% Mizar ND problem: t8_card_1,card_1,110,34 
fof(dh_c1_8__card_1,definition,
    ( ( v1_card_1(c1_8__card_1)
     => ! [A] : 
          ( v1_card_1(A)
         => ( c1_8__card_1 = A
          <=> r2_wellord2(c1_8__card_1,A) ) ) )
   => ! [B] : 
        ( v1_card_1(B)
       => ! [C] : 
            ( v1_card_1(C)
           => ( B = C
            <=> r2_wellord2(B,C) ) ) ) ),
    introduced(definition,[new_symbol(c1_8__card_1),file(card_1,c1_8__card_1)]),
    [interesting(0.8),axiom,file(card_1,c1_8__card_1)]).

fof(dh_c2_8__card_1,definition,
    ( ( v1_card_1(c2_8__card_1)
     => ( c1_8__card_1 = c2_8__card_1
      <=> r2_wellord2(c1_8__card_1,c2_8__card_1) ) )
   => ! [A] : 
        ( v1_card_1(A)
       => ( c1_8__card_1 = A
        <=> r2_wellord2(c1_8__card_1,A) ) ) ),
    introduced(definition,[new_symbol(c2_8__card_1),file(card_1,c2_8__card_1)]),
    [interesting(0.8),axiom,file(card_1,c2_8__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(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(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(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(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_8__card_1,assumption,(
    v1_card_1(c1_8__card_1) ),
    introduced(assumption,[file(card_1,c1_8__card_1)]),
    [interesting(0.8),axiom,file(card_1,c1_8__card_1)]).

fof(dt_c2_8__card_1,assumption,(
    v1_card_1(c2_8__card_1) ),
    introduced(assumption,[file(card_1,c2_8__card_1)]),
    [interesting(0.8),axiom,file(card_1,c2_8__card_1)]).

fof(e1_8__card_1,plain,
    ( c1_8__card_1 = c2_8__card_1
   => r2_wellord2(c1_8__card_1,c2_8__card_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__card_1,dt_c2_8__card_1])],[cc1_ordinal1,cc2_ordinal1,rc1_ordinal1,cc1_card_1,rc1_card_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_c1_8__card_1,dt_c2_8__card_1]),
    [interesting(0.8),file(card_1,e1_8__card_1),[file(card_1,e1_8__card_1)]]).

fof(e6_8__card_1,assumption,(
    r2_wellord2(c1_8__card_1,c2_8__card_1) ),
    introduced(assumption,[file(card_1,e6_8__card_1)]),
    [interesting(0.8),axiom,file(card_1,e6_8__card_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(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(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_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_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(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(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(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(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(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(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(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(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_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(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(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(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

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(dh_c3_8__card_1,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & c1_8__card_1 = A
        & ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_wellord2(B,A)
             => r1_ordinal1(A,B) ) ) )
   => ( v3_ordinal1(c3_8__card_1)
      & c1_8__card_1 = c3_8__card_1
      & ! [C] : 
          ( v3_ordinal1(C)
         => ( r2_wellord2(C,c3_8__card_1)
           => r1_ordinal1(c3_8__card_1,C) ) ) ) ),
    introduced(definition,[new_symbol(c3_8__card_1),file(card_1,c3_8__card_1)]),
    [interesting(0.8),axiom,file(card_1,c3_8__card_1)]).

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(d1_card_1,definition,(
    ! [A] : 
      ( v1_card_1(A)
    <=> ? [B] : 
          ( v3_ordinal1(B)
          & A = B
          & ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_wellord2(C,B)
               => r1_ordinal1(B,C) ) ) ) ) ),
    file(card_1,d1_card_1),
    [interesting(0.9),axiom,file(card_1,d1_card_1)]).

fof(e2_8__card_1,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & c1_8__card_1 = A
      & ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_wellord2(B,A)
           => r1_ordinal1(A,B) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__card_1])],[cc2_funct_1,rc1_funct_1,rc2_funct_1,rc2_ordinal1,rc3_funct_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc2_ordinal1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_funct_1,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,fc1_subset_1,reflexivity_r1_tarski,cc2_ordinal1,rc1_ordinal1,t3_subset,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r1_ordinal1,redefinition_r2_wellord2,dt_c1_8__card_1,cc1_card_1,cc1_ordinal1,rc1_card_1,d1_card_1]),
    [interesting(0.8),file(card_1,e2_8__card_1),[file(card_1,e2_8__card_1)]]).

