% Mizar ND problem: t6_setfam_1,setfam_1,123,63 
fof(dh_c1_5__setfam_1,definition,
    ( ! [A] : 
        ( ! [B] : 
            ( r2_hidden(B,c1_5__setfam_1)
           => r1_tarski(A,B) )
       => ( c1_5__setfam_1 = k1_xboole_0
          | r1_tarski(A,k1_setfam_1(c1_5__setfam_1)) ) )
   => ! [C,D] : 
        ( ! [E] : 
            ( r2_hidden(E,C)
           => r1_tarski(D,E) )
       => ( C = k1_xboole_0
          | r1_tarski(D,k1_setfam_1(C)) ) ) ),
    introduced(definition,[new_symbol(c1_5__setfam_1),file(setfam_1,c1_5__setfam_1)]),
    [interesting(0.8),axiom,file(setfam_1,c1_5__setfam_1)]).

fof(dh_c2_5__setfam_1,definition,
    ( ( ! [A] : 
          ( r2_hidden(A,c1_5__setfam_1)
         => r1_tarski(c2_5__setfam_1,A) )
     => ( c1_5__setfam_1 = k1_xboole_0
        | r1_tarski(c2_5__setfam_1,k1_setfam_1(c1_5__setfam_1)) ) )
   => ! [B] : 
        ( ! [C] : 
            ( r2_hidden(C,c1_5__setfam_1)
           => r1_tarski(B,C) )
       => ( c1_5__setfam_1 = k1_xboole_0
          | r1_tarski(B,k1_setfam_1(c1_5__setfam_1)) ) ) ),
    introduced(definition,[new_symbol(c2_5__setfam_1),file(setfam_1,c2_5__setfam_1)]),
    [interesting(0.8),axiom,file(setfam_1,c2_5__setfam_1)]).

fof(e1_5__setfam_1,assumption,
    ( c1_5__setfam_1 != k1_xboole_0
    & ! [A] : 
        ( r2_hidden(A,c1_5__setfam_1)
       => r1_tarski(c2_5__setfam_1,A) ) ),
    introduced(assumption,[file(setfam_1,e1_5__setfam_1)]),
    [interesting(0.8),axiom,file(setfam_1,e1_5__setfam_1)]).

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

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

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

fof(dt_c1_5__setfam_1,assumption,(
    $true ),
    introduced(assumption,[file(setfam_1,c1_5__setfam_1)]),
    [interesting(0.8),axiom,file(setfam_1,c1_5__setfam_1)]).

fof(dt_c1_5_1__setfam_1,assumption,(
    $true ),
    introduced(assumption,[file(setfam_1,c1_5_1__setfam_1)]),
    [interesting(0.65),axiom,file(setfam_1,c1_5_1__setfam_1)]).

fof(dt_c2_5__setfam_1,assumption,(
    $true ),
    introduced(assumption,[file(setfam_1,c2_5__setfam_1)]),
    [interesting(0.8),axiom,file(setfam_1,c2_5__setfam_1)]).

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

fof(dh_c1_5_1__setfam_1,definition,
    ( ~ ( r2_hidden(c1_5_1__setfam_1,c2_5__setfam_1)
        & ~ r2_hidden(c1_5_1__setfam_1,k1_setfam_1(c1_5__setfam_1)) )
   => ! [A] : 
        ~ ( r2_hidden(A,c2_5__setfam_1)
          & ~ r2_hidden(A,k1_setfam_1(c1_5__setfam_1)) ) ),
    introduced(definition,[new_symbol(c1_5_1__setfam_1),file(setfam_1,c1_5_1__setfam_1)]),
    [interesting(0.65),axiom,file(setfam_1,c1_5_1__setfam_1)]).

fof(e1_5_1__setfam_1,assumption,(
    r2_hidden(c1_5_1__setfam_1,c2_5__setfam_1) ),
    introduced(assumption,[file(setfam_1,e1_5_1__setfam_1)]),
    [interesting(0.65),axiom,file(setfam_1,e1_5_1__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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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(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(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(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

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(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

