% Mizar problem: t56_card_3,card_3,1003,19 
fof(t56_card_3,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r2_hidden(k6_card_3(A),k7_card_3(B)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_finset_1,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,commutativity_k2_tarski,d12_funct_1,d1_card_3,d3_card_3,d3_tarski,d4_card_3,d4_tarski,d4_wellord2,d4_xboole_0,d5_card_1,d5_card_3,d5_funct_1,d5_tarski,d6_card_3,d7_card_3,d8_card_3,d8_funct_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_card_3,dt_k2_mcart_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_tarski,dt_k4_card_3,dt_k4_tarski,dt_k4_xboole_0,dt_k5_card_3,dt_k6_card_3,dt_k7_card_3,dt_k9_relat_1,dt_m1_subset_1,existence_m1_subset_1,fc12_finset_1,fc12_relat_1,fc13_finset_1,fc14_finset_1,fc1_finset_1,fc2_card_1,fc2_finset_1,fc2_ordinal1,fc2_setfam_1,fc3_relat_1,fc3_setfam_1,fc4_ordinal1,fc4_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_card_1,rc1_card_3,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc1_setfam_1,rc2_card_1,rc2_funct_1,rc2_ordinal1,rc2_relat_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc3_relat_1,rc4_finset_1,rc4_funct_1,redefinition_r2_wellord2,reflexivity_r1_tarski,reflexivity_r2_wellord2,s1_partfun1__e2_52_3__card_3,s2_funct_1__e11_52__card_3,s3_funct_1__e2_52__card_3,s3_funct_1__e5_52_6__card_3,symmetry_r2_wellord2,t13_card_1,t1_subset,t1_xboole_1,t21_card_1,t22_ordinal1,t26_card_1,t2_subset,t31_card_3,t32_card_3,t33_card_3,t36_xboole_1,t37_card_3,t38_card_3,t3_boole,t3_card_2,t3_subset,t40_card_3,t4_boole,t4_card_2,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t8_mcart_1,t9_funct_1]),
    [file(card_3,t56_card_3)]).

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_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_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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(cc1_setfam_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    []).

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

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(d1_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_card_3(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => v1_card_1(k1_funct_1(A,B)) ) ) ) ),
    file(card_3,d1_card_3),
    []).

fof(d3_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_card_3(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) ) ) ) ) ) ),
    file(card_3,d3_card_3),
    []).

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_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    []).

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_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    []).

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_card_3,axiom,(
    ! [A,B,C] : 
      ( C = k5_card_3(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & r2_hidden(E,B)
              & D = k1_funct_1(E,A) ) ) ) ),
    file(card_3,d6_card_3),
    []).

fof(d7_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => k6_card_3(A) = k1_card_1(k3_card_3(k2_card_3(A))) ) ),
    file(card_3,d7_card_3),
    []).

fof(d8_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => k7_card_3(A) = k1_card_1(k4_card_3(A)) ) ),
    file(card_3,d8_card_3),
    []).

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_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

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

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_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_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_card_3(A))
        & v1_funct_1(k2_card_3(A)) ) ) ),
    file(card_3,k2_card_3),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_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_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    []).

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

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

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_3,axiom,(
    $true ),
    file(card_3,k5_card_3),
    []).

fof(dt_k6_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => v1_card_1(k6_card_3(A)) ) ),
    file(card_3,k6_card_3),
    []).

fof(dt_k7_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => v1_card_1(k7_card_3(A)) ) ),
    file(card_3,k7_card_3),
    []).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

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

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_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(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_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_setfam_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_1),
    []).

fof(fc3_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    []).

fof(fc3_setfam_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & v1_setfam_1(k2_tarski(A,B)) ) ) ),
    file(setfam_1,fc3_setfam_1),
    []).

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_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc6_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc8_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    []).

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

fof(rc1_card_3,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_card_3(A) ) ),
    file(card_3,rc1_card_3),
    []).

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_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc1_setfam_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_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_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_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_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(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

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_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(s1_partfun1__e2_52_3__card_3,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ? [D] : 
          ( v1_relat_1(D)
          & v1_funct_1(D)
          & k1_relat_1(D) = k1_relat_1(A)
          & ! [E] : 
              ( r2_hidden(E,k1_relat_1(A))
             => ( ( E = k2_mcart_1(C)
                 => k1_funct_1(D,E) = k1_mcart_1(C) )
                & ( E != k2_mcart_1(C)
                 => k1_funct_1(D,E) = k1_funct_1(B,E) ) ) ) ) ) ),
    file(card_3,s1_partfun1__e2_52_3__card_3),
    []).

