% Mizar problem: t35_card_fil,card_fil,1413,71 
fof(t35_card_fil,conjecture,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => ! [B] : 
          ( m2_card_fil(B,A)
         => ~ ( r2_card_fil(A,A,B)
              & r1_tarski(k6_card_fil(A),B)
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
                 => ~ ( k1_card_1(C) = A
                      & ! [D] : ~ ( r2_hidden(D,C)
                          & r2_hidden(D,B) )
                      & ! [D,E] : 
                          ( ( r2_hidden(D,C)
                            & r2_hidden(E,C) )
                         => ( D = E
                            | r1_xboole_0(D,E) ) ) ) ) ) ) ) ),
    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_k3_xboole_0,commutativity_k5_subset_1,connectedness_r1_ordinal1,d10_card_fil,d10_xboole_0,d11_card_fil,d13_funct_1,d17_card_fil,d18_card_fil,d1_binop_1,d1_funct_2,d1_tarski,d3_tarski,d4_card_5,d4_card_fil,d4_wellord2,d5_card_1,d5_funct_1,d5_subset_1,d5_tarski,d7_xboole_0,d8_funct_1,d8_setfam_1,dt_k10_relat_1,dt_k1_binop_1,dt_k1_card_1,dt_k1_card_5,dt_k1_card_fil,dt_k1_funct_1,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_card_fil,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_funct_2,dt_k3_funct_5,dt_k3_subset_1,dt_k3_tarski,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_tarski,dt_k4_xboole_0,dt_k5_card_fil,dt_k5_relat_1,dt_k5_setfam_1,dt_k5_subset_1,dt_k6_card_fil,dt_k7_card_fil,dt_k7_ordinal2,dt_k7_setfam_1,dt_k8_funct_2,dt_m1_card_fil,dt_m1_relset_1,dt_m1_subset_1,dt_m2_card_fil,dt_m2_relset_1,existence_m1_card_fil,existence_m1_relset_1,existence_m1_subset_1,existence_m2_card_fil,existence_m2_relset_1,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc1_card_fil,fc1_finset_1,fc1_funct_1,fc1_subset_1,fc2_card_1,fc2_card_fil,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,fc8_card_5,fraenkel_a_0_0_trees_2,fraenkel_a_0_2_domain_1,fraenkel_a_0_40_fraenkel,fraenkel_a_0_41_fraenkel,fraenkel_a_1_1_card_fil,fraenkel_a_2_3_card_fil,fraenkel_a_3_10_card_fil,fraenkel_a_3_5_card_fil,fraenkel_a_3_6_card_fil,fraenkel_a_3_8_card_fil,fraenkel_a_3_9_card_fil,fraenkel_a_4_0_card_fil,idempotence_k3_xboole_0,idempotence_k5_subset_1,involutiveness_k2_card_fil,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,rc1_card_1,rc1_card_5,rc1_finset_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_k2_card_fil,redefinition_k3_funct_2,redefinition_k4_relset_1,redefinition_k5_setfam_1,redefinition_k5_subset_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_r1_ordinal1,redefinition_r2_wellord2,reflexivity_r1_ordinal1,reflexivity_r1_tarski,reflexivity_r2_wellord2,s20_fraenkel__e2_72_1__card_fil,s2_trees_2__e3_72_4__card_fil,s2_trees_2__e5_72_2__card_fil,s3_funct_2__e8_72__card_fil,s9_domain_1__e1_72_1__card_fil,symmetry_r1_xboole_0,symmetry_r2_wellord2,t106_zfmisc_1,t10_card_fil,t11_card_fil,t129_zfmisc_1,t12_setwiseo,t13_card_1,t13_card_2,t19_card_fil,t1_subset,t1_xboole_1,t22_funct_1,t22_ordinal1,t23_card_1,t23_card_4,t27_card_1,t27_ordinal2,t2_boole,t2_subset,t2_tarski,t32_card_1,t34_card_fil,t36_funct_5,t38_card_5,t3_boole,t3_subset,t46_relat_1,t4_boole,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(card_fil,t35_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_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_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => k5_card_fil(A) = a_1_1_card_fil(A) ) ),
    file(card_fil,d10_card_fil),
    []).

