% Mizar ND problem: t4_grcat_1,grcat_1,61,43 
fof(dh_c1_3__grcat_1,definition,
    ( ( ( ~ v1_xboole_0(c1_3__grcat_1)
        & v1_classes2(c1_3__grcat_1) )
     => ! [A,B] : 
          ( ( r2_hidden(A,B)
            & r2_hidden(B,c1_3__grcat_1) )
         => r2_hidden(A,c1_3__grcat_1) ) )
   => ! [C] : 
        ( ( ~ v1_xboole_0(C)
          & v1_classes2(C) )
       => ! [D,E] : 
            ( ( r2_hidden(D,E)
              & r2_hidden(E,C) )
           => r2_hidden(D,C) ) ) ),
    introduced(definition,[new_symbol(c1_3__grcat_1),file(grcat_1,c1_3__grcat_1)]),
    [interesting(0.8),axiom,file(grcat_1,c1_3__grcat_1)]).

fof(dh_c2_3__grcat_1,definition,
    ( ! [A] : 
        ( ( r2_hidden(c2_3__grcat_1,A)
          & r2_hidden(A,c1_3__grcat_1) )
       => r2_hidden(c2_3__grcat_1,c1_3__grcat_1) )
   => ! [B,C] : 
        ( ( r2_hidden(B,C)
          & r2_hidden(C,c1_3__grcat_1) )
       => r2_hidden(B,c1_3__grcat_1) ) ),
    introduced(definition,[new_symbol(c2_3__grcat_1),file(grcat_1,c2_3__grcat_1)]),
    [interesting(0.8),axiom,file(grcat_1,c2_3__grcat_1)]).

fof(dh_c3_3__grcat_1,definition,
    ( ( ( r2_hidden(c2_3__grcat_1,c3_3__grcat_1)
        & r2_hidden(c3_3__grcat_1,c1_3__grcat_1) )
     => r2_hidden(c2_3__grcat_1,c1_3__grcat_1) )
   => ! [A] : 
        ( ( r2_hidden(c2_3__grcat_1,A)
          & r2_hidden(A,c1_3__grcat_1) )
       => r2_hidden(c2_3__grcat_1,c1_3__grcat_1) ) ),
    introduced(definition,[new_symbol(c3_3__grcat_1),file(grcat_1,c3_3__grcat_1)]),
    [interesting(0.8),axiom,file(grcat_1,c3_3__grcat_1)]).

fof(e1_3__grcat_1,assumption,
    ( r2_hidden(c2_3__grcat_1,c3_3__grcat_1)
    & r2_hidden(c3_3__grcat_1,c1_3__grcat_1) ),
    introduced(assumption,[file(grcat_1,e1_3__grcat_1)]),
    [interesting(0.8),axiom,file(grcat_1,e1_3__grcat_1)]).

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

fof(cc1_classes2,theorem,(
    ! [A] : 
      ( v2_classes1(A)
     => v1_classes1(A) ) ),
    file(classes2,cc1_classes2),
    [interesting(0.9),axiom,file(classes2,cc1_classes2)]).

fof(cc3_classes2,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_classes1(A) )
     => v1_classes2(A) ) ),
    file(classes2,cc3_classes2),
    [interesting(0.9),axiom,file(classes2,cc3_classes2)]).

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(rc1_classes2,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v2_classes1(A)
      & v1_classes2(A) ) ),
    file(classes2,rc1_classes2),
    [interesting(0.9),axiom,file(classes2,rc1_classes2)]).

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_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(cc2_classes2,theorem,(
    ! [A] : 
      ( v1_classes2(A)
     => ( v1_ordinal1(A)
        & v1_classes1(A)
        & v2_classes1(A) ) ) ),
    file(classes2,cc2_classes2),
    [interesting(0.9),axiom,file(classes2,cc2_classes2)]).

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_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(classes2,rc2_classes2),
    [interesting(0.9),axiom,file(classes2,rc2_classes2)]).

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(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(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_c1_3__grcat_1,assumption,
    ( ~ v1_xboole_0(c1_3__grcat_1)
    & v1_classes2(c1_3__grcat_1) ),
    introduced(assumption,[file(grcat_1,c1_3__grcat_1)]),
    [interesting(0.8),axiom,file(grcat_1,c1_3__grcat_1)]).

fof(dt_c2_3__grcat_1,assumption,(
    $true ),
    introduced(assumption,[file(grcat_1,c2_3__grcat_1)]),
    [interesting(0.8),axiom,file(grcat_1,c2_3__grcat_1)]).

fof(dt_c3_3__grcat_1,assumption,(
    $true ),
    introduced(assumption,[file(grcat_1,c3_3__grcat_1)]),
    [interesting(0.8),axiom,file(grcat_1,c3_3__grcat_1)]).

