% Mizar ND problem: t10_card_5,card_5,84,46 
fof(dh_c1_4__card_5,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_hidden(c1_4__card_5,k3_card_3(A))
        <=> ? [B] : 
              ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(c1_4__card_5,k1_funct_1(A,B)) ) ) )
   => ! [C,D] : 
        ( ( v1_relat_1(D)
          & v1_funct_1(D) )
       => ( r2_hidden(C,k3_card_3(D))
        <=> ? [E] : 
              ( r2_hidden(E,k1_relat_1(D))
              & r2_hidden(C,k1_funct_1(D,E)) ) ) ) ),
    introduced(definition,[new_symbol(c1_4__card_5),file(card_5,c1_4__card_5)]),
    [interesting(0.8),axiom,file(card_5,c1_4__card_5)]).

fof(dh_c2_4__card_5,definition,
    ( ( ( v1_relat_1(c2_4__card_5)
        & v1_funct_1(c2_4__card_5) )
     => ( r2_hidden(c1_4__card_5,k3_card_3(c2_4__card_5))
      <=> ? [A] : 
            ( r2_hidden(A,k1_relat_1(c2_4__card_5))
            & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,A)) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ( r2_hidden(c1_4__card_5,k3_card_3(B))
        <=> ? [C] : 
              ( r2_hidden(C,k1_relat_1(B))
              & r2_hidden(c1_4__card_5,k1_funct_1(B,C)) ) ) ) ),
    introduced(definition,[new_symbol(c2_4__card_5),file(card_5,c2_4__card_5)]),
    [interesting(0.8),axiom,file(card_5,c2_4__card_5)]).

fof(e1_4_1__card_5,assumption,(
    r2_hidden(c1_4__card_5,k3_card_3(c2_4__card_5)) ),
    introduced(assumption,[file(card_5,e1_4_1__card_5)]),
    [interesting(0.65),axiom,file(card_5,e1_4_1__card_5)]).

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(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_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_c1_4__card_5,assumption,(
    $true ),
    introduced(assumption,[file(card_5,c1_4__card_5)]),
    [interesting(0.8),axiom,file(card_5,c1_4__card_5)]).

fof(dt_c2_4__card_5,assumption,
    ( v1_relat_1(c2_4__card_5)
    & v1_funct_1(c2_4__card_5) ),
    introduced(assumption,[file(card_5,c2_4__card_5)]),
    [interesting(0.8),axiom,file(card_5,c2_4__card_5)]).

fof(dh_c2_4_1__card_5,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c2_4__card_5))
        & c1_4_1__card_5 = k1_funct_1(c2_4__card_5,A) )
   => ( r2_hidden(c2_4_1__card_5,k1_relat_1(c2_4__card_5))
      & c1_4_1__card_5 = k1_funct_1(c2_4__card_5,c2_4_1__card_5) ) ),
    introduced(definition,[new_symbol(c2_4_1__card_5),file(card_5,c2_4_1__card_5)]),
    [interesting(0.65),axiom,file(card_5,c2_4_1__card_5)]).

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_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_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(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(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_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_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(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(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(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_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

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(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

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(rc1_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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(cc1_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

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_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_arytm_3,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

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

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

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(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(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(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(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(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(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(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_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(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(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(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_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dh_c1_4_1__card_5,definition,
    ( ? [A] : 
        ( r2_hidden(c1_4__card_5,A)
        & r2_hidden(A,k2_relat_1(c2_4__card_5)) )
   => ( r2_hidden(c1_4__card_5,c1_4_1__card_5)
      & r2_hidden(c1_4_1__card_5,k2_relat_1(c2_4__card_5)) ) ),
    introduced(definition,[new_symbol(c1_4_1__card_5),file(card_5,c1_4_1__card_5)]),
    [interesting(0.65),axiom,file(card_5,c1_4_1__card_5)]).

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

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

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_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(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(d4_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    [interesting(0.9),axiom,file(card_3,d4_card_3)]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.9),axiom,file(tarski,d4_tarski)]).

fof(e2_4_1__card_5,plain,(
    ? [A] : 
      ( r2_hidden(c1_4__card_5,A)
      & r2_hidden(A,k2_relat_1(c2_4__card_5)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_arytm_3,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc11_finseq_1,fc2_finseq_1,fc2_ordinal1,fc4_ordinal1,fc6_membered,rc1_finset_1,rc1_membered,rc1_ordinal1,rc2_ordinal1,rc3_funct_1,rc3_ordinal1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc3_ordinal1,rc1_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k3_card_3,dt_k3_tarski,dt_c1_4__card_5,dt_c2_4__card_5,t1_subset,t7_boole,d4_card_3,e1_4_1__card_5,d4_tarski]),
    [interesting(0.65),file(card_5,e2_4_1__card_5),[file(card_5,e2_4_1__card_5)]]).

