% Mizar problem: t39_closure2,closure2,1512,37 
fof(t39_closure2,conjecture,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B))
                & v7_closure2(C,u1_struct_0(A),B)
                & v8_closure2(C,u1_struct_0(A),B)
                & m2_relset_1(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(u1_struct_0(A),B)))
                 => ( D = a_3_1_closure2(A,B,C)
                   => ( v15_closure2(g1_closure2(A,B,D),A)
                      & l1_closure2(g1_closure2(A,B,D),A) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v11_closure2,antisymmetry_r2_hidden,cc10_closure2,cc11_closure2,cc12_closure2,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,cc9_closure2,d12_closure2,d13_closure2,d13_pboole,d19_closure2,d1_closure2,d8_closure2,dt_g1_closure2,dt_k1_closure2,dt_k1_funct_1,dt_k1_mboolean,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_closure2,dt_k5_closure2,dt_k5_mssubfam,dt_k6_closure2,dt_k6_mssubfam,dt_k7_closure2,dt_l1_closure2,dt_l1_struct_0,dt_l2_msualg_1,dt_m1_closure2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m4_pboole,dt_u1_closure2,dt_u1_struct_0,dt_u4_msualg_1,existence_l1_closure2,existence_l1_struct_0,existence_l2_msualg_1,existence_m1_closure2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m4_pboole,fc10_closure2,fc11_closure2,fc12_closure2,fc12_relat_1,fc13_closure2,fc14_closure2,fc14_finset_1,fc15_closure2,fc16_closure2,fc17_closure2,fc18_closure2,fc19_closure2,fc1_msualg_1,fc1_subset_1,fc20_closure2,fc2_closure2,fc2_pboole,fc4_closure2,fc4_relat_1,fc4_subset_1,fc5_closure2,fc8_closure2,fc8_mssubfam,fc9_closure2,fraenkel_a_3_1_closure2,free_g1_closure2,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_mssubfam,rc2_pboole,rc2_relat_1,rc2_subset_1,rc3_closure2,rc3_finset_1,rc3_funct_1,rc3_mssubfam,rc3_pboole,rc3_relat_1,rc4_closure2,rc4_finset_1,rc4_funct_1,rc4_mssubfam,rc5_funct_1,rc5_pboole,rc6_closure2,rc7_closure2,redefinition_k5_closure2,redefinition_k6_closure2,redefinition_k6_mssubfam,redefinition_k7_closure2,redefinition_m1_closure2,redefinition_m2_relset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r2_pboole,reflexivity_r6_pboole,symmetry_r6_pboole,t1_subset,t22_closure2,t25_closure2,t2_subset,t2_tarski,t3_subset,t43_mssubfam,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(closure2,t39_closure2)]).

fof(abstractness_v11_closure2,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l1_closure2(B,A) )
     => ( v11_closure2(B,A)
       => B = g1_closure2(A,u4_msualg_1(A,B),u1_closure2(A,B)) ) ) ),
    file(closure2,v11_closure2),
    []).

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

fof(cc10_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure2(B,A)
         => ( v15_closure2(B,A)
           => v14_closure2(B,A) ) ) ) ),
    file(closure2,cc10_closure2),
    []).

fof(cc11_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure2(B,A)
         => ( v15_closure2(B,A)
           => v16_closure2(B,A) ) ) ) ),
    file(closure2,cc11_closure2),
    []).

fof(cc12_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure2(B,A)
         => ( v13_closure2(B,A)
           => v17_closure2(B,A) ) ) ) ),
    file(closure2,cc12_closure2),
    []).

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(cc9_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure2(B,A)
         => ( v13_closure2(B,A)
           => v12_closure2(B,A) ) ) ) ),
    file(closure2,cc9_closure2),
    []).

fof(d12_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)) )
         => ( v7_closure2(C,A,B)
          <=> ! [D] : 
                ( m1_closure2(D,A,B,k6_closure2(A,B))
               => r2_pboole(A,D,k7_closure2(A,B,C,D)) ) ) ) ) ),
    file(closure2,d12_closure2),
    []).

fof(d13_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)) )
         => ( v8_closure2(C,A,B)
          <=> ! [D] : 
                ( m1_closure2(D,A,B,k6_closure2(A,B))
               => ! [E] : 
                    ( m1_closure2(E,A,B,k6_closure2(A,B))
                   => ( r2_pboole(A,D,E)
                     => r2_pboole(A,k7_closure2(A,B,C,D),k7_closure2(A,B,C,E)) ) ) ) ) ) ) ),
    file(closure2,d13_closure2),
    []).

fof(d13_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,B,C)
          <=> ( r2_pboole(A,B,C)
              & r2_pboole(A,C,B) ) ) ) ) ),
    file(pboole,d13_pboole),
    []).