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

fof(d11_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => k6_card_fil(A) = k2_card_fil(A,k5_card_fil(A)) ) ),
    file(card_fil,d11_card_fil),
    []).

fof(d13_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( r2_hidden(D,k1_relat_1(A))
                & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ),
    file(funct_1,d13_funct_1),
    []).

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

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

fof(d4_card_5,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( v1_card_5(A)
      <=> k1_card_5(A) = A ) ) ),
    file(card_5,d4_card_5),
    []).

fof(d4_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
             => ( r2_card_fil(A,B,C)
              <=> ! [D] : 
                    ( ~ v1_xboole_0(D)
                   => ( ( r1_tarski(D,C)
                        & r2_hidden(k1_card_1(D),B) )
                     => r2_hidden(k3_tarski(D),C) ) ) ) ) ) ) ),
    file(card_fil,d4_card_fil),
    []).

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(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_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,B) = k4_xboole_0(A,B) ) ),
    file(subset_1,d5_subset_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(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

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(d8_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k7_setfam_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> r2_hidden(k3_subset_1(A,D),B) ) ) ) ) ) ),
    file(setfam_1,d8_setfam_1),
    []).

fof(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_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_5,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => v1_card_1(k1_card_5(A)) ) ),
    file(card_5,k1_card_5),
    []).

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_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_card_fil,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_card_fil(B,A) )
     => m2_card_fil(k2_card_fil(A,B),A) ) ),
    file(card_fil,k2_card_fil),
    []).

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)) ) ),
    file(funct_2,k3_funct_2),
    []).

fof(dt_k3_funct_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_5(A))
        & v1_funct_1(k3_funct_5(A)) ) ) ),
    file(funct_5,k3_funct_5),
    []).

fof(dt_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ),
    file(subset_1,k3_subset_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_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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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

fof(dt_k5_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => m1_card_fil(k5_card_fil(A),A) ) ),
    file(card_fil,k5_card_fil),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    []).

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_k6_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => m2_card_fil(k6_card_fil(A),A) ) ),
    file(card_fil,k6_card_fil),
    []).

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_k7_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k7_ordinal2(A)) ),
    file(ordinal2,k7_ordinal2),
    []).

fof(dt_k7_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(setfam_1,k7_setfam_1),
    []).

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_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_card_fil(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ),
    file(card_fil,m1_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_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_card_fil(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ),
    file(card_fil,m2_card_fil),
    []).

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_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_card_fil(B,A) ) ),
    file(card_fil,m1_card_fil),
    []).

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_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m2_card_fil(B,A) ) ),
    file(card_fil,m2_card_fil),
    []).

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_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_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_card_fil,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ~ v1_xboole_0(k7_setfam_1(A,B)) ) ),
    file(card_fil,fc2_card_fil),
    []).

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(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_0_0_trees_2,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_trees_2)
    <=> ? [B] : 
          ( m1_subset_1(B,f1_s2_trees_2)
          & A = f3_s2_trees_2(B)
          & r2_hidden(B,f2_s2_trees_2) ) ) ),
    file(trees_2,a_0_0_trees_2),
    []).

fof(fraenkel_a_0_2_domain_1,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_2_domain_1)
    <=> ? [B,C] : 
          ( m1_subset_1(B,f1_s9_domain_1)
          & m1_subset_1(C,f2_s9_domain_1)
          & A = f4_s9_domain_1(B,C)
          & p1_s9_domain_1(B,C) ) ) ),
    file(domain_1,a_0_2_domain_1),
    []).

fof(fraenkel_a_0_40_fraenkel,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_40_fraenkel)
    <=> ? [B,C] : 
          ( m1_subset_1(B,f1_s20_fraenkel)
          & m1_subset_1(C,f2_s20_fraenkel)
          & A = f3_s20_fraenkel(B,C)
          & C = f4_s20_fraenkel
          & p1_s20_fraenkel(B,C) ) ) ),
    file(fraenkel,a_0_40_fraenkel),
    []).

fof(fraenkel_a_0_41_fraenkel,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_41_fraenkel)
    <=> ? [B] : 
          ( m1_subset_1(B,f1_s20_fraenkel)
          & A = f3_s20_fraenkel(B,f4_s20_fraenkel)
          & p1_s20_fraenkel(B,f4_s20_fraenkel) ) ) ),
    file(fraenkel,a_0_41_fraenkel),
    []).

