% Mizar ND problem: t69_classes2,classes2,1183,35 
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(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(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(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(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(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(cc1_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    [interesting(0.9),axiom,file(card_1,cc1_card_1)]).

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(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_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(rc1_card_1,theorem,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    [interesting(0.9),axiom,file(card_1,rc1_card_1)]).

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_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(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(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(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_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    [interesting(0.9),axiom,file(card_1,k1_card_1)]).

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

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

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(fc4_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_tarski(A))
        & v2_ordinal1(k3_tarski(A))
        & v3_ordinal1(k3_tarski(A)) ) ) ),
    file(ordinal1,fc4_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc4_ordinal1)]).

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

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(dh_c1_62__classes2,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & k1_relat_1(A) = k5_ordinal2
        & ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_hidden(B,k5_ordinal2)
             => k1_funct_1(A,B) = k4_classes1(B) ) ) )
   => ( v1_relat_1(c1_62__classes2)
      & v1_funct_1(c1_62__classes2)
      & v5_ordinal1(c1_62__classes2)
      & k1_relat_1(c1_62__classes2) = k5_ordinal2
      & ! [C] : 
          ( v3_ordinal1(C)
         => ( r2_hidden(C,k5_ordinal2)
           => k1_funct_1(c1_62__classes2,C) = k4_classes1(C) ) ) ) ),
    introduced(definition,[new_symbol(c1_62__classes2),file(classes2,c1_62__classes2)]),
    [interesting(0.8),axiom,file(classes2,c1_62__classes2)]).

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(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(s2_ordinal2__e1_62__classes2,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A)
      & k1_relat_1(A) = k5_ordinal2
      & ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(B,k5_ordinal2)
           => k1_funct_1(A,B) = k4_classes1(B) ) ) ) ),
    file(classes2,s2_ordinal2__e1_62__classes2),
    [interesting(0.9),axiom,file(classes2,s2_ordinal2__e1_62__classes2)]).

fof(e1_62__classes2,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A)
      & k1_relat_1(A) = k5_ordinal2
      & ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(B,k5_ordinal2)
           => k1_funct_1(A,B) = k4_classes1(B) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([])],[cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc3_ordinal1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_classes1,dt_k5_ordinal2,cc1_ordinal1,fc1_ordinal2,fc5_ordinal1,rc4_ordinal1,s2_ordinal2__e1_62__classes2]),
    [interesting(0.8),file(classes2,e1_62__classes2),[file(classes2,e1_62__classes2)]]).

fof(dt_c1_62__classes2,plain,
    ( v1_relat_1(c1_62__classes2)
    & v1_funct_1(c1_62__classes2)
    & v5_ordinal1(c1_62__classes2) ),
    inference(consider,[status(thm),assumptions([])],[dh_c1_62__classes2,e1_62__classes2]),
    [interesting(0.8),file(classes2,c1_62__classes2),[file(classes2,c1_62__classes2)]]).

fof(dh_c1_62_3__classes2,definition,
    ( ( r2_hidden(c1_62_3__classes2,k2_relat_1(c1_62__classes2))
     => r2_hidden(k1_card_1(c1_62_3__classes2),k1_card_1(k5_ordinal2)) )
   => ! [A] : 
        ( r2_hidden(A,k2_relat_1(c1_62__classes2))
       => r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)) ) ),
    introduced(definition,[new_symbol(c1_62_3__classes2),file(classes2,c1_62_3__classes2)]),
    [interesting(0.65),axiom,file(classes2,c1_62_3__classes2)]).

fof(e1_62_3__classes2,assumption,(
    r2_hidden(c1_62_3__classes2,k2_relat_1(c1_62__classes2)) ),
    introduced(assumption,[file(classes2,e1_62_3__classes2)]),
    [interesting(0.65),axiom,file(classes2,e1_62_3__classes2)]).

fof(rc2_card_1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    [interesting(0.9),axiom,file(card_1,rc2_card_1)]).

fof(dt_c1_62_3__classes2,assumption,(
    $true ),
    introduced(assumption,[file(classes2,c1_62_3__classes2)]),
    [interesting(0.65),axiom,file(classes2,c1_62_3__classes2)]).

fof(fc2_card_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ( v1_ordinal1(k1_card_1(A))
        & v2_ordinal1(k1_card_1(A))
        & v3_ordinal1(k1_card_1(A))
        & v1_finset_1(k1_card_1(A))
        & v1_card_1(k1_card_1(A)) ) ) ),
    file(card_1,fc2_card_1),
    [interesting(0.9),axiom,file(card_1,fc2_card_1)]).

