_7_1_3__tops_2])],[e2_7_1_3__tops_2,i3_7_1_3__tops_2]),
    [interesting(0.5),file(tops_2,i2_7_1_3__tops_2),[file(tops_2,i2_7_1_3__tops_2)]]).

fof(i1_7_1_3__tops_2,plain,
    ( r2_hidden(c1_7_1_3__tops_2,k2_relat_1(c1_7_1__tops_2))
  <=> r2_hidden(c1_7_1_3__tops_2,c2_7__tops_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_1_3__tops_2,dt_c2_7__tops_2])],[e1_7_1_3__tops_2,i2_7_1_3__tops_2]),
    [interesting(0.5),file(tops_2,i1_7_1_3__tops_2),[file(tops_2,i1_7_1_3__tops_2)]]).

fof(i1_7_1_3_tmp__tops_2,plain,
    ( r2_hidden(c1_7_1_3__tops_2,k2_relat_1(c1_7_1__tops_2))
  <=> r2_hidden(c1_7_1_3__tops_2,c2_7__tops_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[dt_c1_7_1_3__tops_2])],[dt_c1_7_1_3__tops_2,i1_7_1_3__tops_2]),
    [interesting(0.65),e7_7_1__tops_2]).

fof(e7_7_1__tops_2,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_relat_1(c1_7_1__tops_2))
    <=> r2_hidden(A,c2_7__tops_2) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[i1_7_1_3_tmp__tops_2,dh_c1_7_1_3__tops_2]),
    [interesting(0.65),file(tops_2,e7_7_1__tops_2),[file(tops_2,e7_7_1__tops_2)]]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(e8_7_1__tops_2,plain,(
    k2_relat_1(c1_7_1__tops_2) = c2_7__tops_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[reflexivity_r1_tarski,existence_l1_struct_0,dt_k1_xboole_0,dt_l1_struct_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_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,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,dt_k2_relat_1,dt_c1_7_1__tops_2,dt_c2_7__tops_2,t1_subset,t7_boole,e7_7_1__tops_2,t2_tarski]),
    [interesting(0.65),file(tops_2,e8_7_1__tops_2),[file(tops_2,e8_7_1__tops_2)]]).

fof(t146_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ),
    file(relat_1,t146_relat_1),
    [interesting(0.9),axiom,file(relat_1,t146_relat_1)]).

fof(e9_7_1__tops_2,plain,(
    k9_relat_1(c1_7_1__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) = c2_7__tops_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,fc1_subset_1,t3_subset,involutiveness_k7_setfam_1,dt_k1_relat_1,dt_k2_relat_1,dt_k7_setfam_1,dt_k9_relat_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1__tops_2,dt_c2_7__tops_2,e8_7_1__tops_2,e5_7_1__tops_2,t146_relat_1]),
    [interesting(0.65),file(tops_2,e9_7_1__tops_2),[file(tops_2,e9_7_1__tops_2)]]).

fof(t17_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_finset_1(A)
       => v1_finset_1(k9_relat_1(B,A)) ) ) ),
    file(finset_1,t17_finset_1),
    [interesting(0.9),axiom,file(finset_1,t17_finset_1)]).

fof(e10_7_1__tops_2,plain,(
    v1_finset_1(c2_7__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,e1_7_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,fc1_subset_1,t3_subset,involutiveness_k7_setfam_1,dt_k7_setfam_1,dt_k9_relat_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_1__tops_2,dt_c2_7__tops_2,e9_7_1__tops_2,e1_7_1__tops_2,t17_finset_1]),
    [interesting(0.65),file(tops_2,e10_7_1__tops_2),[file(tops_2,e10_7_1__tops_2)]]).

fof(i2_7_1__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i2_7_1__tops_2)]),
    [interesting(0.65),trivial,file(tops_2,i2_7_1__tops_2)]).

fof(i1_7_1__tops_2,plain,(
    v1_finset_1(c2_7__tops_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,e1_7_1__tops_2])],[e10_7_1__tops_2,i2_7_1__tops_2]),
    [interesting(0.65),file(tops_2,i1_7_1__tops_2),[file(tops_2,i1_7_1__tops_2)]]).

fof(e1_7__tops_2,plain,
    ( v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
   => v1_finset_1(c2_7__tops_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[e1_7_1__tops_2])],[e1_7_1__tops_2,i1_7_1__tops_2]),
    [interesting(0.8),file(tops_2,e1_7__tops_2),[file(tops_2,e1_7__tops_2)]]).

fof(e1_7_2__tops_2,assumption,(
    v1_finset_1(c2_7__tops_2) ),
    introduced(assumption,[file(tops_2,e1_7_2__tops_2)]),
    [interesting(0.65),axiom,file(tops_2,e1_7_2__tops_2)]).

fof(dh_c1_7_2__tops_2,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = c2_7__tops_2
        & ! [B] : 
            ( r2_hidden(B,c2_7__tops_2)
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
               => ( C = B
                 => k1_funct_1(A,B) = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) ) )
   => ( v1_relat_1(c1_7_2__tops_2)
      & v1_funct_1(c1_7_2__tops_2)
      & k1_relat_1(c1_7_2__tops_2) = c2_7__tops_2
      & ! [D] : 
          ( r2_hidden(D,c2_7__tops_2)
         => ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( E = D
               => k1_funct_1(c1_7_2__tops_2,D) = k3_subset_1(u1_struct_0(c1_7__tops_2),E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_7_2__tops_2),file(tops_2,c1_7_2__tops_2)]),
    [interesting(0.65),axiom,file(tops_2,c1_7_2__tops_2)]).

