% Mizar problem: t34_card_fil,card_fil,1169,29 
fof(t34_card_fil,conjecture,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => ? [B] : 
          ( v1_funct_1(B)
          & v1_funct_2(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A))
          & m2_relset_1(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A))
          & r4_card_fil(A,B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_card_1,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relset_1,cc2_card_5,cc2_finset_1,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,cc6_card_fil,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k5_subset_1,connectedness_r1_ordinal1,d10_xboole_0,d17_card_fil,d18_card_fil,d1_binop_1,d1_tarski,d1_xboole_0,d2_funct_2,d2_ordinal1,d2_xboole_0,d3_tarski,d3_xboole_0,d4_tarski,d4_wellord2,d4_xboole_0,d5_card_1,d5_funct_1,d5_tarski,d6_funcop_1,d8_funct_1,dt_k1_binop_1,dt_k1_card_1,dt_k1_card_fil,dt_k1_funct_1,dt_k1_funct_2,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_card_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k3_xboole_0,dt_k4_tarski,dt_k4_xboole_0,dt_k5_subset_1,dt_k7_card_fil,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc1_card_fil,fc1_finset_1,fc1_subset_1,fc2_card_1,fc2_finset_1,fc2_ordinal1,fc2_subset_1,fc3_card_fil,fc3_subset_1,fc4_card_fil,fc4_ordinal1,fc4_subset_1,fc7_card_5,fc7_funcop_1,fc9_finset_1,fraenkel_a_0_0_domain_1,fraenkel_a_3_5_card_fil,fraenkel_a_3_6_card_fil,fraenkel_a_3_7_card_fil,fraenkel_a_5_0_card_fil,fraenkel_a_5_1_card_fil,fraenkel_a_5_2_card_fil,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k5_subset_1,rc1_card_1,rc1_card_5,rc1_finset_1,rc1_funcop_1,rc1_funct_1,rc1_ordinal1,rc1_subset_1,rc2_card_1,rc2_card_5,rc2_card_fil,rc2_funct_1,rc2_ordinal1,rc2_subset_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc4_funct_1,redefinition_k1_card_fil,redefinition_k2_binop_1,redefinition_k5_subset_1,redefinition_m2_relset_1,redefinition_r1_ordinal1,redefinition_r2_wellord2,reflexivity_r1_ordinal1,reflexivity_r1_tarski,reflexivity_r2_wellord2,s1_card_fil__e7_71_6__card_fil,s1_card_fil__e8_71_6__card_fil,s1_wellord2__e2_71__card_fil,s7_domain_1__e1_71_10_3_1_2_1__card_fil,s7_domain_1__e1_71_4__card_fil,s7_funct_2__e12_71__card_fil,symmetry_r2_wellord2,t17_xboole_1,t1_boole,t1_card_4,t1_subset,t1_xboole_1,t21_card_1,t22_ordinal1,t23_card_1,t23_card_4,t24_ordinal1,t25_card_1,t26_ordinal1,t27_card_1,t2_boole,t2_subset,t2_tarski,t32_card_1,t34_xboole_1,t36_card_4,t3_boole,t3_subset,t48_xboole_1,t4_boole,t4_subset,t5_subset,t6_boole,t79_zfmisc_1,t7_boole,t8_boole,t94_zfmisc_1,t9_funct_2]),
    [file(card_fil,t34_card_fil)]).

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

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

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

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_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_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [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),
    []).

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

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

fof(cc6_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & ~ v1_xboole_0(A)
        & ~ v1_finset_1(A)
        & v1_card_1(A)
        & v1_card_5(A) ) ) ),
    file(card_fil,cc6_card_fil),
    []).

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

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_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

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(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d17_card_fil,axiom,(
    ! [A] : 
      ( ( v1_card_1(A)
        & ~ v2_card_1(A) )
     => ! [B] : 
          ( v1_card_1(B)
         => ( B = k7_card_fil(A)
          <=> A = k2_card_1(B) ) ) ) ),
    file(card_fil,d17_card_fil),
    []).