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

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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_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(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(dh_c1_5_1_1__setfam_1,definition,
    ( ( r2_hidden(c1_5_1_1__setfam_1,c1_5__setfam_1)
     => r2_hidden(c1_5_1__setfam_1,c1_5_1_1__setfam_1) )
   => ! [A] : 
        ( r2_hidden(A,c1_5__setfam_1)
       => r2_hidden(c1_5_1__setfam_1,A) ) ),
    introduced(definition,[new_symbol(c1_5_1_1__setfam_1),file(setfam_1,c1_5_1_1__setfam_1)]),
    [interesting(0.5),axiom,file(setfam_1,c1_5_1_1__setfam_1)]).

fof(e1_5_1_1__setfam_1,assumption,(
    r2_hidden(c1_5_1_1__setfam_1,c1_5__setfam_1) ),
    introduced(assumption,[file(setfam_1,e1_5_1_1__setfam_1)]),
    [interesting(0.5),axiom,file(setfam_1,e1_5_1_1__setfam_1)]).

fof(dt_c1_5_1_1__setfam_1,assumption,(
    $true ),
    introduced(assumption,[file(setfam_1,c1_5_1_1__setfam_1)]),
    [interesting(0.5),axiom,file(setfam_1,c1_5_1_1__setfam_1)]).

fof(e2_5_1_1__setfam_1,plain,(
    r1_tarski(c2_5__setfam_1,c1_5_1_1__setfam_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__setfam_1,dt_c1_5_1_1__setfam_1,dt_c2_5__setfam_1,e1_5_1_1__setfam_1,e1_5__setfam_1])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c1_5__setfam_1,dt_c1_5_1_1__setfam_1,dt_c2_5__setfam_1,fc1_xboole_0,t1_subset,t3_subset,t6_boole,t7_boole,e1_5_1_1__setfam_1,e1_5__setfam_1]),
    [interesting(0.5),file(setfam_1,e2_5_1_1__setfam_1),[file(setfam_1,e2_5_1_1__setfam_1)]]).

fof(e3_5_1_1__setfam_1,plain,(
    r2_hidden(c1_5_1__setfam_1,c1_5_1_1__setfam_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__setfam_1,dt_c1_5__setfam_1,dt_c1_5_1_1__setfam_1,dt_c2_5__setfam_1,e1_5_1_1__setfam_1,e1_5__setfam_1,e1_5_1__setfam_1])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_5_1__setfam_1,dt_c1_5_1_1__setfam_1,dt_c2_5__setfam_1,t1_subset,t3_subset,t7_boole,e2_5_1_1__setfam_1,e1_5_1__setfam_1]),
    [interesting(0.5),file(setfam_1,e3_5_1_1__setfam_1),[file(setfam_1,e3_5_1_1__setfam_1)]]).

fof(i3_5_1_1__setfam_1,theorem,(
    $true ),
    introduced(tautology,[file(setfam_1,i3_5_1_1__setfam_1)]),
    [interesting(0.5),trivial,file(setfam_1,i3_5_1_1__setfam_1)]).

fof(i2_5_1_1__setfam_1,plain,(
    r2_hidden(c1_5_1__setfam_1,c1_5_1_1__setfam_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1__setfam_1,dt_c1_5__setfam_1,dt_c1_5_1_1__setfam_1,dt_c2_5__setfam_1,e1_5_1_1__setfam_1,e1_5__setfam_1,e1_5_1__setfam_1])],[e3_5_1_1__setfam_1,i3_5_1_1__setfam_1]),
    [interesting(0.5),file(setfam_1,i2_5_1_1__setfam_1),[file(setfam_1,i2_5_1_1__setfam_1)]]).

fof(i1_5_1_1__setfam_1,plain,
    ( r2_hidden(c1_5_1_1__setfam_1,c1_5__setfam_1)
   => r2_hidden(c1_5_1__setfam_1,c1_5_1_1__setfam_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1__setfam_1,dt_c1_5__setfam_1,dt_c1_5_1_1__setfam_1,dt_c2_5__setfam_1,e1_5__setfam_1,e1_5_1__setfam_1]),discharge_asm(discharge,[e1_5_1_1__setfam_1])],[e1_5_1_1__setfam_1,i2_5_1_1__setfam_1]),
    [interesting(0.5),file(setfam_1,i1_5_1_1__setfam_1),[file(setfam_1,i1_5_1_1__setfam_1)]]).

