% Mizar problem: t25_card_lar,card_lar,817,63 
fof(t25_card_lar,conjecture,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( r2_hidden(k3_card_1(0),k1_card_5(A))
              & v1_card_lar(B,A) )
           => ! [C] : 
                ( v3_ordinal1(C)
               => ~ ( r2_hidden(C,A)
                    & ! [D] : 
                        ( ( v3_ordinal1(D)
                          & v4_ordinal1(D)
                          & ~ v1_finset_1(D) )
                       => ~ ( r2_hidden(D,A)
                            & r2_hidden(C,D)
                            & r2_hidden(D,k4_card_lar(A,B)) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_card_1,cc1_card_5,cc1_card_lar,cc1_ordinal1,cc1_relset_1,cc2_arytm_3,cc2_card_1,cc2_card_5,cc2_card_lar,cc2_ordinal1,cc3_arytm_3,cc3_card_1,cc3_ordinal1,commutativity_k1_nat_1,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xboole_0,connectedness_r1_ordinal1,d1_funct_2,d1_ordinal1,d3_xboole_0,d5_funct_1,d9_card_lar,dt_k1_card_5,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_ordinal1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_card_lar,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_card_1,dt_k3_xboole_0,dt_k4_card_lar,dt_k4_relset_1,dt_k5_numbers,dt_k5_ordinal2,dt_k7_ordinal2,dt_k8_funct_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc1_card_1,fc1_ordinal1,fc1_ordinal2,fc1_ordinal3,fc1_subset_1,fc2_arytm_3,fc2_card_5,fc2_ordinal1,fc2_ordinal3,fc2_subset_1,fc3_ordinal1,fc4_subset_1,fc8_card_5,fraenkel_a_2_0_card_lar,fraenkel_a_2_1_card_lar,idempotence_k2_xboole_0,idempotence_k3_xboole_0,rc1_arytm_3,rc1_card_1,rc1_card_5,rc1_ordinal1,rc1_ordinal2,rc1_subset_1,rc2_card_1,rc2_card_5,rc2_card_lar,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,redefinition_k1_nat_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_ordinal1,reflexivity_r1_ordinal1,reflexivity_r1_tarski,s2_recdef_1__e7_40__card_lar,spc0_boole,spc1_boole,spc1_numerals,t10_card_lar,t10_ordinal1,t12_relset_1,t19_ordinal1,t1_boole,t1_numerals,t1_subset,t1_xboole_1,t23_card_lar,t27_ordinal2,t29_ordinal2,t2_boole,t2_subset,t2_tarski,t3_subset,t41_ordinal1,t4_card_lar,t4_subset,t5_subset,t6_boole,t6_card_lar,t7_boole,t7_card_lar,t8_boole,t8_card_lar]),
    [file(card_lar,t25_card_lar)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_arytm_3,axiom,(
    ! [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),
    []).

fof(cc1_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    []).

fof(cc1_card_5,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(card_5,cc1_card_5),
    []).

fof(cc1_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal1(A) ) ) ),
    file(card_lar,cc1_card_lar),
    []).

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_arytm_3,axiom,(
    ! [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),
    []).

fof(cc2_card_1,axiom,(
    ! [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),
    []).

fof(cc2_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(card_5,cc2_card_5),
    []).

fof(cc2_card_lar,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v3_ordinal1(A)
        & v4_ordinal1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & ~ v1_finset_1(A) ) ) ),
    file(card_lar,cc2_card_lar),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

fof(cc3_card_1,axiom,(
    ! [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),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(connectedness_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
        | r1_ordinal1(B,A) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_ordinal1,axiom,(
    ! [A] : k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A)) ),
    file(ordinal1,d1_ordinal1),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d5_funct_1,axiom,(
    ! [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),
    []).

fof(d9_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => k4_card_lar(A,B) = a_2_0_card_lar(A,B) ) ) ),
    file(card_lar,d9_card_lar),
    []).

