% Mizar problem: t30_osalg_2,osalg_2,978,26 
fof(t30_osalg_2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_osalg_2(C,A,B)
             => ( v2_relat_1(k2_pboole(u1_struct_0(A),k3_osalg_2(A,B),C))
               => v2_relat_1(k9_osalg_2(A,B,C)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_1,cc1_orders_3,cc1_osalg_1,cc2_funct_1,cc7_osalg_1,commutativity_k2_pboole,d10_osalg_2,d11_osalg_2,d16_pboole,d1_xboole_0,d5_pboole,d7_osalg_2,dt_k1_funct_1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_pboole,dt_k3_osalg_2,dt_k5_msualg_2,dt_k5_osalg_2,dt_k8_osalg_2,dt_k9_osalg_2,dt_l1_msualg_1,dt_l1_orders_2,dt_l1_osalg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l2_osalg_1,dt_l3_msualg_1,dt_l3_osalg_1,dt_m1_pboole,dt_m1_subset_1,dt_m2_osalg_2,dt_m4_pboole,dt_u1_struct_0,dt_u4_msualg_1,existence_l1_msualg_1,existence_l1_orders_2,existence_l1_osalg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l2_osalg_1,existence_l3_msualg_1,existence_l3_osalg_1,existence_m1_pboole,existence_m1_subset_1,existence_m2_osalg_2,existence_m4_pboole,fc1_msualg_2,fc1_osalg_2,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_msualg_2,fc3_osalg_2,fc7_msualg_2,fraenkel_a_3_3_osalg_2,idempotence_k2_pboole,rc10_osalg_1,rc11_osalg_1,rc1_funct_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_funct_1,rc3_struct_0,rc5_funct_1,rc5_osalg_1,rc5_struct_0,rc8_osalg_2,reflexivity_r1_tarski,reflexivity_r2_pboole,t18_pboole,t1_subset,t24_osalg_2,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t6_setfam_1,t7_boole,t8_boole]),
    [file(osalg_2,t30_osalg_2)]).

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

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

fof(cc1_orders_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => v1_orders_3(A) ) ) ),
    file(orders_3,cc1_orders_3),
    []).

fof(cc1_osalg_1,axiom,(
    ! [A] : 
      ( l3_osalg_1(A)
     => ( v4_osalg_1(A)
       => ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A) ) ) ) ),
    file(osalg_1,cc1_osalg_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(cc7_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_orders_3(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => v12_osalg_1(B,A) ) ) ),
    file(osalg_1,cc7_osalg_1),
    []).

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

fof(d10_osalg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_osalg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( E = k8_osalg_2(A,B,C,D)
                    <=> ! [F] : 
                          ( r2_hidden(F,E)
                        <=> ? [G] : 
                              ( m2_osalg_2(G,A,B)
                              & r2_hidden(G,k5_osalg_2(A,B,C))
                              & F = k1_funct_1(G,D) ) ) ) ) ) ) ) ),
    file(osalg_2,d10_osalg_2),
    []).

fof(d11_osalg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_osalg_2(C,A,B)
             => ! [D] : 
                  ( m2_osalg_2(D,A,B)
                 => ( D = k9_osalg_2(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_funct_1(D,E) = k1_setfam_1(k8_osalg_2(A,B,C,E)) ) ) ) ) ) ) ),
    file(osalg_2,d11_osalg_2),
    []).

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(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

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(d7_osalg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_osalg_2(C,A,B)
             => k5_osalg_2(A,B,C) = a_3_3_osalg_2(A,B,C) ) ) ) ),
    file(osalg_2,d7_osalg_2),
    []).

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

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_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_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k2_pboole(A,B,C),A) ) ),
    file(pboole,k2_pboole),
    []).

fof(dt_k3_osalg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => m2_osalg_2(k3_osalg_2(A,B),A,B) ) ),
    file(osalg_2,k3_osalg_2),
    []).

fof(dt_k5_msualg_2,axiom,(
    $true ),
    file(msualg_2,k5_msualg_2),
    []).

fof(dt_k5_osalg_2,axiom,(
    $true ),
    file(osalg_2,k5_osalg_2),
    []).

fof(dt_k8_osalg_2,axiom,(
    $true ),
    file(osalg_2,k8_osalg_2),
    []).

fof(dt_k9_osalg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & m2_osalg_2(C,A,B) )
     => m2_osalg_2(k9_osalg_2(A,B,C),A,B) ) ),
    file(osalg_2,k9_osalg_2),
    []).

fof(dt_l1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => l1_struct_0(A) ) ),
    file(msualg_1,l1_msualg_1),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

fof(dt_l1_osalg_1,axiom,(
    ! [A] : 
      ( l1_osalg_1(A)
     => l1_msualg_1(A) ) ),
    file(osalg_1,l1_osalg_1),
    []).

