% Mizar ND problem: t14_card_4,card_4,166,54 
fof(dh_c1_10__card_4,definition,
    ( ( ~ ( ~ v1_finset_1(c1_10__card_4)
          & ! [A] : 
              ~ ( r1_tarski(A,c1_10__card_4)
                & k1_card_1(A) = k3_card_1(0) ) )
      & ~ ( ? [A] : 
              ( r1_tarski(A,c1_10__card_4)
              & k1_card_1(A) = k3_card_1(0) )
          & v1_finset_1(c1_10__card_4) ) )
   => ! [B] : 
        ( ~ ( ~ v1_finset_1(B)
            & ! [C] : 
                ~ ( r1_tarski(C,B)
                  & k1_card_1(C) = k3_card_1(0) ) )
        & ~ ( ? [C] : 
                ( r1_tarski(C,B)
                & k1_card_1(C) = k3_card_1(0) )
            & v1_finset_1(B) ) ) ),
    introduced(definition,[new_symbol(c1_10__card_4),file(card_4,c1_10__card_4)]),
    [interesting(0.8),axiom,file(card_4,c1_10__card_4)]).

fof(e1_10_1__card_4,assumption,(
    ~ v1_finset_1(c1_10__card_4) ),
    introduced(assumption,[file(card_4,e1_10_1__card_4)]),
    [interesting(0.65),axiom,file(card_4,e1_10_1__card_4)]).

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_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

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(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

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(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

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(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_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(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

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(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

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(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(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

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(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

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(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

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(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

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_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(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_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(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_card_1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_card_1(A))
        & v2_ordinal1(k3_card_1(A))
        & v3_ordinal1(k3_card_1(A))
        & v1_card_1(k3_card_1(A)) ) ) ),
    file(card_1,fc1_card_1),
    [interesting(0.9),axiom,file(card_1,fc1_card_1)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

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(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_k3_card_1,axiom,(
    $true ),
    file(card_1,k3_card_1),
    [interesting(0.9),axiom,file(card_1,k3_card_1)]).

fof(dt_c1_10__card_4,assumption,(
    $true ),
    introduced(assumption,[file(card_4,c1_10__card_4)]),
    [interesting(0.8),axiom,file(card_4,c1_10__card_4)]).

fof(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_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(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_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(fc13_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k9_relat_1(A,B)) ) ),
    file(finset_1,fc13_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc13_finset_1)]).

fof(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & 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_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_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(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc2_finset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc2_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_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(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_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(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(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(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(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(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

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(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_1)]).

fof(dh_c1_10_1__card_4,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & k1_relat_1(A) = k1_card_1(c1_10__card_4)
        & k2_relat_1(A) = c1_10__card_4 )
   => ( v1_relat_1(c1_10_1__card_4)
      & v1_funct_1(c1_10_1__card_4)
      & v2_funct_1(c1_10_1__card_4)
      & k1_relat_1(c1_10_1__card_4) = k1_card_1(c1_10__card_4)
      & k2_relat_1(c1_10_1__card_4) = c1_10__card_4 ) ),
    introduced(definition,[new_symbol(c1_10_1__card_4),file(card_4,c1_10_1__card_4)]),
    [interesting(0.65),axiom,file(card_4,c1_10_1__card_4)]).

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_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(d5_card_1,definition,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( B = k1_card_1(A)
      <=> r2_wellord2(A,B) ) ) ),
    file(card_1,d5_card_1),
    [interesting(0.9),axiom,file(card_1,d5_card_1)]).

fof(e5_10_1__card_4,plain,(
    r2_wellord2(k1_card_1(c1_10__card_4),c1_10__card_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4])],[cc1_ordinal1,cc2_ordinal1,rc1_ordinal1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_c1_10__card_4,cc1_card_1,rc1_card_1,d5_card_1]),
    [interesting(0.65),file(card_4,e5_10_1__card_4),[file(card_4,e5_10_1__card_4)]]).

