% Mizar problem: t40_card_fil,card_fil,1692,43 
fof(t40_card_fil,conjecture,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( v7_card_fil(A)
       => v5_card_fil(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_card_1,cc1_card_5,cc1_card_fil,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relset_1,cc2_card_1,cc2_card_5,cc2_finset_1,cc2_funct_1,cc2_ordinal1,cc3_card_1,cc3_card_fil,cc3_ordinal1,cc6_card_fil,commutativity_k2_tarski,commutativity_k3_xboole_0,d10_xboole_0,d12_funct_1,d13_funct_1,d14_card_fil,d16_card_fil,d1_funct_2,d1_setfam_1,d1_tarski,d2_funct_2,d2_tarski,d3_card_2,d3_card_fil,d3_tarski,d4_wellord2,d4_xboole_0,d5_card_1,d5_card_fil,d7_card_fil,dt_k10_relat_1,dt_k1_card_1,dt_k1_card_fil,dt_k1_funct_1,dt_k1_funct_2,dt_k1_numbers,dt_k1_ordinal1,dt_k1_relat_1,dt_k1_setfam_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_card_2,dt_k3_xboole_0,dt_k4_ordinal2,dt_k4_relset_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k7_relat_1,dt_k8_funct_2,dt_k9_relat_1,dt_m1_card_fil,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_card_fil,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc13_finset_1,fc14_finset_1,fc1_card_fil,fc1_finset_1,fc1_ordinal1,fc1_ordinal2,fc1_subset_1,fc2_card_1,fc2_finset_1,fc2_ordinal1,fc2_subset_1,fc3_ordinal1,fc3_subset_1,fc4_funct_1,fc4_subset_1,fc6_card_5,fraenkel_a_0_0_trees_2,fraenkel_a_3_11_card_fil,fraenkel_a_3_12_card_fil,fraenkel_a_4_1_card_fil,fraenkel_a_4_2_card_fil,fraenkel_a_4_3_card_fil,fraenkel_a_4_4_card_fil,idempotence_k3_xboole_0,rc1_card_1,rc1_card_5,rc1_card_fil,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc1_subset_1,rc2_card_1,rc2_card_5,rc2_card_fil,rc2_finset_1,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_k4_relset_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_r2_wellord2,reflexivity_r1_tarski,reflexivity_r2_wellord2,s2_trees_2__e28_77__card_fil,s3_funct_2__e26_77__card_fil,spc2_boole,spc2_numerals,symmetry_r2_wellord2,t11_relset_1,t138_funct_1,t13_finset_1,t148_relat_1,t14_card_1,t167_relat_1,t169_relat_1,t1_card_4,t1_subset,t22_card_2,t22_ordinal1,t23_card_fil,t24_finset_1,t26_card_1,t28_xboole_1,t2_boole,t2_subset,t2_tarski,t36_card_fil,t3_boole,t3_funct_2,t3_subset,t44_card_2,t4_boole,t4_subset,t5_subset,t68_card_1,t6_boole,t7_boole,t7_funct_2,t84_funct_1,t8_boole,t90_relat_1,t9_funct_1]),
    [file(card_fil,t40_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_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ! [B] : 
          ( m1_card_fil(B,A)
         => ( ( v1_card_fil(B,A)
              & v3_card_fil(B,A) )
           => ~ v2_card_fil(B,A) ) ) ) ),
    file(card_fil,cc1_card_fil),
    []).

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_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_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_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_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & v5_card_fil(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,cc3_card_fil),
    []).

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

fof(d12_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    []).

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(d14_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( v5_card_fil(A)
      <=> ! [B] : 
            ( v1_card_1(B)
           => ( r2_hidden(B,A)
             => r2_hidden(k3_card_2(2,B),A) ) ) ) ) ),
    file(card_fil,d14_card_fil),
    []).

fof(d16_card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ( v7_card_fil(A)
      <=> ? [B] : 
            ( m1_card_fil(B,A)
            & r1_card_fil(A,A,B)
            & ~ v2_card_fil(B,A)
            & v3_card_fil(B,A) ) ) ) ),
    file(card_fil,d16_card_fil),
    []).

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_setfam_1,axiom,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    []).

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

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_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

fof(d3_card_2,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => k3_card_2(A,B) = k1_card_1(k1_funct_2(B,A)) ) ) ),
    file(card_2,d3_card_2),
    []).

fof(d3_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))) )
             => ( r1_card_fil(A,B,C)
              <=> ! [D] : 
                    ( ~ v1_xboole_0(D)
                   => ( ( r1_tarski(D,C)
                        & r2_hidden(k1_card_1(D),B) )
                     => r2_hidden(k1_setfam_1(D),C) ) ) ) ) ) ) ),
    file(card_fil,d3_card_fil),
    []).