fof(d19_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure2(B,A)
         => ( v15_closure2(B,A)
          <=> v4_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ) ),
    file(closure2,d19_closure2),
    []).

fof(d1_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( C = k1_closure2(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> m4_pboole(D,A,B) ) ) ) ),
    file(closure2,d1_closure2),
    []).

fof(d8_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)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B)))
               => ( r1_tarski(D,C)
                 => r2_hidden(k6_mssubfam(A,B,k5_closure2(A,B,D)),C) ) ) ) ) ) ),
    file(closure2,d8_closure2),
    []).

fof(dt_g1_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),B))) )
     => ( v11_closure2(g1_closure2(A,B,C),A)
        & l1_closure2(g1_closure2(A,B,C),A) ) ) ),
    file(closure2,g1_closure2),
    []).

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_mboolean,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_pboole(k1_mboolean(A,B),A) ) ),
    file(mboolean,k1_mboolean),
    []).

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

fof(dt_k4_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => m1_pboole(k4_closure2(A,B,C),A) ) ),
    file(closure2,k4_closure2),
    []).

fof(dt_k5_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => m4_pboole(k5_closure2(A,B,C),A,k1_mboolean(A,B)) ) ),
    file(closure2,k5_closure2),
    []).

fof(dt_k5_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m4_pboole(C,A,k1_mboolean(A,B)) )
     => m1_pboole(k5_mssubfam(A,B,C),A) ) ),
    file(mssubfam,k5_mssubfam),
    []).

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_k6_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m4_pboole(C,A,k1_mboolean(A,B)) )
     => m4_pboole(k6_mssubfam(A,B,C),A,B) ) ),
    file(mssubfam,k6_mssubfam),
    []).

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_l1_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure2(B,A)
         => l2_msualg_1(B,A) ) ) ),
    file(closure2,l1_closure2),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_msualg_1,axiom,(
    $true ),
    file(msualg_1,l2_msualg_1),
    []).

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(dt_u1_closure2,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l1_closure2(B,A) )
     => m1_subset_1(u1_closure2(A,B),k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) ) ),
    file(closure2,u1_closure2),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u4_msualg_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A) )
     => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ),
    file(msualg_1,u4_msualg_1),
    []).

fof(existence_l1_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l1_closure2(B,A) ) ),
    file(closure2,l1_closure2),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_msualg_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l2_msualg_1(B,A) ) ),
    file(msualg_1,l2_msualg_1),
    []).

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_closure2,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v14_closure2(B,A)
        & l1_closure2(B,A) )
     => ( v1_fraenkel(u1_closure2(A,B))
        & v3_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure2,fc10_closure2),
    []).

fof(fc11_closure2,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v15_closure2(B,A)
        & l1_closure2(B,A) )
     => ( ~ v1_xboole_0(u1_closure2(A,B))
        & v1_fraenkel(u1_closure2(A,B))
        & v3_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))
        & v4_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))
        & v5_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure2,fc11_closure2),
    []).

fof(fc12_closure2,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v16_closure2(B,A)
        & l1_closure2(B,A) )
     => ( ~ v1_xboole_0(u1_closure2(A,B))
        & v1_fraenkel(u1_closure2(A,B))
        & v5_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure2,fc12_closure2),
    []).

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_closure2,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v17_closure2(B,A)
        & l1_closure2(B,A) )
     => ( ~ v1_xboole_0(u1_closure2(A,B))
        & v1_fraenkel(u1_closure2(A,B))
        & v6_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure2,fc13_closure2),
    []).

fof(fc14_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),B))) )
     => ( v5_msualg_1(g1_closure2(A,B,C),A)
        & v11_closure2(g1_closure2(A,B,C),A) ) ) ),
    file(closure2,fc14_closure2),
    []).

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(fc15_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v1_closure2(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) )
     => ( v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A)
        & v12_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure2,fc15_closure2),
    []).

fof(fc16_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v2_closure2(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) )
     => ( v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A)
        & v12_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A)
        & v13_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure2,fc16_closure2),
    []).

fof(fc17_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v3_closure2(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) )
     => ( v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A)
        & v14_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure2,fc17_closure2),
    []).

fof(fc18_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v4_closure2(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) )
     => ( v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A)
        & v14_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A)
        & v15_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure2,fc18_closure2),
    []).

fof(fc19_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v5_closure2(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) )
     => ( v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A)
        & v16_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure2,fc19_closure2),
    []).

fof(fc1_msualg_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v5_msualg_1(B,A)
        & l2_msualg_1(B,A) )
     => ( v1_relat_1(u4_msualg_1(A,B))
        & v2_relat_1(u4_msualg_1(A,B))
        & v1_funct_1(u4_msualg_1(A,B)) ) ) ),
    file(msualg_1,fc1_msualg_1),
    []).

