% Mizar ND problem: t39_classes2,classes2,820,42 
fof(dh_c1_33__classes2,definition,
    ( ( v2_classes1(c1_33__classes2)
     => v2_classes1(k4_classes1(k1_card_1(c1_33__classes2))) )
   => ! [A] : 
        ( v2_classes1(A)
       => v2_classes1(k4_classes1(k1_card_1(A))) ) ),
    introduced(definition,[new_symbol(c1_33__classes2),file(classes2,c1_33__classes2)]),
    [interesting(0.8),axiom,file(classes2,c1_33__classes2)]).

fof(e1_33__classes2,assumption,(
    v2_classes1(c1_33__classes2) ),
    introduced(assumption,[file(classes2,e1_33__classes2)]),
    [interesting(0.8),axiom,file(classes2,e1_33__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(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(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(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(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(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(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_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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

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

fof(dt_c1_33__classes2,assumption,(
    $true ),
    introduced(assumption,[file(classes2,c1_33__classes2)]),
    [interesting(0.8),axiom,file(classes2,c1_33__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(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(d1_classes1,definition,(
    ! [A] : 
      ( v1_classes1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r1_tarski(C,B) )
         => r2_hidden(C,A) ) ) ),
    file(classes1,d1_classes1),
    [interesting(0.9),axiom,file(classes1,d1_classes1)]).

fof(d2_classes1,definition,(
    ! [A] : 
      ( v2_classes1(A)
    <=> ( v1_classes1(A)
        & ! [B] : 
            ( r2_hidden(B,A)
           => r2_hidden(k1_zfmisc_1(B),A) )
        & ! [B] : 
            ~ ( r1_tarski(B,A)
              & ~ r2_tarski(B,A)
              & ~ r2_hidden(B,A) ) ) ) ),
    file(classes1,d2_classes1),
    [interesting(0.9),axiom,file(classes1,d2_classes1)]).

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(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(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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_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(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(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(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(t47_classes1,theorem,(
    ! [A,B,C] : 
      ( v3_ordinal1(C)
     => ( ( r1_tarski(A,B)
          & r2_hidden(B,k4_classes1(C)) )
       => r2_hidden(A,k4_classes1(C)) ) ) ),
    file(classes1,t47_classes1),
    [interesting(0.9),axiom,file(classes1,t47_classes1)]).

fof(e2_33__classes2,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2)))
        & r1_tarski(B,A) )
     => r2_hidden(B,k4_classes1(k1_card_1(c1_33__classes2))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_33__classes2])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,fc2_ordinal1,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_card_1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_card_1,rc1_ordinal1,rc1_subset_1,rc2_subset_1,rc3_ordinal1,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_card_1,dt_k4_classes1,dt_c1_33__classes2,cc1_ordinal1,t1_subset,t3_subset,t7_boole,t47_classes1]),
    [interesting(0.8),file(classes2,e2_33__classes2),[file(classes2,e2_33__classes2)]]).

fof(symmetry_r2_wellord2,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(reflexivity_r2_wellord2,theorem,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(redefinition_r2_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(e1_33_1__classes2,assumption,(
    c1_33__classes2 != k1_xboole_0 ),
    introduced(assumption,[file(classes2,e1_33_1__classes2)]),
    [interesting(0.65),axiom,file(classes2,e1_33_1__classes2)]).

fof(dh_c1_33_1_1__classes2,definition,
    ( ( r2_hidden(c1_33_1_1__classes2,k4_classes1(k1_card_1(c1_33__classes2)))
     => r2_hidden(k1_zfmisc_1(c1_33_1_1__classes2),k4_classes1(k1_card_1(c1_33__classes2))) )
   => ! [A] : 
        ( r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2)))
       => r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_card_1(c1_33__classes2))) ) ),
    introduced(definition,[new_symbol(c1_33_1_1__classes2),file(classes2,c1_33_1_1__classes2)]),
    [interesting(0.5),axiom,file(classes2,c1_33_1_1__classes2)]).

fof(e1_33_1_1__classes2,assumption,(
    r2_hidden(c1_33_1_1__classes2,k4_classes1(k1_card_1(c1_33__classes2))) ),
    introduced(assumption,[file(classes2,e1_33_1_1__classes2)]),
    [interesting(0.5),axiom,file(classes2,e1_33_1_1__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(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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(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(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(dt_k1_ordinal1,axiom,(
    $true ),
    file(ordinal1,k1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,k1_ordinal1)]).

fof(dt_c1_33_1_1__classes2,assumption,(
    $true ),
    introduced(assumption,[file(classes2,c1_33_1_1__classes2)]),
    [interesting(0.5),axiom,file(classes2,c1_33_1_1__classes2)]).