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(e6_10_1__card_4,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & k1_relat_1(A) = k1_card_1(c1_10__card_4)
      & k2_relat_1(A) = c1_10__card_4 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4])],[cc1_ordinal1,cc2_ordinal1,rc1_ordinal1,cc1_card_1,rc1_card_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_10__card_4,rc1_funct_1,rc3_funct_1,e5_10_1__card_4,d4_wellord2]),
    [interesting(0.65),file(card_4,e6_10_1__card_4),[file(card_4,e6_10_1__card_4)]]).

fof(dt_c1_10_1__card_4,plain,
    ( v1_relat_1(c1_10_1__card_4)
    & v1_funct_1(c1_10_1__card_4) ),
    inference(consider,[status(thm),assumptions([dt_c1_10__card_4])],[dh_c1_10_1__card_4,e6_10_1__card_4]),
    [interesting(0.65),file(card_4,c1_10_1__card_4),[file(card_4,c1_10_1__card_4)]]).

fof(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(de_c2_10_1__card_4,definition,(
    c2_10_1__card_4 = k9_relat_1(c1_10_1__card_4,k3_card_1(0)) ),
    introduced(definition,[new_symbol(c2_10_1__card_4),file(card_4,c2_10_1__card_4)]),
    [interesting(0.65),axiom,file(card_4,c2_10_1__card_4)]).

fof(dt_c2_10_1__card_4,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_card_1,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_ordinal1,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc13_finset_1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_card_1,rc1_finset_1,rc1_membered,rc1_ordinal1,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_finset_1,rc2_ordinal1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc2_funct_1,cc3_card_1,cc3_ordinal1,fc1_card_1,fc2_membered,rc1_funct_1,rc2_funct_1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,dt_k3_card_1,dt_k9_relat_1,dt_c1_10_1__card_4,spc0_numerals,spc0_boole,de_c2_10_1__card_4]),
    [interesting(0.65),file(card_4,c2_10_1__card_4),[file(card_4,c2_10_1__card_4)]]).

fof(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(e7_10_1__card_4,plain,
    ( v2_funct_1(c1_10_1__card_4)
    & k1_relat_1(c1_10_1__card_4) = k1_card_1(c1_10__card_4)
    & k2_relat_1(c1_10_1__card_4) = c1_10__card_4 ),
    inference(consider,[status(thm),assumptions([dt_c1_10__card_4])],[dh_c1_10_1__card_4,e6_10_1__card_4]),
    [interesting(0.65),file(card_4,e7_10_1__card_4),[file(card_4,e7_10_1__card_4)]]).

fof(t144_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ),
    file(relat_1,t144_relat_1),
    [interesting(0.9),axiom,file(relat_1,t144_relat_1)]).

fof(e8_10_1__card_4,plain,(
    r1_tarski(c2_10_1__card_4,c1_10__card_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc11_finseq_1,fc13_finset_1,fc17_finseq_1,fc1_ordinal2,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_xreal_0,rc2_card_1,rc2_finset_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc2_funct_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,cc6_membered,cc9_membered,fc1_card_1,fc2_membered,rc1_ordinal1,rc1_subset_1,rc2_funct_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_card_1,dt_m1_subset_1,cc1_card_1,fc1_subset_1,rc1_card_1,rc1_funct_1,rc3_funct_1,spc0_numerals,spc0_boole,reflexivity_r1_tarski,dt_k1_card_1,dt_k1_relat_1,dt_k2_relat_1,dt_k9_relat_1,dt_c1_10__card_4,dt_c1_10_1__card_4,dt_c2_10_1__card_4,de_c2_10_1__card_4,t3_subset,e7_10_1__card_4,t144_relat_1]),
    [interesting(0.65),file(card_4,e8_10_1__card_4),[file(card_4,e8_10_1__card_4)]]).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    [interesting(0.9),axiom,file(relat_1,k7_relat_1)]).

fof(fc4_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc4_funct_1)]).

fof(t1_card_4,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> v1_finset_1(k1_card_1(A)) ) ),
    file(card_4,t1_card_4),
    [interesting(0.9),axiom,file(card_4,t1_card_4)]).

fof(e2_10_1__card_4,plain,(
    ~ v1_finset_1(k1_card_1(c1_10__card_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4,e1_10_1__card_4])],[cc1_card_1,cc1_ordinal1,cc2_ordinal1,rc1_card_1,rc1_ordinal1,rc2_card_1,dt_k1_card_1,dt_c1_10__card_4,fc2_card_1,e1_10_1__card_4,t1_card_4]),
    [interesting(0.65),file(card_4,e2_10_1__card_4),[file(card_4,e2_10_1__card_4)]]).