fof(cc2_card_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc2_card_1),
    [interesting(0.9),axiom,file(card_1,cc2_card_1)]).

fof(cc3_card_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_finset_1(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc3_card_1),
    [interesting(0.9),axiom,file(card_1,cc3_card_1)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dh_c2_62_3__classes2,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_62__classes2))
        & c1_62_3__classes2 = k1_funct_1(c1_62__classes2,A) )
   => ( r2_hidden(c2_62_3__classes2,k1_relat_1(c1_62__classes2))
      & c1_62_3__classes2 = k1_funct_1(c1_62__classes2,c2_62_3__classes2) ) ),
    introduced(definition,[new_symbol(c2_62_3__classes2),file(classes2,c2_62_3__classes2)]),
    [interesting(0.65),axiom,file(classes2,c2_62_3__classes2)]).

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_62_3__classes2,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_62__classes2))
      & c1_62_3__classes2 = k1_funct_1(c1_62__classes2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc3_ordinal1,fc5_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_62__classes2,dt_c1_62_3__classes2,t1_subset,t7_boole,e1_62_3__classes2,d5_funct_1]),
    [interesting(0.65),file(classes2,e2_62_3__classes2),[file(classes2,e2_62_3__classes2)]]).

fof(dt_c2_62_3__classes2,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[dh_c2_62_3__classes2,e2_62_3__classes2]),
    [interesting(0.65),file(classes2,c2_62_3__classes2),[file(classes2,c2_62_3__classes2)]]).

fof(de_c3_62_3__classes2,definition,(
    c3_62_3__classes2 = c2_62_3__classes2 ),
    introduced(definition,[new_symbol(c3_62_3__classes2),file(classes2,c3_62_3__classes2)]),
    [interesting(0.65),axiom,file(classes2,c3_62_3__classes2)]).

fof(e3_62_3__classes2,plain,
    ( r2_hidden(c2_62_3__classes2,k1_relat_1(c1_62__classes2))
    & c1_62_3__classes2 = k1_funct_1(c1_62__classes2,c2_62_3__classes2) ),
    inference(consider,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[dh_c2_62_3__classes2,e2_62_3__classes2]),
    [interesting(0.65),file(classes2,e3_62_3__classes2),[file(classes2,e3_62_3__classes2)]]).

fof(t23_ordinal1,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t23_ordinal1)]).

fof(e4_62_3__classes2,plain,(
    v3_ordinal1(c2_62_3__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,fc2_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc2_ordinal1,cc3_ordinal1,fc5_ordinal1,rc1_ordinal1,rc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_c1_62__classes2,dt_c1_62_3__classes2,dt_c2_62_3__classes2,cc1_ordinal1,t1_subset,t7_boole,e3_62_3__classes2,t23_ordinal1]),
    [interesting(0.65),file(classes2,e4_62_3__classes2),[file(classes2,e4_62_3__classes2)]]).

fof(dt_c3_62_3__classes2,plain,(
    v3_ordinal1(c3_62_3__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[cc2_ordinal1,rc1_ordinal1,dt_c2_62_3__classes2,cc1_ordinal1,de_c3_62_3__classes2,e4_62_3__classes2]),
    [interesting(0.65),file(classes2,c3_62_3__classes2),[file(classes2,c3_62_3__classes2)]]).

fof(e2_62__classes2,plain,
    ( k1_relat_1(c1_62__classes2) = k5_ordinal2
    & ! [A] : 
        ( v3_ordinal1(A)
       => ( r2_hidden(A,k5_ordinal2)
         => k1_funct_1(c1_62__classes2,A) = k4_classes1(A) ) ) ),
    inference(consider,[status(thm),assumptions([])],[dh_c1_62__classes2,e1_62__classes2]),
    [interesting(0.8),file(classes2,e2_62__classes2),[file(classes2,e2_62__classes2)]]).

fof(e5_62_3__classes2,plain,(
    c1_62_3__classes2 = k4_classes1(c3_62_3__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,fc2_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc2_ordinal1,cc3_ordinal1,fc5_ordinal1,rc1_ordinal1,rc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_classes1,dt_k5_ordinal2,dt_c1_62__classes2,dt_c1_62_3__classes2,dt_c2_62_3__classes2,dt_c3_62_3__classes2,de_c3_62_3__classes2,cc1_ordinal1,fc1_ordinal2,t1_subset,t7_boole,e2_62__classes2,e3_62_3__classes2]),
    [interesting(0.65),file(classes2,e5_62_3__classes2),[file(classes2,e5_62_3__classes2)]]).