fof(s2_funct_1__e4_7_2__tops_2,theorem,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
     => ( ( ! [C,D,E] : 
              ( ( r2_hidden(C,B)
                & ! [F] : 
                    ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                   => ( F = C
                     => D = k3_subset_1(u1_struct_0(A),F) ) )
                & ! [G] : 
                    ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                   => ( G = C
                     => E = k3_subset_1(u1_struct_0(A),G) ) ) )
             => D = E )
          & ! [C] : 
              ~ ( r2_hidden(C,B)
                & ! [D] : 
                    ~ ! [H] : 
                        ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                       => ( H = C
                         => D = k3_subset_1(u1_struct_0(A),H) ) ) ) )
       => ? [C] : 
            ( v1_relat_1(C)
            & v1_funct_1(C)
            & k1_relat_1(C) = B
            & ! [D] : 
                ( r2_hidden(D,B)
               => ! [I] : 
                    ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                   => ( I = D
                     => k1_funct_1(C,D) = k3_subset_1(u1_struct_0(A),I) ) ) ) ) ) ) ),
    file(tops_2,s2_funct_1__e4_7_2__tops_2),
    [interesting(0.9),axiom,file(tops_2,s2_funct_1__e4_7_2__tops_2)]).

fof(dh_c1_7_2_1__tops_2,definition,
    ( ! [A,B] : 
        ( ( r2_hidden(c1_7_2_1__tops_2,c2_7__tops_2)
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = c1_7_2_1__tops_2
               => A = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) )
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = c1_7_2_1__tops_2
               => B = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) )
       => A = B )
   => ! [D,E,F] : 
        ( ( r2_hidden(D,c2_7__tops_2)
          & ! [G] : 
              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( G = D
               => E = k3_subset_1(u1_struct_0(c1_7__tops_2),G) ) )
          & ! [G] : 
              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( G = D
               => F = k3_subset_1(u1_struct_0(c1_7__tops_2),G) ) ) )
       => E = F ) ),
    introduced(definition,[new_symbol(c1_7_2_1__tops_2),file(tops_2,c1_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_2_1__tops_2)]).

fof(dh_c2_7_2_1__tops_2,definition,
    ( ! [A] : 
        ( ( r2_hidden(c1_7_2_1__tops_2,c2_7__tops_2)
          & ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( B = c1_7_2_1__tops_2
               => c2_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) )
          & ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( B = c1_7_2_1__tops_2
               => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) )
       => c2_7_2_1__tops_2 = A )
   => ! [C,D] : 
        ( ( r2_hidden(c1_7_2_1__tops_2,c2_7__tops_2)
          & ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( E = c1_7_2_1__tops_2
               => C = k3_subset_1(u1_struct_0(c1_7__tops_2),E) ) )
          & ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( E = c1_7_2_1__tops_2
               => D = k3_subset_1(u1_struct_0(c1_7__tops_2),E) ) ) )
       => C = D ) ),
    introduced(definition,[new_symbol(c2_7_2_1__tops_2),file(tops_2,c2_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c2_7_2_1__tops_2)]).

fof(dh_c3_7_2_1__tops_2,definition,
    ( ( ( r2_hidden(c1_7_2_1__tops_2,c2_7__tops_2)
        & ! [A] : 
            ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
           => ( A = c1_7_2_1__tops_2
             => c2_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) )
        & ! [A] : 
            ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
           => ( A = c1_7_2_1__tops_2
             => c3_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) )
     => c2_7_2_1__tops_2 = c3_7_2_1__tops_2 )
   => ! [B] : 
        ( ( r2_hidden(c1_7_2_1__tops_2,c2_7__tops_2)
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = c1_7_2_1__tops_2
               => c2_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) )
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = c1_7_2_1__tops_2
               => B = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) )
       => c2_7_2_1__tops_2 = B ) ),
    introduced(definition,[new_symbol(c3_7_2_1__tops_2),file(tops_2,c3_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c3_7_2_1__tops_2)]).

fof(e1_7_2_1__tops_2,assumption,(
    r2_hidden(c1_7_2_1__tops_2,c2_7__tops_2) ),
    introduced(assumption,[file(tops_2,e1_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e1_7_2_1__tops_2)]).

fof(e2_7_2_1__tops_2,assumption,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( A = c1_7_2_1__tops_2
       => c2_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) ),
    introduced(assumption,[file(tops_2,e2_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e2_7_2_1__tops_2)]).

fof(e3_7_2_1__tops_2,assumption,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( A = c1_7_2_1__tops_2
       => c3_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) ),
    introduced(assumption,[file(tops_2,e3_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e3_7_2_1__tops_2)]).

fof(dt_c1_7_2_1__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c1_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_2_1__tops_2)]).

fof(dt_c2_7_2_1__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c2_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c2_7_2_1__tops_2)]).

fof(dt_c3_7_2_1__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c3_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c3_7_2_1__tops_2)]).

fof(de_c4_7_2_1__tops_2,definition,(
    c4_7_2_1__tops_2 = c1_7_2_1__tops_2 ),
    introduced(definition,[new_symbol(c4_7_2_1__tops_2),file(tops_2,c4_7_2_1__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c4_7_2_1__tops_2)]).

