% Mizar problem: t28_heyting3,heyting3,1069,73 
fof(t28_heyting3,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => m1_subset_1(k4_heyting3(A,B),u1_struct_0(k1_heyting3(k5_numbers,k6_domain_1(k5_numbers,B)))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,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_abian,cc1_finseq_1,cc1_finset_1,cc1_finsub_1,cc1_lattice3,cc1_lattices,cc1_membered,cc1_nat_1,cc1_realset1,cc1_relset_1,cc1_substlat,cc1_xreal_0,cc1_yellow_0,cc1_yellow_3,cc20_membered,cc2_finset_1,cc2_finsub_1,cc2_lattice3,cc2_lattices,cc2_membered,cc2_nat_1,cc2_substlat,cc2_xreal_0,cc2_yellow_0,cc2_yellow_3,cc3_finsub_1,cc3_lattices,cc3_membered,cc3_nat_1,cc3_xreal_0,cc3_yellow_0,cc3_yellow_3,cc4_lattices,cc4_membered,cc4_xreal_0,cc4_yellow_0,cc5_xreal_0,cc5_yellow_0,cc6_membered,cc6_xreal_0,cc7_lattices,cc7_xreal_0,cc8_xreal_0,cc9_membered,connectedness_r1_xreal_0,d1_heyting3,d1_substlat,d2_lattice3,d4_heyting3,dt_g1_orders_2,dt_g3_lattices,dt_k1_heyting3,dt_k1_numbers,dt_k1_substlat,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_heyting3,dt_k2_lattice3,dt_k2_zfmisc_1,dt_k3_heyting3,dt_k3_lattice3,dt_k4_heyting3,dt_k4_partfun1,dt_k5_finsub_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_substlat,dt_k6_domain_1,dt_k9_filter_1,dt_l1_lattices,dt_l1_orders_2,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_lattices,dt_u1_orders_2,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_orders_2,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc11_membered,fc13_yellow_3,fc14_finset_1,fc17_abian,fc1_finset_1,fc1_finsub_1,fc1_heyting3,fc1_ordinal2,fc1_partfun1,fc1_struct_0,fc1_subset_1,fc1_substlat,fc1_yellow_0,fc1_yellow_1,fc2_finseq_1,fc2_finsub_1,fc2_heyting3,fc2_membered,fc2_subset_1,fc2_substlat,fc2_yellow_1,fc3_heyting3,fc3_lattices,fc3_realset1,fc3_substlat,fc3_yellow_1,fc4_heyting3,fc4_lattice3,fc4_subset_1,fc4_substlat,fc5_heyting3,fc5_membered,fc6_heyting3,fc6_membered,fc7_membered,fc8_membered,fc9_membered,fraenkel_a_1_0_heyting3,fraenkel_a_2_0_substlat,free_g1_orders_2,free_g3_lattices,l21_heyting3,l40_heyting3,rc10_lattices,rc11_lattices,rc1_finseq_1,rc1_finset_1,rc1_lattice3,rc1_membered,rc1_nat_1,rc1_partfun1,rc1_pre_circ,rc1_realset1,rc1_subset_1,rc1_substlat,rc1_xreal_0,rc1_yellow_0,rc1_yellow_3,rc2_finseq_1,rc2_finset_1,rc2_lattice3,rc2_nat_1,rc2_partfun1,rc2_realset1,rc2_subset_1,rc2_substlat,rc2_xreal_0,rc2_yellow_0,rc3_finseq_1,rc3_finset_1,rc3_lattices,rc3_nat_1,rc3_struct_0,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc5_struct_0,rc6_finseq_1,rc6_lattices,rc7_finseq_1,rc8_finseq_1,rc9_lattices,redefinition_k2_lattice3,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,t1_real,t1_subset,t21_heyting3,t26_heyting3,t27_heyting3,t2_real,t2_subset,t2_tarski,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(heyting3,t28_heyting3)]).

fof(abstractness_v1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_orders_2(A)
       => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ),
    file(orders_2,v1_orders_2),
    []).

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_abian,axiom,(
    ! [A] : 
      ( v2_setfam_1(A)
     => v1_realset1(A) ) ),
    file(abian,cc1_abian),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    []).

fof(cc1_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc1_lattice3),
    []).

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_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

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(cc1_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
     => v1_finset_1(C) ) ),
    file(substlat,cc1_substlat),
    []).

fof(cc1_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

fof(cc1_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v3_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v1_lattice3(A)
          & v2_lattice3(A) ) ) ) ),
    file(yellow_0,cc1_yellow_0),
    []).

fof(cc1_yellow_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => v1_yellow_3(A) ) ) ),
    file(yellow_3,cc1_yellow_3),
    []).

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_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

fof(cc2_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc2_lattice3),
    []).

