% Mizar ND problem: t11_tops_2,tops_2,106,45 
fof(dh_c1_5__tops_2,definition,
    ( ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_5__tops_2)))
       => ( A != k1_xboole_0
         => k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,A)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,A)) ) )
   => ! [B,C] : 
        ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B)))
       => ( C != k1_xboole_0
         => k6_setfam_1(B,k7_setfam_1(B,C)) = k3_subset_1(B,k5_setfam_1(B,C)) ) ) ),
    introduced(definition,[new_symbol(c1_5__tops_2),file(tops_2,c1_5__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c1_5__tops_2)]).

fof(dh_c2_5__tops_2,definition,
    ( ( m1_subset_1(c2_5__tops_2,k1_zfmisc_1(k1_zfmisc_1(c1_5__tops_2)))
     => ( c2_5__tops_2 != k1_xboole_0
       => k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,c2_5__tops_2)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,c2_5__tops_2)) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_5__tops_2)))
       => ( A != k1_xboole_0
         => k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,A)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,A)) ) ) ),
    introduced(definition,[new_symbol(c2_5__tops_2),file(tops_2,c2_5__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c2_5__tops_2)]).

fof(e1_5__tops_2,assumption,(
    c2_5__tops_2 != k1_xboole_0 ),
    introduced(assumption,[file(tops_2,e1_5__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,e1_5__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(fc37_membered,theorem,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k4_xboole_0(A,B)) ) ),
    file(membered,fc37_membered),
    [interesting(0.9),axiom,file(membered,fc37_membered)]).

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

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

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

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

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

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

fof(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(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k1_setfam_1)]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_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(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(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(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(redefinition_k5_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(redefinition_k6_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_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_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_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

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

fof(dt_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_c1_5__tops_2,assumption,(
    $true ),
    introduced(assumption,[file(tops_2,c1_5__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c1_5__tops_2)]).

fof(dt_c2_5__tops_2,assumption,(
    m1_subset_1(c2_5__tops_2,k1_zfmisc_1(k1_zfmisc_1(c1_5__tops_2))) ),
    introduced(assumption,[file(tops_2,c2_5__tops_2)]),
    [interesting(0.8),axiom,file(tops_2,c2_5__tops_2)]).

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

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

fof(dt_k2_subset_1,axiom,(
    ! [A] : m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A)) ),
    file(subset_1,k2_subset_1),
    [interesting(0.9),axiom,file(subset_1,k2_subset_1)]).

fof(dt_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    [interesting(0.9),axiom,file(subset_1,k6_subset_1)]).

fof(t47_setfam_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( B != k1_xboole_0
       => k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B)) = k6_setfam_1(A,k7_setfam_1(A,B)) ) ) ),
    file(setfam_1,t47_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,t47_setfam_1)]).

fof(e2_5__tops_2,plain,(
    k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,c2_5__tops_2)) = k6_subset_1(c1_5__tops_2,k2_subset_1(c1_5__tops_2),k5_setfam_1(c1_5__tops_2,c2_5__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__tops_2,dt_c2_5__tops_2,e1_5__tops_2])],[antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,dt_k1_setfam_1,dt_k3_tarski,dt_k4_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_boole,t4_boole,t7_boole,t8_boole,involutiveness_k7_setfam_1,existence_m1_subset_1,redefinition_k5_setfam_1,redefinition_k6_setfam_1,redefinition_k6_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_subset_1,dt_k5_setfam_1,dt_k6_setfam_1,dt_k6_subset_1,dt_k7_setfam_1,dt_m1_subset_1,dt_c1_5__tops_2,dt_c2_5__tops_2,fc1_subset_1,fc6_membered,t3_subset,t6_boole,e1_5__tops_2,t47_setfam_1]),
    [interesting(0.8),file(tops_2,e2_5__tops_2),[file(tops_2,e2_5__tops_2)]]).

fof(d4_subset_1,definition,(
    ! [A] : k2_subset_1(A) = A ),
    file(subset_1,d4_subset_1),
    [interesting(0.9),axiom,file(subset_1,d4_subset_1)]).