fof(t57_card_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v1_finset_1(k4_classes1(A)) ) ),
    file(card_3,t57_card_3),
    [interesting(0.9),axiom,file(card_3,t57_card_3)]).

fof(e6_62_3__classes2,plain,(
    v1_finset_1(c1_62_3__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_card_1,fc2_ordinal1,rc1_card_1,rc2_card_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc2_card_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,fc1_subset_1,fc5_ordinal1,rc1_ordinal1,rc1_subset_1,rc2_subset_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k4_classes1,dt_k5_numbers,dt_k5_ordinal2,dt_m2_subset_1,dt_c1_62__classes2,dt_c1_62_3__classes2,dt_c2_62_3__classes2,dt_c3_62_3__classes2,de_c3_62_3__classes2,cc1_ordinal1,fc1_ordinal2,t1_subset,t7_boole,e5_62_3__classes2,e2_62__classes2,e3_62_3__classes2,t57_card_3]),
    [interesting(0.65),file(classes2,e6_62_3__classes2),[file(classes2,e6_62_3__classes2)]]).

fof(t58_card_3,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)) ) ),
    file(card_3,t58_card_3),
    [interesting(0.9),axiom,file(card_3,t58_card_3)]).

fof(e7_62_3__classes2,plain,(
    r2_hidden(k1_card_1(c1_62_3__classes2),k1_card_1(k5_ordinal2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,fc2_ordinal1,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_card_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k5_ordinal2,dt_c1_62_3__classes2,fc1_ordinal2,fc2_card_1,t1_subset,t7_boole,e6_62_3__classes2,t58_card_3]),
    [interesting(0.65),file(classes2,e7_62_3__classes2),[file(classes2,e7_62_3__classes2)]]).

fof(i3_62_3__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i3_62_3__classes2)]),
    [interesting(0.65),trivial,file(classes2,i3_62_3__classes2)]).

fof(i2_62_3__classes2,plain,(
    r2_hidden(k1_card_1(c1_62_3__classes2),k1_card_1(k5_ordinal2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_62_3__classes2,e1_62_3__classes2])],[e7_62_3__classes2,i3_62_3__classes2]),
    [interesting(0.65),file(classes2,i2_62_3__classes2),[file(classes2,i2_62_3__classes2)]]).

fof(i1_62_3__classes2,plain,
    ( r2_hidden(c1_62_3__classes2,k2_relat_1(c1_62__classes2))
   => r2_hidden(k1_card_1(c1_62_3__classes2),k1_card_1(k5_ordinal2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_62_3__classes2]),discharge_asm(discharge,[e1_62_3__classes2])],[e1_62_3__classes2,i2_62_3__classes2]),
    [interesting(0.65),file(classes2,i1_62_3__classes2),[file(classes2,i1_62_3__classes2)]]).

fof(i1_62_3_tmp__classes2,plain,
    ( r2_hidden(c1_62_3__classes2,k2_relat_1(c1_62__classes2))
   => r2_hidden(k1_card_1(c1_62_3__classes2),k1_card_1(k5_ordinal2)) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_62_3__classes2])],[dt_c1_62_3__classes2,i1_62_3__classes2]),
    [interesting(0.8),e7_62__classes2]).

fof(e7_62__classes2,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_relat_1(c1_62__classes2))
     => r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)) ) ),
    inference(let,[status(thm),assumptions([])],[i1_62_3_tmp__classes2,dh_c1_62_3__classes2]),
    [interesting(0.8),file(classes2,e7_62__classes2),[file(classes2,e7_62__classes2)]]).

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(reflexivity_r1_ordinal1,theorem,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => r1_ordinal1(A,A) ) ),
    file(ordinal1,r1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,r1_ordinal1)]).

fof(connectedness_r1_ordinal1,theorem,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
        | r1_ordinal1(B,A) ) ) ),
    file(ordinal1,r1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,r1_ordinal1)]).

fof(redefinition_r1_ordinal1,definition,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
      <=> r1_tarski(A,B) ) ) ),
    file(ordinal1,r1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,r1_ordinal1)]).

