% Mizar problem: t19_msualg_8,msualg_8,1045,31 
fof(t19_msualg_8,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => v1_msualg_7(k6_msualg_5(A,B),k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_lattices,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_closure2,cc1_finset_1,cc1_fraenkel,cc1_lattices,cc1_membered,cc1_msualg_5,cc1_msualg_6,cc1_msualg_7,cc1_pboole,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_lattices,cc2_membered,cc2_pboole,cc3_lattices,cc3_membered,cc4_lattices,cc4_membered,cc4_msualg_6,d2_msualg_7,d6_msualg_5,dt_g3_lattices,dt_k16_lattice3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_msualg_5,dt_k6_msualg_5,dt_l1_lattices,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_lattices,dt_l2_msualg_1,dt_l3_lattices,dt_l3_msualg_1,dt_m1_msualg_4,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_nat_lat,dt_m2_relset_1,dt_u1_lattices,dt_u1_struct_0,dt_u2_lattices,dt_u4_msualg_1,existence_l1_lattices,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_lattices,existence_l2_msualg_1,existence_l3_lattices,existence_l3_msualg_1,existence_m1_msualg_4,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_nat_lat,existence_m2_relset_1,fc14_finset_1,fc1_msualg_1,fc1_msualg_5,fc1_msualg_7,fc1_struct_0,fc1_subset_1,fc2_msualg_7,fc3_lattices,fc4_subset_1,fc6_membered,free_g3_lattices,rc11_lattices,rc1_finset_1,rc1_fraenkel,rc1_membered,rc1_msualg_5,rc1_msualg_6,rc1_msualg_7,rc1_pboole,rc1_subset_1,rc2_partfun1,rc2_pboole,rc2_subset_1,rc3_finset_1,rc3_lattices,rc3_pboole,rc3_struct_0,rc4_finset_1,rc5_struct_0,rc6_lattices,rc9_lattices,redefinition_m2_relset_1,reflexivity_r1_tarski,t11_msualg_8,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(msualg_8,t19_msualg_8)]).

fof(abstractness_v3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( v3_lattices(A)
       => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ),
    file(lattices,v3_lattices),
    []).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

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_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) ) ) ) ),
    file(lattices,cc1_lattices),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc1_msualg_5,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ! [C] : 
          ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
         => ( v3_msualg_4(C,A,B)
           => ( v1_msualg_4(C)
              & v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) ) ) ),
    file(msualg_5,cc1_msualg_5),
    []).

fof(cc1_msualg_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ( v5_msualg_1(B,A)
           => v1_msualg_6(B,A) ) ) ) ),
    file(msualg_6,cc1_msualg_6),
    []).

fof(cc1_msualg_7,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m2_nat_lat(B,A)
         => ( v1_msualg_7(B,A)
           => v4_lattice3(B) ) ) ) ),
    file(msualg_7,cc1_msualg_7),
    []).

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(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

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_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v10_lattices(A) ) ) ) ),
    file(lattices,cc2_lattices),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

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_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v15_lattices(A) ) ) ) ),
    file(lattices,cc3_lattices),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc4_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v15_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) ) ) ) ),
    file(lattices,cc4_lattices),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc4_msualg_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] : 
          ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
         => ( v3_msualg_4(C,A,B)
           => ( v2_relat_1(C)
              & ~ v3_relat_1(C)
              & v1_msualg_4(C) ) ) ) ) ),
    file(msualg_6,cc4_msualg_6),
    []).

fof(d2_msualg_7,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m2_nat_lat(B,A)
         => ( v1_msualg_7(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
               => r2_hidden(k16_lattice3(A,C),u1_struct_0(B)) ) ) ) ) ),
    file(msualg_7,d2_msualg_7),
    []).

fof(d6_msualg_5,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v3_lattices(C)
                & m2_nat_lat(C,k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))) )
             => ( C = k6_msualg_5(A,B)
              <=> ! [D] : 
                    ( r2_hidden(D,u1_struct_0(C))
                  <=> ( v3_msualg_4(D,A,B)
                      & v4_msualg_4(D,A,B)
                      & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ) ),
    file(msualg_5,d6_msualg_5),
    []).

fof(dt_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( v3_lattices(g3_lattices(A,B,C))
        & l3_lattices(g3_lattices(A,B,C)) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(dt_k16_lattice3,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)) ) ),
    file(lattice3,k16_lattice3),
    []).

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_k5_msualg_5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k5_msualg_5(A,B))
        & v3_lattices(k5_msualg_5(A,B))
        & v10_lattices(k5_msualg_5(A,B))
        & l3_lattices(k5_msualg_5(A,B)) ) ) ),
    file(msualg_5,k5_msualg_5),
    []).

fof(dt_k6_msualg_5,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ( v3_lattices(k6_msualg_5(A,B))
        & m2_nat_lat(k6_msualg_5(A,B),k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))) ) ) ),
    file(msualg_5,k6_msualg_5),
    []).

fof(dt_l1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l1_lattices),
    []).

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

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

fof(dt_l2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l2_lattices),
    []).

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

fof(dt_l3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) ),
    file(lattices,l3_lattices),
    []).

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_m1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m1_msualg_4(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(msualg_4,m1_msualg_4),
    []).

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_nat_lat,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m2_nat_lat(B,A)
         => ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) ) ) ) ),
    file(nat_lat,m2_nat_lat),
    []).