fof(dt_k1_card_5,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => v1_card_1(k1_card_5(A)) ) ),
    file(card_5,k1_card_5),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_card_lar,axiom,(
    ! [A,B,C] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A)
        & m1_subset_1(B,k1_zfmisc_1(A))
        & v3_ordinal1(C) )
     => m1_subset_1(k2_card_lar(A,B,C),B) ) ),
    file(card_lar,k2_card_lar),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

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

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_card_1,axiom,(
    $true ),
    file(card_1,k3_card_1),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_card_lar,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_card_lar(A,B),k1_zfmisc_1(A)) ) ),
    file(card_lar,k4_card_lar),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k7_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k7_ordinal2(A)) ),
    file(ordinal2,k7_ordinal2),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_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),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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),
    []).

fof(fc1_card_1,axiom,(
    ! [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),
    []).

fof(fc1_ordinal1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) ),
    file(ordinal1,fc1_ordinal1),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc1_ordinal3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( v1_ordinal1(k2_xboole_0(A,B))
        & v2_ordinal1(k2_xboole_0(A,B))
        & v3_ordinal1(k2_xboole_0(A,B)) ) ) ),
    file(ordinal3,fc1_ordinal3),
    []).

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

fof(fc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A))
        & v4_ordinal2(k1_ordinal1(A)) ) ) ),
    file(arytm_3,fc2_arytm_3),
    []).

fof(fc2_card_5,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k3_card_1(A))
        & v1_ordinal1(k3_card_1(A))
        & v2_ordinal1(k3_card_1(A))
        & v3_ordinal1(k3_card_1(A))
        & ~ v1_finset_1(k3_card_1(A))
        & v1_card_1(k3_card_1(A)) ) ) ),
    file(card_5,fc2_card_5),
    []).

fof(fc2_ordinal1,axiom,
    ( 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),
    []).

fof(fc2_ordinal3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( v1_ordinal1(k3_xboole_0(A,B))
        & v2_ordinal1(k3_xboole_0(A,B))
        & v3_ordinal1(k3_xboole_0(A,B)) ) ) ),
    file(ordinal3,fc2_ordinal3),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A)) ) ) ),
    file(ordinal1,fc3_ordinal1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc8_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( ~ v1_xboole_0(k1_card_5(A))
        & v1_ordinal1(k1_card_5(A))
        & v2_ordinal1(k1_card_5(A))
        & v3_ordinal1(k1_card_5(A))
        & ~ v1_finset_1(k1_card_5(A))
        & v1_card_1(k1_card_5(A)) ) ) ),
    file(card_5,fc8_card_5),
    []).

fof(fraenkel_a_2_0_card_lar,axiom,(
    ! [A,B,C] : 
      ( ( v3_ordinal1(B)
        & v4_ordinal1(B)
        & ~ v1_finset_1(B)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ( r2_hidden(A,a_2_0_card_lar(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,B)
            & A = D
            & ~ v1_finset_1(D)
            & v4_ordinal1(D)
            & k7_ordinal2(k3_xboole_0(C,D)) = D ) ) ) ),
    file(card_lar,a_2_0_card_lar),
    []).

fof(fraenkel_a_2_1_card_lar,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v1_card_4(B)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ( r2_hidden(A,a_2_1_card_lar(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,B)
            & A = D
            & ~ v1_finset_1(D)
            & v4_ordinal1(D)
            & k7_ordinal2(k3_xboole_0(C,D)) = D ) ) ) ),
    file(card_lar,a_2_1_card_lar),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

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

fof(rc1_card_1,axiom,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    []).

fof(rc1_card_5,axiom,(
    ? [A] : ~ v1_finset_1(A) ),
    file(card_5,rc1_card_5),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_ordinal2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal1(A) ) ),
    file(ordinal2,rc1_ordinal2),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc2_card_1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    []).

fof(rc2_card_5,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_5,rc2_card_5),
    []).

fof(rc2_card_lar,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_ordinal1(B)
          & v2_ordinal1(B)
          & v3_ordinal1(B)
          & v4_ordinal1(B)
          & ~ v1_finset_1(B)
          & v1_card_1(B) ) ) ),
    file(card_lar,rc2_card_lar),
    []).