fof(dh_c2_33_1_1__classes2,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & r2_hidden(A,k1_card_1(c1_33__classes2))
        & r2_hidden(c1_33_1_1__classes2,k4_classes1(A)) )
   => ( v3_ordinal1(c2_33_1_1__classes2)
      & r2_hidden(c2_33_1_1__classes2,k1_card_1(c1_33__classes2))
      & r2_hidden(c1_33_1_1__classes2,k4_classes1(c2_33_1_1__classes2)) ) ),
    introduced(definition,[new_symbol(c2_33_1_1__classes2),file(classes2,c2_33_1_1__classes2)]),
    [interesting(0.5),axiom,file(classes2,c2_33_1_1__classes2)]).

fof(t46_card_1,theorem,(
    ! [A] : 
      ( r2_wellord2(A,k1_xboole_0)
    <=> A = k1_xboole_0 ) ),
    file(card_1,t46_card_1),
    [interesting(0.9),axiom,file(card_1,t46_card_1)]).

fof(e2_33_1__classes2,plain,(
    ~ r2_wellord2(c1_33__classes2,k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_33__classes2,e1_33_1__classes2])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,t1_subset,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_xboole_0,dt_c1_33__classes2,fc2_ordinal1,t6_boole,e1_33_1__classes2,t46_card_1]),
    [interesting(0.65),file(classes2,e2_33_1__classes2),[file(classes2,e2_33_1__classes2)]]).

fof(t20_classes2,theorem,(
    ! [A] : 
      ( v2_classes1(A)
     => v4_ordinal1(k1_card_1(A)) ) ),
    file(classes2,t20_classes2),
    [interesting(0.9),axiom,file(classes2,t20_classes2)]).

fof(t21_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    [interesting(0.9),axiom,file(card_1,t21_card_1)]).

fof(t47_card_1,theorem,(
    k1_card_1(k1_xboole_0) = k1_xboole_0 ),
    file(card_1,t47_card_1),
    [interesting(0.9),axiom,file(card_1,t47_card_1)]).

fof(e3_33_1__classes2,plain,
    ( k1_card_1(c1_33__classes2) != k1_xboole_0
    & v4_ordinal1(k1_card_1(c1_33__classes2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,t1_subset,cc1_card_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_k1_xboole_0,dt_c1_33__classes2,cc1_classes2,fc2_ordinal1,t6_boole,e2_33_1__classes2,e1_33__classes2,t20_classes2,t21_card_1,t47_card_1]),
    [interesting(0.65),file(classes2,e3_33_1__classes2),[file(classes2,e3_33_1__classes2)]]).

fof(t35_classes1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
       => ( A = k1_xboole_0
          | ! [B] : 
              ( r2_hidden(B,k4_classes1(A))
            <=> ? [C] : 
                  ( v3_ordinal1(C)
                  & r2_hidden(C,A)
                  & r2_hidden(B,k4_classes1(C)) ) ) ) ) ) ),
    file(classes1,t35_classes1),
    [interesting(0.9),axiom,file(classes1,t35_classes1)]).

fof(e2_33_1_1__classes2,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & r2_hidden(A,k1_card_1(c1_33__classes2))
      & r2_hidden(c1_33_1_1__classes2,k4_classes1(A)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_33_1_1__classes2,e1_33_1_1__classes2,dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[existence_m1_subset_1,dt_m1_subset_1,cc1_card_1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_xboole_0,dt_k4_classes1,dt_c1_33__classes2,dt_c1_33_1_1__classes2,cc1_ordinal1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,e1_33_1_1__classes2,e3_33_1__classes2,t35_classes1]),
    [interesting(0.5),file(classes2,e2_33_1_1__classes2),[file(classes2,e2_33_1_1__classes2)]]).

fof(dt_c2_33_1_1__classes2,plain,(
    v3_ordinal1(c2_33_1_1__classes2) ),
    inference(consider,[status(thm),assumptions([dt_c1_33_1_1__classes2,e1_33_1_1__classes2,dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[dh_c2_33_1_1__classes2,e2_33_1_1__classes2]),
    [interesting(0.5),file(classes2,c2_33_1_1__classes2),[file(classes2,c2_33_1_1__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(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(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(e3_33_1_1__classes2,plain,
    ( r2_hidden(c2_33_1_1__classes2,k1_card_1(c1_33__classes2))
    & r2_hidden(c1_33_1_1__classes2,k4_classes1(c2_33_1_1__classes2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_33_1_1__classes2,e1_33_1_1__classes2,dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[dh_c2_33_1_1__classes2,e2_33_1_1__classes2]),
    [interesting(0.5),file(classes2,e3_33_1_1__classes2),[file(classes2,e3_33_1_1__classes2)]]).

fof(t48_classes1,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,k4_classes1(B))
      <=> r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B))) ) ) ),
    file(classes1,t48_classes1),
    [interesting(0.9),axiom,file(classes1,t48_classes1)]).

