% Mizar problem: t30_closure1,closure1,1321,43 
fof(t30_closure1,conjecture,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_closure1(C,u1_struct_0(A),B)
                & v2_closure1(C,u1_struct_0(A),B)
                & m3_pboole(C,u1_struct_0(A),k7_mssubfam(u1_struct_0(A),B),k7_mssubfam(u1_struct_0(A),B)) )
             => ! [D] : 
                  ( m4_pboole(D,u1_struct_0(A),k1_mboolean(u1_struct_0(A),B))
                 => ( r6_pboole(u1_struct_0(A),D,k6_closure1(u1_struct_0(A),k7_mssubfam(u1_struct_0(A),B),C))
                   => ( v9_closure1(g1_closure1(A,B,D),A)
                      & l1_closure1(g1_closure1(A,B,D),A) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v5_closure1,antisymmetry_r2_hidden,cc1_finset_1,cc1_funct_1,cc1_mssubfam,cc1_pboole,cc1_relset_1,cc2_closure1,cc2_finset_1,cc2_funct_1,cc2_mssubfam,cc2_pboole,cc3_closure1,cc3_mssubfam,cc3_pboole,cc4_closure1,cc4_mssubfam,cc5_closure1,cc5_mssubfam,cc6_mssubfam,cc7_mssubfam,cc8_mssubfam,d13_closure1,d13_pboole,d17_pralg_1,d18_pboole,d1_mboolean,d23_pboole,d2_closure1,d2_mssubfam,d3_pboole,d5_pboole,d6_mssubfam,d9_closure1,dt_g1_closure1,dt_k15_pralg_1,dt_k1_closure1,dt_k1_funct_1,dt_k1_mboolean,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_closure1,dt_k5_mssubfam,dt_k6_closure1,dt_k6_mssubfam,dt_k7_mssubfam,dt_k8_setfam_1,dt_l1_closure1,dt_l1_struct_0,dt_l2_msualg_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_pboole,dt_m2_relset_1,dt_m3_pboole,dt_m4_pboole,dt_u1_closure1,dt_u1_struct_0,dt_u4_msualg_1,existence_l1_closure1,existence_l1_struct_0,existence_l2_msualg_1,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_pboole,existence_m2_relset_1,existence_m3_pboole,existence_m4_pboole,fc10_closure1,fc11_closure1,fc12_closure1,fc13_closure1,fc14_closure1,fc14_finset_1,fc15_closure1,fc16_closure1,fc1_msualg_1,fc1_subset_1,fc1_xboole_0,fc2_pboole,fc3_closure1,fc4_closure1,fc4_subset_1,fc5_closure1,fc6_closure1,fc7_closure1,fc7_funcop_1,fc8_closure1,fc8_mssubfam,fc9_closure1,free_g1_closure1,rc1_closure1,rc1_finset_1,rc1_funcop_1,rc1_funct_1,rc1_mssubfam,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_mssubfam,rc2_pboole,rc2_subset_1,rc2_xboole_0,rc3_closure1,rc3_finset_1,rc3_funct_1,rc3_mssubfam,rc3_pboole,rc4_closure1,rc4_finset_1,rc4_funct_1,rc4_mssubfam,rc4_pboole,rc5_funct_1,rc5_mssubfam,rc5_pboole,redefinition_k1_closure1,redefinition_k3_closure1,redefinition_k6_mssubfam,redefinition_k7_mssubfam,redefinition_m2_relset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r2_pboole,reflexivity_r6_pboole,symmetry_r6_pboole,t11_mssubfam,t19_mboolean,t1_subset,t25_closure1,t28_closure1,t2_mssubfam,t2_subset,t3_subset,t4_mssubfam,t4_subset,t5_subset,t6_boole,t7_boole,t7_funct_2,t8_boole]),
    [file(closure1,t30_closure1)]).

fof(abstractness_v5_closure1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l1_closure1(B,A) )
     => ( v5_closure1(B,A)
       => B = g1_closure1(A,u4_msualg_1(A,B),u1_closure1(A,B)) ) ) ),
    file(closure1,v5_closure1),
    []).

