% Mizar ND problem: t4_card_1,card_1,84,38 
fof(dh_c1_6__card_1,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & r2_wellord2(c1_6__card_1,A) )
   => ! [B] : 
      ? [C] : 
        ( v3_ordinal1(C)
        & r2_wellord2(B,C) ) ),
    introduced(definition,[new_symbol(c1_6__card_1),file(card_1,c1_6__card_1)]),
    [interesting(0.8),axiom,file(card_1,c1_6__card_1)]).

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(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(dt_c1_6__card_1,assumption,(
    $true ),
    introduced(assumption,[file(card_1,c1_6__card_1)]),
    [interesting(0.8),axiom,file(card_1,c1_6__card_1)]).

fof(dt_k2_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k2_wellord1(A,B)) ) ),
    file(wellord1,k2_wellord1),
    [interesting(0.9),axiom,file(wellord1,k2_wellord1)]).

fof(dt_k2_wellord2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v3_ordinal1(k2_wellord2(A)) ) ),
    file(wellord2,k2_wellord2),
    [interesting(0.9),axiom,file(wellord2,k2_wellord2)]).

fof(dh_c2_6__card_1,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & r2_wellord1(A,c1_6__card_1) )
   => ( v1_relat_1(c2_6__card_1)
      & r2_wellord1(c2_6__card_1,c1_6__card_1) ) ),
    introduced(definition,[new_symbol(c2_6__card_1),file(card_1,c2_6__card_1)]),
    [interesting(0.8),axiom,file(card_1,c2_6__card_1)]).

fof(t26_wellord2,theorem,(
    ! [A] : 
    ? [B] : 
      ( v1_relat_1(B)
      & r2_wellord1(B,A) ) ),
    file(wellord2,t26_wellord2),
    [interesting(0.9),axiom,file(wellord2,t26_wellord2)]).

fof(e1_6__card_1,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & r2_wellord1(A,c1_6__card_1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__card_1])],[dt_c1_6__card_1,t26_wellord2]),
    [interesting(0.8),file(card_1,e1_6__card_1),[file(card_1,e1_6__card_1)]]).

fof(dt_c2_6__card_1,plain,(
    v1_relat_1(c2_6__card_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__card_1])],[dh_c2_6__card_1,e1_6__card_1]),
    [interesting(0.8),file(card_1,c2_6__card_1),[file(card_1,c2_6__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(de_c4_6__card_1,definition,(
    c4_6__card_1 = k2_wellord2(k2_wellord1(c2_6__card_1,c1_6__card_1)) ),
    introduced(definition,[new_symbol(c4_6__card_1),file(card_1,c4_6__card_1)]),
    [interesting(0.8),axiom,file(card_1,c4_6__card_1)]).

fof(dt_c4_6__card_1,plain,(
    v3_ordinal1(c4_6__card_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__card_1])],[cc2_ordinal1,rc1_ordinal1,dt_k2_wellord1,dt_k2_wellord2,dt_c1_6__card_1,dt_c2_6__card_1,cc1_ordinal1,de_c4_6__card_1]),
    [interesting(0.8),file(card_1,c4_6__card_1),[file(card_1,c4_6__card_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(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dh_c5_6__card_1,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & r3_wellord1(k2_wellord1(c2_6__card_1,c1_6__card_1),k1_wellord2(c4_6__card_1),A) )
   => ( v1_relat_1(c5_6__card_1)
      & v1_funct_1(c5_6__card_1)
      & r3_wellord1(k2_wellord1(c2_6__card_1,c1_6__card_1),k1_wellord2(c4_6__card_1),c5_6__card_1) ) ),
    introduced(definition,[new_symbol(c5_6__card_1),file(card_1,c5_6__card_1)]),
    [interesting(0.8),axiom,file(card_1,c5_6__card_1)]).

fof(dt_k1_wellord2,axiom,(
    ! [A] : v1_relat_1(k1_wellord2(A)) ),
    file(wellord2,k1_wellord2),
    [interesting(0.9),axiom,file(wellord2,k1_wellord2)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    [interesting(0.9),axiom,file(relat_1,k3_relat_1)]).

fof(e2_6__card_1,plain,(
    r2_wellord1(c2_6__card_1,c1_6__card_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__card_1])],[dh_c2_6__card_1,e1_6__card_1]),
    [interesting(0.8),file(card_1,e2_6__card_1),[file(card_1,e2_6__card_1)]]).

fof(t25_wellord2,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r2_wellord1(B,A)
       => ( k3_relat_1(k2_wellord1(B,A)) = A
          & v2_wellord1(k2_wellord1(B,A)) ) ) ) ),
    file(wellord2,t25_wellord2),
    [interesting(0.9),axiom,file(wellord2,t25_wellord2)]).

