% Mizar ND problem: t79_classes2,classes2,1442,14 
fof(dh_c1_73__classes2,definition,
    ( ( ( ~ v1_xboole_0(c1_73__classes2)
        & v1_classes2(c1_73__classes2) )
     => ( r1_tarski(k13_classes2,c1_73__classes2)
        & r1_tarski(k1_classes1(k1_xboole_0),c1_73__classes2)
        & r1_tarski(k16_classes2(k1_xboole_0),c1_73__classes2) ) )
   => ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & v1_classes2(A) )
       => ( r1_tarski(k13_classes2,A)
          & r1_tarski(k1_classes1(k1_xboole_0),A)
          & r1_tarski(k16_classes2(k1_xboole_0),A) ) ) ),
    introduced(definition,[new_symbol(c1_73__classes2),file(classes2,c1_73__classes2)]),
    [interesting(0.8),axiom,file(classes2,c1_73__classes2)]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_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_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

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_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_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(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(cc2_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]).

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(cc3_ordinal1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]).

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(fc2_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( v1_ordinal1(k2_ordinal2(A))
        & v2_ordinal1(k2_ordinal2(A))
        & v3_ordinal1(k2_ordinal2(A)) ) ) ),
    file(classes2,fc2_classes2),
    [interesting(0.9),axiom,file(classes2,fc2_classes2)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc3_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( v1_ordinal1(k1_classes1(A))
        & ~ v1_xboole_0(k1_classes1(A))
        & v1_classes1(k1_classes1(A))
        & v2_classes1(k1_classes1(A))
        & v1_classes2(k1_classes1(A)) ) ) ),
    file(classes2,fc3_classes2),
    [interesting(0.9),axiom,file(classes2,fc3_classes2)]).

fof(fc6_classes2,theorem,(
    ! [A] : 
      ( v1_ordinal1(A)
     => ( v1_ordinal1(k1_classes1(A))
        & ~ v1_xboole_0(k1_classes1(A))
        & v1_classes1(k1_classes1(A))
        & v2_classes1(k1_classes1(A))
        & v1_classes2(k1_classes1(A)) ) ) ),
    file(classes2,fc6_classes2),
    [interesting(0.9),axiom,file(classes2,fc6_classes2)]).

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(rc1_ordinal1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]).

fof(rc1_ordinal2,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal1(A) ) ),
    file(ordinal2,rc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,rc1_ordinal2)]).

fof(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

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_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_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]).

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(rc3_ordinal1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]).

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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(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_k13_classes2,axiom,
    ( ~ v1_xboole_0(k13_classes2)
    & v1_classes2(k13_classes2) ),
    file(classes2,k13_classes2),
    [interesting(0.9),axiom,file(classes2,k13_classes2)]).

fof(dt_k15_classes2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k15_classes2(A))
      & v1_classes2(k15_classes2(A)) ) ),
    file(classes2,k15_classes2),
    [interesting(0.9),axiom,file(classes2,k15_classes2)]).

fof(dt_k16_classes2,axiom,(
    $true ),
    file(classes2,k16_classes2),
    [interesting(0.9),axiom,file(classes2,k16_classes2)]).

fof(dt_k1_classes1,axiom,(
    $true ),
    file(classes1,k1_classes1),
    [interesting(0.9),axiom,file(classes1,k1_classes1)]).

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_ordinal1,axiom,(
    $true ),
    file(ordinal1,k1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,k1_ordinal1)]).

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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k2_ordinal2,axiom,(
    $true ),
    file(ordinal2,k2_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k2_ordinal2)]).

fof(dt_k3_card_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    [interesting(0.9),axiom,file(card_3,k3_card_3)]).

fof(dt_k4_classes1,axiom,(
    $true ),
    file(classes1,k4_classes1),
    [interesting(0.9),axiom,file(classes1,k4_classes1)]).

fof(dt_c1_73__classes2,assumption,
    ( ~ v1_xboole_0(c1_73__classes2)
    & v1_classes2(c1_73__classes2) ),
    introduced(assumption,[file(classes2,c1_73__classes2)]),
    [interesting(0.8),axiom,file(classes2,c1_73__classes2)]).