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

fof(t25_classes2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ( ( v4_ordinal1(k1_relat_1(A))
          & ! [B] : 
              ( v3_ordinal1(B)
             => ( r2_hidden(B,k1_relat_1(A))
               => k1_funct_1(A,B) = k4_classes1(B) ) ) )
       => k4_classes1(k1_relat_1(A)) = k3_card_3(A) ) ) ),
    file(classes2,t25_classes2),
    [interesting(0.9),axiom,file(classes2,t25_classes2)]).

fof(t19_ordinal2,theorem,
    ( r2_hidden(k1_xboole_0,k5_ordinal2)
    & v4_ordinal1(k5_ordinal2)
    & ! [A] : 
        ( v3_ordinal1(A)
       => ( ( r2_hidden(k1_xboole_0,A)
            & v4_ordinal1(A) )
         => r1_ordinal1(k5_ordinal2,A) ) ) ),
    file(ordinal2,t19_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,t19_ordinal2)]).

fof(e1_62_1__classes2,plain,(
    k4_classes1(k5_ordinal2) = k3_card_3(c1_62__classes2) ),
    inference(mizar_by,[status(thm),assumptions([])],[dt_k1_zfmisc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_subset_1,dt_m1_subset_1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t2_subset,t3_subset,t8_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k3_card_3,dt_k4_classes1,dt_k5_ordinal2,dt_c1_62__classes2,cc1_ordinal1,fc1_ordinal2,fc2_ordinal1,fc5_ordinal1,rc4_ordinal1,t1_subset,t6_boole,t7_boole,e2_62__classes2,t25_classes2,t19_ordinal2]),
    [interesting(0.65),file(classes2,e1_62_1__classes2),[file(classes2,e1_62_1__classes2)]]).

fof(d4_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    [interesting(0.9),axiom,file(card_3,d4_card_3)]).

fof(e2_62_1__classes2,plain,(
    k3_card_3(c1_62__classes2) = k3_tarski(k2_relat_1(c1_62__classes2)) ),
    inference(mizar_by,[status(thm),assumptions([])],[rc4_ordinal1,dt_k2_relat_1,dt_k3_card_3,dt_k3_tarski,dt_c1_62__classes2,d4_card_3]),
    [interesting(0.65),file(classes2,e2_62_1__classes2),[file(classes2,e2_62_1__classes2)]]).

fof(e3_62__classes2,plain,(
    k4_classes1(k5_ordinal2) = k3_tarski(k2_relat_1(c1_62__classes2)) ),
    inference(iterative_eq,[status(thm),assumptions([])],[e1_62_1__classes2,e2_62_1__classes2]),
    [interesting(0.8),file(classes2,e3_62__classes2),[file(classes2,e3_62__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(e4_62__classes2,plain,(
    r1_tarski(k5_ordinal2,k4_classes1(k5_ordinal2)) ),
    inference(mizar_by,[status(thm),assumptions([])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_ordinal1,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_ordinal1,rc1_subset_1,rc2_subset_1,rc3_ordinal1,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,dt_k4_classes1,dt_k5_ordinal2,cc1_ordinal1,fc1_ordinal2,t3_subset,t44_classes1]),
    [interesting(0.8),file(classes2,e4_62__classes2),[file(classes2,e4_62__classes2)]]).

fof(symmetry_r3_xboole_0,theorem,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
     => r3_xboole_0(B,A) ) ),
    file(xboole_0,r3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r3_xboole_0)]).

fof(reflexivity_r3_xboole_0,theorem,(
    ! [A,B] : r3_xboole_0(A,A) ),
    file(xboole_0,r3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r3_xboole_0)]).

fof(dh_c1_62_2__classes2,definition,
    ( ! [A] : 
        ( ( r2_hidden(c1_62_2__classes2,k2_relat_1(c1_62__classes2))
          & r2_hidden(A,k2_relat_1(c1_62__classes2)) )
       => r3_xboole_0(c1_62_2__classes2,A) )
   => ! [B,C] : 
        ( ( r2_hidden(B,k2_relat_1(c1_62__classes2))
          & r2_hidden(C,k2_relat_1(c1_62__classes2)) )
       => r3_xboole_0(B,C) ) ),
    introduced(definition,[new_symbol(c1_62_2__classes2),file(classes2,c1_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,c1_62_2__classes2)]).

fof(dh_c2_62_2__classes2,definition,
    ( ( ( r2_hidden(c1_62_2__classes2,k2_relat_1(c1_62__classes2))
        & r2_hidden(c2_62_2__classes2,k2_relat_1(c1_62__classes2)) )
     => r3_xboole_0(c1_62_2__classes2,c2_62_2__classes2) )
   => ! [A] : 
        ( ( r2_hidden(c1_62_2__classes2,k2_relat_1(c1_62__classes2))
          & r2_hidden(A,k2_relat_1(c1_62__classes2)) )
       => r3_xboole_0(c1_62_2__classes2,A) ) ),
    introduced(definition,[new_symbol(c2_62_2__classes2),file(classes2,c2_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,c2_62_2__classes2)]).