fof(dt_c1_4_1__card_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[dh_c1_4_1__card_5,e2_4_1__card_5]),
    [interesting(0.65),file(card_5,c1_4_1__card_5),[file(card_5,c1_4_1__card_5)]]).

fof(e3_4_1__card_5,plain,
    ( r2_hidden(c1_4__card_5,c1_4_1__card_5)
    & r2_hidden(c1_4_1__card_5,k2_relat_1(c2_4__card_5)) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[dh_c1_4_1__card_5,e2_4_1__card_5]),
    [interesting(0.65),file(card_5,e3_4_1__card_5),[file(card_5,e3_4_1__card_5)]]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e4_4_1__card_5,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c2_4__card_5))
      & c1_4_1__card_5 = k1_funct_1(c2_4__card_5,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_arytm_3,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_finset_1,rc1_membered,rc1_ordinal1,rc2_ordinal1,rc3_funct_1,rc3_ordinal1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc3_ordinal1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_4__card_5,dt_c1_4_1__card_5,dt_c2_4__card_5,rc1_funct_1,t1_subset,t7_boole,e3_4_1__card_5,d5_funct_1]),
    [interesting(0.65),file(card_5,e4_4_1__card_5),[file(card_5,e4_4_1__card_5)]]).

fof(dt_c2_4_1__card_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[dh_c2_4_1__card_5,e4_4_1__card_5]),
    [interesting(0.65),file(card_5,c2_4_1__card_5),[file(card_5,c2_4_1__card_5)]]).

fof(e5_4_1__card_5,plain,
    ( r2_hidden(c2_4_1__card_5,k1_relat_1(c2_4__card_5))
    & c1_4_1__card_5 = k1_funct_1(c2_4__card_5,c2_4_1__card_5) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[dh_c2_4_1__card_5,e4_4_1__card_5]),
    [interesting(0.65),file(card_5,e5_4_1__card_5),[file(card_5,e5_4_1__card_5)]]).

fof(e6_4_1__card_5,plain,
    ( r2_hidden(c2_4_1__card_5,k1_relat_1(c2_4__card_5))
    & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,c2_4_1__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_arytm_3,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_finset_1,rc1_membered,rc1_ordinal1,rc2_ordinal1,rc3_funct_1,rc3_ordinal1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc3_ordinal1,rc1_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_4__card_5,dt_c1_4_1__card_5,dt_c2_4__card_5,dt_c2_4_1__card_5,t1_subset,t7_boole,e3_4_1__card_5,e5_4_1__card_5]),
    [interesting(0.65),file(card_5,e6_4_1__card_5),[file(card_5,e6_4_1__card_5)]]).

fof(i3_4_1__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i3_4_1__card_5)]),
    [interesting(0.65),trivial,file(card_5,i3_4_1__card_5)]).

fof(i2_4_1__card_5,plain,
    ( r2_hidden(c2_4_1__card_5,k1_relat_1(c2_4__card_5))
    & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,c2_4_1__card_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[e6_4_1__card_5,i3_4_1__card_5]),
    [interesting(0.65),file(card_5,i2_4_1__card_5),[file(card_5,i2_4_1__card_5)]]).

fof(i1_4_1__card_5,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c2_4__card_5))
      & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,A)) ) ),
    inference(take,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e1_4_1__card_5])],[rc1_funct_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_c1_4__card_5,dt_c2_4__card_5,dt_c2_4_1__card_5,i2_4_1__card_5]),
    [interesting(0.65),file(card_5,i1_4_1__card_5),[file(card_5,i1_4_1__card_5)]]).

fof(e1_4__card_5,plain,(
    ~ ( r2_hidden(c1_4__card_5,k3_card_3(c2_4__card_5))
      & ! [A] : 
          ~ ( r2_hidden(A,k1_relat_1(c2_4__card_5))
            & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5]),discharge_asm(discharge,[e1_4_1__card_5])],[e1_4_1__card_5,i1_4_1__card_5]),
    [interesting(0.8),file(card_5,e1_4__card_5),[file(card_5,e1_4__card_5)]]).

fof(e2_4__card_5,assumption,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c2_4__card_5))
      & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,A)) ) ),
    introduced(assumption,[file(card_5,e2_4__card_5)]),
    [interesting(0.8),axiom,file(card_5,e2_4__card_5)]).

fof(dh_c3_4__card_5,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c2_4__card_5))
        & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,A)) )
   => ( r2_hidden(c3_4__card_5,k1_relat_1(c2_4__card_5))
      & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,c3_4__card_5)) ) ),
    introduced(definition,[new_symbol(c3_4__card_5),file(card_5,c3_4__card_5)]),
    [interesting(0.8),axiom,file(card_5,c3_4__card_5)]).

fof(dt_c3_4__card_5,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e2_4__card_5])],[dh_c3_4__card_5,e2_4__card_5]),
    [interesting(0.8),file(card_5,c3_4__card_5),[file(card_5,c3_4__card_5)]]).