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

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_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_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_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure1(B,A)
         => ( v7_closure1(B,A)
           => v6_closure1(B,A) ) ) ) ),
    file(closure1,cc2_closure1),
    []).

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_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure1(B,A)
         => ( v9_closure1(B,A)
           => v8_closure1(B,A) ) ) ) ),
    file(closure1,cc3_closure1),
    []).

fof(cc3_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v2_mssubfam(C,A,B)
           => v1_mssubfam(C,A,B) ) ) ) ),
    file(mssubfam,cc3_mssubfam),
    []).

fof(cc3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => v1_funcop_1(D) ) ) ),
    file(pboole,cc3_pboole),
    []).

fof(cc4_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure1(B,A)
         => ( v9_closure1(B,A)
           => v10_closure1(B,A) ) ) ) ),
    file(closure1,cc4_closure1),
    []).

fof(cc4_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v4_mssubfam(C,A,B)
           => v3_mssubfam(C,A,B) ) ) ) ),
    file(mssubfam,cc4_mssubfam),
    []).

fof(cc5_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure1(B,A)
         => ( v7_closure1(B,A)
           => v11_closure1(B,A) ) ) ) ),
    file(closure1,cc5_closure1),
    []).

fof(cc5_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v4_mssubfam(C,A,B)
           => v5_mssubfam(C,A,B) ) ) ) ),
    file(mssubfam,cc5_mssubfam),
    []).

fof(cc6_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v5_mssubfam(C,A,B)
           => v2_relat_1(C) ) ) ) ),
    file(mssubfam,cc6_mssubfam),
    []).

fof(cc7_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v2_mssubfam(C,A,B)
           => v6_mssubfam(C,A,B) ) ) ) ),
    file(mssubfam,cc7_mssubfam),
    []).

fof(cc8_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v6_mssubfam(C,A,B)
           => v2_relat_1(C) ) ) ) ),
    file(mssubfam,cc8_mssubfam),
    []).

fof(d13_closure1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m3_pboole(C,A,B,B)
         => ! [D] : 
              ( m4_pboole(D,A,B)
             => ( D = k6_closure1(A,B,C)
              <=> ! [E,F] : 
                    ( r2_hidden(F,A)
                   => ( r2_hidden(E,k1_funct_1(D,F))
                    <=> ? [G] : 
                          ( v1_relat_1(G)
                          & v1_funct_1(G)
                          & G = k1_funct_1(C,F)
                          & r2_hidden(E,k1_relat_1(G))
                          & k1_funct_1(G,E) = E ) ) ) ) ) ) ) ),
    file(closure1,d13_closure1),
    []).

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(d17_pralg_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k15_pralg_1(A,B)
              <=> ( k1_relat_1(C) = k1_relat_1(A)
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(A))
                     => k1_funct_1(C,D) = k1_funct_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(pralg_1,d17_pralg_1),
    []).

fof(d18_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(pboole,d18_pboole),
    []).

fof(d1_mboolean,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k1_mboolean(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k1_zfmisc_1(k1_funct_1(B,D)) ) ) ) ) ),
    file(mboolean,d1_mboolean),
    []).

fof(d23_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( m4_pboole(C,A,B)
          <=> r2_pboole(A,C,B) ) ) ) ),
    file(pboole,d23_pboole),
    []).

fof(d2_closure1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m3_pboole(C,A,k7_mssubfam(A,B),k7_mssubfam(A,B))
         => ( v1_closure1(C,A,B)
          <=> ! [D] : 
                ( m2_pboole(D,A,k7_mssubfam(A,B))
               => r2_pboole(A,D,k3_closure1(A,B,C,D)) ) ) ) ) ),
    file(closure1,d2_closure1),
    []).