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_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc2_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
     => ( v1_finset_1(C)
        & v1_fraenkel(C) ) ) ),
    file(substlat,cc2_substlat),
    []).

fof(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

fof(cc2_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v3_lattice3(A) ) ) ) ),
    file(yellow_0,cc2_yellow_0),
    []).

fof(cc2_yellow_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ~ v1_yellow_3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(yellow_3,cc2_yellow_3),
    []).

fof(cc3_finsub_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
     => v1_finset_1(B) ) ),
    file(finsub_1,cc3_finsub_1),
    []).

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(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(cc3_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    []).

fof(cc3_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v3_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v3_yellow_0(A) ) ) ) ),
    file(yellow_0,cc3_yellow_0),
    []).

fof(cc3_yellow_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & ~ v1_yellow_3(A) ) ) ) ),
    file(yellow_3,cc3_yellow_3),
    []).

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_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    []).

fof(cc4_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_yellow_0(A)
       => ( v1_yellow_0(A)
          & v2_yellow_0(A) ) ) ) ),
    file(yellow_0,cc4_yellow_0),
    []).

fof(cc5_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    []).

fof(cc5_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( v1_yellow_0(A)
          & v2_yellow_0(A) )
       => v3_yellow_0(A) ) ) ),
    file(yellow_0,cc5_yellow_0),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc6_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    []).

fof(cc7_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v12_lattices(A) ) ) ) ),
    file(lattices,cc7_lattices),
    []).

fof(cc7_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    []).

fof(cc8_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d1_heyting3,axiom,(
    ! [A,B] : k1_heyting3(A,B) = k3_lattice3(k5_substlat(A,B)) ),
    file(heyting3,d1_heyting3),
    []).

fof(d1_substlat,axiom,(
    ! [A,B] : k1_substlat(A,B) = a_2_0_substlat(A,B) ),
    file(substlat,d1_substlat),
    []).

fof(d2_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)) ) ),
    file(lattice3,d2_lattice3),
    []).

fof(d4_heyting3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k5_finsub_1(k4_partfun1(k5_numbers,k6_domain_1(k5_numbers,B))))
             => ( C = k4_heyting3(A,B)
              <=> ! [D] : 
                    ( r2_hidden(D,C)
                  <=> ~ ( ! [E] : 
                            ( ( ~ v1_xboole_0(E)
                              & m2_subset_1(E,k1_numbers,k5_numbers) )
                           => ~ ( r1_xreal_0(E,A)
                                & D = k2_heyting3(E,B) ) )
                        & D != k3_heyting3(A,B) ) ) ) ) ) ) ),
    file(heyting3,d4_heyting3),
    []).

fof(dt_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( v1_orders_2(g1_orders_2(A,B))
        & l1_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,g1_orders_2),
    []).

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_k1_heyting3,axiom,(
    ! [A,B] : l1_orders_2(k1_heyting3(A,B)) ),
    file(heyting3,k1_heyting3),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_substlat,axiom,(
    ! [A,B] : m1_subset_1(k1_substlat(A,B),k1_zfmisc_1(k5_finsub_1(k4_partfun1(A,B)))) ),
    file(substlat,k1_substlat),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_heyting3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k2_heyting3(A,B),k4_partfun1(k5_numbers,k6_domain_1(k5_numbers,B))) ) ),
    file(heyting3,k2_heyting3),
    []).

fof(dt_k2_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_relat_2(k2_lattice3(A))
        & v4_relat_2(k2_lattice3(A))
        & v8_relat_2(k2_lattice3(A))
        & v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(lattice3,k2_lattice3),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_heyting3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k3_heyting3(A,B),k4_partfun1(k5_numbers,k6_domain_1(k5_numbers,B))) ) ),
    file(heyting3,k3_heyting3),
    []).

fof(dt_k3_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & l1_orders_2(k3_lattice3(A)) ) ) ),
    file(lattice3,k3_lattice3),
    []).

fof(dt_k4_heyting3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k4_heyting3(A,B),k5_finsub_1(k4_partfun1(k5_numbers,k6_domain_1(k5_numbers,B)))) ) ),
    file(heyting3,k4_heyting3),
    []).

fof(dt_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    []).

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_substlat,axiom,(
    ! [A,B] : 
      ( v3_lattices(k5_substlat(A,B))
      & l3_lattices(k5_substlat(A,B)) ) ),
    file(substlat,k5_substlat),
    []).

fof(dt_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(dt_k9_filter_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => v1_relat_1(k9_filter_1(A)) ) ),
    file(filter_1,k9_filter_1),
    []).

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

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

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_l3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) ),
    file(lattices,l3_lattices),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_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_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(orders_2,u1_orders_2),
    []).

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(existence_l1_lattices,axiom,(
    ? [A] : l1_lattices(A) ),
    file(lattices,l1_lattices),
    []).