fof(fraenkel_a_1_1_card_fil,axiom,(
    ! [A,B] : 
      ( ~ v1_finset_1(B)
     => ( r2_hidden(A,a_1_1_card_fil(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(B))
            & A = C
            & r2_hidden(k1_card_1(k1_card_fil(B,C)),k1_card_1(B)) ) ) ) ),
    file(card_fil,a_1_1_card_fil),
    []).

fof(fraenkel_a_2_3_card_fil,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_finset_1(B)
        & v1_card_1(B)
        & ~ v2_card_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,k7_card_fil(B))
        & m2_relset_1(C,B,k7_card_fil(B)) )
     => ( r2_hidden(A,a_2_3_card_fil(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k7_card_fil(B))
            & A = k7_ordinal2(k3_funct_2(B,k7_card_fil(B),C,k1_tarski(D)))
            & r2_hidden(D,k7_card_fil(B)) ) ) ) ),
    file(card_fil,a_2_3_card_fil),
    []).

fof(fraenkel_a_3_10_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_10_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k2_zfmisc_1(k7_card_fil(B),B))
            & A = k8_funct_2(k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B),C,E)
            & r2_hidden(E,k2_zfmisc_1(k7_card_fil(B),k1_tarski(D))) ) ) ) ),
    file(card_fil,a_3_10_card_fil),
    []).

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_8_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_8_card_fil(B,C,D))
      <=> ? [E,F] : 
            ( m1_subset_1(E,k7_card_fil(B))
            & m1_subset_1(F,B)
            & A = k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,E,F)
            & F = D
            & r2_hidden(E,k7_card_fil(B)) ) ) ) ),
    file(card_fil,a_3_8_card_fil),
    []).

fof(fraenkel_a_3_9_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_9_card_fil(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k2_zfmisc_1(k7_card_fil(B),B))
            & A = k1_funct_1(C,E)
            & r2_hidden(E,k2_zfmisc_1(k7_card_fil(B),k1_tarski(D))) ) ) ) ),
    file(card_fil,a_3_9_card_fil),
    []).

fof(fraenkel_a_4_0_card_fil,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ 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))
        & v1_funct_1(D)
        & v1_funct_2(D,B,k7_card_fil(B))
        & m2_relset_1(D,B,k7_card_fil(B))
        & m1_subset_1(E,k7_card_fil(B)) )
     => ( r2_hidden(A,a_4_0_card_fil(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,B)
            & A = k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,E,F)
            & k8_funct_2(B,k7_card_fil(B),D,F) = E ) ) ) ),
    file(card_fil,a_4_0_card_fil),
    []).

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(involutiveness_k2_card_fil,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_card_fil(B,A) )
     => k2_card_fil(A,k2_card_fil(A,B)) = B ) ),
    file(card_fil,k2_card_fil),
    []).

fof(involutiveness_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,k3_subset_1(A,B)) = B ) ),
    file(subset_1,k3_subset_1),
    []).

fof(involutiveness_k7_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k7_setfam_1(A,k7_setfam_1(A,B)) = B ) ),
    file(setfam_1,k7_setfam_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_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_k2_card_fil,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_card_fil(B,A) )
     => k2_card_fil(A,B) = k7_setfam_1(A,B) ) ),
    file(card_fil,k2_card_fil),
    []).

fof(redefinition_k3_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k3_funct_2(A,B,C,D) = k10_relat_1(C,D) ) ),
    file(funct_2,k3_funct_2),
    []).

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_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_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_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_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(s20_fraenkel__e2_72_1__card_fil,axiom,(
    a_0_40_fraenkel = a_0_41_fraenkel ),
    file(card_fil,s20_fraenkel__e2_72_1__card_fil),
    []).

fof(s2_trees_2__e3_72_4__card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => r1_tarski(k1_card_1(a_0_0_trees_2),k1_card_1(k7_card_fil(A))) ) ),
    file(card_fil,s2_trees_2__e3_72_4__card_fil),
    []).

fof(s2_trees_2__e5_72_2__card_fil,axiom,(
    ! [A,B] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A)
        & m1_subset_1(B,A) )
     => r1_tarski(k1_card_1(a_0_0_trees_2),k1_card_1(k2_zfmisc_1(k7_card_fil(A),k1_tarski(B)))) ) ),
    file(card_fil,s2_trees_2__e5_72_2__card_fil),
    []).