fof(e1_62_2__classes2,assumption,(
    r2_hidden(c1_62_2__classes2,k2_relat_1(c1_62__classes2)) ),
    introduced(assumption,[file(classes2,e1_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,e1_62_2__classes2)]).

fof(e4_62_2__classes2,assumption,(
    r2_hidden(c2_62_2__classes2,k2_relat_1(c1_62__classes2)) ),
    introduced(assumption,[file(classes2,e4_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,e4_62_2__classes2)]).

fof(dt_c1_62_2__classes2,assumption,(
    $true ),
    introduced(assumption,[file(classes2,c1_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,c1_62_2__classes2)]).

fof(dt_c2_62_2__classes2,assumption,(
    $true ),
    introduced(assumption,[file(classes2,c2_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,c2_62_2__classes2)]).

fof(dh_c3_62_2__classes2,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_62__classes2))
        & c1_62_2__classes2 = k1_funct_1(c1_62__classes2,A) )
   => ( r2_hidden(c3_62_2__classes2,k1_relat_1(c1_62__classes2))
      & c1_62_2__classes2 = k1_funct_1(c1_62__classes2,c3_62_2__classes2) ) ),
    introduced(definition,[new_symbol(c3_62_2__classes2),file(classes2,c3_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,c3_62_2__classes2)]).

fof(e2_62_2__classes2,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_62__classes2))
      & c1_62_2__classes2 = k1_funct_1(c1_62__classes2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc3_ordinal1,fc5_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_62__classes2,dt_c1_62_2__classes2,t1_subset,t7_boole,e1_62_2__classes2,d5_funct_1]),
    [interesting(0.65),file(classes2,e2_62_2__classes2),[file(classes2,e2_62_2__classes2)]]).

fof(dt_c3_62_2__classes2,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2])],[dh_c3_62_2__classes2,e2_62_2__classes2]),
    [interesting(0.65),file(classes2,c3_62_2__classes2),[file(classes2,c3_62_2__classes2)]]).

fof(dh_c4_62_2__classes2,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_62__classes2))
        & c2_62_2__classes2 = k1_funct_1(c1_62__classes2,A) )
   => ( r2_hidden(c4_62_2__classes2,k1_relat_1(c1_62__classes2))
      & c2_62_2__classes2 = k1_funct_1(c1_62__classes2,c4_62_2__classes2) ) ),
    introduced(definition,[new_symbol(c4_62_2__classes2),file(classes2,c4_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,c4_62_2__classes2)]).

fof(e5_62_2__classes2,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_62__classes2))
      & c2_62_2__classes2 = k1_funct_1(c1_62__classes2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_62_2__classes2,e4_62_2__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc3_ordinal1,fc5_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_62__classes2,dt_c2_62_2__classes2,t1_subset,t7_boole,e4_62_2__classes2,d5_funct_1]),
    [interesting(0.65),file(classes2,e5_62_2__classes2),[file(classes2,e5_62_2__classes2)]]).

fof(dt_c4_62_2__classes2,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_62_2__classes2,e4_62_2__classes2])],[dh_c4_62_2__classes2,e5_62_2__classes2]),
    [interesting(0.65),file(classes2,c4_62_2__classes2),[file(classes2,c4_62_2__classes2)]]).

fof(de_c5_62_2__classes2,definition,(
    c5_62_2__classes2 = c3_62_2__classes2 ),
    introduced(definition,[new_symbol(c5_62_2__classes2),file(classes2,c5_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,c5_62_2__classes2)]).

fof(e3_62_2__classes2,plain,
    ( r2_hidden(c3_62_2__classes2,k1_relat_1(c1_62__classes2))
    & c1_62_2__classes2 = k1_funct_1(c1_62__classes2,c3_62_2__classes2) ),
    inference(consider,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2])],[dh_c3_62_2__classes2,e2_62_2__classes2]),
    [interesting(0.65),file(classes2,e3_62_2__classes2),[file(classes2,e3_62_2__classes2)]]).