fof(e3_6__card_1,plain,
    ( k3_relat_1(k2_wellord1(c2_6__card_1,c1_6__card_1)) = c1_6__card_1
    & v2_wellord1(k2_wellord1(c2_6__card_1,c1_6__card_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__card_1])],[dt_k2_wellord1,dt_k3_relat_1,dt_c1_6__card_1,dt_c2_6__card_1,e2_6__card_1,t25_wellord2]),
    [interesting(0.8),file(card_1,e3_6__card_1),[file(card_1,e3_6__card_1)]]).

fof(d2_wellord2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
       => ! [B] : 
            ( v3_ordinal1(B)
           => ( B = k2_wellord2(A)
            <=> r4_wellord1(A,k1_wellord2(B)) ) ) ) ) ),
    file(wellord2,d2_wellord2),
    [interesting(0.9),axiom,file(wellord2,d2_wellord2)]).

fof(e4_6__card_1,plain,(
    r4_wellord1(k2_wellord1(c2_6__card_1,c1_6__card_1),k1_wellord2(c4_6__card_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__card_1])],[cc2_ordinal1,rc1_ordinal1,dt_k1_wellord2,dt_k2_wellord1,dt_k2_wellord2,dt_k3_relat_1,dt_c1_6__card_1,dt_c2_6__card_1,dt_c4_6__card_1,de_c4_6__card_1,cc1_ordinal1,e3_6__card_1,d2_wellord2]),
    [interesting(0.8),file(card_1,e4_6__card_1),[file(card_1,e4_6__card_1)]]).

fof(d8_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & r3_wellord1(A,B,C) ) ) ) ) ),
    file(wellord1,d8_wellord1),
    [interesting(0.9),axiom,file(wellord1,d8_wellord1)]).

fof(e5_6__card_1,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & r3_wellord1(k2_wellord1(c2_6__card_1,c1_6__card_1),k1_wellord2(c4_6__card_1),A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__card_1])],[cc2_ordinal1,rc1_ordinal1,dt_k2_wellord2,cc1_ordinal1,dt_k1_wellord2,dt_k2_wellord1,dt_c1_6__card_1,dt_c2_6__card_1,dt_c4_6__card_1,de_c4_6__card_1,rc1_funct_1,e4_6__card_1,d8_wellord1]),
    [interesting(0.8),file(card_1,e5_6__card_1),[file(card_1,e5_6__card_1)]]).

fof(dt_c5_6__card_1,plain,
    ( v1_relat_1(c5_6__card_1)
    & v1_funct_1(c5_6__card_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__card_1])],[dh_c5_6__card_1,e5_6__card_1]),
    [interesting(0.8),file(card_1,c5_6__card_1),[file(card_1,c5_6__card_1)]]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(d4_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & k2_relat_1(C) = B ) ) ),
    file(wellord2,d4_wellord2),
    [interesting(0.9),axiom,file(wellord2,d4_wellord2)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_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(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

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(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

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(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_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(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

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_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc2_finset_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]).

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_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_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_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_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(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_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

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(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(e6_6__card_1,plain,(
    r3_wellord1(k2_wellord1(c2_6__card_1,c1_6__card_1),k1_wellord2(c4_6__card_1),c5_6__card_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__card_1])],[dh_c5_6__card_1,e5_6__card_1]),
    [interesting(0.8),file(card_1,e6_6__card_1),[file(card_1,e6_6__card_1)]]).

fof(d7_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r3_wellord1(A,B,C)
              <=> ( k1_relat_1(C) = k3_relat_1(A)
                  & k2_relat_1(C) = k3_relat_1(B)
                  & v2_funct_1(C)
                  & ! [D,E] : 
                      ( r2_hidden(k4_tarski(D,E),A)
                    <=> ( r2_hidden(D,k3_relat_1(A))
                        & r2_hidden(E,k3_relat_1(A))
                        & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) ) ) ) ) ) ) ) ),
    file(wellord1,d7_wellord1),
    [interesting(0.9),axiom,file(wellord1,d7_wellord1)]).