fof(t7_card_4,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_finset_1(A)
      <=> r2_hidden(A,k5_ordinal2) ) ) ),
    file(card_4,t7_card_4),
    [interesting(0.9),axiom,file(card_4,t7_card_4)]).

fof(t83_card_1,theorem,(
    k3_card_1(0) = k5_ordinal2 ),
    file(card_1,t83_card_1),
    [interesting(0.9),axiom,file(card_1,t83_card_1)]).

fof(e3_10_1__card_4,plain,(
    ~ r2_hidden(k1_card_1(c1_10__card_4),k3_card_1(0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4,e1_10_1__card_4])],[reflexivity_r1_tarski,cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_card_1,cc2_membered,cc2_ordinal1,cc3_card_1,cc3_membered,cc3_ordinal1,cc4_membered,fc2_membered,rc1_card_1,rc1_finset_1,rc1_membered,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k3_card_1,dt_k5_ordinal2,dt_c1_10__card_4,cc1_ordinal1,fc1_card_1,fc1_ordinal2,fc2_card_1,fc5_membered,t1_subset,t7_boole,spc0_numerals,spc0_boole,e2_10_1__card_4,t7_card_4,t83_card_1]),
    [interesting(0.65),file(card_4,e3_10_1__card_4),[file(card_4,e3_10_1__card_4)]]).

fof(t14_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,B)
          <=> ~ r1_tarski(B,A) ) ) ) ),
    file(card_1,t14_card_1),
    [interesting(0.9),axiom,file(card_1,t14_card_1)]).

fof(e4_10_1__card_4,plain,(
    r1_tarski(k3_card_1(0),k1_card_1(c1_10__card_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4,e1_10_1__card_4])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_ordinal2,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_xreal_0,rc2_card_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,cc6_membered,cc9_membered,fc1_card_1,fc1_subset_1,fc2_membered,rc1_ordinal1,rc1_subset_1,rc2_subset_1,rc3_ordinal1,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_card_1,dt_k3_card_1,dt_c1_10__card_4,cc1_card_1,rc1_card_1,t1_subset,t3_subset,t7_boole,spc0_numerals,spc0_boole,e3_10_1__card_4,t14_card_1]),
    [interesting(0.65),file(card_4,e4_10_1__card_4),[file(card_4,e4_10_1__card_4)]]).

fof(t84_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v2_funct_1(B)
       => v2_funct_1(k7_relat_1(B,A)) ) ) ),
    file(funct_1,t84_funct_1),
    [interesting(0.9),axiom,file(funct_1,t84_funct_1)]).

fof(t91_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    [interesting(0.9),axiom,file(relat_1,t91_relat_1)]).

fof(t148_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A) ) ),
    file(relat_1,t148_relat_1),
    [interesting(0.9),axiom,file(relat_1,t148_relat_1)]).

fof(e1_10_1_1__card_4,plain,
    ( v2_funct_1(k7_relat_1(c1_10_1__card_4,k3_card_1(0)))
    & k1_relat_1(k7_relat_1(c1_10_1__card_4,k3_card_1(0))) = k3_card_1(0)
    & k2_relat_1(k7_relat_1(c1_10_1__card_4,k3_card_1(0))) = c2_10_1__card_4 ),
    inference(mizar_by,[status(thm),assumptions([e1_10_1__card_4,dt_c1_10__card_4])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_ordinal1,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc11_finseq_1,fc13_finset_1,fc17_finseq_1,fc1_ordinal2,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_finset_1,rc2_ordinal1,rc2_xreal_0,rc3_finset_1,rc3_ordinal1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc2_funct_1,cc3_card_1,cc3_ordinal1,cc6_membered,cc9_membered,fc1_card_1,fc1_subset_1,fc2_membered,rc1_card_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_card_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_1,dt_k7_relat_1,dt_k9_relat_1,dt_c1_10__card_4,dt_c1_10_1__card_4,dt_c2_10_1__card_4,de_c2_10_1__card_4,fc4_funct_1,rc1_funct_1,rc3_funct_1,t3_subset,spc0_numerals,spc0_boole,e4_10_1__card_4,e7_10_1__card_4,t84_funct_1,t91_relat_1,t148_relat_1]),
    [interesting(0.5),file(card_4,e1_10_1_1__card_4),[file(card_4,e1_10_1_1__card_4)]]).