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

fof(fc20_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v6_closure2(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) )
     => ( v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A)
        & v17_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure2,fc20_closure2),
    []).

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_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_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ( v1_relat_1(k4_closure2(A,B,C))
        & v3_relat_1(k4_closure2(A,B,C))
        & v1_funct_1(k4_closure2(A,B,C))
        & v1_pre_circ(k4_closure2(A,B,C),A) ) ) ),
    file(closure2,fc4_closure2),
    []).

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_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ( v1_relat_1(k4_closure2(A,B,C))
        & v2_relat_1(k4_closure2(A,B,C))
        & v1_funct_1(k4_closure2(A,B,C)) ) ) ),
    file(closure2,fc5_closure2),
    []).

fof(fc8_closure2,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v12_closure2(B,A)
        & l1_closure2(B,A) )
     => ( v1_fraenkel(u1_closure2(A,B))
        & v1_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure2,fc8_closure2),
    []).

fof(fc8_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k1_mboolean(A,B))
        & v2_relat_1(k1_mboolean(A,B))
        & v1_funct_1(k1_mboolean(A,B))
        & v1_pre_circ(k1_mboolean(A,B),A) ) ) ),
    file(mssubfam,fc8_mssubfam),
    []).

fof(fc9_closure2,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v13_closure2(B,A)
        & l1_closure2(B,A) )
     => ( ~ v1_xboole_0(u1_closure2(A,B))
        & v1_fraenkel(u1_closure2(A,B))
        & v1_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))
        & v2_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))
        & v6_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure2,fc9_closure2),
    []).

fof(fraenkel_a_3_1_closure2,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(B)
        & m1_pboole(C,u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C))
        & v7_closure2(D,u1_struct_0(B),C)
        & v8_closure2(D,u1_struct_0(B),C)
        & m2_relset_1(D,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) )
     => ( r2_hidden(A,a_3_1_closure2(B,C,D))
      <=> ? [E] : 
            ( m1_closure2(E,u1_struct_0(B),C,k6_closure2(u1_struct_0(B),C))
            & A = E
            & r6_pboole(u1_struct_0(B),k7_closure2(u1_struct_0(B),C,D,E),E) ) ) ) ),
    file(closure2,a_3_1_closure2),
    []).

fof(free_g1_closure2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),B))) )
     => ! [D,E,F] : 
          ( g1_closure2(A,B,C) = g1_closure2(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(closure2,g1_closure2),
    []).

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_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(mssubfam,rc2_mssubfam),
    []).

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_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
          & v1_relat_1(C)
          & v3_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) ),
    file(mssubfam,rc3_mssubfam),
    []).

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(rc4_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) ),
    file(mssubfam,rc4_mssubfam),
    []).

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(rc6_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( l1_closure2(B,A)
          & v11_closure2(B,A) ) ) ),
    file(closure2,rc6_closure2),
    []).

fof(rc7_closure2,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( l1_closure2(B,A)
          & v5_msualg_1(B,A)
          & v11_closure2(B,A)
          & v12_closure2(B,A)
          & v13_closure2(B,A)
          & v14_closure2(B,A)
          & v15_closure2(B,A)
          & v16_closure2(B,A)
          & v17_closure2(B,A) ) ) ),
    file(closure2,rc7_closure2),
    []).

fof(redefinition_k5_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => k5_closure2(A,B,C) = k4_closure2(A,B,C) ) ),
    file(closure2,k5_closure2),
    []).

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_k6_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m4_pboole(C,A,k1_mboolean(A,B)) )
     => k6_mssubfam(A,B,C) = k5_mssubfam(A,B,C) ) ),
    file(mssubfam,k6_mssubfam),
    []).

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_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(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

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

fof(reflexivity_r2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r2_pboole(A,B,B) ) ),
    file(pboole,r2_pboole),
    []).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

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

fof(t22_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B)))
             => ( r2_hidden(C,D)
               => r1_pboole(A,C,k5_closure2(A,B,D)) ) ) ) ) ),
    file(closure2,t22_closure2),
    []).

fof(t25_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ! [D] : 
              ( m4_pboole(D,A,B)
             => ( ! [E] : 
                    ( m1_pboole(E,A)
                   => ( r2_hidden(E,C)
                     => r2_pboole(A,D,E) ) )
               => r2_pboole(A,D,k6_mssubfam(A,B,k5_closure2(A,B,C))) ) ) ) ) ),
    file(closure2,t25_closure2),
    []).

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

fof(t43_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => ( r1_pboole(A,C,D)
               => r2_pboole(A,k6_mssubfam(A,B,D),C) ) ) ) ) ),
    file(mssubfam,t43_mssubfam),
    []).

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),
    []).