fof(e7_6__card_1,plain,
    ( k1_relat_1(c5_6__card_1) = k3_relat_1(k2_wellord1(c2_6__card_1,c1_6__card_1))
    & k2_relat_1(c5_6__card_1) = k3_relat_1(k1_wellord2(c4_6__card_1))
    & v2_funct_1(c5_6__card_1)
    & ! [A,B] : 
        ( r2_hidden(k4_tarski(A,B),k2_wellord1(c2_6__card_1,c1_6__card_1))
      <=> ( r2_hidden(A,k3_relat_1(k2_wellord1(c2_6__card_1,c1_6__card_1)))
          & r2_hidden(B,k3_relat_1(k2_wellord1(c2_6__card_1,c1_6__card_1)))
          & r2_hidden(k4_tarski(k1_funct_1(c5_6__card_1,A),k1_funct_1(c5_6__card_1,B)),k1_wellord2(c4_6__card_1)) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__card_1])],[rc4_funct_1,dt_k1_xboole_0,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_k2_wellord2,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_funct_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_wellord2,dt_k2_relat_1,dt_k2_wellord1,dt_k3_relat_1,dt_k4_tarski,dt_c1_6__card_1,dt_c2_6__card_1,dt_c4_6__card_1,dt_c5_6__card_1,de_c4_6__card_1,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,d5_tarski,e6_6__card_1,d7_wellord1]),
    [interesting(0.8),file(card_1,e7_6__card_1),[file(card_1,e7_6__card_1)]]).

fof(d1_wellord2,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k1_wellord2(A)
      <=> ( k3_relat_1(B) = A
          & ! [C,D] : 
              ( ( r2_hidden(C,A)
                & r2_hidden(D,A) )
             => ( r2_hidden(k4_tarski(C,D),B)
              <=> r1_tarski(C,D) ) ) ) ) ) ),
    file(wellord2,d1_wellord2),
    [interesting(0.9),axiom,file(wellord2,d1_wellord2)]).

fof(e8_6__card_1,plain,
    ( v2_funct_1(c5_6__card_1)
    & k1_relat_1(c5_6__card_1) = c1_6__card_1
    & k2_relat_1(c5_6__card_1) = c4_6__card_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__card_1])],[rc4_funct_1,dt_k1_xboole_0,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_wellord2,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_funct_1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_funct_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_wellord2,dt_k2_relat_1,dt_k2_wellord1,dt_k3_relat_1,dt_k4_tarski,dt_c1_6__card_1,dt_c2_6__card_1,dt_c4_6__card_1,dt_c5_6__card_1,de_c4_6__card_1,t1_subset,t3_subset,t7_boole,d5_tarski,e2_6__card_1,e7_6__card_1,t25_wellord2,d1_wellord2]),
    [interesting(0.8),file(card_1,e8_6__card_1),[file(card_1,e8_6__card_1)]]).

fof(i4_6__card_1,theorem,(
    $true ),
    introduced(tautology,[file(card_1,i4_6__card_1)]),
    [interesting(0.8),trivial,file(card_1,i4_6__card_1)]).

fof(i3_6__card_1,plain,
    ( v2_funct_1(c5_6__card_1)
    & k1_relat_1(c5_6__card_1) = c1_6__card_1
    & k2_relat_1(c5_6__card_1) = c4_6__card_1 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__card_1])],[e8_6__card_1,i4_6__card_1]),
    [interesting(0.8),file(card_1,i3_6__card_1),[file(card_1,i3_6__card_1)]]).

fof(i2_6__card_1,plain,(
    r2_wellord2(c1_6__card_1,c4_6__card_1) ),
    inference(take,[status(thm),assumptions([dt_c1_6__card_1])],[cc2_ordinal1,rc1_ordinal1,cc1_ordinal1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_relat_1,dt_k2_relat_1,dt_c1_6__card_1,dt_c4_6__card_1,dt_c5_6__card_1,rc1_funct_1,rc3_funct_1,d4_wellord2,i3_6__card_1]),
    [interesting(0.8),file(card_1,i2_6__card_1),[file(card_1,i2_6__card_1)]]).

fof(i1_6__card_1,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & r2_wellord2(c1_6__card_1,A) ) ),
    inference(take,[status(thm),assumptions([dt_c1_6__card_1])],[cc2_ordinal1,rc1_ordinal1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_c1_6__card_1,dt_c4_6__card_1,cc1_ordinal1,i2_6__card_1]),
    [interesting(0.8),file(card_1,i1_6__card_1),[file(card_1,i1_6__card_1)]]).

fof(i1_6_tmp__card_1,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & r2_wellord2(c1_6__card_1,A) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__card_1])],[dt_c1_6__card_1,i1_6__card_1]),
    [interesting(1),t4_card_1]).

fof(t4_card_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( v3_ordinal1(B)
      & r2_wellord2(A,B) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__card_1,dh_c1_6__card_1]),
    [interesting(1),file(card_1,t4_card_1),[file(card_1,t4_card_1)]]).