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_u1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => ( v1_funct_1(u1_lattices(A))
        & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u1_lattices),
    []).

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

fof(dt_u2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => ( v1_funct_1(u2_lattices(A))
        & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u2_lattices),
    []).

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_lattices,axiom,(
    ? [A] : l1_lattices(A) ),
    file(lattices,l1_lattices),
    []).

fof(existence_l1_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) ),
    file(msualg_1,l1_msualg_1),
    []).

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

fof(existence_l2_lattices,axiom,(
    ? [A] : l2_lattices(A) ),
    file(lattices,l2_lattices),
    []).

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_l3_lattices,axiom,(
    ? [A] : l3_lattices(A) ),
    file(lattices,l3_lattices),
    []).

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_m1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m1_msualg_4(D,A,B,C) ) ),
    file(msualg_4,m1_msualg_4),
    []).

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_nat_lat,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ? [B] : m2_nat_lat(B,A) ) ),
    file(nat_lat,m2_nat_lat),
    []).

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

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc1_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_msualg_5,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ( ~ v3_struct_0(k6_msualg_5(A,B))
        & v3_lattices(k6_msualg_5(A,B))
        & v4_lattices(k6_msualg_5(A,B))
        & v5_lattices(k6_msualg_5(A,B))
        & v6_lattices(k6_msualg_5(A,B))
        & v7_lattices(k6_msualg_5(A,B))
        & v8_lattices(k6_msualg_5(A,B))
        & v9_lattices(k6_msualg_5(A,B))
        & v10_lattices(k6_msualg_5(A,B))
        & v13_lattices(k6_msualg_5(A,B))
        & v14_lattices(k6_msualg_5(A,B))
        & v15_lattices(k6_msualg_5(A,B)) ) ) ),
    file(msualg_5,fc1_msualg_5),
    []).

fof(fc1_msualg_7,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k5_msualg_5(A,B))
        & v3_lattices(k5_msualg_5(A,B))
        & v4_lattices(k5_msualg_5(A,B))
        & v5_lattices(k5_msualg_5(A,B))
        & v6_lattices(k5_msualg_5(A,B))
        & v7_lattices(k5_msualg_5(A,B))
        & v8_lattices(k5_msualg_5(A,B))
        & v9_lattices(k5_msualg_5(A,B))
        & v10_lattices(k5_msualg_5(A,B))
        & v13_lattices(k5_msualg_5(A,B))
        & v14_lattices(k5_msualg_5(A,B))
        & v15_lattices(k5_msualg_5(A,B)) ) ) ),
    file(msualg_7,fc1_msualg_7),
    []).

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(fc2_msualg_7,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k5_msualg_5(A,B))
        & v3_lattices(k5_msualg_5(A,B))
        & v4_lattices(k5_msualg_5(A,B))
        & v5_lattices(k5_msualg_5(A,B))
        & v6_lattices(k5_msualg_5(A,B))
        & v7_lattices(k5_msualg_5(A,B))
        & v8_lattices(k5_msualg_5(A,B))
        & v9_lattices(k5_msualg_5(A,B))
        & v10_lattices(k5_msualg_5(A,B))
        & v13_lattices(k5_msualg_5(A,B))
        & v14_lattices(k5_msualg_5(A,B))
        & v15_lattices(k5_msualg_5(A,B))
        & v4_lattice3(k5_msualg_5(A,B)) ) ) ),
    file(msualg_7,fc2_msualg_7),
    []).

fof(fc3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g3_lattices(A,B,C))
        & v3_lattices(g3_lattices(A,B,C)) ) ) ),
    file(lattices,fc3_lattices),
    []).

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(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(free_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ! [D,E,F] : 
          ( g3_lattices(A,B,C) = g3_lattices(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(rc11_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A)
      & v15_lattices(A) ) ),
    file(lattices,rc11_lattices),
    []).

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_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(rc1_msualg_5,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m1_msualg_4(C,A,B,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v2_msualg_4(C,A,B) ) ) ),
    file(msualg_5,rc1_msualg_5),
    []).

fof(rc1_msualg_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ? [B] : 
          ( l3_msualg_1(B,A)
          & v5_msualg_1(B,A)
          & v1_msualg_6(B,A) ) ) ),
    file(msualg_6,rc1_msualg_6),
    []).

fof(rc1_msualg_7,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ? [B] : 
          ( m2_nat_lat(B,A)
          & ~ v3_struct_0(B)
          & v4_lattices(B)
          & v5_lattices(B)
          & v6_lattices(B)
          & v7_lattices(B)
          & v8_lattices(B)
          & v9_lattices(B)
          & v10_lattices(B)
          & v4_lattice3(B) ) ) ),
    file(msualg_7,rc1_msualg_7),
    []).

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(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

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(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_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & v3_lattices(A) ) ),
    file(lattices,rc3_lattices),
    []).

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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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(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(rc6_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A) ) ),
    file(lattices,rc6_lattices),
    []).

fof(rc9_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A) ) ),
    file(lattices,rc9_lattices),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(t11_msualg_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B))))
             => ( v3_msualg_4(k16_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),A,B)
                & v4_msualg_4(k16_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),A,B)
                & m1_msualg_4(k16_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ),
    file(msualg_8,t11_msualg_8),
    []).

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

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).