fof(e4_7_2_1__tops_2,plain,(
    m1_subset_1(c1_7_2_1__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7__tops_2,e1_7_2_1__tops_2])],[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,t8_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e1_7_2_1__tops_2]),
    [interesting(0.5),file(tops_2,e4_7_2_1__tops_2),[file(tops_2,e4_7_2_1__tops_2)]]).

fof(dt_c4_7_2_1__tops_2,plain,(
    m1_subset_1(c4_7_2_1__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7__tops_2,e1_7_2_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,fc1_subset_1,t3_subset,de_c4_7_2_1__tops_2,e4_7_2_1__tops_2]),
    [interesting(0.5),file(tops_2,c4_7_2_1__tops_2),[file(tops_2,c4_7_2_1__tops_2)]]).

fof(e5_7_2_1__tops_2,plain,(
    c2_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),c4_7_2_1__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7_2_1__tops_2,dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7__tops_2,e1_7_2_1__tops_2,e2_7_2_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7_2_1__tops_2,dt_c4_7_2_1__tops_2,de_c4_7_2_1__tops_2,fc1_subset_1,t3_subset,e2_7_2_1__tops_2]),
    [interesting(0.5),file(tops_2,e5_7_2_1__tops_2),[file(tops_2,e5_7_2_1__tops_2)]]).

fof(e6_7_2_1__tops_2,plain,(
    c2_7_2_1__tops_2 = c3_7_2_1__tops_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_7_2_1__tops_2,dt_c2_7_2_1__tops_2,dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7__tops_2,e1_7_2_1__tops_2,e2_7_2_1__tops_2,e3_7_2_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7_2_1__tops_2,dt_c3_7_2_1__tops_2,dt_c4_7_2_1__tops_2,de_c4_7_2_1__tops_2,fc1_subset_1,t3_subset,e5_7_2_1__tops_2,e3_7_2_1__tops_2]),
    [interesting(0.5),file(tops_2,e6_7_2_1__tops_2),[file(tops_2,e6_7_2_1__tops_2)]]).

fof(i3_7_2_1__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i3_7_2_1__tops_2)]),
    [interesting(0.5),trivial,file(tops_2,i3_7_2_1__tops_2)]).

fof(i2_7_2_1__tops_2,plain,(
    c2_7_2_1__tops_2 = c3_7_2_1__tops_2 ),
    inference(conclusion,[status(thm),assumptions([dt_c3_7_2_1__tops_2,dt_c2_7_2_1__tops_2,dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7__tops_2,e1_7_2_1__tops_2,e2_7_2_1__tops_2,e3_7_2_1__tops_2])],[e6_7_2_1__tops_2,i3_7_2_1__tops_2]),
    [interesting(0.5),file(tops_2,i2_7_2_1__tops_2),[file(tops_2,i2_7_2_1__tops_2)]]).

fof(i1_7_2_1__tops_2,plain,
    ( ( r2_hidden(c1_7_2_1__tops_2,c2_7__tops_2)
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( A = c1_7_2_1__tops_2
           => c2_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) )
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( A = c1_7_2_1__tops_2
           => c3_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) )
   => c2_7_2_1__tops_2 = c3_7_2_1__tops_2 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_7_2_1__tops_2,dt_c2_7_2_1__tops_2,dt_c1_7__tops_2,dt_c1_7_2_1__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[e1_7_2_1__tops_2,e2_7_2_1__tops_2,e3_7_2_1__tops_2])],[e1_7_2_1__tops_2,e2_7_2_1__tops_2,e3_7_2_1__tops_2,i2_7_2_1__tops_2]),
    [interesting(0.5),file(tops_2,i1_7_2_1__tops_2),[file(tops_2,i1_7_2_1__tops_2)]]).

fof(i1_7_2_1_tmp__tops_2,plain,
    ( ( r2_hidden(c1_7_2_1__tops_2,c2_7__tops_2)
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( A = c1_7_2_1__tops_2
           => c2_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) )
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( A = c1_7_2_1__tops_2
           => c3_7_2_1__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) )
   => c2_7_2_1__tops_2 = c3_7_2_1__tops_2 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[dt_c1_7_2_1__tops_2,dt_c2_7_2_1__tops_2,dt_c3_7_2_1__tops_2])],[dt_c1_7_2_1__tops_2,dt_c2_7_2_1__tops_2,dt_c3_7_2_1__tops_2,i1_7_2_1__tops_2]),
    [interesting(0.65),e2_7_2__tops_2]).

fof(e2_7_2__tops_2,plain,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,c2_7__tops_2)
        & ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
           => ( D = A
             => B = k3_subset_1(u1_struct_0(c1_7__tops_2),D) ) )
        & ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
           => ( D = A
             => C = k3_subset_1(u1_struct_0(c1_7__tops_2),D) ) ) )
     => B = C ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[i1_7_2_1_tmp__tops_2,dh_c1_7_2_1__tops_2,dh_c2_7_2_1__tops_2,dh_c3_7_2_1__tops_2]),
    [interesting(0.65),file(tops_2,e2_7_2__tops_2),[file(tops_2,e2_7_2__tops_2)]]).