fof(i1_5_1_1_tmp__setfam_1,plain,
    ( r2_hidden(c1_5_1_1__setfam_1,c1_5__setfam_1)
   => r2_hidden(c1_5_1__setfam_1,c1_5_1_1__setfam_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1__setfam_1,dt_c1_5__setfam_1,dt_c2_5__setfam_1,e1_5__setfam_1,e1_5_1__setfam_1]),discharge_asm(discharge,[dt_c1_5_1_1__setfam_1])],[dt_c1_5_1_1__setfam_1,i1_5_1_1__setfam_1]),
    [interesting(0.65),e2_5_1__setfam_1]).

fof(e2_5_1__setfam_1,plain,(
    ! [A] : 
      ( r2_hidden(A,c1_5__setfam_1)
     => r2_hidden(c1_5_1__setfam_1,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5_1__setfam_1,dt_c1_5__setfam_1,dt_c2_5__setfam_1,e1_5__setfam_1,e1_5_1__setfam_1])],[i1_5_1_1_tmp__setfam_1,dh_c1_5_1_1__setfam_1]),
    [interesting(0.65),file(setfam_1,e2_5_1__setfam_1),[file(setfam_1,e2_5_1__setfam_1)]]).

fof(d1_setfam_1,definition,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,d1_setfam_1)]).

fof(e3_5_1__setfam_1,plain,(
    r2_hidden(c1_5_1__setfam_1,k1_setfam_1(c1_5__setfam_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__setfam_1,dt_c1_5__setfam_1,dt_c2_5__setfam_1,e1_5_1__setfam_1,e1_5__setfam_1])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_setfam_1,dt_k1_xboole_0,dt_c1_5__setfam_1,dt_c1_5_1__setfam_1,dt_c2_5__setfam_1,fc1_xboole_0,t1_subset,t3_subset,t6_boole,t7_boole,e2_5_1__setfam_1,e1_5__setfam_1,d1_setfam_1]),
    [interesting(0.65),file(setfam_1,e3_5_1__setfam_1),[file(setfam_1,e3_5_1__setfam_1)]]).

fof(i3_5_1__setfam_1,theorem,(
    $true ),
    introduced(tautology,[file(setfam_1,i3_5_1__setfam_1)]),
    [interesting(0.65),trivial,file(setfam_1,i3_5_1__setfam_1)]).

fof(i2_5_1__setfam_1,plain,(
    r2_hidden(c1_5_1__setfam_1,k1_setfam_1(c1_5__setfam_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1__setfam_1,dt_c1_5__setfam_1,dt_c2_5__setfam_1,e1_5_1__setfam_1,e1_5__setfam_1])],[e3_5_1__setfam_1,i3_5_1__setfam_1]),
    [interesting(0.65),file(setfam_1,i2_5_1__setfam_1),[file(setfam_1,i2_5_1__setfam_1)]]).

fof(i1_5_1__setfam_1,plain,(
    ~ ( r2_hidden(c1_5_1__setfam_1,c2_5__setfam_1)
      & ~ r2_hidden(c1_5_1__setfam_1,k1_setfam_1(c1_5__setfam_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1__setfam_1,dt_c1_5__setfam_1,dt_c2_5__setfam_1,e1_5__setfam_1]),discharge_asm(discharge,[e1_5_1__setfam_1])],[e1_5_1__setfam_1,i2_5_1__setfam_1]),
    [interesting(0.65),file(setfam_1,i1_5_1__setfam_1),[file(setfam_1,i1_5_1__setfam_1)]]).

fof(i1_5_1_tmp__setfam_1,plain,(
    ~ ( r2_hidden(c1_5_1__setfam_1,c2_5__setfam_1)
      & ~ r2_hidden(c1_5_1__setfam_1,k1_setfam_1(c1_5__setfam_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__setfam_1,dt_c2_5__setfam_1,e1_5__setfam_1]),discharge_asm(discharge,[dt_c1_5_1__setfam_1])],[dt_c1_5_1__setfam_1,i1_5_1__setfam_1]),
    [interesting(0.8),e2_5__setfam_1]).