fof(s2_funct_1__e11_52__card_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( ! [C,D,E] : 
              ( ( r2_hidden(C,k3_card_3(k2_card_3(A)))
                & ? [F] : 
                    ( v1_relat_1(F)
                    & v1_funct_1(F)
                    & D = F
                    & k1_relat_1(F) = k1_relat_1(A)
                    & ! [G] : 
                        ( r2_hidden(G,k1_relat_1(A))
                       => ( ( k2_mcart_1(C) = G
                           => k1_funct_1(F,G) = k1_mcart_1(C) )
                          & ( k2_mcart_1(C) != G
                           => k1_funct_1(F,G) = k1_funct_1(B,G) ) ) ) )
                & ? [H] : 
                    ( v1_relat_1(H)
                    & v1_funct_1(H)
                    & E = H
                    & k1_relat_1(H) = k1_relat_1(A)
                    & ! [I] : 
                        ( r2_hidden(I,k1_relat_1(A))
                       => ( ( k2_mcart_1(C) = I
                           => k1_funct_1(H,I) = k1_mcart_1(C) )
                          & ( k2_mcart_1(C) != I
                           => k1_funct_1(H,I) = k1_funct_1(B,I) ) ) ) ) )
             => D = E )
          & ! [C] : ~ ( r2_hidden(C,k3_card_3(k2_card_3(A)))
              & ! [D] : ~ ? [J] : 
                    ( v1_relat_1(J)
                    & v1_funct_1(J)
                    & D = J
                    & k1_relat_1(J) = k1_relat_1(A)
                    & ! [K] : 
                        ( r2_hidden(K,k1_relat_1(A))
                       => ( ( k2_mcart_1(C) = K
                           => k1_funct_1(J,K) = k1_mcart_1(C) )
                          & ( k2_mcart_1(C) != K
                           => k1_funct_1(J,K) = k1_funct_1(B,K) ) ) ) ) ) )
       => ? [C] : 
            ( v1_relat_1(C)
            & v1_funct_1(C)
            & k1_relat_1(C) = k3_card_3(k2_card_3(A))
            & ! [D] : 
                ( r2_hidden(D,k3_card_3(k2_card_3(A)))
               => ? [L] : 
                    ( v1_relat_1(L)
                    & v1_funct_1(L)
                    & k1_funct_1(C,D) = L
                    & k1_relat_1(L) = k1_relat_1(A)
                    & ! [M] : 
                        ( r2_hidden(M,k1_relat_1(A))
                       => ( ( k2_mcart_1(D) = M
                           => k1_funct_1(L,M) = k1_mcart_1(D) )
                          & ( k2_mcart_1(D) != M
                           => k1_funct_1(L,M) = k1_funct_1(B,M) ) ) ) ) ) ) ) ) ),
    file(card_3,s2_funct_1__e11_52__card_3),
    []).

fof(s3_funct_1__e2_52__card_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_card_3(B) )
     => ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & k1_relat_1(C) = k1_relat_1(A)
          & ! [D] : 
              ( r2_hidden(D,k1_relat_1(A))
             => k1_funct_1(C,D) = k4_xboole_0(k1_funct_1(B,D),k1_funct_1(A,D)) ) ) ) ),
    file(card_3,s3_funct_1__e2_52__card_3),
    []).

fof(s3_funct_1__e5_52_6__card_3,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_card_3(B)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ? [D] : 
          ( v1_relat_1(D)
          & v1_funct_1(D)
          & k1_relat_1(D) = k1_relat_1(A)
          & ! [E] : 
              ( r2_hidden(E,k1_relat_1(A))
             => k1_funct_1(D,E) = k4_xboole_0(k1_funct_1(B,E),k5_card_3(E,k9_relat_1(C,k1_funct_1(k2_card_3(A),E)))) ) ) ) ),
    file(card_3,s3_funct_1__e5_52_6__card_3),
    []).

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

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

fof(t31_card_3,axiom,(
    ! [A,B] : r1_tarski(k1_card_1(k5_card_3(B,A)),k1_card_1(A)) ),
    file(card_3,t31_card_3),
    []).

fof(t32_card_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ~ ( r2_hidden(A,k3_card_3(k2_card_3(B)))
          & ! [C,D] : A != k4_tarski(C,D) ) ) ),
    file(card_3,t32_card_3),
    []).

fof(t33_card_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k3_card_3(k2_card_3(B)))
      <=> ( r2_hidden(k2_mcart_1(A),k1_relat_1(B))
          & r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A)))
          & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ) ) ),
    file(card_3,t33_card_3),
    []).

fof(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t37_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k4_card_3(A) = k1_xboole_0
      <=> r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ),
    file(card_3,t37_card_3),
    []).

fof(t38_card_3,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))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r1_tarski(k4_card_3(A),k4_card_3(B)) ) ) ) ),
    file(card_3,t38_card_3),
    []).

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

fof(t3_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_tarski(k1_card_1(k9_relat_1(B,A)),k1_card_1(A)) ) ),
    file(card_2,t3_card_2),
    []).

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

fof(t40_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k1_card_1(k1_funct_1(k2_card_3(A),B)) = k1_funct_1(A,B) ) ) ),
    file(card_3,t40_card_3),
    []).

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

fof(t4_card_2,axiom,(
    ! [A,B] : ~ ( r2_hidden(k1_card_1(A),k1_card_1(B))
      & k4_xboole_0(B,A) = k1_xboole_0 ) ),
    file(card_2,t4_card_2),
    []).

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),
    []).

fof(t8_mcart_1,axiom,(
    ! [A] : 
      ( ? [B,C] : A = k4_tarski(B,C)
     => k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A ) ),
    file(mcart_1,t8_mcart_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),
    []).