fof(d18_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A))
            & m2_relset_1(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) )
         => ( r4_card_fil(A,B)
          <=> ( ! [C] : 
                  ( m1_subset_1(C,k7_card_fil(A))
                 => ! [D] : 
                      ( m1_subset_1(D,A)
                     => ! [E] : 
                          ( m1_subset_1(E,A)
                         => ( D != E
                           => v1_xboole_0(k5_subset_1(A,k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,C,D),k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,C,E))) ) ) ) )
              & ! [C] : 
                  ( m1_subset_1(C,A)
                 => ! [D] : 
                      ( m1_subset_1(D,k7_card_fil(A))
                     => ! [E] : 
                          ( m1_subset_1(E,k7_card_fil(A))
                         => ( D != E
                           => v1_xboole_0(k5_subset_1(A,k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,D,C),k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,E,C))) ) ) ) )
              & ! [C] : 
                  ( m1_subset_1(C,k7_card_fil(A))
                 => r1_tarski(k1_card_1(k1_card_fil(A,k3_tarski(a_3_5_card_fil(A,B,C)))),k7_card_fil(A)) )
              & ! [C] : 
                  ( m1_subset_1(C,A)
                 => r1_tarski(k1_card_1(k1_card_fil(A,k3_tarski(a_3_6_card_fil(A,B,C)))),k7_card_fil(A)) ) ) ) ) ) ),
    file(card_fil,d18_card_fil),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d2_funct_2,axiom,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    []).

fof(d2_ordinal1,axiom,(
    ! [A] : 
      ( v1_ordinal1(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => r1_tarski(B,A) ) ) ),
    file(ordinal1,d2_ordinal1),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

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

fof(d4_wellord2,axiom,(
    ! [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),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

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

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

fof(d6_funcop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funcop_1(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => ( v1_relat_1(k1_funct_1(A,B))
              & v1_funct_1(k1_funct_1(A,B)) ) ) ) ) ),
    file(funcop_1,d6_funcop_1),
    []).

fof(d8_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

fof(dt_k1_card_fil,axiom,(
    ! [A,B] : m1_subset_1(k1_card_fil(A,B),k1_zfmisc_1(A)) ),
    file(card_fil,k1_card_fil),
    []).

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

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

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_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(dt_k2_card_1,axiom,(
    ! [A] : v1_card_1(k2_card_1(A)) ),
    file(card_1,k2_card_1),
    []).

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

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

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

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

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

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

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_k7_card_fil,axiom,(
    ! [A] : 
      ( ( v1_card_1(A)
        & ~ v2_card_1(A) )
     => v1_card_1(k7_card_fil(A)) ) ),
    file(card_fil,k7_card_fil),
    []).

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(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(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc12_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc1_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ( v1_ordinal1(k1_card_1(A))
        & v2_ordinal1(k1_card_1(A))
        & v3_ordinal1(k1_card_1(A))
        & ~ v1_xboole_0(k1_card_1(A))
        & ~ v1_finset_1(k1_card_1(A))
        & v1_card_1(k1_card_1(A)) ) ) ),
    file(card_fil,fc1_card_fil),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

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

fof(fc2_card_1,axiom,(
    ! [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),
    []).

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

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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( v1_ordinal1(k2_card_1(A))
        & v2_ordinal1(k2_card_1(A))
        & v3_ordinal1(k2_card_1(A))
        & ~ v1_xboole_0(k2_card_1(A))
        & ~ v1_finset_1(k2_card_1(A))
        & v1_card_1(k2_card_1(A))
        & ~ v2_card_1(k2_card_1(A)) ) ) ),
    file(card_fil,fc3_card_fil),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => ( v1_ordinal1(k7_card_fil(A))
        & v2_ordinal1(k7_card_fil(A))
        & v3_ordinal1(k7_card_fil(A))
        & ~ v1_xboole_0(k7_card_fil(A))
        & ~ v1_finset_1(k7_card_fil(A))
        & v1_card_1(k7_card_fil(A)) ) ) ),
    file(card_fil,fc4_card_fil),
    []).

fof(fc4_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_tarski(A))
        & v2_ordinal1(k3_tarski(A))
        & v3_ordinal1(k3_tarski(A)) ) ) ),
    file(ordinal1,fc4_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(fc7_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( ~ v1_xboole_0(k2_card_1(A))
        & v1_ordinal1(k2_card_1(A))
        & v2_ordinal1(k2_card_1(A))
        & v3_ordinal1(k2_card_1(A))
        & ~ v1_finset_1(k2_card_1(A))
        & v1_card_1(k2_card_1(A)) ) ) ),
    file(card_5,fc7_card_5),
    []).

fof(fc7_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    []).

fof(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

fof(fraenkel_a_0_0_domain_1,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_domain_1)
    <=> ? [B] : 
          ( m1_subset_1(B,f1_s7_domain_1)
          & A = B
          & p1_s7_domain_1(B) ) ) ),
    file(domain_1,a_0_0_domain_1),
    []).