fof(t41_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
      <=> ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_hidden(B,A)
             => r2_hidden(k1_ordinal1(B),A) ) ) ) ) ),
    file(ordinal1,t41_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,t41_ordinal1)]).

fof(e4_33_1_1__classes2,plain,
    ( r2_hidden(k1_ordinal1(c2_33_1_1__classes2),k1_card_1(c1_33__classes2))
    & r2_hidden(k1_zfmisc_1(c1_33_1_1__classes2),k4_classes1(k1_ordinal1(c2_33_1_1__classes2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_33_1_1__classes2,e1_33_1_1__classes2,dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[reflexivity_r1_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_card_1,cc2_ordinal1,cc3_ordinal1,fc2_subset_1,rc1_card_1,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_ordinal1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_classes1,dt_c1_33__classes2,dt_c1_33_1_1__classes2,dt_c2_33_1_1__classes2,cc1_ordinal1,fc1_ordinal1,fc1_subset_1,fc2_ordinal1,fc3_ordinal1,t1_subset,t6_boole,t7_boole,d1_ordinal1,e3_33_1__classes2,e3_33_1_1__classes2,t48_classes1,t41_ordinal1]),
    [interesting(0.5),file(classes2,e4_33_1_1__classes2),[file(classes2,e4_33_1_1__classes2)]]).

fof(e5_33_1_1__classes2,plain,(
    r2_hidden(k1_zfmisc_1(c1_33_1_1__classes2),k4_classes1(k1_card_1(c1_33__classes2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_33_1_1__classes2,e1_33_1_1__classes2,dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[reflexivity_r1_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_card_1,cc2_ordinal1,cc3_ordinal1,fc2_subset_1,rc1_card_1,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_ordinal1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_classes1,dt_c1_33__classes2,dt_c1_33_1_1__classes2,dt_c2_33_1_1__classes2,cc1_ordinal1,fc1_ordinal1,fc1_subset_1,fc2_ordinal1,fc3_ordinal1,t1_subset,t6_boole,t7_boole,d1_ordinal1,e4_33_1_1__classes2,e3_33_1__classes2,t35_classes1]),
    [interesting(0.5),file(classes2,e5_33_1_1__classes2),[file(classes2,e5_33_1_1__classes2)]]).

fof(i3_33_1_1__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i3_33_1_1__classes2)]),
    [interesting(0.5),trivial,file(classes2,i3_33_1_1__classes2)]).

fof(i2_33_1_1__classes2,plain,(
    r2_hidden(k1_zfmisc_1(c1_33_1_1__classes2),k4_classes1(k1_card_1(c1_33__classes2))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_33_1_1__classes2,e1_33_1_1__classes2,dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[e5_33_1_1__classes2,i3_33_1_1__classes2]),
    [interesting(0.5),file(classes2,i2_33_1_1__classes2),[file(classes2,i2_33_1_1__classes2)]]).

fof(i1_33_1_1__classes2,plain,
    ( r2_hidden(c1_33_1_1__classes2,k4_classes1(k1_card_1(c1_33__classes2)))
   => r2_hidden(k1_zfmisc_1(c1_33_1_1__classes2),k4_classes1(k1_card_1(c1_33__classes2))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_33_1_1__classes2,dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2]),discharge_asm(discharge,[e1_33_1_1__classes2])],[e1_33_1_1__classes2,i2_33_1_1__classes2]),
    [interesting(0.5),file(classes2,i1_33_1_1__classes2),[file(classes2,i1_33_1_1__classes2)]]).

fof(i1_33_1_1_tmp__classes2,plain,
    ( r2_hidden(c1_33_1_1__classes2,k4_classes1(k1_card_1(c1_33__classes2)))
   => r2_hidden(k1_zfmisc_1(c1_33_1_1__classes2),k4_classes1(k1_card_1(c1_33__classes2))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2]),discharge_asm(discharge,[dt_c1_33_1_1__classes2])],[dt_c1_33_1_1__classes2,i1_33_1_1__classes2]),
    [interesting(0.65),e4_33_1__classes2]).

fof(e4_33_1__classes2,plain,(
    ! [A] : 
      ( r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2)))
     => r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_card_1(c1_33__classes2))) ) ),
    inference(let,[status(thm),assumptions([dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[i1_33_1_1_tmp__classes2,dh_c1_33_1_1__classes2]),
    [interesting(0.65),file(classes2,e4_33_1__classes2),[file(classes2,e4_33_1__classes2)]]).

fof(i2_33_1__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i2_33_1__classes2)]),
    [interesting(0.65),trivial,file(classes2,i2_33_1__classes2)]).

fof(i1_33_1__classes2,plain,(
    ! [A] : 
      ( r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2)))
     => r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_card_1(c1_33__classes2))) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_33__classes2,e1_33_1__classes2,e1_33__classes2])],[e4_33_1__classes2,i2_33_1__classes2]),
    [interesting(0.65),file(classes2,i1_33_1__classes2),[file(classes2,i1_33_1__classes2)]]).