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

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

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc10_membered,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    []).

fof(fc11_membered,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    []).

fof(fc13_yellow_3,axiom,(
    ! [A] : 
      ( ( ~ v1_yellow_3(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(u1_orders_2(A))
        & v1_relat_1(u1_orders_2(A)) ) ) ),
    file(yellow_3,fc13_yellow_3),
    []).

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(fc17_abian,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_zfmisc_1(A))
        & ~ v2_setfam_1(k1_zfmisc_1(A)) ) ) ),
    file(abian,fc17_abian),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    []).

fof(fc1_heyting3,axiom,(
    ! [A,B] : v1_funct_1(k2_zfmisc_1(A,k1_tarski(B))) ),
    file(heyting3,fc1_heyting3),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc1_partfun1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ),
    file(partfun1,fc1_partfun1),
    []).

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_substlat,axiom,(
    ! [A,B] : ~ v1_xboole_0(k1_substlat(A,B)) ),
    file(substlat,fc1_substlat),
    []).

fof(fc1_yellow_0,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k1_tarski(A),k1_tarski(A))
     => ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B))
        & v1_orders_2(g1_orders_2(k1_tarski(A),B))
        & v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ),
    file(yellow_0,fc1_yellow_0),
    []).

fof(fc1_yellow_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & v1_lattice3(k3_lattice3(A))
        & v2_lattice3(k3_lattice3(A)) ) ) ),
    file(yellow_1,fc1_yellow_1),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A)) ) ),
    file(finsub_1,fc2_finsub_1),
    []).

fof(fc2_heyting3,axiom,(
    ! [A,B] : 
      ( ~ v3_struct_0(k1_heyting3(A,B))
      & v1_lattice3(k1_heyting3(A,B))
      & v2_lattice3(k1_heyting3(A,B)) ) ),
    file(heyting3,fc2_heyting3),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_substlat,axiom,(
    ! [A,B] : 
      ( ~ v3_struct_0(k5_substlat(A,B))
      & v3_lattices(k5_substlat(A,B)) ) ),
    file(substlat,fc2_substlat),
    []).

fof(fc2_yellow_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & v2_yellow_0(k3_lattice3(A))
        & v1_lattice3(k3_lattice3(A))
        & v2_lattice3(k3_lattice3(A)) ) ) ),
    file(yellow_1,fc2_yellow_1),
    []).

fof(fc3_heyting3,axiom,(
    ! [A,B] : 
      ( ~ v3_struct_0(k1_heyting3(A,B))
      & v2_orders_2(k1_heyting3(A,B))
      & v3_orders_2(k1_heyting3(A,B))
      & v4_orders_2(k1_heyting3(A,B))
      & v1_lattice3(k1_heyting3(A,B))
      & v2_lattice3(k1_heyting3(A,B)) ) ),
    file(heyting3,fc3_heyting3),
    []).

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(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc3_substlat,axiom,(
    ! [A,B] : 
      ( ~ v3_struct_0(k5_substlat(A,B))
      & v3_lattices(k5_substlat(A,B))
      & v4_lattices(k5_substlat(A,B))
      & v5_lattices(k5_substlat(A,B))
      & v6_lattices(k5_substlat(A,B))
      & v7_lattices(k5_substlat(A,B))
      & v8_lattices(k5_substlat(A,B))
      & v9_lattices(k5_substlat(A,B))
      & v10_lattices(k5_substlat(A,B)) ) ),
    file(substlat,fc3_substlat),
    []).

fof(fc3_yellow_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & v1_yellow_0(k3_lattice3(A))
        & v1_lattice3(k3_lattice3(A))
        & v2_lattice3(k3_lattice3(A)) ) ) ),
    file(yellow_1,fc3_yellow_1),
    []).

fof(fc4_heyting3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => v1_finset_1(k2_heyting3(A,B)) ) ),
    file(heyting3,fc4_heyting3),
    []).

fof(fc4_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A)) ) ) ),
    file(lattice3,fc4_lattice3),
    []).

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(fc4_substlat,axiom,(
    ! [A,B] : 
      ( ~ v3_struct_0(k5_substlat(A,B))
      & v3_lattices(k5_substlat(A,B))
      & v4_lattices(k5_substlat(A,B))
      & v5_lattices(k5_substlat(A,B))
      & v6_lattices(k5_substlat(A,B))
      & v7_lattices(k5_substlat(A,B))
      & v8_lattices(k5_substlat(A,B))
      & v9_lattices(k5_substlat(A,B))
      & v10_lattices(k5_substlat(A,B))
      & v11_lattices(k5_substlat(A,B))
      & v12_lattices(k5_substlat(A,B))
      & v13_lattices(k5_substlat(A,B))
      & v14_lattices(k5_substlat(A,B))
      & v15_lattices(k5_substlat(A,B)) ) ),
    file(substlat,fc4_substlat),
    []).

fof(fc5_heyting3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => v1_finset_1(k3_heyting3(A,B)) ) ),
    file(heyting3,fc5_heyting3),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc6_heyting3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k2_heyting3(A,B))
        & v1_finset_1(k2_heyting3(A,B)) ) ) ),
    file(heyting3,fc6_heyting3),
    []).