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_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_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_card_fil(B,A)
         => ( v1_card_fil(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(A))
               => ( r2_hidden(C,B)
                 => k1_card_1(C) = k1_card_1(A) ) ) ) ) ) ),
    file(card_fil,d5_card_fil),
    []).

fof(d7_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_card_fil(B,A)
         => ( v3_card_fil(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(A))
               => ( r2_hidden(C,B)
                  | r2_hidden(k1_card_fil(A,C),B) ) ) ) ) ) ),
    file(card_fil,d7_card_fil),
    []).

fof(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_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_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_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_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_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_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => v1_card_1(k3_card_2(A,B)) ) ),
    file(card_2,k3_card_2),
    []).

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

fof(dt_k4_ordinal2,axiom,
    ( v3_ordinal1(k4_ordinal2)
    & ~ v1_xboole_0(k4_ordinal2) ),
    file(ordinal2,k4_ordinal2),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

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_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_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_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

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_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_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(fc13_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k9_relat_1(A,B)) ) ),
    file(finset_1,fc13_finset_1),
    []).

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

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

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(fc6_card_5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & ~ v1_finset_1(B)
        & v1_card_1(B) )
     => ( ~ v1_xboole_0(k3_card_2(A,B))
        & v1_ordinal1(k3_card_2(A,B))
        & v2_ordinal1(k3_card_2(A,B))
        & v3_ordinal1(k3_card_2(A,B))
        & ~ v1_finset_1(k3_card_2(A,B))
        & v1_card_1(k3_card_2(A,B)) ) ) ),
    file(card_5,fc6_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_3_11_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_finset_1(C)
        & v1_card_1(C)
        & m1_subset_1(D,C) )
     => ( r2_hidden(A,a_3_11_card_fil(B,C,D))
      <=> ? [E] : 
            ( v1_funct_1(E)
            & v1_funct_2(E,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & m2_relset_1(E,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & A = E
            & r2_hidden(E,B)
            & k8_funct_2(C,k2_tarski(k1_xboole_0,k4_ordinal2),E,D) = k1_xboole_0 ) ) ) ),
    file(card_fil,a_3_11_card_fil),
    []).

fof(fraenkel_a_3_12_card_fil,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_finset_1(C)
        & v1_card_1(C)
        & m1_subset_1(D,C) )
     => ( r2_hidden(A,a_3_12_card_fil(B,C,D))
      <=> ? [E] : 
            ( v1_funct_1(E)
            & v1_funct_2(E,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & m2_relset_1(E,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & A = E
            & r2_hidden(E,B)
            & k8_funct_2(C,k2_tarski(k1_xboole_0,k4_ordinal2),E,D) = k4_ordinal2 ) ) ) ),
    file(card_fil,a_3_12_card_fil),
    []).

fof(fraenkel_a_4_1_card_fil,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_finset_1(C)
        & v1_card_1(C)
        & m1_subset_1(D,C)
        & m1_subset_1(E,k2_tarski(k1_xboole_0,k4_ordinal2)) )
     => ( r2_hidden(A,a_4_1_card_fil(B,C,D,E))
      <=> ? [F] : 
            ( v1_funct_1(F)
            & v1_funct_2(F,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & m2_relset_1(F,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & A = F
            & r2_hidden(F,B)
            & k1_funct_1(F,D) = E ) ) ) ),
    file(card_fil,a_4_1_card_fil),
    []).

fof(fraenkel_a_4_2_card_fil,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_finset_1(C)
        & v1_card_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,C,k2_tarski(k1_xboole_0,k4_ordinal2))
        & m2_relset_1(D,C,k2_tarski(k1_xboole_0,k4_ordinal2))
        & m1_subset_1(E,C) )
     => ( r2_hidden(A,a_4_2_card_fil(B,C,D,E))
      <=> ? [F] : 
            ( v1_funct_1(F)
            & v1_funct_2(F,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & m2_relset_1(F,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & A = F
            & r2_hidden(F,B)
            & k1_funct_1(F,E) = k8_funct_2(C,k2_tarski(k1_xboole_0,k4_ordinal2),D,E) ) ) ) ),
    file(card_fil,a_4_2_card_fil),
    []).

fof(fraenkel_a_4_3_card_fil,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_finset_1(C)
        & v1_card_1(C)
        & v1_relat_1(D)
        & v1_funct_1(D)
        & v1_funct_1(E)
        & v1_funct_2(E,C,k2_tarski(k1_xboole_0,k4_ordinal2))
        & m2_relset_1(E,C,k2_tarski(k1_xboole_0,k4_ordinal2)) )
     => ( r2_hidden(A,a_4_3_card_fil(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,C)
            & A = k10_relat_1(D,a_4_4_card_fil(B,C,E,F))
            & r2_hidden(F,C) ) ) ) ),
    file(card_fil,a_4_3_card_fil),
    []).