fof(d2_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k5_mssubfam(A,B,C)
              <=> ! [E] : ~ ( r2_hidden(E,A)
                    & ! [F] : 
                        ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,E))))
                       => ~ ( F = k1_funct_1(C,E)
                            & k1_funct_1(D,E) = k8_setfam_1(k1_funct_1(B,E),F) ) ) ) ) ) ) ) ),
    file(mssubfam,d2_mssubfam),
    []).

fof(d3_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    []).

fof(d5_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    []).

fof(d6_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v4_mssubfam(C,A,B)
          <=> ! [D] : 
                ( m4_pboole(D,A,k1_mboolean(A,B))
               => ( r2_pboole(A,D,C)
                 => r1_pboole(A,k6_mssubfam(A,B,D),C) ) ) ) ) ) ),
    file(mssubfam,d6_mssubfam),
    []).

fof(d9_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure1(B,A)
         => ( v9_closure1(B,A)
          <=> v4_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ) ),
    file(closure1,d9_closure1),
    []).

fof(dt_g1_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & m1_pboole(B,u1_struct_0(A))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),B)) )
     => ( v5_closure1(g1_closure1(A,B,C),A)
        & l1_closure1(g1_closure1(A,B,C),A) ) ) ),
    file(closure1,g1_closure1),
    []).

fof(dt_k15_pralg_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k15_pralg_1(A,B))
        & v1_funct_1(k15_pralg_1(A,B)) ) ) ),
    file(pralg_1,k15_pralg_1),
    []).

fof(dt_k1_closure1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k1_closure1(A,B,C),A) ) ),
    file(closure1,k1_closure1),
    []).

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

fof(dt_k3_closure1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(B,A)
        & m3_pboole(C,A,k7_mssubfam(A,B),k7_mssubfam(A,B))
        & m2_pboole(D,A,k7_mssubfam(A,B)) )
     => m2_pboole(k3_closure1(A,B,C,D),A,k7_mssubfam(A,B)) ) ),
    file(closure1,k3_closure1),
    []).

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_closure1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m3_pboole(C,A,B,B) )
     => m4_pboole(k6_closure1(A,B,C),A,B) ) ),
    file(closure1,k6_closure1),
    []).

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_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_mssubfam(k7_mssubfam(A,B),A,B)
        & v2_mssubfam(k7_mssubfam(A,B),A,B)
        & v3_mssubfam(k7_mssubfam(A,B),A,B)
        & v4_mssubfam(k7_mssubfam(A,B),A,B)
        & v5_mssubfam(k7_mssubfam(A,B),A,B)
        & v6_mssubfam(k7_mssubfam(A,B),A,B)
        & m4_pboole(k7_mssubfam(A,B),A,k1_mboolean(A,B)) ) ) ),
    file(mssubfam,k7_mssubfam),
    []).

fof(dt_k8_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k8_setfam_1),
    []).

fof(dt_l1_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_closure1(B,A)
         => l2_msualg_1(B,A) ) ) ),
    file(closure1,l1_closure1),
    []).

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_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_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m2_pboole(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pboole,m2_pboole),
    []).

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_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    []).

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_closure1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l1_closure1(B,A) )
     => m4_pboole(u1_closure1(A,B),u1_struct_0(A),k1_mboolean(u1_struct_0(A),u4_msualg_1(A,B))) ) ),
    file(closure1,u1_closure1),
    []).

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_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l1_closure1(B,A) ) ),
    file(closure1,l1_closure1),
    []).

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_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_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : m2_pboole(C,A,B) ) ),
    file(pboole,m2_pboole),
    []).

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

fof(existence_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    []).