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(fc7_membered,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    []).

fof(fc8_membered,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    []).

fof(fc9_membered,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    []).

fof(fraenkel_a_1_0_heyting3,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( r2_hidden(A,a_1_0_heyting3(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k5_finsub_1(k4_partfun1(k5_numbers,k6_domain_1(k5_numbers,B))))
            & A = C
            & ! [D] : 
                ( r2_hidden(D,C)
               => v1_finset_1(D) )
            & ! [D] : 
                ( m1_subset_1(D,k4_partfun1(k5_numbers,k6_domain_1(k5_numbers,B)))
               => ! [E] : 
                    ( m1_subset_1(E,k4_partfun1(k5_numbers,k6_domain_1(k5_numbers,B)))
                   => ( ( r2_hidden(D,C)
                        & r2_hidden(E,C)
                        & r1_tarski(D,E) )
                     => D = E ) ) ) ) ) ) ),
    file(heyting3,a_1_0_heyting3),
    []).

fof(fraenkel_a_2_0_substlat,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(A,a_2_0_substlat(B,C))
    <=> ? [D] : 
          ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C)))
          & A = D
          & ! [E] : 
              ( r2_hidden(E,D)
             => v1_finset_1(E) )
          & ! [E] : 
              ( m1_subset_1(E,k4_partfun1(B,C))
             => ! [F] : 
                  ( m1_subset_1(F,k4_partfun1(B,C))
                 => ( ( r2_hidden(E,D)
                      & r2_hidden(F,D)
                      & r1_tarski(E,F) )
                   => E = F ) ) ) ) ) ),
    file(substlat,a_2_0_substlat),
    []).

fof(free_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ! [C,D] : 
          ( g1_orders_2(A,B) = g1_orders_2(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(orders_2,g1_orders_2),
    []).

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(l21_heyting3,axiom,(
    ! [A,B] : k1_substlat(A,B) = u1_struct_0(k1_heyting3(A,B)) ),
    file(heyting3,l21_heyting3),
    []).

fof(l40_heyting3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( r2_hidden(C,k4_heyting3(A,B))
             => v1_finset_1(C) ) ) ) ),
    file(heyting3,l40_heyting3),
    []).

fof(rc10_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)
      & v11_lattices(A)
      & v12_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A) ) ),
    file(lattices,rc10_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_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

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

fof(rc1_lattice3,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v3_lattice3(A) ) ),
    file(lattice3,rc1_lattice3),
    []).

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_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_pre_circ,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(pre_circ,rc1_pre_circ),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

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_substlat,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
      & ~ v1_xboole_0(C) ) ),
    file(substlat,rc1_substlat),
    []).

fof(rc1_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

fof(rc1_yellow_0,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v3_realset2(A) ) ),
    file(yellow_0,rc1_yellow_0),
    []).

fof(rc1_yellow_3,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & ~ v1_yellow_3(A) ) ),
    file(yellow_3,rc1_yellow_3),
    []).

fof(rc2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    []).

fof(rc2_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

fof(rc2_lattice3,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A) ) ),
    file(lattice3,rc2_lattice3),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_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_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

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_substlat,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_subset_1(C,k4_partfun1(A,B))
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_finset_1(C) ) ),
    file(substlat,rc2_substlat),
    []).

fof(rc2_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    []).

fof(rc2_yellow_0,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A) ) ),
    file(yellow_0,rc2_yellow_0),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

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

fof(rc3_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_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(rc4_xreal_0,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    []).

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_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

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

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

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_k2_lattice3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k2_lattice3(A) = k9_filter_1(A) ) ),
    file(lattice3,k2_lattice3),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    []).

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_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(t1_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    []).

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

fof(t21_heyting3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ r1_tarski(k2_heyting3(A,B),k3_heyting3(C,B)) ) ) ) ),
    file(heyting3,t21_heyting3),
    []).

fof(t26_heyting3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_tarski(k2_heyting3(A,B),k2_heyting3(C,B))
               => A = C ) ) ) ) ),
    file(heyting3,t26_heyting3),
    []).

fof(t27_heyting3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_tarski(k3_heyting3(A,B),k2_heyting3(C,B))
              <=> ~ r1_xreal_0(C,A) ) ) ) ) ),
    file(heyting3,t27_heyting3),
    []).

fof(t2_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    []).

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_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    []).

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

fof(t4_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    []).

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_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    []).

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_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    []).

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

fof(t7_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    []).

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

fof(t8_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    []).