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

fof(cc1_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]).

fof(fc1_classes1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_classes1(A)) ),
    file(classes1,fc1_classes1),
    [interesting(0.9),axiom,file(classes1,fc1_classes1)]).

fof(fc1_classes2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_classes1(A))
      & v1_classes1(k1_classes1(A))
      & v2_classes1(k1_classes1(A)) ) ),
    file(classes2,fc1_classes2),
    [interesting(0.9),axiom,file(classes2,fc1_classes2)]).

fof(fc1_ordinal1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) ),
    file(ordinal1,fc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc1_ordinal1)]).

fof(fc2_ordinal1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(fc3_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A)) ) ) ),
    file(ordinal1,fc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc3_ordinal1)]).

fof(fc4_classes2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k1_classes1(A))
        & ~ v1_xboole_0(k1_classes1(A))
        & v1_classes1(k1_classes1(A))
        & v2_classes1(k1_classes1(A))
        & v1_classes2(k1_classes1(A)) ) ) ),
    file(classes2,fc4_classes2),
    [interesting(0.9),axiom,file(classes2,fc4_classes2)]).

fof(fc5_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ( v1_ordinal1(k1_relat_1(A))
        & v2_ordinal1(k1_relat_1(A))
        & v3_ordinal1(k1_relat_1(A)) ) ) ),
    file(ordinal1,fc5_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc5_ordinal1)]).

fof(fc7_classes2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => v1_ordinal1(k4_classes1(A)) ) ),
    file(classes2,fc7_classes2),
    [interesting(0.9),axiom,file(classes2,fc7_classes2)]).

fof(fc8_classes2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k16_classes2(A))
        & ~ v1_xboole_0(k16_classes2(A))
        & v1_classes1(k16_classes2(A))
        & v2_classes1(k16_classes2(A))
        & v1_classes2(k16_classes2(A)) ) ) ),
    file(classes2,fc8_classes2),
    [interesting(0.9),axiom,file(classes2,fc8_classes2)]).

fof(rc4_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A) ) ),
    file(ordinal1,rc4_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc4_ordinal1)]).

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(d2_classes2,definition,(
    k13_classes2 = k1_classes1(k1_xboole_0) ),
    file(classes2,d2_classes2),
    [interesting(0.9),axiom,file(classes2,d2_classes2)]).

fof(d1_ordinal1,definition,(
    ! [A] : k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A)) ),
    file(ordinal1,d1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,d1_ordinal1)]).

fof(t55_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( k2_ordinal2(A) != k1_xboole_0
        & v4_ordinal1(k2_ordinal2(A)) ) ) ),
    file(classes2,t55_classes2),
    [interesting(0.9),axiom,file(classes2,t55_classes2)]).

fof(e1_73__classes2,plain,(
    k1_xboole_0 != k2_ordinal2(c1_73__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_73__classes2])],[existence_m1_subset_1,dt_m1_subset_1,rc2_classes2,t2_subset,antisymmetry_r2_hidden,cc1_classes2,cc1_ordinal1,cc2_ordinal1,cc3_classes2,rc1_classes2,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t1_subset,dt_k1_xboole_0,dt_k2_ordinal2,dt_c1_73__classes2,cc2_classes2,cc3_ordinal1,fc2_classes2,fc2_ordinal1,t6_boole,t7_boole,t8_boole,t55_classes2]),
    [interesting(0.8),file(classes2,e1_73__classes2),[file(classes2,e1_73__classes2)]]).

fof(t54_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => A = k4_classes1(k2_ordinal2(A)) ) ),
    file(classes2,t54_classes2),
    [interesting(0.9),axiom,file(classes2,t54_classes2)]).

fof(t44_classes1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => r1_tarski(A,k4_classes1(A)) ) ),
    file(classes1,t44_classes1),
    [interesting(0.9),axiom,file(classes1,t44_classes1)]).

fof(t10_ordinal3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( A != k1_xboole_0
       => r2_hidden(k1_xboole_0,A) ) ) ),
    file(ordinal3,t10_ordinal3),
    [interesting(0.9),axiom,file(ordinal3,t10_ordinal3)]).

fof(e2_73__classes2,plain,
    ( r2_hidden(k1_xboole_0,k2_ordinal2(c1_73__classes2))
    & k4_classes1(k2_ordinal2(c1_73__classes2)) = c1_73__classes2
    & r1_tarski(k2_ordinal2(c1_73__classes2),k4_classes1(k2_ordinal2(c1_73__classes2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_73__classes2])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_classes2,cc2_ordinal1,cc3_classes2,fc1_subset_1,rc1_classes2,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_classes2,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t2_subset,t4_subset,t5_subset,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_ordinal2,dt_k4_classes1,dt_c1_73__classes2,cc1_ordinal1,cc2_classes2,cc3_ordinal1,fc2_classes2,fc2_ordinal1,fc7_classes2,t1_subset,t3_subset,t6_boole,t7_boole,t8_boole,e1_73__classes2,t54_classes2,t44_classes1,t10_ordinal3]),
    [interesting(0.8),file(classes2,e2_73__classes2),[file(classes2,e2_73__classes2)]]).