fof(i2_10_1_1__card_4,theorem,(
    $true ),
    introduced(tautology,[file(card_4,i2_10_1_1__card_4)]),
    [interesting(0.5),trivial,file(card_4,i2_10_1_1__card_4)]).

fof(i1_10_1_1__card_4,plain,
    ( v2_funct_1(k7_relat_1(c1_10_1__card_4,k3_card_1(0)))
    & k1_relat_1(k7_relat_1(c1_10_1__card_4,k3_card_1(0))) = k3_card_1(0)
    & k2_relat_1(k7_relat_1(c1_10_1__card_4,k3_card_1(0))) = c2_10_1__card_4 ),
    inference(conclusion,[status(thm),assumptions([e1_10_1__card_4,dt_c1_10__card_4])],[e1_10_1_1__card_4,i2_10_1_1__card_4]),
    [interesting(0.5),file(card_4,i1_10_1_1__card_4),[file(card_4,i1_10_1_1__card_4)]]).

fof(e9_10_1__card_4,plain,(
    r2_wellord2(k3_card_1(0),c2_10_1__card_4) ),
    inference(take,[status(thm),assumptions([e1_10_1__card_4,dt_c1_10__card_4])],[dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_card_1,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_ordinal1,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_card_1,rc1_finset_1,rc1_membered,rc1_ordinal1,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_finset_1,rc2_ordinal1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_ordinal1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc2_funct_1,cc3_card_1,cc3_ordinal1,fc1_card_1,fc2_membered,rc2_funct_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_1,dt_k7_relat_1,dt_c1_10_1__card_4,dt_c2_10_1__card_4,fc4_funct_1,rc1_funct_1,rc3_funct_1,spc0_numerals,spc0_boole,d4_wellord2,i1_10_1_1__card_4]),
    [interesting(0.65),file(card_4,e9_10_1__card_4),[file(card_4,e9_10_1__card_4)]]).

fof(e10_10_1__card_4,plain,(
    k1_card_1(c2_10_1__card_4) = k3_card_1(0) ),
    inference(mizar_by,[status(thm),assumptions([e1_10_1__card_4,dt_c1_10__card_4])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc2_finset_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc13_finset_1,fc1_ordinal2,fc1_subset_1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_funct_1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k9_relat_1,dt_m1_subset_1,dt_m2_subset_1,dt_c1_10_1__card_4,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,fc1_card_1,fc2_membered,rc1_ordinal1,rc3_ordinal1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_k3_card_1,dt_c2_10_1__card_4,de_c2_10_1__card_4,cc1_card_1,rc1_card_1,spc0_numerals,spc0_boole,e9_10_1__card_4,d5_card_1]),
    [interesting(0.65),file(card_4,e10_10_1__card_4),[file(card_4,e10_10_1__card_4)]]).

fof(i4_10_1__card_4,theorem,(
    $true ),
    introduced(tautology,[file(card_4,i4_10_1__card_4)]),
    [interesting(0.65),trivial,file(card_4,i4_10_1__card_4)]).

fof(i3_10_1__card_4,plain,(
    k1_card_1(c2_10_1__card_4) = k3_card_1(0) ),
    inference(conclusion,[status(thm),assumptions([e1_10_1__card_4,dt_c1_10__card_4])],[e10_10_1__card_4,i4_10_1__card_4]),
    [interesting(0.65),file(card_4,i3_10_1__card_4),[file(card_4,i3_10_1__card_4)]]).

fof(i2_10_1__card_4,plain,
    ( r1_tarski(c2_10_1__card_4,c1_10__card_4)
    & k1_card_1(c2_10_1__card_4) = k3_card_1(0) ),
    inference(conclusion,[status(thm),assumptions([e1_10_1__card_4,dt_c1_10__card_4])],[e8_10_1__card_4,i3_10_1__card_4]),
    [interesting(0.65),file(card_4,i2_10_1__card_4),[file(card_4,i2_10_1__card_4)]]).