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

fof(fc10_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v1_mssubfam(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),u4_msualg_1(A,B))) )
     => ( v5_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A)
        & v6_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure1,fc10_closure1),
    []).

fof(fc11_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v2_mssubfam(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),u4_msualg_1(A,B))) )
     => ( v5_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A)
        & v6_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A)
        & v7_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure1,fc11_closure1),
    []).

fof(fc12_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v3_mssubfam(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),u4_msualg_1(A,B))) )
     => ( v5_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A)
        & v8_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure1,fc12_closure1),
    []).

fof(fc13_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v4_mssubfam(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),u4_msualg_1(A,B))) )
     => ( v5_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A)
        & v8_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A)
        & v9_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure1,fc13_closure1),
    []).

fof(fc14_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v5_mssubfam(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),u4_msualg_1(A,B))) )
     => ( v5_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A)
        & v10_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure1,fc14_closure1),
    []).

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_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A)
        & v6_mssubfam(C,u1_struct_0(A),u4_msualg_1(A,B))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),u4_msualg_1(A,B))) )
     => ( v5_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A)
        & v11_closure1(g1_closure1(A,u4_msualg_1(A,B),C),A) ) ) ),
    file(closure1,fc15_closure1),
    []).

fof(fc16_closure1,axiom,(
    ! [A,B,C] : 
      ( ( v3_relat_1(B)
        & m1_pboole(B,A)
        & m3_pboole(C,A,B,B) )
     => ( v1_relat_1(k6_closure1(A,B,C))
        & v3_relat_1(k6_closure1(A,B,C))
        & v1_funct_1(k6_closure1(A,B,C))
        & v1_pre_circ(k6_closure1(A,B,C),A) ) ) ),
    file(closure1,fc16_closure1),
    []).

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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

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(fc3_closure1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v6_closure1(B,A)
        & l1_closure1(B,A) )
     => ( v1_relat_1(u1_closure1(A,B))
        & v1_funct_1(u1_closure1(A,B))
        & v1_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure1,fc3_closure1),
    []).

fof(fc4_closure1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v7_closure1(B,A)
        & l1_closure1(B,A) )
     => ( v1_relat_1(u1_closure1(A,B))
        & v2_relat_1(u1_closure1(A,B))
        & v1_funct_1(u1_closure1(A,B))
        & v1_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B))
        & v2_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B))
        & v6_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure1,fc4_closure1),
    []).

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_closure1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v8_closure1(B,A)
        & l1_closure1(B,A) )
     => ( v1_relat_1(u1_closure1(A,B))
        & v1_funct_1(u1_closure1(A,B))
        & v3_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure1,fc5_closure1),
    []).

fof(fc6_closure1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v9_closure1(B,A)
        & l1_closure1(B,A) )
     => ( v1_relat_1(u1_closure1(A,B))
        & v2_relat_1(u1_closure1(A,B))
        & v1_funct_1(u1_closure1(A,B))
        & v3_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B))
        & v4_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B))
        & v5_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure1,fc6_closure1),
    []).

fof(fc7_closure1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v10_closure1(B,A)
        & l1_closure1(B,A) )
     => ( v1_relat_1(u1_closure1(A,B))
        & v2_relat_1(u1_closure1(A,B))
        & v1_funct_1(u1_closure1(A,B))
        & v5_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure1,fc7_closure1),
    []).

fof(fc7_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    []).

fof(fc8_closure1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v11_closure1(B,A)
        & l1_closure1(B,A) )
     => ( v1_relat_1(u1_closure1(A,B))
        & v2_relat_1(u1_closure1(A,B))
        & v1_funct_1(u1_closure1(A,B))
        & v6_mssubfam(u1_closure1(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(closure1,fc8_closure1),
    []).

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_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),B)) )
     => ( v5_msualg_1(g1_closure1(A,B,C),A)
        & v5_closure1(g1_closure1(A,B,C),A) ) ) ),
    file(closure1,fc9_closure1),
    []).

fof(free_g1_closure1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & m1_pboole(B,u1_struct_0(A))
        & m4_pboole(C,u1_struct_0(A),k1_mboolean(u1_struct_0(A),B)) )
     => ! [D,E,F] : 
          ( g1_closure1(A,B,C) = g1_closure1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(closure1,g1_closure1),
    []).

fof(rc1_closure1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m2_pboole(C,A,k7_mssubfam(A,B))
          & v1_relat_1(C)
          & v3_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) ),
    file(closure1,rc1_closure1),
    []).