fof(rc2_ordinal1,axiom,(
    ? [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),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_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,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(redefinition_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
      <=> r1_tarski(A,B) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(reflexivity_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => r1_ordinal1(A,A) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(s2_recdef_1__e7_40__card_lar,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A))
        & m2_subset_1(C,A,B) )
     => ( ! [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
           => ! [E] : 
                ( m1_subset_1(E,B)
               => ? [F] : 
                    ( m1_subset_1(F,B)
                    & r2_hidden(E,F) ) ) )
       => ? [D] : 
            ( v1_funct_1(D)
            & v1_funct_2(D,k5_numbers,B)
            & m2_relset_1(D,k5_numbers,B)
            & k8_funct_2(k5_numbers,B,D,0) = C
            & ! [E] : 
                ( m2_subset_1(E,k1_numbers,k5_numbers)
               => r2_hidden(k8_funct_2(k5_numbers,B,D,E),k8_funct_2(k5_numbers,B,D,k1_nat_1(E,1))) ) ) ) ) ),
    file(card_lar,s2_recdef_1__e7_40__card_lar),
    []).

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

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(t10_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ( ( v1_card_lar(C,A)
                  & r2_hidden(B,A) )
               => ( r2_hidden(k2_card_lar(A,C,B),C)
                  & r2_hidden(B,k2_card_lar(A,C,B)) ) ) ) ) ) ),
    file(card_lar,t10_card_lar),
    []).

fof(t10_ordinal1,axiom,(
    ! [A] : r2_hidden(A,k1_ordinal1(A)) ),
    file(ordinal1,t10_ordinal1),
    []).

fof(t12_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    []).

fof(t19_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v1_ordinal1(C)
             => ( ( r2_hidden(C,A)
                  & r2_hidden(A,B) )
               => r2_hidden(C,B) ) ) ) ) ),
    file(ordinal1,t19_ordinal1),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t23_card_lar,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_card_4(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( r2_hidden(k3_card_1(0),k1_card_5(A))
           => ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k5_numbers,B)
                  & m2_relset_1(C,k5_numbers,B) )
               => r2_hidden(k7_ordinal2(k2_relat_1(C)),A) ) ) ) ) ),
    file(card_lar,t23_card_lar),
    []).

fof(t27_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r2_hidden(A,B)
         => r2_hidden(A,k7_ordinal2(B)) ) ) ),
    file(ordinal2,t27_ordinal2),
    []).

fof(t29_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : ~ ( r2_hidden(A,k7_ordinal2(B))
          & ! [C] : 
              ( v3_ordinal1(C)
             => ~ ( r2_hidden(C,B)
                  & r1_ordinal1(A,C) ) ) ) ) ),
    file(ordinal2,t29_ordinal2),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

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

fof(t4_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ! [C] : 
                ( v3_ordinal1(C)
               => ~ ( r2_hidden(C,B)
                    & ! [D] : 
                        ( v3_ordinal1(D)
                       => ~ ( r2_hidden(D,B)
                            & r2_hidden(C,D) ) ) ) )
           => ( v1_xboole_0(B)
              | ( v3_ordinal1(k7_ordinal2(B))
                & v4_ordinal1(k7_ordinal2(B))
                & ~ v1_finset_1(k7_ordinal2(B)) ) ) ) ) ) ),
    file(card_lar,t4_card_lar),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t6_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal1(B)
            & ~ v1_finset_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ~ ( k7_ordinal2(k3_xboole_0(C,B)) != B
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ~ ( r2_hidden(D,B)
                          & r1_tarski(k3_xboole_0(C,B),D) ) ) ) ) ) ) ),
    file(card_lar,t6_card_lar),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t7_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_card_lar(B,A)
          <=> ! [C] : 
                ( v3_ordinal1(C)
               => ~ ( r2_hidden(C,A)
                    & ! [D] : 
                        ( v3_ordinal1(D)
                       => ~ ( r2_hidden(D,B)
                            & r1_ordinal1(C,D) ) ) ) ) ) ) ) ),
    file(card_lar,t7_card_lar),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t8_card_lar,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ~ ( v1_card_lar(B,A)
              & v1_xboole_0(B) ) ) ) ),
    file(card_lar,t8_card_lar),
    []).