% Mizar problem: t36_closure1,closure1,1716,32 
fof(t36_closure1,conjecture,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v5_mssubfam(C,A,B)
            & m4_pboole(C,A,k1_mboolean(A,B)) )
         => ! [D] : 
              ( m3_pboole(D,A,k7_mssubfam(A,B),k7_mssubfam(A,B))
             => ( ! [E] : 
                    ( m2_pboole(E,A,k7_mssubfam(A,B))
                   => ! [F] : 
                        ( ( v2_relat_1(F)
                          & m4_pboole(F,A,k1_mboolean(A,B)) )
                       => ( ! [G] : 
                              ( m1_pboole(G,A)
                             => ( r1_pboole(A,G,F)
                              <=> ( r1_pboole(A,G,C)
                                  & r2_pboole(A,E,G) ) ) )
                         => r6_pboole(A,k3_closure1(A,B,D,E),k6_mssubfam(A,B,F)) ) ) )
               => ( v1_closure1(D,A,B)
                  & v2_closure1(D,A,B) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_funct_1,cc1_mssubfam,cc1_pboole,cc2_finset_1,cc2_funct_1,cc2_mssubfam,cc2_pboole,cc3_mssubfam,cc3_pboole,cc4_mssubfam,cc5_mssubfam,cc6_mssubfam,cc7_mssubfam,cc8_mssubfam,d16_pboole,d2_closure1,d3_closure1,d5_pboole,dt_k15_pralg_1,dt_k1_funct_1,dt_k1_mboolean,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_closure1,dt_k5_mssubfam,dt_k6_mssubfam,dt_k7_mssubfam,dt_m1_pboole,dt_m1_subset_1,dt_m2_pboole,dt_m3_pboole,dt_m4_pboole,existence_m1_pboole,existence_m1_subset_1,existence_m2_pboole,existence_m3_pboole,existence_m4_pboole,fc1_subset_1,fc1_xboole_0,fc2_pboole,fc7_funcop_1,fc8_mssubfam,fraenkel_a_2_0_closure1,fraenkel_a_5_0_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_finset_1,rc3_funct_1,rc3_mssubfam,rc3_pboole,rc4_finset_1,rc4_funct_1,rc4_mssubfam,rc4_pboole,rc5_funct_1,rc5_mssubfam,rc5_pboole,redefinition_k3_closure1,redefinition_k6_mssubfam,redefinition_k7_mssubfam,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r2_pboole,reflexivity_r6_pboole,symmetry_r6_pboole,t1_closure1,t1_subset,t2_subset,t2_tarski,t31_closure1,t32_closure1,t3_subset,t45_mssubfam,t46_mssubfam,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(closure1,t36_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(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_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_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_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(d16_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v2_relat_1(B)
      <=> ! [C] : ~ ( r2_hidden(C,A)
            & v1_xboole_0(k1_funct_1(B,C)) ) ) ) ),
    file(pboole,d16_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(d3_closure1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m3_pboole(C,A,k7_mssubfam(A,B),k7_mssubfam(A,B))
         => ( v2_closure1(C,A,B)
          <=> ! [D] : 
                ( m2_pboole(D,A,k7_mssubfam(A,B))
               => ! [E] : 
                    ( m2_pboole(E,A,k7_mssubfam(A,B))
                   => ( r2_pboole(A,D,E)
                     => r2_pboole(A,k3_closure1(A,B,C,D),k3_closure1(A,B,C,E)) ) ) ) ) ) ) ),
    file(closure1,d3_closure1),
    []).

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(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_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_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_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_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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

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_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(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(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_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(fraenkel_a_2_0_closure1,axiom,(
    ! [A,B,C] : 
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_2_0_closure1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,B)
            & A = D
            & r1_tarski(C,D) ) ) ) ),
    file(closure1,a_2_0_closure1),
    []).

fof(fraenkel_a_5_0_closure1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_pboole(C,B)
        & m2_pboole(D,B,k7_mssubfam(B,C))
        & ~ v1_xboole_0(F) )
     => ( r2_hidden(A,a_5_0_closure1(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,F)
            & A = G
            & r1_tarski(k1_funct_1(D,E),G) ) ) ) ),
    file(closure1,a_5_0_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_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_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_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_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_closure1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( r1_tarski(B,C)
         => r1_tarski(a_2_0_closure1(A,C),a_2_0_closure1(A,B)) ) ) ),
    file(closure1,t1_closure1),
    []).

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

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(t31_closure1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v5_mssubfam(C,A,B)
            & m4_pboole(C,A,k1_mboolean(A,B)) )
         => ! [D] : 
              ( m2_pboole(D,A,k7_mssubfam(A,B))
             => ? [E] : 
                  ( v2_relat_1(E)
                  & m4_pboole(E,A,k1_mboolean(A,B))
                  & ! [F] : 
                      ( m1_pboole(F,A)
                     => ( r1_pboole(A,F,E)
                      <=> ( r1_pboole(A,F,C)
                          & r2_pboole(A,D,F) ) ) ) ) ) ) ) ),
    file(closure1,t31_closure1),
    []).

fof(t32_closure1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v5_mssubfam(C,A,B)
            & m4_pboole(C,A,k1_mboolean(A,B)) )
         => ! [D] : 
              ( m2_pboole(D,A,k7_mssubfam(A,B))
             => ! [E] : 
                  ( ( v2_relat_1(E)
                    & m4_pboole(E,A,k1_mboolean(A,B)) )
                 => ( ! [F] : 
                        ( m1_pboole(F,A)
                       => ( r1_pboole(A,F,E)
                        <=> ( r1_pboole(A,F,C)
                            & r2_pboole(A,D,F) ) ) )
                   => ! [F,G] : 
                        ( ~ v1_xboole_0(G)
                       => ( ( r2_hidden(F,A)
                            & G = k1_funct_1(C,F) )
                         => k1_funct_1(E,F) = a_5_0_closure1(A,B,D,F,G) ) ) ) ) ) ) ) ),
    file(closure1,t32_closure1),
    []).

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

fof(t45_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( ( v2_relat_1(D)
                & m4_pboole(D,A,k1_mboolean(A,C)) )
             => ( ! [E] : 
                    ( m1_pboole(E,A)
                   => ( r1_pboole(A,E,D)
                     => r2_pboole(A,B,E) ) )
               => r2_pboole(A,B,k6_mssubfam(A,C,D)) ) ) ) ) ),
    file(mssubfam,t45_mssubfam),
    []).

fof(t46_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => ( r2_pboole(A,C,D)
               => r2_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,C)) ) ) ) ) ),
    file(mssubfam,t46_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),
    []).