fof(e6_62_2__classes2,plain,
    ( r2_hidden(c4_62_2__classes2,k1_relat_1(c1_62__classes2))
    & c2_62_2__classes2 = k1_funct_1(c1_62__classes2,c4_62_2__classes2) ),
    inference(consider,[status(thm),assumptions([dt_c2_62_2__classes2,e4_62_2__classes2])],[dh_c4_62_2__classes2,e5_62_2__classes2]),
    [interesting(0.65),file(classes2,e6_62_2__classes2),[file(classes2,e6_62_2__classes2)]]).

fof(e7_62_2__classes2,plain,
    ( v3_ordinal1(c3_62_2__classes2)
    & v3_ordinal1(c4_62_2__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2,dt_c2_62_2__classes2,e4_62_2__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,fc2_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc2_ordinal1,cc3_ordinal1,fc5_ordinal1,rc1_ordinal1,rc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_c1_62__classes2,dt_c1_62_2__classes2,dt_c2_62_2__classes2,dt_c3_62_2__classes2,dt_c4_62_2__classes2,cc1_ordinal1,t1_subset,t7_boole,e3_62_2__classes2,e6_62_2__classes2,t23_ordinal1]),
    [interesting(0.65),file(classes2,e7_62_2__classes2),[file(classes2,e7_62_2__classes2)]]).

fof(dt_c5_62_2__classes2,plain,(
    v3_ordinal1(c5_62_2__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2,dt_c2_62_2__classes2,e4_62_2__classes2])],[cc2_ordinal1,rc1_ordinal1,dt_c3_62_2__classes2,dt_c4_62_2__classes2,cc1_ordinal1,de_c5_62_2__classes2,e7_62_2__classes2]),
    [interesting(0.65),file(classes2,c5_62_2__classes2),[file(classes2,c5_62_2__classes2)]]).

fof(de_c6_62_2__classes2,definition,(
    c6_62_2__classes2 = c4_62_2__classes2 ),
    introduced(definition,[new_symbol(c6_62_2__classes2),file(classes2,c6_62_2__classes2)]),
    [interesting(0.65),axiom,file(classes2,c6_62_2__classes2)]).

fof(dt_c6_62_2__classes2,plain,(
    v3_ordinal1(c6_62_2__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2,dt_c2_62_2__classes2,e4_62_2__classes2])],[cc2_ordinal1,rc1_ordinal1,dt_c3_62_2__classes2,dt_c4_62_2__classes2,cc1_ordinal1,de_c6_62_2__classes2,e7_62_2__classes2]),
    [interesting(0.65),file(classes2,c6_62_2__classes2),[file(classes2,c6_62_2__classes2)]]).

fof(e8_62_2__classes2,plain,
    ( c1_62_2__classes2 = k4_classes1(c5_62_2__classes2)
    & c2_62_2__classes2 = k4_classes1(c6_62_2__classes2)
    & ( r1_ordinal1(c5_62_2__classes2,c6_62_2__classes2)
      | r1_ordinal1(c6_62_2__classes2,c5_62_2__classes2) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2,dt_c2_62_2__classes2,e4_62_2__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc2_ordinal1,rc1_subset_1,rc2_subset_1,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_subset_1,dt_m1_subset_1,cc2_ordinal1,cc3_ordinal1,fc5_ordinal1,rc1_ordinal1,rc3_ordinal1,rc4_ordinal1,t2_subset,t3_subset,t6_boole,t8_boole,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,antisymmetry_r2_hidden,redefinition_r1_ordinal1,dt_k1_funct_1,dt_k1_relat_1,dt_k4_classes1,dt_k5_ordinal2,dt_c1_62__classes2,dt_c1_62_2__classes2,dt_c2_62_2__classes2,dt_c3_62_2__classes2,dt_c4_62_2__classes2,dt_c5_62_2__classes2,dt_c6_62_2__classes2,de_c5_62_2__classes2,de_c6_62_2__classes2,cc1_ordinal1,fc1_ordinal2,t1_subset,t7_boole,e2_62__classes2,e3_62_2__classes2,e6_62_2__classes2]),
    [interesting(0.65),file(classes2,e8_62_2__classes2),[file(classes2,e8_62_2__classes2)]]).

fof(t43_classes1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
          <=> r1_tarski(k4_classes1(A),k4_classes1(B)) ) ) ) ),
    file(classes1,t43_classes1),
    [interesting(0.9),axiom,file(classes1,t43_classes1)]).