fof(fraenkel_a_3_5_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v2_card_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B))
        & m2_relset_1(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B))
        & m1_subset_1(D,k7_card_fil(B)) )
     => ( r2_hidden(A,a_3_5_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,B)
            & A = k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,D,E)
            & r2_hidden(E,B) ) ) ) ),
    file(card_fil,a_3_5_card_fil),
    []).

fof(fraenkel_a_3_6_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v2_card_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B))
        & m2_relset_1(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B))
        & m1_subset_1(D,B) )
     => ( r2_hidden(A,a_3_6_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k7_card_fil(B))
            & A = k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,E,D)
            & r2_hidden(E,k7_card_fil(B)) ) ) ) ),
    file(card_fil,a_3_6_card_fil),
    []).

fof(fraenkel_a_3_7_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v2_card_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,B) )
     => ( r2_hidden(A,a_3_7_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,C)
            & A = E
            & r2_hidden(D,E) ) ) ) ),
    file(card_fil,a_3_7_card_fil),
    []).

fof(fraenkel_a_5_0_card_fil,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v2_card_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_funcop_1(C)
        & ~ v1_xboole_0(D)
        & m1_subset_1(E,k7_card_fil(B))
        & m1_subset_1(F,B) )
     => ( r2_hidden(A,a_5_0_card_fil(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,D)
            & A = G
            & k1_funct_1(k1_funct_1(C,G),E) = F ) ) ) ),
    file(card_fil,a_5_0_card_fil),
    []).

fof(fraenkel_a_5_1_card_fil,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v2_card_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_funcop_1(C)
        & ~ v1_xboole_0(D)
        & m1_subset_1(E,k7_card_fil(B))
        & m1_subset_1(F,D) )
     => ( r2_hidden(A,a_5_1_card_fil(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,D)
            & A = G
            & k1_funct_1(k1_funct_1(C,G),E) = k1_funct_1(k1_funct_1(C,F),E) ) ) ) ),
    file(card_fil,a_5_1_card_fil),
    []).

fof(fraenkel_a_5_2_card_fil,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v2_card_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_funcop_1(C)
        & ~ v1_xboole_0(D)
        & m1_subset_1(E,B)
        & m1_subset_1(F,k7_card_fil(B)) )
     => ( r2_hidden(A,a_5_2_card_fil(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,D)
            & A = G
            & k1_funct_1(k1_funct_1(C,G),F) = E ) ) ) ),
    file(card_fil,a_5_2_card_fil),
    []).

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(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

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_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_funcop_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    []).

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

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

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_fil,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & ~ v1_xboole_0(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A)
      & ~ v2_card_1(A) ) ),
    file(card_fil,rc2_card_fil),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

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_finset_1,axiom,(
    ! [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),
    []).

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

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

fof(rc4_finset_1,axiom,(
    ! [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),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(redefinition_k1_card_fil,axiom,(
    ! [A,B] : k1_card_fil(A,B) = k4_xboole_0(A,B) ),
    file(card_fil,k1_card_fil),
    []).

fof(redefinition_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(redefinition_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

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_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
      <=> r1_tarski(A,B) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(redefinition_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    []).

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(reflexivity_r2_wellord2,axiom,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    []).

fof(s1_card_fil__e7_71_6__card_fil,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_funcop_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,k7_card_fil(A))
        & m1_subset_1(E,A)
        & m1_subset_1(F,C) )
     => ( r2_hidden(F,a_5_0_card_fil(A,B,C,D,E))
       => k1_funct_1(k1_funct_1(B,F),D) = E ) ) ),
    file(card_fil,s1_card_fil__e7_71_6__card_fil),
    []).

fof(s1_card_fil__e8_71_6__card_fil,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_funcop_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,k7_card_fil(A))
        & m1_subset_1(E,A)
        & m1_subset_1(F,C) )
     => ( r2_hidden(F,a_5_0_card_fil(A,B,C,D,E))
       => k1_funct_1(k1_funct_1(B,F),D) = E ) ) ),
    file(card_fil,s1_card_fil__e8_71_6__card_fil),
    []).

