% Mizar problem: t38_closure2,closure2,1279,67 
fof(t38_closure2,conjecture,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B))
            & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B))
                & m2_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) )
             => ( ( v10_closure2(C,A,B)
                  & v10_closure2(D,A,B) )
               => v10_closure2(k8_closure2(A,B,D,C),A,B) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_altcat_1,cc1_closure2,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_funct_2,cc1_mssubfam,cc1_pboole,cc1_relat_1,cc1_relset_1,cc2_closure2,cc2_finset_1,cc2_funct_1,cc2_mssubfam,cc2_pboole,cc3_closure2,cc4_closure2,cc5_closure2,cc5_funct_2,cc6_closure2,cc6_funct_2,cc7_closure2,cc8_closure2,commutativity_k2_pboole,d15_closure2,d1_funct_2,dt_k1_closure2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_closure2,dt_k2_pboole,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_relat_1,dt_k6_closure2,dt_k7_closure2,dt_k8_closure2,dt_m1_closure2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m4_pboole,existence_m1_closure2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m4_pboole,fc10_relat_1,fc12_relat_1,fc14_finset_1,fc1_funct_1,fc1_subset_1,fc2_closure2,fc2_mssubfam,fc2_pboole,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,idempotence_k2_pboole,rc1_closure2,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_funct_2,rc1_mssubfam,rc1_pboole,rc1_relat_1,rc1_subset_1,rc2_closure2,rc2_funct_1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc3_closure2,rc3_finset_1,rc3_funct_1,rc3_pboole,rc3_relat_1,rc4_closure2,rc4_finset_1,rc4_funct_1,rc5_funct_1,rc5_pboole,redefinition_k2_closure2,redefinition_k4_relset_1,redefinition_k6_closure2,redefinition_k7_closure2,redefinition_k8_closure2,redefinition_m1_closure2,redefinition_m2_relset_1,reflexivity_r1_tarski,t11_closure2,t1_subset,t23_funct_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(closure2,t38_closure2)]).

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

fof(cc1_altcat_1,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_fraenkel(B) ) ) ),
    file(altcat_1,cc1_altcat_1),
    []).

fof(cc1_closure2,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_fraenkel(A) ) ),
    file(closure2,cc1_closure2),
    []).

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

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v3_relat_1(B)
       => v1_pre_circ(B,A) ) ) ),
    file(mssubfam,cc1_mssubfam),
    []).

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

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(cc2_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v2_closure2(C,A,B)
           => ( v1_fraenkel(C)
              & v1_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc2_closure2),
    []).

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_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( m4_pboole(C,A,B)
         => v1_pre_circ(C,A) ) ) ),
    file(mssubfam,cc2_mssubfam),
    []).

fof(cc2_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(cc3_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v4_closure2(C,A,B)
           => ( v1_fraenkel(C)
              & v3_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc3_closure2),
    []).

fof(cc4_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v4_closure2(C,A,B)
           => ( v1_fraenkel(C)
              & v5_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc4_closure2),
    []).

fof(cc5_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v5_closure2(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v1_fraenkel(C) ) ) ) ) ),
    file(closure2,cc5_closure2),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v2_closure2(C,A,B)
           => ( v1_fraenkel(C)
              & v6_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc6_closure2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(cc7_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v6_closure2(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v1_fraenkel(C) ) ) ) ) ),
    file(closure2,cc7_closure2),
    []).

fof(cc8_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B))
              & v10_closure2(C,A,B) )
           => ( ~ v1_xboole_0(C)
              & v1_funct_1(C)
              & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B))
              & v1_partfun1(C,k6_closure2(A,B),k6_closure2(A,B))
              & v8_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc8_closure2),
    []).

fof(commutativity_k2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k2_pboole(A,B,C) = k2_pboole(A,C,B) ) ),
    file(pboole,k2_pboole),
    []).

fof(d15_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B))
            & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) )
         => ( v10_closure2(C,A,B)
          <=> ! [D] : 
                ( m1_closure2(D,A,B,k6_closure2(A,B))
               => ! [E] : 
                    ( m1_closure2(E,A,B,k6_closure2(A,B))
                   => k1_funct_1(C,k2_pboole(A,D,E)) = k2_pboole(A,k7_closure2(A,B,C,D),k7_closure2(A,B,C,E)) ) ) ) ) ) ),
    file(closure2,d15_closure2),
    []).

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(dt_k1_closure2,axiom,(
    $true ),
    file(closure2,k1_closure2),
    []).

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_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_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_subset_1(k2_closure2(A,B),k1_zfmisc_1(k1_closure2(A,B))) ) ),
    file(closure2,k2_closure2),
    []).

fof(dt_k2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k2_pboole(A,B,C),A) ) ),
    file(pboole,k2_pboole),
    []).