fof(dt_c3_8__card_1,plain,(
    v3_ordinal1(c3_8__card_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_8__card_1])],[dh_c3_8__card_1,e2_8__card_1]),
    [interesting(0.8),file(card_1,c3_8__card_1),[file(card_1,c3_8__card_1)]]).

fof(dh_c4_8__card_1,definition,
    ( ? [A] : 
        ( v3_ordinal1(A)
        & c2_8__card_1 = A
        & ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_wellord2(B,A)
             => r1_ordinal1(A,B) ) ) )
   => ( v3_ordinal1(c4_8__card_1)
      & c2_8__card_1 = c4_8__card_1
      & ! [C] : 
          ( v3_ordinal1(C)
         => ( r2_wellord2(C,c4_8__card_1)
           => r1_ordinal1(c4_8__card_1,C) ) ) ) ),
    introduced(definition,[new_symbol(c4_8__card_1),file(card_1,c4_8__card_1)]),
    [interesting(0.8),axiom,file(card_1,c4_8__card_1)]).

fof(e4_8__card_1,plain,(
    ? [A] : 
      ( v3_ordinal1(A)
      & c2_8__card_1 = A
      & ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_wellord2(B,A)
           => r1_ordinal1(A,B) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_8__card_1])],[cc2_funct_1,rc1_funct_1,rc2_funct_1,rc2_ordinal1,rc3_funct_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc2_ordinal1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_funct_1,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,fc1_subset_1,reflexivity_r1_tarski,cc2_ordinal1,rc1_ordinal1,t3_subset,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r1_ordinal1,redefinition_r2_wellord2,dt_c2_8__card_1,cc1_card_1,cc1_ordinal1,rc1_card_1,d1_card_1]),
    [interesting(0.8),file(card_1,e4_8__card_1),[file(card_1,e4_8__card_1)]]).

fof(dt_c4_8__card_1,plain,(
    v3_ordinal1(c4_8__card_1) ),
    inference(consider,[status(thm),assumptions([dt_c2_8__card_1])],[dh_c4_8__card_1,e4_8__card_1]),
    [interesting(0.8),file(card_1,c4_8__card_1),[file(card_1,c4_8__card_1)]]).

fof(e3_8__card_1,plain,
    ( c1_8__card_1 = c3_8__card_1
    & ! [A] : 
        ( v3_ordinal1(A)
       => ( r2_wellord2(A,c3_8__card_1)
         => r1_ordinal1(c3_8__card_1,A) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_8__card_1])],[dh_c3_8__card_1,e2_8__card_1]),
    [interesting(0.8),file(card_1,e3_8__card_1),[file(card_1,e3_8__card_1)]]).

fof(e5_8__card_1,plain,
    ( c2_8__card_1 = c4_8__card_1
    & ! [A] : 
        ( v3_ordinal1(A)
       => ( r2_wellord2(A,c4_8__card_1)
         => r1_ordinal1(c4_8__card_1,A) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c2_8__card_1])],[dh_c4_8__card_1,e4_8__card_1]),
    [interesting(0.8),file(card_1,e5_8__card_1),[file(card_1,e5_8__card_1)]]).

fof(e8_8__card_1,plain,(
    r1_ordinal1(c3_8__card_1,c4_8__card_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__card_1,dt_c2_8__card_1,e6_8__card_1])],[cc2_funct_1,rc1_funct_1,rc2_funct_1,rc2_ordinal1,rc3_funct_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc2_ordinal1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_funct_1,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,fc1_subset_1,reflexivity_r1_tarski,cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,t3_subset,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r1_ordinal1,redefinition_r2_wellord2,dt_c1_8__card_1,dt_c2_8__card_1,dt_c3_8__card_1,dt_c4_8__card_1,cc1_ordinal1,e3_8__card_1,e5_8__card_1,e6_8__card_1]),
    [interesting(0.8),file(card_1,e8_8__card_1),[file(card_1,e8_8__card_1)]]).

fof(e7_8__card_1,plain,
    ( r1_ordinal1(c4_8__card_1,c3_8__card_1)
    & r2_wellord2(c2_8__card_1,c1_8__card_1) ),
    inference(mizar_by,[status(thm),assumptions([e6_8__card_1,dt_c1_8__card_1,dt_c2_8__card_1])],[cc2_funct_1,rc1_funct_1,rc2_funct_1,rc2_ordinal1,rc3_funct_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc2_ordinal1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_funct_1,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,fc1_subset_1,reflexivity_r1_tarski,cc1_card_1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,t3_subset,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r1_ordinal1,redefinition_r2_wellord2,dt_c1_8__card_1,dt_c2_8__card_1,dt_c3_8__card_1,dt_c4_8__card_1,cc1_ordinal1,e6_8__card_1,e3_8__card_1,e5_8__card_1]),
    [interesting(0.8),file(card_1,e7_8__card_1),[file(card_1,e7_8__card_1)]]).