fof(i1_10_1__card_4,plain,(
    ? [A] : 
      ( r1_tarski(A,c1_10__card_4)
      & k1_card_1(A) = k3_card_1(0) ) ),
    inference(take,[status(thm),assumptions([e1_10_1__card_4,dt_c1_10__card_4])],[dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_ordinal1,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc2_card_1,fc5_membered,rc1_finset_1,rc1_membered,rc1_ordinal1,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_ordinal1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc3_card_1,cc3_ordinal1,fc1_card_1,fc2_membered,rc1_card_1,reflexivity_r1_tarski,dt_k1_card_1,dt_k3_card_1,dt_c1_10__card_4,dt_c2_10_1__card_4,spc0_numerals,spc0_boole,i2_10_1__card_4]),
    [interesting(0.65),file(card_4,i1_10_1__card_4),[file(card_4,i1_10_1__card_4)]]).

fof(e1_10__card_4,plain,(
    ~ ( ~ v1_finset_1(c1_10__card_4)
      & ! [A] : 
          ~ ( r1_tarski(A,c1_10__card_4)
            & k1_card_1(A) = k3_card_1(0) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__card_4]),discharge_asm(discharge,[e1_10_1__card_4])],[e1_10_1__card_4,i1_10_1__card_4]),
    [interesting(0.8),file(card_4,e1_10__card_4),[file(card_4,e1_10__card_4)]]).

fof(e2_10__card_4,assumption,(
    ? [A] : 
      ( r1_tarski(A,c1_10__card_4)
      & k1_card_1(A) = k3_card_1(0) ) ),
    introduced(assumption,[file(card_4,e2_10__card_4)]),
    [interesting(0.8),axiom,file(card_4,e2_10__card_4)]).

fof(dh_c2_10__card_4,definition,
    ( ? [A] : 
        ( r1_tarski(A,c1_10__card_4)
        & k1_card_1(A) = k3_card_1(0) )
   => ( r1_tarski(c2_10__card_4,c1_10__card_4)
      & k1_card_1(c2_10__card_4) = k3_card_1(0) ) ),
    introduced(definition,[new_symbol(c2_10__card_4),file(card_4,c2_10__card_4)]),
    [interesting(0.8),axiom,file(card_4,c2_10__card_4)]).

fof(dt_c2_10__card_4,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e2_10__card_4])],[dh_c2_10__card_4,e2_10__card_4]),
    [interesting(0.8),file(card_4,c2_10__card_4),[file(card_4,c2_10__card_4)]]).

fof(e3_10__card_4,plain,
    ( r1_tarski(c2_10__card_4,c1_10__card_4)
    & k1_card_1(c2_10__card_4) = k3_card_1(0) ),
    inference(consider,[status(thm),assumptions([e2_10__card_4])],[dh_c2_10__card_4,e2_10__card_4]),
    [interesting(0.8),file(card_4,e3_10__card_4),[file(card_4,e3_10__card_4)]]).

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(e4_10__card_4,plain,(
    r1_tarski(k1_card_1(c2_10__card_4),k1_card_1(c1_10__card_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4,e2_10__card_4])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_ordinal1,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_ordinal2,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_xreal_0,rc3_finset_1,rc3_ordinal1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc3_card_1,cc3_ordinal1,cc6_membered,cc9_membered,fc1_card_1,fc1_subset_1,fc2_membered,rc1_card_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_card_1,dt_k3_card_1,dt_c1_10__card_4,dt_c2_10__card_4,t3_subset,spc0_numerals,spc0_boole,e3_10__card_4,t27_card_1]),
    [interesting(0.8),file(card_4,e4_10__card_4),[file(card_4,e4_10__card_4)]]).

