% Mizar problem: t15_lattice5,lattice5,1248,15 
fof(t15_lattice5,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v5_yellow_0(B,k1_lattice5(A))
            & v6_yellow_0(B,k1_lattice5(A))
            & m1_yellow_0(B,k1_lattice5(A)) )
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ! [D] : 
                    ( ( v1_partfun1(D,A,A)
                      & v3_relat_2(D)
                      & v8_relat_2(D)
                      & m2_relset_1(D,A,A) )
                   => ! [E] : 
                        ( ( v1_partfun1(E,A,A)
                          & v3_relat_2(E)
                          & v8_relat_2(E)
                          & m2_relset_1(E,A,A) )
                       => ! [F,G] : ~ ( r2_hidden(D,u1_struct_0(B))
                            & r2_hidden(E,u1_struct_0(B))
                            & r2_hidden(k4_tarski(F,G),k5_eqrel_1(A,D,E))
                            & ! [H] : 
                                ( ( ~ v1_xboole_0(H)
                                  & m2_finseq_1(H,A) )
                               => ~ ( k3_finseq_1(H) = k1_nat_1(C,2)
                                    & r1_lattice5(A,H,F,G,D,E) ) ) ) ) )
               => ( ! [D] : 
                      ( ( v1_partfun1(D,A,A)
                        & v3_relat_2(D)
                        & v8_relat_2(D)
                        & m2_relset_1(D,A,A) )
                     => ~ ( r2_hidden(D,u1_struct_0(B))
                          & D != k13_cqc_sim1(A) ) )
                  | r1_xreal_0(k3_lattice5(A,B),C) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v3_lattices,antisymmetry_r2_hidden,cc1_abian,cc1_arytm_3,cc1_card_1,cc1_finseq_1,cc1_lattice3,cc1_lattices,cc1_ordinal1,cc1_partfun1,cc1_relset_1,cc1_yellow_0,cc2_arytm_3,cc2_card_1,cc2_int_1,cc2_lattice3,cc2_lattices,cc2_ordinal1,cc2_yellow_0,cc3_arytm_3,cc3_card_1,cc3_int_1,cc3_ordinal1,cc3_yellow_0,cc4_int_1,cc4_yellow_0,cc5_yellow_0,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k5_eqrel_1,connectedness_r1_xreal_0,d1_lattice5,d2_lattice3,d4_lattice5,d5_tarski,d9_relat_2,dt_g1_orders_2,dt_g3_lattices,dt_k13_cqc_sim1,dt_k1_card_1,dt_k1_fraenkel,dt_k1_funct_2,dt_k1_lattice5,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_lattice3,dt_k2_msualg_5,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_lattice3,dt_k3_lattice5,dt_k3_relat_1,dt_k4_tarski,dt_k5_eqrel_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_relat_1,dt_k9_filter_1,dt_l1_lattices,dt_l1_orders_2,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_finseq_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_0,dt_m2_finseq_1,dt_m2_fraenkel,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_finseq_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m2_finseq_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc17_abian,fc1_int_1,fc1_lattice5,fc1_numbers,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_yellow_0,fc1_yellow_1,fc2_card_1,fc2_finseq_1,fc2_lattice5,fc2_ordinal1,fc2_partfun1,fc2_subset_1,fc3_lattices,fc3_subset_1,fc4_lattice3,fc4_subset_1,fc6_int_1,free_g1_orders_2,free_g3_lattices,idempotence_k5_eqrel_1,rc1_arytm_3,rc1_card_1,rc1_finseq_1,rc1_int_1,rc1_lattice3,rc1_ordinal1,rc1_partfun1,rc1_pralg_1,rc1_subset_1,rc1_yellow_0,rc2_card_1,rc2_finseq_1,rc2_int_1,rc2_lattice3,rc2_lattice5,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc2_yellow_0,rc3_finseq_1,rc3_lattices,rc3_ordinal1,rc3_partfun1,rc3_struct_0,rc4_finseq_1,rc5_struct_0,rc6_finseq_1,rc6_lattices,rc7_finseq_1,rc8_finseq_1,rc9_lattices,redefinition_k13_cqc_sim1,redefinition_k1_fraenkel,redefinition_k1_nat_1,redefinition_k2_lattice3,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t14_lattice5,t16_eqrel_1,t1_real,t1_subset,t28_nat_1,t29_nat_1,t2_real,t2_subset,t38_nat_1,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(lattice5,t15_lattice5)]).

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

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    []).

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_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_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc1_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

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_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(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc2_card_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)
        & v1_card_1(A) ) ) ),
    file(card_1,cc2_card_1),
    []).

fof(cc2_int_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)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_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_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

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(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

fof(cc3_card_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_finset_1(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc3_card_1),
    []).

fof(cc3_int_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

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(cc4_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

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_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(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(commutativity_k5_eqrel_1,axiom,(
    ! [A,B,C] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A)
        & v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m1_relset_1(C,A,A) )
     => k5_eqrel_1(A,B,C) = k5_eqrel_1(A,C,B) ) ),
    file(eqrel_1,k5_eqrel_1),
    []).