fof(e3_5__tops_2,plain,(
    k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,c2_5__tops_2)) = k4_xboole_0(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,c2_5__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__tops_2,dt_c2_5__tops_2,e1_5__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,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,rc1_membered,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_setfam_1,dt_k1_zfmisc_1,dt_k3_tarski,dt_m1_subset_1,fc1_subset_1,t3_subset,involutiveness_k7_setfam_1,redefinition_k5_setfam_1,redefinition_k6_setfam_1,redefinition_k6_subset_1,dt_k2_subset_1,dt_k4_xboole_0,dt_k5_setfam_1,dt_k6_setfam_1,dt_k6_subset_1,dt_k7_setfam_1,dt_c1_5__tops_2,dt_c2_5__tops_2,e2_5__tops_2,d4_subset_1]),
    [interesting(0.8),file(tops_2,e3_5__tops_2),[file(tops_2,e3_5__tops_2)]]).

fof(d5_subset_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,B) = k4_xboole_0(A,B) ) ),
    file(subset_1,d5_subset_1),
    [interesting(0.9),axiom,file(subset_1,d5_subset_1)]).

fof(e4_5__tops_2,plain,(
    k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,c2_5__tops_2)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,c2_5__tops_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__tops_2,dt_c2_5__tops_2,e1_5__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,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,rc1_membered,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,reflexivity_r1_tarski,dt_k1_setfam_1,dt_k3_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,existence_m1_subset_1,redefinition_k5_setfam_1,redefinition_k6_setfam_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k4_xboole_0,dt_k5_setfam_1,dt_k6_setfam_1,dt_k7_setfam_1,dt_m1_subset_1,dt_c1_5__tops_2,dt_c2_5__tops_2,fc1_subset_1,t3_subset,e3_5__tops_2,d5_subset_1]),
    [interesting(0.8),file(tops_2,e4_5__tops_2),[file(tops_2,e4_5__tops_2)]]).

fof(i4_5__tops_2,theorem,(
    $true ),
    introduced(tautology,[file(tops_2,i4_5__tops_2)]),
    [interesting(0.8),trivial,file(tops_2,i4_5__tops_2)]).

fof(i3_5__tops_2,plain,(
    k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,c2_5__tops_2)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,c2_5__tops_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__tops_2,dt_c2_5__tops_2,e1_5__tops_2])],[e4_5__tops_2,i4_5__tops_2]),
    [interesting(0.8),file(tops_2,i3_5__tops_2),[file(tops_2,i3_5__tops_2)]]).

fof(i2_5__tops_2,plain,
    ( c2_5__tops_2 != k1_xboole_0
   => k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,c2_5__tops_2)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,c2_5__tops_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__tops_2,dt_c2_5__tops_2]),discharge_asm(discharge,[e1_5__tops_2])],[e1_5__tops_2,i3_5__tops_2]),
    [interesting(0.8),file(tops_2,i2_5__tops_2),[file(tops_2,i2_5__tops_2)]]).

fof(i2_5_tmp__tops_2,plain,
    ( m1_subset_1(c2_5__tops_2,k1_zfmisc_1(k1_zfmisc_1(c1_5__tops_2)))
   => ( c2_5__tops_2 != k1_xboole_0
     => k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,c2_5__tops_2)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,c2_5__tops_2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__tops_2]),discharge_asm(discharge,[dt_c2_5__tops_2])],[dt_c2_5__tops_2,i2_5__tops_2]),
    [interesting(0.8),i1_5__tops_2]).

fof(i1_5__tops_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_5__tops_2)))
     => ( A != k1_xboole_0
       => k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,A)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__tops_2])],[i2_5_tmp__tops_2,dh_c2_5__tops_2]),
    [interesting(0.8),file(tops_2,i1_5__tops_2),[file(tops_2,i1_5__tops_2)]]).

fof(i1_5_tmp__tops_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_5__tops_2)))
     => ( A != k1_xboole_0
       => k6_setfam_1(c1_5__tops_2,k7_setfam_1(c1_5__tops_2,A)) = k3_subset_1(c1_5__tops_2,k5_setfam_1(c1_5__tops_2,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__tops_2])],[dt_c1_5__tops_2,i1_5__tops_2]),
    [interesting(1),t11_tops_2]).

fof(t11_tops_2,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( B != k1_xboole_0
       => k6_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k5_setfam_1(A,B)) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__tops_2,dh_c1_5__tops_2]),
    [interesting(1),file(tops_2,t11_tops_2),[file(tops_2,t11_tops_2)]]).