fof(dh_c1_7_2_2__tops_2,definition,
    ( ~ ( r2_hidden(c1_7_2_2__tops_2,c2_7__tops_2)
        & ! [A] : 
            ~ ! [B] : 
                ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
               => ( B = c1_7_2_2__tops_2
                 => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) )
   => ! [C] : 
        ~ ( r2_hidden(C,c2_7__tops_2)
          & ! [D] : 
              ~ ! [E] : 
                  ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
                 => ( E = C
                   => D = k3_subset_1(u1_struct_0(c1_7__tops_2),E) ) ) ) ),
    introduced(definition,[new_symbol(c1_7_2_2__tops_2),file(tops_2,c1_7_2_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_2_2__tops_2)]).

fof(e1_7_2_2__tops_2,assumption,(
    r2_hidden(c1_7_2_2__tops_2,c2_7__tops_2) ),
    introduced(assumption,[file(tops_2,e1_7_2_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e1_7_2_2__tops_2)]).

fof(dt_c1_7_2_2__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c1_7_2_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_2_2__tops_2)]).

fof(de_c2_7_2_2__tops_2,definition,(
    c2_7_2_2__tops_2 = c1_7_2_2__tops_2 ),
    introduced(definition,[new_symbol(c2_7_2_2__tops_2),file(tops_2,c2_7_2_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c2_7_2_2__tops_2)]).

fof(e2_7_2_2__tops_2,plain,(
    m1_subset_1(c1_7_2_2__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2,e1_7_2_2__tops_2])],[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,t8_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e1_7_2_2__tops_2]),
    [interesting(0.5),file(tops_2,e2_7_2_2__tops_2),[file(tops_2,e2_7_2_2__tops_2)]]).

fof(dt_c2_7_2_2__tops_2,plain,(
    m1_subset_1(c2_7_2_2__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2,e1_7_2_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,fc1_subset_1,t3_subset,de_c2_7_2_2__tops_2,e2_7_2_2__tops_2]),
    [interesting(0.5),file(tops_2,c2_7_2_2__tops_2),[file(tops_2,c2_7_2_2__tops_2)]]).

fof(de_c3_7_2_2__tops_2,definition,(
    c3_7_2_2__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_2_2__tops_2) ),
    introduced(definition,[new_symbol(c3_7_2_2__tops_2),file(tops_2,c3_7_2_2__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c3_7_2_2__tops_2)]).

fof(e3_7_2_2__tops_2,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2,e1_7_2_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,dt_c1_7_2_2__tops_2,fc1_subset_1,t3_subset,involutiveness_k3_subset_1,dt_k3_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c2_7_2_2__tops_2,de_c2_7_2_2__tops_2]),
    [interesting(0.5),file(tops_2,e3_7_2_2__tops_2),[file(tops_2,e3_7_2_2__tops_2)]]).

fof(dt_c3_7_2_2__tops_2,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2,e1_7_2_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,dt_c1_7_2_2__tops_2,fc1_subset_1,t3_subset,involutiveness_k3_subset_1,dt_k3_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c2_7_2_2__tops_2,de_c2_7_2_2__tops_2,de_c3_7_2_2__tops_2,e3_7_2_2__tops_2]),
    [interesting(0.5),file(tops_2,c3_7_2_2__tops_2),[file(tops_2,c3_7_2_2__tops_2)]]).

fof(e4_7_2_2__tops_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( A = c1_7_2_2__tops_2
       => c3_7_2_2__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2,e1_7_2_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,dt_c2_7_2_2__tops_2,de_c2_7_2_2__tops_2,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c3_7_2_2__tops_2,de_c3_7_2_2__tops_2,fc1_subset_1,t3_subset]),
    [interesting(0.5),file(tops_2,e4_7_2_2__tops_2),[file(tops_2,e4_7_2_2__tops_2)]]).

fof(i4_7_2_2__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i4_7_2_2__tops_2)]),
    [interesting(0.5),trivial,file(tops_2,i4_7_2_2__tops_2)]).

fof(i3_7_2_2__tops_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( A = c1_7_2_2__tops_2
       => c3_7_2_2__tops_2 = k3_subset_1(u1_struct_0(c1_7__tops_2),A) ) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2,e1_7_2_2__tops_2])],[e4_7_2_2__tops_2,i4_7_2_2__tops_2]),
    [interesting(0.5),file(tops_2,i3_7_2_2__tops_2),[file(tops_2,i3_7_2_2__tops_2)]]).

fof(i2_7_2_2__tops_2,plain,(
    ? [A] : 
    ! [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
     => ( B = c1_7_2_2__tops_2
       => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) ),
    inference(take,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2,e1_7_2_2__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,rc1_membered,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,involutiveness_k3_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c3_7_2_2__tops_2,fc1_subset_1,i3_7_2_2__tops_2]),
    [interesting(0.5),file(tops_2,i2_7_2_2__tops_2),[file(tops_2,i2_7_2_2__tops_2)]]).

fof(i1_7_2_2__tops_2,plain,(
    ~ ( r2_hidden(c1_7_2_2__tops_2,c2_7__tops_2)
      & ! [A] : 
          ~ ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( B = c1_7_2_2__tops_2
               => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_2__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[e1_7_2_2__tops_2])],[e1_7_2_2__tops_2,i2_7_2_2__tops_2]),
    [interesting(0.5),file(tops_2,i1_7_2_2__tops_2),[file(tops_2,i1_7_2_2__tops_2)]]).