fof(s1_wellord2__e2_71__card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => ( ! [B] : ~ ( r2_hidden(B,k1_card_fil(k2_card_1(k7_card_fil(A)),k7_card_fil(A)))
            & ! [C] : ~ ( r2_hidden(C,k1_funct_2(k7_card_fil(A),k2_card_1(k7_card_fil(A))))
                & ? [D] : 
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & C = D
                    & v2_funct_1(D)
                    & k1_relat_1(D) = k7_card_fil(A)
                    & k2_relat_1(D) = B ) ) )
       => ? [B] : 
            ( v1_relat_1(B)
            & v1_funct_1(B)
            & k1_relat_1(B) = k1_card_fil(k2_card_1(k7_card_fil(A)),k7_card_fil(A))
            & r1_tarski(k2_relat_1(B),k1_funct_2(k7_card_fil(A),k2_card_1(k7_card_fil(A))))
            & ! [C] : 
                ( r2_hidden(C,k1_card_fil(k2_card_1(k7_card_fil(A)),k7_card_fil(A)))
               => ? [E] : 
                    ( v1_relat_1(E)
                    & v1_funct_1(E)
                    & k1_funct_1(B,C) = E
                    & v2_funct_1(E)
                    & k1_relat_1(E) = k7_card_fil(A)
                    & k2_relat_1(E) = C ) ) ) ) ) ),
    file(card_fil,s1_wellord2__e2_71__card_fil),
    []).

fof(s7_domain_1__e1_71_10_3_1_2_1__card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(A)) ) ),
    file(card_fil,s7_domain_1__e1_71_10_3_1_2_1__card_fil),
    []).

fof(s7_domain_1__e1_71_4__card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(A)) ) ),
    file(card_fil,s7_domain_1__e1_71_4__card_fil),
    []).

fof(s7_funct_2__e12_71__card_fil,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_funcop_1(B)
        & ~ v1_xboole_0(C) )
     => ( ! [D] : 
            ( m1_subset_1(D,k7_card_fil(A))
           => ! [E] : 
                ( m1_subset_1(E,A)
               => ? [F] : 
                    ( m1_subset_1(F,k1_zfmisc_1(C))
                    & F = a_5_0_card_fil(A,B,C,D,E) ) ) )
       => ? [D] : 
            ( v1_funct_1(D)
            & v1_funct_2(D,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(C))
            & m2_relset_1(D,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(C))
            & ! [E] : 
                ( m1_subset_1(E,k7_card_fil(A))
               => ! [F] : 
                    ( m1_subset_1(F,A)
                   => k1_funct_1(D,k4_tarski(E,F)) = a_5_0_card_fil(A,B,C,E,F) ) ) ) ) ) ),
    file(card_fil,s7_funct_2__e12_71__card_fil),
    []).

fof(symmetry_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    []).

fof(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    []).

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

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

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(t21_card_1,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    []).

fof(t22_ordinal1,axiom,(
    ! [A] : 
      ( v1_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r1_tarski(A,B)
                  & r2_hidden(B,C) )
               => r2_hidden(A,C) ) ) ) ) ),
    file(ordinal1,t22_ordinal1),
    []).

fof(t23_card_1,axiom,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( r1_tarski(A,B)
       => r1_tarski(k1_card_1(A),B) ) ) ),
    file(card_1,t23_card_1),
    []).

fof(t23_card_4,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,k2_card_1(B))
          <=> r1_tarski(A,B) ) ) ) ),
    file(card_4,t23_card_4),
    []).

fof(t24_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ~ ( ~ r2_hidden(A,B)
              & A != B
              & ~ r2_hidden(B,A) ) ) ) ),
    file(ordinal1,t24_ordinal1),
    []).

fof(t25_card_1,axiom,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( r2_hidden(A,B)
       => r2_hidden(k1_card_1(A),B) ) ) ),
    file(card_1,t25_card_1),
    []).

fof(t26_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
            | r2_hidden(B,A) ) ) ) ),
    file(ordinal1,t26_ordinal1),
    []).

fof(t27_card_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_card_1(A),k1_card_1(B)) ) ),
    file(card_1,t27_card_1),
    []).

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(t32_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => r2_hidden(A,k2_card_1(A)) ) ),
    file(card_1,t32_card_1),
    []).

fof(t34_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)) ) ),
    file(xboole_1,t34_xboole_1),
    []).

fof(t36_card_4,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ( v1_finset_1(A)
        | ( r2_wellord2(k2_xboole_0(A,B),A)
          & k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A) ) ) ) ),
    file(card_4,t36_card_4),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t48_xboole_1,axiom,(
    ! [A,B] : k4_xboole_0(A,k4_xboole_0(A,B)) = k3_xboole_0(A,B) ),
    file(xboole_1,t48_xboole_1),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t79_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ) ),
    file(zfmisc_1,t79_zfmisc_1),
    []).

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

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

fof(t94_zfmisc_1,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(C,B) )
     => r1_tarski(k3_tarski(A),B) ) ),
    file(zfmisc_1,t94_zfmisc_1),
    []).

fof(t9_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(B,C)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(D)
            & v1_funct_2(D,A,C)
            & m2_relset_1(D,A,C) ) ) ) ) ),
    file(funct_2,t9_funct_2),
    []).