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

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

fof(dt_k5_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_k6_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_closure2(k6_closure2(A,B),A,B)
        & v2_closure2(k6_closure2(A,B),A,B)
        & v3_closure2(k6_closure2(A,B),A,B)
        & v4_closure2(k6_closure2(A,B),A,B)
        & v5_closure2(k6_closure2(A,B),A,B)
        & v6_closure2(k6_closure2(A,B),A,B)
        & m1_subset_1(k6_closure2(A,B),k1_zfmisc_1(k1_closure2(A,B))) ) ) ),
    file(closure2,k6_closure2),
    []).

fof(dt_k7_closure2,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B))
        & m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B))
        & m1_subset_1(D,k6_closure2(A,B)) )
     => m1_closure2(k7_closure2(A,B,C,D),A,B,k6_closure2(A,B)) ) ),
    file(closure2,k7_closure2),
    []).

fof(dt_k8_closure2,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B))
        & m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B))
        & v1_funct_1(D)
        & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B))
        & m1_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) )
     => ( v1_funct_1(k8_closure2(A,B,C,D))
        & v1_funct_2(k8_closure2(A,B,C,D),k6_closure2(A,B),k6_closure2(A,B))
        & m2_relset_1(k8_closure2(A,B,C,D),k6_closure2(A,B),k6_closure2(A,B)) ) ) ),
    file(closure2,k8_closure2),
    []).

fof(dt_m1_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ! [D] : 
          ( m1_closure2(D,A,B,C)
         => m4_pboole(D,A,B) ) ) ),
    file(closure2,m1_closure2),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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

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

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

fof(dt_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pboole,m4_pboole),
    []).

fof(existence_m1_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ? [D] : m1_closure2(D,A,B,C) ) ),
    file(closure2,m1_closure2),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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

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

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

fof(existence_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : m4_pboole(C,A,B) ) ),
    file(pboole,m4_pboole),
    []).

fof(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_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(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_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_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( ~ v1_xboole_0(k1_closure2(A,B))
        & v1_fraenkel(k1_closure2(A,B))
        & v1_pralg_2(k1_closure2(A,B)) ) ) ),
    file(closure2,fc2_closure2),
    []).

fof(fc2_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A)
        & v1_pre_circ(C,A)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k2_pboole(A,B,C))
        & v1_funct_1(k2_pboole(A,B,C))
        & v1_pre_circ(k2_pboole(A,B,C),A) ) ) ),
    file(mssubfam,fc2_mssubfam),
    []).

fof(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_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(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(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(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    []).

fof(idempotence_k2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k2_pboole(A,B,B) = B ) ),
    file(pboole,k2_pboole),
    []).

fof(rc1_closure2,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_fraenkel(A) ) ),
    file(closure2,rc1_closure2),
    []).

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

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

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

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v3_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) ),
    file(mssubfam,rc1_mssubfam),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

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

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_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
          & ~ v1_xboole_0(C)
          & v1_fraenkel(C)
          & v1_pralg_2(C) ) ) ),
    file(closure2,rc2_closure2),
    []).

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_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
          & v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & v1_finset_1(C)
          & v1_fraenkel(C) ) ) ),
    file(closure2,rc3_closure2),
    []).

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_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc4_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
          & ~ v1_xboole_0(C)
          & v1_fraenkel(C)
          & v1_pralg_2(C)
          & v1_closure2(C,A,B)
          & v2_closure2(C,A,B)
          & v3_closure2(C,A,B)
          & v4_closure2(C,A,B)
          & v5_closure2(C,A,B)
          & v6_closure2(C,A,B) ) ) ),
    file(closure2,rc4_closure2),
    []).

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(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

fof(rc5_pboole,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(pboole,rc5_pboole),
    []).

fof(redefinition_k2_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => k2_closure2(A,B) = k1_closure2(A,B) ) ),
    file(closure2,k2_closure2),
    []).

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_k6_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => k6_closure2(A,B) = k1_closure2(A,B) ) ),
    file(closure2,k6_closure2),
    []).

fof(redefinition_k7_closure2,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B))
        & m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B))
        & m1_subset_1(D,k6_closure2(A,B)) )
     => k7_closure2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(closure2,k7_closure2),
    []).

fof(redefinition_k8_closure2,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B))
        & m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B))
        & v1_funct_1(D)
        & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B))
        & m1_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) )
     => k8_closure2(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(closure2,k8_closure2),
    []).

fof(redefinition_m1_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ! [D] : 
          ( m1_closure2(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(closure2,m1_closure2),
    []).

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

fof(t11_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_closure2(C,A,B,k2_closure2(A,B))
         => ! [D] : 
              ( m1_closure2(D,A,B,k2_closure2(A,B))
             => r2_hidden(k2_pboole(A,C,D),k2_closure2(A,B)) ) ) ) ),
    file(closure2,t11_closure2),
    []).

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

fof(t23_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(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_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(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

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),
    []).