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_8__card_1,plain,(
    c1_8__card_1 = c2_8__card_1 ),
    inference(mizar_by,[status(thm),assumptions([e6_8__card_1,dt_c1_8__card_1,dt_c2_8__card_1])],[cc2_funct_1,rc1_funct_1,rc2_funct_1,rc2_ordinal1,rc3_funct_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc2_ordinal1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_funct_1,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,cc1_card_1,cc2_ordinal1,fc1_subset_1,rc1_card_1,rc1_ordinal1,reflexivity_r1_ordinal1,connectedness_r1_ordinal1,reflexivity_r1_tarski,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r1_ordinal1,redefinition_r2_wellord2,dt_c1_8__card_1,dt_c2_8__card_1,dt_c3_8__card_1,dt_c4_8__card_1,cc1_ordinal1,t3_subset,e8_8__card_1,e3_8__card_1,e5_8__card_1,e7_8__card_1,d10_xboole_0]),
    [interesting(0.8),file(card_1,e9_8__card_1),[file(card_1,e9_8__card_1)]]).

fof(i5_8__card_1,theorem,(
    $true ),
    introduced(tautology,[file(card_1,i5_8__card_1)]),
    [interesting(0.8),trivial,file(card_1,i5_8__card_1)]).

fof(i4_8__card_1,plain,(
    c1_8__card_1 = c2_8__card_1 ),
    inference(conclusion,[status(thm),assumptions([e6_8__card_1,dt_c1_8__card_1,dt_c2_8__card_1])],[e9_8__card_1,i5_8__card_1]),
    [interesting(0.8),file(card_1,i4_8__card_1),[file(card_1,i4_8__card_1)]]).

fof(i3_8__card_1,plain,
    ( r2_wellord2(c1_8__card_1,c2_8__card_1)
   => c1_8__card_1 = c2_8__card_1 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__card_1,dt_c2_8__card_1]),discharge_asm(discharge,[e6_8__card_1])],[e6_8__card_1,i4_8__card_1]),
    [interesting(0.8),file(card_1,i3_8__card_1),[file(card_1,i3_8__card_1)]]).

fof(i2_8__card_1,plain,
    ( c1_8__card_1 = c2_8__card_1
  <=> r2_wellord2(c1_8__card_1,c2_8__card_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__card_1,dt_c2_8__card_1])],[e1_8__card_1,i3_8__card_1]),
    [interesting(0.8),file(card_1,i2_8__card_1),[file(card_1,i2_8__card_1)]]).

fof(i2_8_tmp__card_1,plain,
    ( v1_card_1(c2_8__card_1)
   => ( c1_8__card_1 = c2_8__card_1
    <=> r2_wellord2(c1_8__card_1,c2_8__card_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__card_1]),discharge_asm(discharge,[dt_c2_8__card_1])],[dt_c2_8__card_1,i2_8__card_1]),
    [interesting(0.8),i1_8__card_1]).

fof(i1_8__card_1,plain,(
    ! [A] : 
      ( v1_card_1(A)
     => ( c1_8__card_1 = A
      <=> r2_wellord2(c1_8__card_1,A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__card_1])],[i2_8_tmp__card_1,dh_c2_8__card_1]),
    [interesting(0.8),file(card_1,i1_8__card_1),[file(card_1,i1_8__card_1)]]).

fof(i1_8_tmp__card_1,plain,
    ( v1_card_1(c1_8__card_1)
   => ! [A] : 
        ( v1_card_1(A)
       => ( c1_8__card_1 = A
        <=> r2_wellord2(c1_8__card_1,A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__card_1])],[dt_c1_8__card_1,i1_8__card_1]),
    [interesting(1),t8_card_1]).

fof(t8_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( A = B
          <=> r2_wellord2(A,B) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__card_1,dh_c1_8__card_1]),
    [interesting(1),file(card_1,t8_card_1),[file(card_1,t8_card_1)]]).