fof(e3_33__classes2,plain,
    ( c1_33__classes2 != k1_xboole_0
   => ! [A] : 
        ( r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2)))
       => r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_card_1(c1_33__classes2))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_33__classes2,e1_33__classes2]),discharge_asm(discharge,[e1_33_1__classes2])],[e1_33_1__classes2,i1_33_1__classes2]),
    [interesting(0.8),file(classes2,e3_33__classes2),[file(classes2,e3_33__classes2)]]).

fof(t37_classes2,theorem,(
    ! [A,B] : 
      ~ ( v2_classes1(A)
        & r1_tarski(B,k4_classes1(k1_card_1(A)))
        & ~ r2_wellord2(B,k4_classes1(k1_card_1(A)))
        & ~ r2_hidden(B,k4_classes1(k1_card_1(A))) ) ),
    file(classes2,t37_classes2),
    [interesting(0.9),axiom,file(classes2,t37_classes2)]).

fof(t33_classes1,theorem,(
    k4_classes1(k1_xboole_0) = k1_xboole_0 ),
    file(classes1,t33_classes1),
    [interesting(0.9),axiom,file(classes1,t33_classes1)]).

fof(e4_33__classes2,plain,
    ( ! [A] : 
        ~ ( r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2)))
          & ~ r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_card_1(c1_33__classes2))) )
    & ! [A] : 
        ~ ( r1_tarski(A,k4_classes1(k1_card_1(c1_33__classes2)))
          & ~ r2_tarski(A,k4_classes1(k1_card_1(c1_33__classes2)))
          & ~ r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_33__classes2,e1_33__classes2])],[existence_m1_subset_1,dt_m1_subset_1,cc1_card_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_card_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_classes1,dt_c1_33__classes2,cc1_classes2,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,e3_33__classes2,e1_33__classes2,t37_classes2,t47_card_1,t33_classes1]),
    [interesting(0.8),file(classes2,e4_33__classes2),[file(classes2,e4_33__classes2)]]).

fof(i4_33__classes2,theorem,(
    $true ),
    introduced(tautology,[file(classes2,i4_33__classes2)]),
    [interesting(0.8),trivial,file(classes2,i4_33__classes2)]).

fof(i3_33__classes2,plain,
    ( ! [A] : 
        ~ ( r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2)))
          & ~ r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_card_1(c1_33__classes2))) )
    & ! [A] : 
        ~ ( r1_tarski(A,k4_classes1(k1_card_1(c1_33__classes2)))
          & ~ r2_tarski(A,k4_classes1(k1_card_1(c1_33__classes2)))
          & ~ r2_hidden(A,k4_classes1(k1_card_1(c1_33__classes2))) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_33__classes2,e1_33__classes2])],[e4_33__classes2,i4_33__classes2]),
    [interesting(0.8),file(classes2,i3_33__classes2),[file(classes2,i3_33__classes2)]]).

fof(i2_33__classes2,plain,(
    v2_classes1(k4_classes1(k1_card_1(c1_33__classes2))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_33__classes2,e1_33__classes2])],[cc2_ordinal1,rc1_ordinal1,rc3_ordinal1,cc1_card_1,cc1_ordinal1,cc3_ordinal1,rc1_card_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_card_1,dt_k1_zfmisc_1,dt_k4_classes1,dt_c1_33__classes2,cc1_classes2,fc1_subset_1,d1_classes1,d2_classes1,e2_33__classes2,i3_33__classes2]),
    [interesting(0.8),file(classes2,i2_33__classes2),[file(classes2,i2_33__classes2)]]).

fof(i1_33__classes2,plain,
    ( v2_classes1(c1_33__classes2)
   => v2_classes1(k4_classes1(k1_card_1(c1_33__classes2))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_33__classes2]),discharge_asm(discharge,[e1_33__classes2])],[e1_33__classes2,i2_33__classes2]),
    [interesting(0.8),file(classes2,i1_33__classes2),[file(classes2,i1_33__classes2)]]).

fof(i1_33_tmp__classes2,plain,
    ( v2_classes1(c1_33__classes2)
   => v2_classes1(k4_classes1(k1_card_1(c1_33__classes2))) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_33__classes2])],[dt_c1_33__classes2,i1_33__classes2]),
    [interesting(1),t39_classes2]).

fof(t39_classes2,theorem,(
    ! [A] : 
      ( v2_classes1(A)
     => v2_classes1(k4_classes1(k1_card_1(A))) ) ),
    inference(let,[status(thm),assumptions([])],[i1_33_tmp__classes2,dh_c1_33__classes2]),
    [interesting(1),file(classes2,t39_classes2),[file(classes2,t39_classes2)]]).