fof(e9_62_2__classes2,plain,
    ( r1_tarski(c1_62_2__classes2,c2_62_2__classes2)
    | r1_tarski(c2_62_2__classes2,c1_62_2__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2,dt_c2_62_2__classes2,e4_62_2__classes2])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_ordinal1,t1_subset,t4_subset,t5_subset,cc3_ordinal1,rc1_subset_1,rc2_subset_1,rc3_ordinal1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c3_62_2__classes2,dt_c4_62_2__classes2,cc2_ordinal1,fc1_subset_1,rc1_ordinal1,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,redefinition_r1_ordinal1,dt_k4_classes1,dt_c1_62_2__classes2,dt_c2_62_2__classes2,dt_c5_62_2__classes2,dt_c6_62_2__classes2,de_c5_62_2__classes2,de_c6_62_2__classes2,cc1_ordinal1,t3_subset,e8_62_2__classes2,t43_classes1]),
    [interesting(0.65),file(classes2,e9_62_2__classes2),[file(classes2,e9_62_2__classes2)]]).

fof(d9_xboole_0,definition,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        | r1_tarski(B,A) ) ) ),
    file(xboole_0,d9_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d9_xboole_0)]).

fof(e10_62_2__classes2,plain,(
    r3_xboole_0(c1_62_2__classes2,c2_62_2__classes2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2,dt_c2_62_2__classes2,e4_62_2__classes2])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,t1_subset,t4_subset,t5_subset,t8_boole,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,symmetry_r3_xboole_0,reflexivity_r3_xboole_0,dt_c1_62_2__classes2,dt_c2_62_2__classes2,t3_subset,e9_62_2__classes2,d9_xboole_0]),
    [interesting(0.65),file(classes2,e10_62_2__classes2),[file(classes2,e10_62_2__classes2)]]).

fof(i5_62_2__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i5_62_2__classes2)]),
    [interesting(0.65),trivial,file(classes2,i5_62_2__classes2)]).

fof(i4_62_2__classes2,plain,(
    r3_xboole_0(c1_62_2__classes2,c2_62_2__classes2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2,dt_c2_62_2__classes2,e4_62_2__classes2])],[e10_62_2__classes2,i5_62_2__classes2]),
    [interesting(0.65),file(classes2,i4_62_2__classes2),[file(classes2,i4_62_2__classes2)]]).

fof(i3_62_2__classes2,plain,
    ( r2_hidden(c2_62_2__classes2,k2_relat_1(c1_62__classes2))
   => r3_xboole_0(c1_62_2__classes2,c2_62_2__classes2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_62_2__classes2,e1_62_2__classes2,dt_c2_62_2__classes2]),discharge_asm(discharge,[e4_62_2__classes2])],[e4_62_2__classes2,i4_62_2__classes2]),
    [interesting(0.65),file(classes2,i3_62_2__classes2),[file(classes2,i3_62_2__classes2)]]).

fof(i2_62_2__classes2,plain,
    ( ( r2_hidden(c1_62_2__classes2,k2_relat_1(c1_62__classes2))
      & r2_hidden(c2_62_2__classes2,k2_relat_1(c1_62__classes2)) )
   => r3_xboole_0(c1_62_2__classes2,c2_62_2__classes2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_62_2__classes2,dt_c2_62_2__classes2]),discharge_asm(discharge,[e1_62_2__classes2])],[e1_62_2__classes2,i3_62_2__classes2]),
    [interesting(0.65),file(classes2,i2_62_2__classes2),[file(classes2,i2_62_2__classes2)]]).

fof(i2_62_2_tmp__classes2,plain,
    ( ( r2_hidden(c1_62_2__classes2,k2_relat_1(c1_62__classes2))
      & r2_hidden(c2_62_2__classes2,k2_relat_1(c1_62__classes2)) )
   => r3_xboole_0(c1_62_2__classes2,c2_62_2__classes2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_62_2__classes2]),discharge_asm(discharge,[dt_c2_62_2__classes2])],[dt_c2_62_2__classes2,i2_62_2__classes2]),
    [interesting(0.65),i1_62_2__classes2]).

fof(i1_62_2__classes2,plain,(
    ! [A] : 
      ( ( r2_hidden(c1_62_2__classes2,k2_relat_1(c1_62__classes2))
        & r2_hidden(A,k2_relat_1(c1_62__classes2)) )
     => r3_xboole_0(c1_62_2__classes2,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_62_2__classes2])],[i2_62_2_tmp__classes2,dh_c2_62_2__classes2]),
    [interesting(0.65),file(classes2,i1_62_2__classes2),[file(classes2,i1_62_2__classes2)]]).