fof(i1_7_2_2_tmp__tops_2,plain,(
    ~ ( r2_hidden(c1_7_2_2__tops_2,c2_7__tops_2)
      & ! [A] : 
          ~ ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( B = c1_7_2_2__tops_2
               => A = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[dt_c1_7_2_2__tops_2])],[dt_c1_7_2_2__tops_2,i1_7_2_2__tops_2]),
    [interesting(0.65),e3_7_2__tops_2]).

fof(e3_7_2__tops_2,plain,(
    ! [A] : 
      ~ ( r2_hidden(A,c2_7__tops_2)
        & ! [B] : 
            ~ ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
               => ( C = A
                 => B = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[i1_7_2_2_tmp__tops_2,dh_c1_7_2_2__tops_2]),
    [interesting(0.65),file(tops_2,e3_7_2__tops_2),[file(tops_2,e3_7_2__tops_2)]]).

fof(e4_7_2__tops_2,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = c2_7__tops_2
      & ! [B] : 
          ( r2_hidden(B,c2_7__tops_2)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
             => ( C = B
               => k1_funct_1(A,B) = k3_subset_1(u1_struct_0(c1_7__tops_2),C) ) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__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,rc1_membered,cc15_membered,rc1_subset_1,rc2_subset_1,involutiveness_k3_subset_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c2_7__tops_2,fc1_subset_1,s2_funct_1__e4_7_2__tops_2,e2_7_2__tops_2,e3_7_2__tops_2]),
    [interesting(0.65),file(tops_2,e4_7_2__tops_2),[file(tops_2,e4_7_2__tops_2)]]).

fof(dt_c1_7_2__tops_2,plain,
    ( v1_relat_1(c1_7_2__tops_2)
    & v1_funct_1(c1_7_2__tops_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[dh_c1_7_2__tops_2,e4_7_2__tops_2]),
    [interesting(0.65),file(tops_2,c1_7_2__tops_2),[file(tops_2,c1_7_2__tops_2)]]).

fof(dh_c1_7_2_3__tops_2,definition,
    ( ( r2_hidden(c1_7_2_3__tops_2,k2_relat_1(c1_7_2__tops_2))
    <=> r2_hidden(c1_7_2_3__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) )
   => ! [A] : 
        ( r2_hidden(A,k2_relat_1(c1_7_2__tops_2))
      <=> r2_hidden(A,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ) ),
    introduced(definition,[new_symbol(c1_7_2_3__tops_2),file(tops_2,c1_7_2_3__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_2_3__tops_2)]).

fof(e1_7_2_3_1__tops_2,assumption,(
    r2_hidden(c1_7_2_3__tops_2,k2_relat_1(c1_7_2__tops_2)) ),
    introduced(assumption,[file(tops_2,e1_7_2_3_1__tops_2)]),
    [interesting(0.35),axiom,file(tops_2,e1_7_2_3_1__tops_2)]).

fof(dt_c1_7_2_3__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c1_7_2_3__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c1_7_2_3__tops_2)]).

fof(dh_c1_7_2_3_1__tops_2,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_7_2__tops_2))
        & c1_7_2_3__tops_2 = k1_funct_1(c1_7_2__tops_2,A) )
   => ( r2_hidden(c1_7_2_3_1__tops_2,k1_relat_1(c1_7_2__tops_2))
      & c1_7_2_3__tops_2 = k1_funct_1(c1_7_2__tops_2,c1_7_2_3_1__tops_2) ) ),
    introduced(definition,[new_symbol(c1_7_2_3_1__tops_2),file(tops_2,c1_7_2_3_1__tops_2)]),
    [interesting(0.35),axiom,file(tops_2,c1_7_2_3_1__tops_2)]).

fof(e2_7_2_3_1__tops_2,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_7_2__tops_2))
      & c1_7_2_3__tops_2 = k1_funct_1(c1_7_2__tops_2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_7_2__tops_2,dt_c1_7_2_3__tops_2,t1_subset,t7_boole,e1_7_2_3_1__tops_2,d5_funct_1]),
    [interesting(0.35),file(tops_2,e2_7_2_3_1__tops_2),[file(tops_2,e2_7_2_3_1__tops_2)]]).

fof(dt_c1_7_2_3_1__tops_2,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[dh_c1_7_2_3_1__tops_2,e2_7_2_3_1__tops_2]),
    [interesting(0.35),file(tops_2,c1_7_2_3_1__tops_2),[file(tops_2,c1_7_2_3_1__tops_2)]]).

fof(de_c2_7_2_3_1__tops_2,definition,(
    c2_7_2_3_1__tops_2 = c1_7_2_3_1__tops_2 ),
    introduced(definition,[new_symbol(c2_7_2_3_1__tops_2),file(tops_2,c2_7_2_3_1__tops_2)]),
    [interesting(0.35),axiom,file(tops_2,c2_7_2_3_1__tops_2)]).

fof(e5_7_2__tops_2,plain,(
    k1_relat_1(c1_7_2__tops_2) = c2_7__tops_2 ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[dh_c1_7_2__tops_2,e4_7_2__tops_2]),
    [interesting(0.65),file(tops_2,e5_7_2__tops_2),[file(tops_2,e5_7_2__tops_2)]]).

fof(e3_7_2_3_1__tops_2,plain,(
    r2_hidden(c1_7_2_3_1__tops_2,k1_relat_1(c1_7_2__tops_2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[dh_c1_7_2_3_1__tops_2,e2_7_2_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e3_7_2_3_1__tops_2),[file(tops_2,e3_7_2_3_1__tops_2)]]).