fof(fraenkel_a_4_4_card_fil,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_finset_1(C)
        & v1_card_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,C,k2_tarski(k1_xboole_0,k4_ordinal2))
        & m2_relset_1(D,C,k2_tarski(k1_xboole_0,k4_ordinal2))
        & m1_subset_1(E,C) )
     => ( r2_hidden(A,a_4_4_card_fil(B,C,D,E))
      <=> ? [F] : 
            ( v1_funct_1(F)
            & v1_funct_2(F,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & m2_relset_1(F,C,k2_tarski(k1_xboole_0,k4_ordinal2))
            & A = F
            & r2_hidden(F,B)
            & k8_funct_2(C,k2_tarski(k1_xboole_0,k4_ordinal2),F,E) = k8_funct_2(C,k2_tarski(k1_xboole_0,k4_ordinal2),D,E) ) ) ) ),
    file(card_fil,a_4_4_card_fil),
    []).

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

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_card_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ? [B] : 
          ( m1_card_fil(B,A)
          & ~ v1_xboole_0(B)
          & ~ v2_card_fil(B,A)
          & v3_card_fil(B,A) ) ) ),
    file(card_fil,rc1_card_fil),
    []).

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_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

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_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_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    []).

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(s2_trees_2__e28_77__card_fil,axiom,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => r1_tarski(k1_card_1(a_0_0_trees_2),k1_card_1(A)) ) ),
    file(card_fil,s2_trees_2__e28_77__card_fil),
    []).

fof(s3_funct_2__e26_77__card_fil,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A)
        & m1_card_fil(B,A)
        & ~ v1_finset_1(D)
        & v1_card_1(D)
        & v1_relat_1(E)
        & v1_funct_1(E) )
     => ( ! [F] : 
            ( m1_subset_1(F,D)
           => ? [G] : 
                ( m1_subset_1(G,k2_tarski(k1_xboole_0,k4_ordinal2))
                & r2_hidden(k10_relat_1(E,a_4_1_card_fil(C,D,F,G)),B) ) )
       => ? [F] : 
            ( v1_funct_1(F)
            & v1_funct_2(F,D,k2_tarski(k1_xboole_0,k4_ordinal2))
            & m2_relset_1(F,D,k2_tarski(k1_xboole_0,k4_ordinal2))
            & ! [G] : 
                ( m1_subset_1(G,D)
               => r2_hidden(k10_relat_1(E,a_4_2_card_fil(C,D,F,G)),B) ) ) ) ) ),
    file(card_fil,s3_funct_2__e26_77__card_fil),
    []).

fof(spc2_boole,axiom,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    []).

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

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

fof(t11_relset_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    []).

fof(t138_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => k10_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) ) ),
    file(funct_1,t138_funct_1),
    []).

fof(t13_finset_1,axiom,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    []).

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

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

fof(t167_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k10_relat_1(B,A),k1_relat_1(B)) ) ),
    file(relat_1,t167_relat_1),
    []).

fof(t169_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A) ) ),
    file(relat_1,t169_relat_1),
    []).

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(t22_card_2,axiom,
    ( 2 = k2_tarski(k1_xboole_0,k4_ordinal2)
    & 2 = k1_ordinal1(k4_ordinal2) ),
    file(card_2,t22_card_2),
    []).

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_fil,axiom,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ! [B] : 
          ( m1_card_fil(B,A)
         => ( ( v3_card_fil(B,A)
              & r1_card_fil(A,k1_card_1(A),B) )
           => ( v2_card_fil(B,A)
              | v1_card_fil(B,A) ) ) ) ) ),
    file(card_fil,t23_card_fil),
    []).

fof(t24_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> v1_finset_1(k1_zfmisc_1(A)) ) ),
    file(finset_1,t24_finset_1),
    []).

fof(t26_card_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_card_1(A),k1_card_1(B))
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(card_1,t26_card_1),
    []).

fof(t28_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_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(t36_card_fil,axiom,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ~ ( r1_tarski(B,k1_card_1(A))
          & ! [C] : ~ ( r1_tarski(C,A)
              & k1_card_1(C) = B ) ) ) ),
    file(card_fil,t36_card_fil),
    []).

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

fof(t3_funct_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funct_1(A)
        & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A))
        & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) ),
    file(funct_2,t3_funct_2),
    []).

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

fof(t44_card_2,axiom,(
    ! [A] : k3_card_2(2,k1_card_1(A)) = k1_card_1(k1_zfmisc_1(A)) ),
    file(card_2,t44_card_2),
    []).

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(t68_card_1,axiom,(
    ! [A,B] : 
      ( ( r2_wellord2(A,B)
        & v1_finset_1(A) )
     => v1_finset_1(B) ) ),
    file(card_1,t68_card_1),
    []).

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(t7_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) ),
    file(funct_2,t7_funct_2),
    []).

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

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

fof(t90_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    []).

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).