fof(e3_4__card_5,plain,
    ( r2_hidden(c3_4__card_5,k1_relat_1(c2_4__card_5))
    & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,c3_4__card_5)) ),
    inference(consider,[status(thm),assumptions([e2_4__card_5])],[dh_c3_4__card_5,e2_4__card_5]),
    [interesting(0.8),file(card_5,e3_4__card_5),[file(card_5,e3_4__card_5)]]).

fof(e4_4__card_5,plain,(
    r2_hidden(k1_funct_1(c2_4__card_5,c3_4__card_5),k2_relat_1(c2_4__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e2_4__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_arytm_3,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc6_membered,rc1_finset_1,rc1_membered,rc1_ordinal1,rc2_ordinal1,rc3_funct_1,rc3_ordinal1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc3_ordinal1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_4__card_5,dt_c2_4__card_5,dt_c3_4__card_5,rc1_funct_1,t1_subset,t7_boole,e3_4__card_5,d5_funct_1]),
    [interesting(0.8),file(card_5,e4_4__card_5),[file(card_5,e4_4__card_5)]]).

fof(e5_4__card_5,plain,(
    r2_hidden(c1_4__card_5,k3_card_3(c2_4__card_5)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e2_4__card_5])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_arytm_3,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc4_ordinal1,fc6_membered,rc1_finset_1,rc1_membered,rc1_ordinal1,rc2_ordinal1,rc3_funct_1,rc3_ordinal1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc3_ordinal1,rc1_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_card_3,dt_k3_tarski,dt_c1_4__card_5,dt_c2_4__card_5,dt_c3_4__card_5,t1_subset,t7_boole,d4_card_3,e4_4__card_5,e3_4__card_5,d4_tarski]),
    [interesting(0.8),file(card_5,e5_4__card_5),[file(card_5,e5_4__card_5)]]).

fof(i5_4__card_5,theorem,(
    $true ),
    introduced(tautology,[file(card_5,i5_4__card_5)]),
    [interesting(0.8),trivial,file(card_5,i5_4__card_5)]).

fof(i4_4__card_5,plain,(
    r2_hidden(c1_4__card_5,k3_card_3(c2_4__card_5)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5,e2_4__card_5])],[e5_4__card_5,i5_4__card_5]),
    [interesting(0.8),file(card_5,i4_4__card_5),[file(card_5,i4_4__card_5)]]).

fof(i3_4__card_5,plain,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c2_4__card_5))
        & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,A)) )
   => r2_hidden(c1_4__card_5,k3_card_3(c2_4__card_5)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5]),discharge_asm(discharge,[e2_4__card_5])],[e2_4__card_5,i4_4__card_5]),
    [interesting(0.8),file(card_5,i3_4__card_5),[file(card_5,i3_4__card_5)]]).

fof(i2_4__card_5,plain,
    ( r2_hidden(c1_4__card_5,k3_card_3(c2_4__card_5))
  <=> ? [A] : 
        ( r2_hidden(A,k1_relat_1(c2_4__card_5))
        & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,A)) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__card_5,dt_c2_4__card_5])],[e1_4__card_5,i3_4__card_5]),
    [interesting(0.8),file(card_5,i2_4__card_5),[file(card_5,i2_4__card_5)]]).

fof(i2_4_tmp__card_5,plain,
    ( ( v1_relat_1(c2_4__card_5)
      & v1_funct_1(c2_4__card_5) )
   => ( r2_hidden(c1_4__card_5,k3_card_3(c2_4__card_5))
    <=> ? [A] : 
          ( r2_hidden(A,k1_relat_1(c2_4__card_5))
          & r2_hidden(c1_4__card_5,k1_funct_1(c2_4__card_5,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__card_5]),discharge_asm(discharge,[dt_c2_4__card_5])],[dt_c2_4__card_5,i2_4__card_5]),
    [interesting(0.8),i1_4__card_5]).

fof(i1_4__card_5,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r2_hidden(c1_4__card_5,k3_card_3(A))
      <=> ? [B] : 
            ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(c1_4__card_5,k1_funct_1(A,B)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__card_5])],[i2_4_tmp__card_5,dh_c2_4__card_5]),
    [interesting(0.8),file(card_5,i1_4__card_5),[file(card_5,i1_4__card_5)]]).

fof(i1_4_tmp__card_5,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r2_hidden(c1_4__card_5,k3_card_3(A))
      <=> ? [B] : 
            ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(c1_4__card_5,k1_funct_1(A,B)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__card_5])],[dt_c1_4__card_5,i1_4__card_5]),
    [interesting(1),t10_card_5]).

fof(t10_card_5,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k3_card_3(B))
      <=> ? [C] : 
            ( r2_hidden(C,k1_relat_1(B))
            & r2_hidden(A,k1_funct_1(B,C)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__card_5,dh_c1_4__card_5]),
    [interesting(1),file(card_5,t10_card_5),[file(card_5,t10_card_5)]]).