fof(e5_7_2_3_1__tops_2,plain,(
    m1_subset_1(c1_7_2_3_1__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c1_7_2_3_1__tops_2,dt_c2_7__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e5_7_2__tops_2,e3_7_2_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e5_7_2_3_1__tops_2),[file(tops_2,e5_7_2_3_1__tops_2)]]).

fof(dt_c2_7_2_3_1__tops_2,plain,(
    m1_subset_1(c2_7_2_3_1__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_3_1__tops_2,fc1_subset_1,t3_subset,de_c2_7_2_3_1__tops_2,e5_7_2_3_1__tops_2]),
    [interesting(0.35),file(tops_2,c2_7_2_3_1__tops_2),[file(tops_2,c2_7_2_3_1__tops_2)]]).

fof(e6_7_2_3_1__tops_2,plain,
    ( r2_hidden(c2_7_2_3_1__tops_2,c2_7__tops_2)
    & k3_subset_1(u1_struct_0(c1_7__tops_2),k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_2_3_1__tops_2)) = c2_7_2_3_1__tops_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__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,involutiveness_k3_subset_1,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k3_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c1_7_2_3_1__tops_2,dt_c2_7__tops_2,dt_c2_7_2_3_1__tops_2,de_c2_7_2_3_1__tops_2,t1_subset,t7_boole,e5_7_2__tops_2,e3_7_2_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e6_7_2_3_1__tops_2),[file(tops_2,e6_7_2_3_1__tops_2)]]).

fof(e7_7_2_3_1__tops_2,plain,(
    r2_hidden(k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_2_3_1__tops_2),k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,dt_c1_7_2_3_1__tops_2,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c2_7_2_3_1__tops_2,de_c2_7_2_3_1__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e6_7_2_3_1__tops_2,d8_setfam_1]),
    [interesting(0.35),file(tops_2,e7_7_2_3_1__tops_2),[file(tops_2,e7_7_2_3_1__tops_2)]]).

fof(e6_7_2__tops_2,plain,(
    ! [A] : 
      ( r2_hidden(A,c2_7__tops_2)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__tops_2)))
         => ( B = A
           => k1_funct_1(c1_7_2__tops_2,A) = k3_subset_1(u1_struct_0(c1_7__tops_2),B) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[dh_c1_7_2__tops_2,e4_7_2__tops_2]),
    [interesting(0.65),file(tops_2,e6_7_2__tops_2),[file(tops_2,e6_7_2__tops_2)]]).

fof(e4_7_2_3_1__tops_2,plain,(
    c1_7_2_3__tops_2 = k1_funct_1(c1_7_2__tops_2,c1_7_2_3_1__tops_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[dh_c1_7_2_3_1__tops_2,e2_7_2_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e4_7_2_3_1__tops_2),[file(tops_2,e4_7_2_3_1__tops_2)]]).

fof(e8_7_2_3_1__tops_2,plain,(
    r2_hidden(c1_7_2_3__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c1_7_2_3__tops_2,dt_c1_7_2_3_1__tops_2,dt_c2_7__tops_2,dt_c2_7_2_3_1__tops_2,de_c2_7_2_3_1__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e7_7_2_3_1__tops_2,e5_7_2__tops_2,e6_7_2__tops_2,e3_7_2_3_1__tops_2,e4_7_2_3_1__tops_2]),
    [interesting(0.35),file(tops_2,e8_7_2_3_1__tops_2),[file(tops_2,e8_7_2_3_1__tops_2)]]).

fof(i2_7_2_3_1__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i2_7_2_3_1__tops_2)]),
    [interesting(0.35),trivial,file(tops_2,i2_7_2_3_1__tops_2)]).

fof(i1_7_2_3_1__tops_2,plain,(
    r2_hidden(c1_7_2_3__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2,e1_7_2_3_1__tops_2])],[e8_7_2_3_1__tops_2,i2_7_2_3_1__tops_2]),
    [interesting(0.35),file(tops_2,i1_7_2_3_1__tops_2),[file(tops_2,i1_7_2_3_1__tops_2)]]).

fof(e1_7_2_3__tops_2,plain,
    ( r2_hidden(c1_7_2_3__tops_2,k2_relat_1(c1_7_2__tops_2))
   => r2_hidden(c1_7_2_3__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,dt_c1_7_2_3__tops_2]),discharge_asm(discharge,[e1_7_2_3_1__tops_2])],[e1_7_2_3_1__tops_2,i1_7_2_3_1__tops_2]),
    [interesting(0.5),file(tops_2,e1_7_2_3__tops_2),[file(tops_2,e1_7_2_3__tops_2)]]).

fof(e2_7_2_3__tops_2,assumption,(
    r2_hidden(c1_7_2_3__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    introduced(assumption,[file(tops_2,e2_7_2_3__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,e2_7_2_3__tops_2)]).

fof(de_c2_7_2_3__tops_2,definition,(
    c2_7_2_3__tops_2 = c1_7_2_3__tops_2 ),
    introduced(definition,[new_symbol(c2_7_2_3__tops_2),file(tops_2,c2_7_2_3__tops_2)]),
    [interesting(0.5),axiom,file(tops_2,c2_7_2_3__tops_2)]).