fof(e5_10__card_4,plain,(
    ~ r2_hidden(k1_card_1(c1_10__card_4),k3_card_1(0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4,e2_10__card_4])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_ordinal2,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_xreal_0,rc2_card_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,cc6_membered,cc9_membered,fc1_card_1,fc1_subset_1,fc2_membered,rc1_ordinal1,rc1_subset_1,rc2_subset_1,rc3_ordinal1,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_card_1,dt_k3_card_1,dt_c1_10__card_4,dt_c2_10__card_4,cc1_card_1,rc1_card_1,t1_subset,t3_subset,t7_boole,spc0_numerals,spc0_boole,e4_10__card_4,e3_10__card_4,t14_card_1]),
    [interesting(0.8),file(card_4,e5_10__card_4),[file(card_4,e5_10__card_4)]]).

fof(t2_card_4,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> r2_hidden(k1_card_1(A),k3_card_1(0)) ) ),
    file(card_4,t2_card_4),
    [interesting(0.9),axiom,file(card_4,t2_card_4)]).

fof(e6_10__card_4,plain,(
    ~ v1_finset_1(c1_10__card_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__card_4,e2_10__card_4])],[reflexivity_r1_tarski,cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t3_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_card_1,cc2_ordinal1,cc3_card_1,cc3_ordinal1,fc1_card_1,fc2_membered,rc1_card_1,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc3_ordinal1,t1_numerals,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_card_1,dt_k3_card_1,dt_c1_10__card_4,fc2_card_1,t1_subset,t7_boole,spc0_numerals,spc0_boole,e5_10__card_4,t2_card_4]),
    [interesting(0.8),file(card_4,e6_10__card_4),[file(card_4,e6_10__card_4)]]).

fof(i4_10__card_4,theorem,(
    $true ),
    introduced(tautology,[file(card_4,i4_10__card_4)]),
    [interesting(0.8),trivial,file(card_4,i4_10__card_4)]).

fof(i3_10__card_4,plain,(
    ~ v1_finset_1(c1_10__card_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_10__card_4,e2_10__card_4])],[e6_10__card_4,i4_10__card_4]),
    [interesting(0.8),file(card_4,i3_10__card_4),[file(card_4,i3_10__card_4)]]).

fof(i2_10__card_4,plain,(
    ~ ( ? [A] : 
          ( r1_tarski(A,c1_10__card_4)
          & k1_card_1(A) = k3_card_1(0) )
      & v1_finset_1(c1_10__card_4) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__card_4]),discharge_asm(discharge,[e2_10__card_4])],[e2_10__card_4,i3_10__card_4]),
    [interesting(0.8),file(card_4,i2_10__card_4),[file(card_4,i2_10__card_4)]]).

fof(i1_10__card_4,plain,
    ( ~ ( ~ v1_finset_1(c1_10__card_4)
        & ! [A] : 
            ~ ( r1_tarski(A,c1_10__card_4)
              & k1_card_1(A) = k3_card_1(0) ) )
    & ~ ( ? [A] : 
            ( r1_tarski(A,c1_10__card_4)
            & k1_card_1(A) = k3_card_1(0) )
        & v1_finset_1(c1_10__card_4) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_10__card_4])],[e1_10__card_4,i2_10__card_4]),
    [interesting(0.8),file(card_4,i1_10__card_4),[file(card_4,i1_10__card_4)]]).

fof(i1_10_tmp__card_4,plain,
    ( ~ ( ~ v1_finset_1(c1_10__card_4)
        & ! [A] : 
            ~ ( r1_tarski(A,c1_10__card_4)
              & k1_card_1(A) = k3_card_1(0) ) )
    & ~ ( ? [A] : 
            ( r1_tarski(A,c1_10__card_4)
            & k1_card_1(A) = k3_card_1(0) )
        & v1_finset_1(c1_10__card_4) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_10__card_4])],[dt_c1_10__card_4,i1_10__card_4]),
    [interesting(1),t14_card_4]).

fof(t14_card_4,theorem,(
    ! [A] : 
      ( ~ ( ~ v1_finset_1(A)
          & ! [B] : 
              ~ ( r1_tarski(B,A)
                & k1_card_1(B) = k3_card_1(0) ) )
      & ~ ( ? [B] : 
              ( r1_tarski(B,A)
              & k1_card_1(B) = k3_card_1(0) )
          & v1_finset_1(A) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_10_tmp__card_4,dh_c1_10__card_4]),
    [interesting(1),file(card_4,t14_card_4),[file(card_4,t14_card_4)]]).