fof(e2_5__setfam_1,plain,(
    r1_tarski(c2_5__setfam_1,k1_setfam_1(c1_5__setfam_1)) ),
    inference(let,[status(thm),assumptions([dt_c1_5__setfam_1,dt_c2_5__setfam_1,e1_5__setfam_1])],[i1_5_1_tmp__setfam_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_setfam_1,dt_c1_5__setfam_1,dt_c2_5__setfam_1,d3_tarski,dh_c1_5_1__setfam_1]),
    [interesting(0.8),file(setfam_1,e2_5__setfam_1),[file(setfam_1,e2_5__setfam_1)]]).

fof(i4_5__setfam_1,theorem,(
    $true ),
    introduced(tautology,[file(setfam_1,i4_5__setfam_1)]),
    [interesting(0.8),trivial,file(setfam_1,i4_5__setfam_1)]).

fof(i3_5__setfam_1,plain,(
    r1_tarski(c2_5__setfam_1,k1_setfam_1(c1_5__setfam_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__setfam_1,dt_c2_5__setfam_1,e1_5__setfam_1])],[e2_5__setfam_1,i4_5__setfam_1]),
    [interesting(0.8),file(setfam_1,i3_5__setfam_1),[file(setfam_1,i3_5__setfam_1)]]).

fof(i2_5__setfam_1,plain,
    ( ! [A] : 
        ( r2_hidden(A,c1_5__setfam_1)
       => r1_tarski(c2_5__setfam_1,A) )
   => ( c1_5__setfam_1 = k1_xboole_0
      | r1_tarski(c2_5__setfam_1,k1_setfam_1(c1_5__setfam_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__setfam_1,dt_c2_5__setfam_1]),discharge_asm(discharge,[e1_5__setfam_1])],[e1_5__setfam_1,i3_5__setfam_1]),
    [interesting(0.8),file(setfam_1,i2_5__setfam_1),[file(setfam_1,i2_5__setfam_1)]]).

fof(i2_5_tmp__setfam_1,plain,
    ( ! [A] : 
        ( r2_hidden(A,c1_5__setfam_1)
       => r1_tarski(c2_5__setfam_1,A) )
   => ( c1_5__setfam_1 = k1_xboole_0
      | r1_tarski(c2_5__setfam_1,k1_setfam_1(c1_5__setfam_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__setfam_1]),discharge_asm(discharge,[dt_c2_5__setfam_1])],[dt_c2_5__setfam_1,i2_5__setfam_1]),
    [interesting(0.8),i1_5__setfam_1]).

fof(i1_5__setfam_1,plain,(
    ! [A] : 
      ( ! [B] : 
          ( r2_hidden(B,c1_5__setfam_1)
         => r1_tarski(A,B) )
     => ( c1_5__setfam_1 = k1_xboole_0
        | r1_tarski(A,k1_setfam_1(c1_5__setfam_1)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__setfam_1])],[i2_5_tmp__setfam_1,dh_c2_5__setfam_1]),
    [interesting(0.8),file(setfam_1,i1_5__setfam_1),[file(setfam_1,i1_5__setfam_1)]]).

fof(i1_5_tmp__setfam_1,plain,(
    ! [A] : 
      ( ! [B] : 
          ( r2_hidden(B,c1_5__setfam_1)
         => r1_tarski(A,B) )
     => ( c1_5__setfam_1 = k1_xboole_0
        | r1_tarski(A,k1_setfam_1(c1_5__setfam_1)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__setfam_1])],[dt_c1_5__setfam_1,i1_5__setfam_1]),
    [interesting(1),t6_setfam_1]).

fof(t6_setfam_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(B,C) )
     => ( A = k1_xboole_0
        | r1_tarski(B,k1_setfam_1(A)) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__setfam_1,dh_c1_5__setfam_1]),
    [interesting(1),file(setfam_1,t6_setfam_1),[file(setfam_1,t6_setfam_1)]]).