fof(e3_7_2_3__tops_2,plain,(
    m1_subset_1(c1_7_2_3__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_3__tops_2,dt_c2_7__tops_2,e2_7_2_3__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_3__tops_2,dt_c2_7__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e2_7_2_3__tops_2]),
    [interesting(0.5),file(tops_2,e3_7_2_3__tops_2),[file(tops_2,e3_7_2_3__tops_2)]]).

fof(dt_c2_7_2_3__tops_2,plain,(
    m1_subset_1(c2_7_2_3__tops_2,k1_zfmisc_1(u1_struct_0(c1_7__tops_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_3__tops_2,dt_c2_7__tops_2,e2_7_2_3__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_3__tops_2,fc1_subset_1,t3_subset,de_c2_7_2_3__tops_2,e3_7_2_3__tops_2]),
    [interesting(0.5),file(tops_2,c2_7_2_3__tops_2),[file(tops_2,c2_7_2_3__tops_2)]]).

fof(e4_7_2_3__tops_2,plain,(
    r2_hidden(k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_2_3__tops_2),c2_7__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_3__tops_2,dt_c2_7__tops_2,e2_7_2_3__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2_3__tops_2,dt_c2_7__tops_2,dt_c2_7_2_3__tops_2,de_c2_7_2_3__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e2_7_2_3__tops_2,d8_setfam_1]),
    [interesting(0.5),file(tops_2,e4_7_2_3__tops_2),[file(tops_2,e4_7_2_3__tops_2)]]).

fof(e6_7_2_3__tops_2,plain,(
    k1_funct_1(c1_7_2__tops_2,k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_2_3__tops_2)) = k3_subset_1(u1_struct_0(c1_7__tops_2),k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_2_3__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c1_7_2_3__tops_2,dt_c2_7__tops_2,e2_7_2_3__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,dt_c1_7_2_3__tops_2,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c2_7__tops_2,dt_c2_7_2_3__tops_2,de_c2_7_2_3__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e6_7_2__tops_2,e4_7_2_3__tops_2]),
    [interesting(0.5),file(tops_2,e6_7_2_3__tops_2),[file(tops_2,e6_7_2_3__tops_2)]]).

fof(e5_7_2_3__tops_2,plain,(
    r2_hidden(k3_subset_1(u1_struct_0(c1_7__tops_2),c2_7_2_3__tops_2),k1_relat_1(c1_7_2__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7_2_3__tops_2,dt_c1_7__tops_2,dt_c2_7__tops_2,e2_7_2_3__tops_2])],[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,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c1_7_2_3__tops_2,dt_c2_7__tops_2,dt_c2_7_2_3__tops_2,de_c2_7_2_3__tops_2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e5_7_2__tops_2,e2_7_2_3__tops_2,d8_setfam_1]),
    [interesting(0.5),file(tops_2,e5_7_2_3__tops_2),[file(tops_2,e5_7_2_3__tops_2)]]).

fof(e7_7_2_3__tops_2,plain,(
    r2_hidden(c1_7_2_3__tops_2,k2_relat_1(c1_7_2__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7_2_3__tops_2,dt_c1_7__tops_2,dt_c2_7__tops_2,e2_7_2_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,involutiveness_k3_subset_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_subset_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c1_7_2_3__tops_2,dt_c2_7_2_3__tops_2,de_c2_7_2_3__tops_2,t1_subset,t7_boole,e6_7_2_3__tops_2,e5_7_2_3__tops_2,d5_funct_1]),
    [interesting(0.5),file(tops_2,e7_7_2_3__tops_2),[file(tops_2,e7_7_2_3__tops_2)]]).

fof(i4_7_2_3__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i4_7_2_3__tops_2)]),
    [interesting(0.5),trivial,file(tops_2,i4_7_2_3__tops_2)]).

fof(i3_7_2_3__tops_2,plain,(
    r2_hidden(c1_7_2_3__tops_2,k2_relat_1(c1_7_2__tops_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7_2_3__tops_2,dt_c1_7__tops_2,dt_c2_7__tops_2,e2_7_2_3__tops_2])],[e7_7_2_3__tops_2,i4_7_2_3__tops_2]),
    [interesting(0.5),file(tops_2,i3_7_2_3__tops_2),[file(tops_2,i3_7_2_3__tops_2)]]).

fof(i2_7_2_3__tops_2,plain,
    ( r2_hidden(c1_7_2_3__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
   => r2_hidden(c1_7_2_3__tops_2,k2_relat_1(c1_7_2__tops_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7_2_3__tops_2,dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[e2_7_2_3__tops_2])],[e2_7_2_3__tops_2,i3_7_2_3__tops_2]),
    [interesting(0.5),file(tops_2,i2_7_2_3__tops_2),[file(tops_2,i2_7_2_3__tops_2)]]).

fof(i1_7_2_3__tops_2,plain,
    ( r2_hidden(c1_7_2_3__tops_2,k2_relat_1(c1_7_2__tops_2))
  <=> r2_hidden(c1_7_2_3__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7_2_3__tops_2,dt_c1_7__tops_2,dt_c2_7__tops_2])],[e1_7_2_3__tops_2,i2_7_2_3__tops_2]),
    [interesting(0.5),file(tops_2,i1_7_2_3__tops_2),[file(tops_2,i1_7_2_3__tops_2)]]).