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

fof(rc1_funcop_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    []).

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

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_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(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

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_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( l1_closure1(B,A)
          & v5_closure1(B,A) ) ) ),
    file(closure1,rc3_closure1),
    []).

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(rc4_closure1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( l1_closure1(B,A)
          & v5_msualg_1(B,A)
          & v5_closure1(B,A)
          & v6_closure1(B,A)
          & v7_closure1(B,A)
          & v8_closure1(B,A)
          & v9_closure1(B,A)
          & v10_closure1(B,A)
          & v11_closure1(B,A) ) ) ),
    file(closure1,rc4_closure1),
    []).

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(rc4_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) ),
    file(pboole,rc4_pboole),
    []).

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_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)
          & v1_mssubfam(C,A,B)
          & v2_mssubfam(C,A,B)
          & v3_mssubfam(C,A,B)
          & v4_mssubfam(C,A,B)
          & v5_mssubfam(C,A,B)
          & v6_mssubfam(C,A,B) ) ) ),
    file(mssubfam,rc5_mssubfam),
    []).

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_k1_closure1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k1_closure1(A,B,C) = k15_pralg_1(B,C) ) ),
    file(closure1,k1_closure1),
    []).

fof(redefinition_k3_closure1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(B,A)
        & m3_pboole(C,A,k7_mssubfam(A,B),k7_mssubfam(A,B))
        & m2_pboole(D,A,k7_mssubfam(A,B)) )
     => k3_closure1(A,B,C,D) = k15_pralg_1(C,D) ) ),
    file(closure1,k3_closure1),
    []).

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_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => k7_mssubfam(A,B) = k1_mboolean(A,B) ) ),
    file(mssubfam,k7_mssubfam),
    []).

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(t11_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
           => m2_pboole(B,A,C) ) ) ) ),
    file(mssubfam,t11_mssubfam),
    []).

fof(t19_mboolean,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> r1_pboole(A,B,k1_mboolean(A,C)) ) ) ) ),
    file(mboolean,t19_mboolean),
    []).

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

fof(t25_closure1,axiom,(
    ! [A,B,C] : 
      ( m1_pboole(C,B)
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ! [E] : 
              ( m3_pboole(E,B,k7_mssubfam(B,C),k7_mssubfam(B,C))
             => ( ( v2_closure1(E,B,C)
                  & r2_hidden(A,B)
                  & D = k1_funct_1(E,A) )
               => ! [F] : 
                    ( m1_subset_1(F,k1_zfmisc_1(k1_funct_1(C,A)))
                   => ! [G] : 
                        ( m1_subset_1(G,k1_zfmisc_1(k1_funct_1(C,A)))
                       => ( r1_tarski(F,G)
                         => r1_tarski(k1_funct_1(D,F),k1_funct_1(D,G)) ) ) ) ) ) ) ) ),
    file(closure1,t25_closure1),
    []).

fof(t28_closure1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,B)
             => ( ( r1_pboole(A,C,B)
                  & r6_pboole(A,k1_closure1(A,D,C),C) )
              <=> r1_pboole(A,C,k6_closure1(A,B,D)) ) ) ) ) ),
    file(closure1,t28_closure1),
    []).

fof(t2_mssubfam,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( r2_hidden(B,C)
       => r1_tarski(k8_setfam_1(A,C),B) ) ) ),
    file(mssubfam,t2_mssubfam),
    []).

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_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( r2_hidden(D,B)
               => r1_tarski(C,D) )
           => r1_tarski(C,k8_setfam_1(A,B)) ) ) ) ),
    file(mssubfam,t4_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(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(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).