fof(l81_classes2,plain,
    ( k16_classes2(k1_xboole_0) = k13_classes2
    & ! [A] : 
        ( v3_ordinal1(A)
       => k16_classes2(k1_ordinal1(A)) = k1_classes1(k16_classes2(A)) )
    & ! [A] : 
        ( v3_ordinal1(A)
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B)
              & v5_ordinal1(B) )
           => ( ( v4_ordinal1(A)
                & k1_relat_1(B) = A
                & ! [C] : 
                    ( v3_ordinal1(C)
                   => ( r2_hidden(C,A)
                     => k1_funct_1(B,C) = k16_classes2(C) ) ) )
             => ( A = k1_xboole_0
                | k16_classes2(A) = k15_classes2(k3_card_3(B)) ) ) ) ) ),
    file(classes2,l81_classes2),
    [interesting(0.9),axiom,file(classes2,l81_classes2)]).

fof(t5_classes2,theorem,(
    ! [A,B] : 
      ( ( v2_classes1(A)
        & r2_hidden(B,A) )
     => r1_tarski(k1_classes1(B),A) ) ),
    file(classes2,t5_classes2),
    [interesting(0.9),axiom,file(classes2,t5_classes2)]).

fof(e3_73__classes2,plain,
    ( r1_tarski(k13_classes2,c1_73__classes2)
    & r1_tarski(k1_classes1(k1_xboole_0),c1_73__classes2)
    & r1_tarski(k16_classes2(k1_xboole_0),c1_73__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_73__classes2])],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xboole_0,dt_m1_subset_1,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,fc1_subset_1,fc2_classes2,fc2_subset_1,fc3_classes2,fc6_classes2,rc1_classes2,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc1_subset_1,rc2_classes2,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k13_classes2,dt_k15_classes2,dt_k16_classes2,dt_k1_classes1,dt_k1_funct_1,dt_k1_ordinal1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_ordinal2,dt_k3_card_3,dt_k4_classes1,dt_c1_73__classes2,cc1_classes2,cc1_ordinal1,fc1_classes1,fc1_classes2,fc1_ordinal1,fc2_ordinal1,fc3_ordinal1,fc4_classes2,fc5_ordinal1,fc7_classes2,fc8_classes2,rc4_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d2_classes2,d1_ordinal1,e2_73__classes2,l81_classes2,t5_classes2]),
    [interesting(0.8),file(classes2,e3_73__classes2),[file(classes2,e3_73__classes2)]]).

fof(i2_73__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i2_73__classes2)]),
    [interesting(0.8),trivial,file(classes2,i2_73__classes2)]).

fof(i1_73__classes2,plain,
    ( r1_tarski(k13_classes2,c1_73__classes2)
    & r1_tarski(k1_classes1(k1_xboole_0),c1_73__classes2)
    & r1_tarski(k16_classes2(k1_xboole_0),c1_73__classes2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_73__classes2])],[e3_73__classes2,i2_73__classes2]),
    [interesting(0.8),file(classes2,i1_73__classes2),[file(classes2,i1_73__classes2)]]).

fof(i1_73_tmp__classes2,plain,
    ( ( ~ v1_xboole_0(c1_73__classes2)
      & v1_classes2(c1_73__classes2) )
   => ( r1_tarski(k13_classes2,c1_73__classes2)
      & r1_tarski(k1_classes1(k1_xboole_0),c1_73__classes2)
      & r1_tarski(k16_classes2(k1_xboole_0),c1_73__classes2) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_73__classes2])],[dt_c1_73__classes2,i1_73__classes2]),
    [interesting(1),t79_classes2]).

fof(t79_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( r1_tarski(k13_classes2,A)
        & r1_tarski(k1_classes1(k1_xboole_0),A)
        & r1_tarski(k16_classes2(k1_xboole_0),A) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_73_tmp__classes2,dh_c1_73__classes2]),
    [interesting(1),file(classes2,t79_classes2),[file(classes2,t79_classes2)]]).