fof(i1_7_2_3_tmp__tops_2,plain,
    ( r2_hidden(c1_7_2_3__tops_2,k2_relat_1(c1_7_2__tops_2))
  <=> r2_hidden(c1_7_2_3__tops_2,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[dt_c1_7_2_3__tops_2])],[dt_c1_7_2_3__tops_2,i1_7_2_3__tops_2]),
    [interesting(0.65),e7_7_2__tops_2]).

fof(e7_7_2__tops_2,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_relat_1(c1_7_2__tops_2))
    <=> r2_hidden(A,k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[i1_7_2_3_tmp__tops_2,dh_c1_7_2_3__tops_2]),
    [interesting(0.65),file(tops_2,e7_7_2__tops_2),[file(tops_2,e7_7_2__tops_2)]]).

fof(e8_7_2__tops_2,plain,(
    k2_relat_1(c1_7_2__tops_2) = k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__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,involutiveness_k7_setfam_1,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k7_setfam_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c2_7__tops_2,t1_subset,t7_boole,e7_7_2__tops_2,t2_tarski]),
    [interesting(0.65),file(tops_2,e8_7_2__tops_2),[file(tops_2,e8_7_2__tops_2)]]).

fof(e9_7_2__tops_2,plain,(
    k9_relat_1(c1_7_2__tops_2,c2_7__tops_2) = k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,fc1_subset_1,t3_subset,involutiveness_k7_setfam_1,dt_k1_relat_1,dt_k2_relat_1,dt_k7_setfam_1,dt_k9_relat_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c2_7__tops_2,e8_7_2__tops_2,e5_7_2__tops_2,t146_relat_1]),
    [interesting(0.65),file(tops_2,e9_7_2__tops_2),[file(tops_2,e9_7_2__tops_2)]]).

fof(e10_7_2__tops_2,plain,(
    v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,e1_7_2__tops_2])],[antisymmetry_r2_hidden,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,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,fc1_subset_1,t3_subset,involutiveness_k7_setfam_1,dt_k7_setfam_1,dt_k9_relat_1,dt_u1_struct_0,dt_c1_7__tops_2,dt_c1_7_2__tops_2,dt_c2_7__tops_2,e9_7_2__tops_2,e1_7_2__tops_2,t17_finset_1]),
    [interesting(0.65),file(tops_2,e10_7_2__tops_2),[file(tops_2,e10_7_2__tops_2)]]).

fof(i2_7_2__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i2_7_2__tops_2)]),
    [interesting(0.65),trivial,file(tops_2,i2_7_2__tops_2)]).

fof(i1_7_2__tops_2,plain,(
    v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2,e1_7_2__tops_2])],[e10_7_2__tops_2,i2_7_2__tops_2]),
    [interesting(0.65),file(tops_2,i1_7_2__tops_2),[file(tops_2,i1_7_2__tops_2)]]).

fof(e2_7__tops_2,plain,
    ( v1_finset_1(c2_7__tops_2)
   => v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2]),discharge_asm(discharge,[e1_7_2__tops_2])],[e1_7_2__tops_2,i1_7_2__tops_2]),
    [interesting(0.8),file(tops_2,e2_7__tops_2),[file(tops_2,e2_7__tops_2)]]).

fof(i4_7__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i4_7__tops_2)]),
    [interesting(0.8),trivial,file(tops_2,i4_7__tops_2)]).

fof(i3_7__tops_2,plain,
    ( v1_finset_1(c2_7__tops_2)
   => v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[e2_7__tops_2,i4_7__tops_2]),
    [interesting(0.8),file(tops_2,i3_7__tops_2),[file(tops_2,i3_7__tops_2)]]).

fof(i2_7__tops_2,plain,
    ( v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
  <=> v1_finset_1(c2_7__tops_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__tops_2,dt_c2_7__tops_2])],[e1_7__tops_2,i3_7__tops_2]),
    [interesting(0.8),file(tops_2,i2_7__tops_2),[file(tops_2,i2_7__tops_2)]]).

fof(i2_7_tmp__tops_2,plain,
    ( m1_subset_1(c2_7__tops_2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_7__tops_2))))
   => ( v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),c2_7__tops_2))
    <=> v1_finset_1(c2_7__tops_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__tops_2]),discharge_asm(discharge,[dt_c2_7__tops_2])],[dt_c2_7__tops_2,i2_7__tops_2]),
    [interesting(0.8),i1_7__tops_2]).

fof(i1_7__tops_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_7__tops_2))))
     => ( v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),A))
      <=> v1_finset_1(A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__tops_2])],[i2_7_tmp__tops_2,dh_c2_7__tops_2]),
    [interesting(0.8),file(tops_2,i1_7__tops_2),[file(tops_2,i1_7__tops_2)]]).

fof(i1_7_tmp__tops_2,plain,
    ( l1_struct_0(c1_7__tops_2)
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(c1_7__tops_2))))
       => ( v1_finset_1(k7_setfam_1(u1_struct_0(c1_7__tops_2),A))
        <=> v1_finset_1(A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__tops_2])],[dt_c1_7__tops_2,i1_7__tops_2]),
    [interesting(1),t13_tops_2]).

fof(t13_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_finset_1(k7_setfam_1(u1_struct_0(A),B))
          <=> v1_finset_1(B) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__tops_2,dh_c1_7__tops_2]),
    [interesting(1),file(tops_2,t13_tops_2),[file(tops_2,t13_tops_2)]]).