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_l2_osalg_1,axiom,(
    ! [A] : 
      ( l2_osalg_1(A)
     => ( l1_msualg_1(A)
        & l1_orders_2(A) ) ) ),
    file(osalg_1,l2_osalg_1),
    []).

fof(dt_l3_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => l2_msualg_1(B,A) ) ) ),
    file(msualg_1,l3_msualg_1),
    []).

fof(dt_l3_osalg_1,axiom,(
    ! [A] : 
      ( l3_osalg_1(A)
     => ( l1_osalg_1(A)
        & l2_osalg_1(A) ) ) ),
    file(osalg_1,l3_osalg_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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_osalg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] : 
          ( m2_osalg_2(C,A,B)
         => m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) ),
    file(osalg_2,m2_osalg_2),
    []).

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_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_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) ),
    file(msualg_1,l1_msualg_1),
    []).

fof(existence_l1_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

fof(existence_l1_osalg_1,axiom,(
    ? [A] : l1_osalg_1(A) ),
    file(osalg_1,l1_osalg_1),
    []).

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_l2_osalg_1,axiom,(
    ? [A] : l2_osalg_1(A) ),
    file(osalg_1,l2_osalg_1),
    []).

fof(existence_l3_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] : l3_msualg_1(B,A) ) ),
    file(msualg_1,l3_msualg_1),
    []).

fof(existence_l3_osalg_1,axiom,(
    ? [A] : l3_osalg_1(A) ),
    file(osalg_1,l3_osalg_1),
    []).

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_osalg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] : m2_osalg_2(C,A,B) ) ),
    file(osalg_2,m2_osalg_2),
    []).

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

fof(fc1_msualg_2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k2_pboole(A,B,C))
        & v2_relat_1(k2_pboole(A,B,C))
        & v1_funct_1(k2_pboole(A,B,C)) ) ) ),
    file(msualg_2,fc1_msualg_2),
    []).

fof(fc1_osalg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & m2_osalg_2(C,A,B) )
     => ~ v1_xboole_0(k5_osalg_2(A,B,C)) ) ),
    file(osalg_2,fc1_osalg_2),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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_msualg_2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k2_pboole(A,C,B))
        & v2_relat_1(k2_pboole(A,C,B))
        & v1_funct_1(k2_pboole(A,C,B)) ) ) ),
    file(msualg_2,fc2_msualg_2),
    []).

fof(fc3_osalg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & m2_osalg_2(C,A,B)
        & m1_subset_1(D,u1_struct_0(A)) )
     => ~ v1_xboole_0(k8_osalg_2(A,B,C,D)) ) ),
    file(osalg_2,fc3_osalg_2),
    []).

fof(fc7_msualg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
     => ~ v1_xboole_0(k5_msualg_2(A,B,C)) ) ),
    file(msualg_2,fc7_msualg_2),
    []).

fof(fraenkel_a_3_3_osalg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_1(B)
        & v12_osalg_1(C,B)
        & l3_msualg_1(C,B)
        & m2_osalg_2(D,B,C) )
     => ( r2_hidden(A,a_3_3_osalg_2(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k5_msualg_2(B,C,D))
            & A = E
            & v11_osalg_1(E,B)
            & m1_pboole(E,u1_struct_0(B)) ) ) ) ),
    file(osalg_2,a_3_3_osalg_2),
    []).

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

fof(rc10_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_pboole(B,u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A) ) ) ),
    file(osalg_1,rc10_osalg_1),
    []).

fof(rc11_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_pboole(B,u1_struct_0(A))
          & v1_relat_1(B)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A) ) ) ),
    file(osalg_1,rc11_osalg_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_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(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_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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_osalg_1,axiom,(
    ? [A] : 
      ( l1_osalg_1(A)
      & ~ v3_struct_0(A)
      & ~ v2_msualg_1(A) ) ),
    file(osalg_1,rc5_osalg_1),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc8_osalg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] : 
          ( m2_osalg_2(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v3_msualg_2(C,A,B) ) ) ),
    file(osalg_2,rc8_osalg_2),
    []).

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(t18_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,D,C) )
               => r2_pboole(A,k2_pboole(A,B,D),C) ) ) ) ) ),
    file(pboole,t18_pboole),
    []).

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

fof(t24_osalg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_osalg_2(C,A,B)
             => ! [D] : 
                  ( m2_osalg_2(D,A,B)
                 => ( r2_hidden(D,k5_osalg_2(A,B,C))
                  <=> ( v3_msualg_2(D,A,B)
                      & r2_pboole(u1_struct_0(A),k3_osalg_2(A,B),D)
                      & r2_pboole(u1_struct_0(A),C,D) ) ) ) ) ) ) ),
    file(osalg_2,t24_osalg_2),
    []).

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(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(t6_setfam_1,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(B,C) )
     => ( A = k1_xboole_0
        | r1_tarski(B,k1_setfam_1(A)) ) ) ),
    file(setfam_1,t6_setfam_1),
    []).

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),
    []).