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(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(d2_ordinal1,definition,(
    ! [A] : 
      ( v1_ordinal1(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => r1_tarski(B,A) ) ) ),
    file(ordinal1,d2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,d2_ordinal1)]).

fof(e2_3__grcat_1,plain,(
    r1_tarski(c3_3__grcat_1,c1_3__grcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__grcat_1,dt_c2_3__grcat_1,dt_c3_3__grcat_1,e1_3__grcat_1])],[dt_k1_xboole_0,cc1_classes2,cc3_classes2,fc1_xboole_0,rc1_classes2,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc2_classes2,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_classes2,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_3__grcat_1,dt_c2_3__grcat_1,dt_c3_3__grcat_1,t1_subset,t3_subset,t7_boole,e1_3__grcat_1,d2_ordinal1]),
    [interesting(0.8),file(grcat_1,e2_3__grcat_1),[file(grcat_1,e2_3__grcat_1)]]).

fof(e3_3__grcat_1,plain,(
    r2_hidden(c2_3__grcat_1,c1_3__grcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__grcat_1,dt_c2_3__grcat_1,dt_c3_3__grcat_1,e1_3__grcat_1])],[dt_k1_xboole_0,cc1_classes2,cc3_classes2,fc1_xboole_0,rc1_classes2,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc2_classes2,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_classes2,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_3__grcat_1,dt_c2_3__grcat_1,dt_c3_3__grcat_1,t1_subset,t3_subset,t7_boole,e2_3__grcat_1,e1_3__grcat_1]),
    [interesting(0.8),file(grcat_1,e3_3__grcat_1),[file(grcat_1,e3_3__grcat_1)]]).

fof(i5_3__grcat_1,theorem,(
    $true ),
    introduced(tautology,[file(grcat_1,i5_3__grcat_1)]),
    [interesting(0.8),trivial,file(grcat_1,i5_3__grcat_1)]).

fof(i4_3__grcat_1,plain,(
    r2_hidden(c2_3__grcat_1,c1_3__grcat_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__grcat_1,dt_c2_3__grcat_1,dt_c3_3__grcat_1,e1_3__grcat_1])],[e3_3__grcat_1,i5_3__grcat_1]),
    [interesting(0.8),file(grcat_1,i4_3__grcat_1),[file(grcat_1,i4_3__grcat_1)]]).

fof(i3_3__grcat_1,plain,
    ( ( r2_hidden(c2_3__grcat_1,c3_3__grcat_1)
      & r2_hidden(c3_3__grcat_1,c1_3__grcat_1) )
   => r2_hidden(c2_3__grcat_1,c1_3__grcat_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__grcat_1,dt_c2_3__grcat_1,dt_c3_3__grcat_1]),discharge_asm(discharge,[e1_3__grcat_1])],[e1_3__grcat_1,i4_3__grcat_1]),
    [interesting(0.8),file(grcat_1,i3_3__grcat_1),[file(grcat_1,i3_3__grcat_1)]]).

fof(i3_3_tmp__grcat_1,plain,
    ( ( r2_hidden(c2_3__grcat_1,c3_3__grcat_1)
      & r2_hidden(c3_3__grcat_1,c1_3__grcat_1) )
   => r2_hidden(c2_3__grcat_1,c1_3__grcat_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__grcat_1,dt_c2_3__grcat_1]),discharge_asm(discharge,[dt_c3_3__grcat_1])],[dt_c3_3__grcat_1,i3_3__grcat_1]),
    [interesting(0.8),i2_3__grcat_1]).

fof(i2_3__grcat_1,plain,(
    ! [A] : 
      ( ( r2_hidden(c2_3__grcat_1,A)
        & r2_hidden(A,c1_3__grcat_1) )
     => r2_hidden(c2_3__grcat_1,c1_3__grcat_1) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__grcat_1,dt_c2_3__grcat_1])],[i3_3_tmp__grcat_1,dh_c3_3__grcat_1]),
    [interesting(0.8),file(grcat_1,i2_3__grcat_1),[file(grcat_1,i2_3__grcat_1)]]).

fof(i2_3_tmp__grcat_1,plain,(
    ! [A] : 
      ( ( r2_hidden(c2_3__grcat_1,A)
        & r2_hidden(A,c1_3__grcat_1) )
     => r2_hidden(c2_3__grcat_1,c1_3__grcat_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__grcat_1]),discharge_asm(discharge,[dt_c2_3__grcat_1])],[dt_c2_3__grcat_1,i2_3__grcat_1]),
    [interesting(0.8),i1_3__grcat_1]).

fof(i1_3__grcat_1,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,B)
        & r2_hidden(B,c1_3__grcat_1) )
     => r2_hidden(A,c1_3__grcat_1) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__grcat_1])],[i2_3_tmp__grcat_1,dh_c2_3__grcat_1]),
    [interesting(0.8),file(grcat_1,i1_3__grcat_1),[file(grcat_1,i1_3__grcat_1)]]).

fof(i1_3_tmp__grcat_1,plain,
    ( ( ~ v1_xboole_0(c1_3__grcat_1)
      & v1_classes2(c1_3__grcat_1) )
   => ! [A,B] : 
        ( ( r2_hidden(A,B)
          & r2_hidden(B,c1_3__grcat_1) )
       => r2_hidden(A,c1_3__grcat_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__grcat_1])],[dt_c1_3__grcat_1,i1_3__grcat_1]),
    [interesting(1),t4_grcat_1]).

fof(t4_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B,C] : 
          ( ( r2_hidden(B,C)
            & r2_hidden(C,A) )
         => r2_hidden(B,A) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__grcat_1,dh_c1_3__grcat_1]),
    [interesting(1),file(grcat_1,t4_grcat_1),[file(grcat_1,t4_grcat_1)]]).