fof(s3_funct_2__e8_72__card_fil,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A)
        & m2_card_fil(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A))
        & m2_relset_1(C,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) )
     => ( ! [D] : 
            ( m1_subset_1(D,A)
           => ? [E] : 
                ( m1_subset_1(E,k7_card_fil(A))
                & ~ r2_hidden(k1_binop_1(C,E,D),B) ) )
       => ? [D] : 
            ( v1_funct_1(D)
            & v1_funct_2(D,A,k7_card_fil(A))
            & m2_relset_1(D,A,k7_card_fil(A))
            & ! [E] : 
                ( m1_subset_1(E,A)
               => ~ r2_hidden(k1_binop_1(C,k8_funct_2(A,k7_card_fil(A),D,E),E),B) ) ) ) ) ),
    file(card_fil,s3_funct_2__e8_72__card_fil),
    []).

fof(s9_domain_1__e1_72_1__card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v2_card_1(A) )
     => m1_subset_1(a_0_2_domain_1,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(card_fil,s9_domain_1__e1_72_1__card_fil),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

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

fof(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    []).

fof(t10_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_card_fil(B,A)
         => ! [C] : 
              ( m2_card_fil(C,A)
             => ( ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(A))
                   => ~ ( r2_hidden(D,B)
                        & r2_hidden(D,k2_card_fil(A,B)) ) )
                & ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(A))
                   => ~ ( r2_hidden(D,C)
                        & r2_hidden(D,k7_setfam_1(A,C)) ) ) ) ) ) ) ),
    file(card_fil,t10_card_fil),
    []).

fof(t11_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_card_fil(B,A)
         => r2_hidden(k1_xboole_0,B) ) ) ),
    file(card_fil,t11_card_fil),
    []).

fof(t129_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D)))
    <=> ( r2_hidden(A,C)
        & B = D ) ) ),
    file(zfmisc_1,t129_zfmisc_1),
    []).

fof(t12_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => r2_hidden(D,k3_funct_2(B,A,C,k1_tarski(k8_funct_2(B,A,C,D)))) ) ) ) ) ),
    file(setwiseo,t12_setwiseo),
    []).

fof(t13_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,B)
          <=> ( r1_tarski(A,B)
              & A != B ) ) ) ) ),
    file(card_1,t13_card_1),
    []).

fof(t13_card_2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,k2_zfmisc_1(A,k1_tarski(B)))
      & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,k1_tarski(B))) ) ),
    file(card_2,t13_card_2),
    []).

fof(t19_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( r2_hidden(B,k6_card_fil(A))
          <=> r2_hidden(k1_card_1(B),k1_card_1(A)) ) ) ) ),
    file(card_fil,t19_card_fil),
    []).

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(t22_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_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(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(t27_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r2_hidden(A,B)
         => r2_hidden(A,k7_ordinal2(B)) ) ) ),
    file(ordinal2,t27_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(t32_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => r2_hidden(A,k2_card_1(A)) ) ),
    file(card_1,t32_card_1),
    []).

fof(t34_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) ) ) ),
    file(card_fil,t34_card_fil),
    []).

fof(t36_funct_5,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ~ ( k2_zfmisc_1(A,B) != k1_xboole_0
          & k1_relat_1(D) = k2_zfmisc_1(A,B)
          & r2_hidden(C,A)
          & ! [E] : 
              ( ( v1_relat_1(E)
                & v1_funct_1(E) )
             => ~ ( k1_funct_1(k3_funct_5(D),C) = E
                  & k1_relat_1(E) = B
                  & r1_tarski(k2_relat_1(E),k2_relat_1(D))
                  & ! [F] : 
                      ( r2_hidden(F,B)
                     => k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(C,F)) ) ) ) ) ) ),
    file(funct_5,t36_funct_5),
    []).

fof(t38_card_5,axiom,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( ( r1_tarski(A,B)
          & r2_hidden(k1_card_1(A),k1_card_5(B)) )
       => ( r2_hidden(k7_ordinal2(A),B)
          & r2_hidden(k3_tarski(A),B) ) ) ) ),
    file(card_5,t38_card_5),
    []).

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(t46_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_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(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),
    []).