fof(i1_62_2_tmp__classes2,plain,(
    ! [A] : 
      ( ( r2_hidden(c1_62_2__classes2,k2_relat_1(c1_62__classes2))
        & r2_hidden(A,k2_relat_1(c1_62__classes2)) )
     => r3_xboole_0(c1_62_2__classes2,A) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_62_2__classes2])],[dt_c1_62_2__classes2,i1_62_2__classes2]),
    [interesting(0.8),e5_62__classes2]).

fof(e5_62__classes2,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,k2_relat_1(c1_62__classes2))
        & r2_hidden(B,k2_relat_1(c1_62__classes2)) )
     => r3_xboole_0(A,B) ) ),
    inference(let,[status(thm),assumptions([])],[i1_62_2_tmp__classes2,dh_c1_62_2__classes2]),
    [interesting(0.8),file(classes2,e5_62__classes2),[file(classes2,e5_62__classes2)]]).

fof(d9_ordinal1,definition,(
    ! [A] : 
      ( v6_ordinal1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => r3_xboole_0(B,C) ) ) ),
    file(ordinal1,d9_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,d9_ordinal1)]).

fof(e6_62__classes2,plain,(
    v6_ordinal1(k2_relat_1(c1_62__classes2)) ),
    inference(mizar_by,[status(thm),assumptions([])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc3_ordinal1,rc4_ordinal1,t2_subset,t6_boole,antisymmetry_r2_hidden,symmetry_r3_xboole_0,reflexivity_r3_xboole_0,dt_k2_relat_1,dt_c1_62__classes2,t1_subset,t7_boole,e5_62__classes2,d9_ordinal1]),
    [interesting(0.8),file(classes2,e6_62__classes2),[file(classes2,e6_62__classes2)]]).

fof(t27_card_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_card_1(A),k1_card_1(B)) ) ),
    file(card_1,t27_card_1),
    [interesting(0.9),axiom,file(card_1,t27_card_1)]).

fof(t62_card_3,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( ( ! [C] : 
                ( r2_hidden(C,B)
               => r2_hidden(k1_card_1(C),A) )
            & v6_ordinal1(B) )
         => r1_tarski(k1_card_1(k3_tarski(B)),A) ) ) ),
    file(card_3,t62_card_3),
    [interesting(0.9),axiom,file(card_3,t62_card_3)]).

fof(e8_62__classes2,plain,
    ( r1_tarski(k1_card_1(k4_classes1(k5_ordinal2)),k1_card_1(k5_ordinal2))
    & r1_tarski(k1_card_1(k5_ordinal2),k1_card_1(k4_classes1(k5_ordinal2))) ),
    inference(mizar_by,[status(thm),assumptions([])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,fc2_ordinal1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,fc4_ordinal1,rc1_ordinal1,rc1_subset_1,rc2_subset_1,rc3_ordinal1,rc4_ordinal1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_card_1,dt_k2_relat_1,dt_k3_tarski,dt_k4_classes1,dt_k5_ordinal2,dt_c1_62__classes2,cc1_card_1,fc1_ordinal2,rc1_card_1,t1_subset,t3_subset,t7_boole,e7_62__classes2,e3_62__classes2,e4_62__classes2,e6_62__classes2,t27_card_1,t62_card_3]),
    [interesting(0.8),file(classes2,e8_62__classes2),[file(classes2,e8_62__classes2)]]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(e9_62__classes2,plain,(
    k1_card_1(k4_classes1(k5_ordinal2)) = k1_card_1(k5_ordinal2) ),
    inference(mizar_by,[status(thm),assumptions([])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_ordinal1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_card_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_card_1,rc1_ordinal1,rc1_subset_1,rc2_subset_1,rc3_ordinal1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_card_1,dt_k4_classes1,dt_k5_ordinal2,fc1_ordinal2,t3_subset,e8_62__classes2,d10_xboole_0]),
    [interesting(0.8),file(classes2,e9_62__classes2),[file(classes2,e9_62__classes2)]]).

fof(i1_62__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i1_62__classes2)]),
    [interesting(0.8),trivial,file(classes2,i1_62__classes2)]).

fof(t69_classes2,theorem,(
    k1_card_1(k4_classes1(k5_ordinal2)) = k1_card_1(k5_ordinal2) ),
    inference(conclusion,[status(thm),assumptions([])],[e9_62__classes2,i1_62__classes2]),
    [interesting(1),file(classes2,t69_classes2),[file(classes2,t69_classes2)]]).