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_lattice5,axiom,(
    ! [A] : k1_lattice5(A) = k3_lattice3(k2_msualg_5(A)) ),
    file(lattice5,d1_lattice5),
    []).

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_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v5_yellow_0(B,k1_lattice5(A))
            & v6_yellow_0(B,k1_lattice5(A))
            & m1_yellow_0(B,k1_lattice5(A)) )
         => ~ ( ? [C] : 
                  ( v1_partfun1(C,A,A)
                  & v3_relat_2(C)
                  & v8_relat_2(C)
                  & m2_relset_1(C,A,A)
                  & r2_hidden(C,u1_struct_0(B))
                  & C != k13_cqc_sim1(A) )
              & ? [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & ! [D] : 
                      ( ( v1_partfun1(D,A,A)
                        & v3_relat_2(D)
                        & v8_relat_2(D)
                        & m2_relset_1(D,A,A) )
                     => ! [E] : 
                          ( ( v1_partfun1(E,A,A)
                            & v3_relat_2(E)
                            & v8_relat_2(E)
                            & m2_relset_1(E,A,A) )
                         => ! [F,G] : ~ ( r2_hidden(D,u1_struct_0(B))
                              & r2_hidden(E,u1_struct_0(B))
                              & r2_hidden(k4_tarski(F,G),k5_eqrel_1(A,D,E))
                              & ! [H] : 
                                  ( ( ~ v1_xboole_0(H)
                                    & m2_finseq_1(H,A) )
                                 => ~ ( k3_finseq_1(H) = C
                                      & r1_lattice5(A,H,F,G,D,E) ) ) ) ) ) )
              & ~ ! [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ( C = k3_lattice5(A,B)
                    <=> ( ! [D] : 
                            ( ( v1_partfun1(D,A,A)
                              & v3_relat_2(D)
                              & v8_relat_2(D)
                              & m2_relset_1(D,A,A) )
                           => ! [E] : 
                                ( ( v1_partfun1(E,A,A)
                                  & v3_relat_2(E)
                                  & v8_relat_2(E)
                                  & m2_relset_1(E,A,A) )
                               => ! [F,G] : ~ ( r2_hidden(D,u1_struct_0(B))
                                    & r2_hidden(E,u1_struct_0(B))
                                    & r2_hidden(k4_tarski(F,G),k5_eqrel_1(A,D,E))
                                    & ! [H] : 
                                        ( ( ~ v1_xboole_0(H)
                                          & m2_finseq_1(H,A) )
                                       => ~ ( k3_finseq_1(H) = k1_nat_1(C,2)
                                            & r1_lattice5(A,H,F,G,D,E) ) ) ) ) )
                        & ? [D] : 
                            ( v1_partfun1(D,A,A)
                            & v3_relat_2(D)
                            & v8_relat_2(D)
                            & m2_relset_1(D,A,A)
                            & ? [E] : 
                                ( v1_partfun1(E,A,A)
                                & v3_relat_2(E)
                                & v8_relat_2(E)
                                & m2_relset_1(E,A,A)
                                & ? [F,G] : 
                                    ( r2_hidden(D,u1_struct_0(B))
                                    & r2_hidden(E,u1_struct_0(B))
                                    & r2_hidden(k4_tarski(F,G),k5_eqrel_1(A,D,E))
                                    & ! [H] : 
                                        ( ( ~ v1_xboole_0(H)
                                          & m2_finseq_1(H,A) )
                                       => ~ ( k3_finseq_1(H) = k1_nat_1(C,1)
                                            & r1_lattice5(A,H,F,G,D,E) ) ) ) ) ) ) ) ) ) ) ) ),
    file(lattice5,d4_lattice5),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d9_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_2(A)
      <=> r1_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d9_relat_2),
    []).

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_k13_cqc_sim1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m2_fraenkel(k13_cqc_sim1(A),A,A,k1_fraenkel(A,A)) ) ),
    file(cqc_sim1,k13_cqc_sim1),
    []).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

fof(dt_k1_lattice5,axiom,(
    ! [A] : 
      ( v2_orders_2(k1_lattice5(A))
      & v3_orders_2(k1_lattice5(A))
      & v4_orders_2(k1_lattice5(A))
      & l1_orders_2(k1_lattice5(A)) ) ),
    file(lattice5,k1_lattice5),
    []).

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

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

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_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_msualg_5,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k2_msualg_5(A))
      & v3_lattices(k2_msualg_5(A))
      & v10_lattices(k2_msualg_5(A))
      & l3_lattices(k2_msualg_5(A)) ) ),
    file(msualg_5,k2_msualg_5),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    []).

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_k3_lattice5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v5_yellow_0(B,k1_lattice5(A))
        & v6_yellow_0(B,k1_lattice5(A))
        & m1_yellow_0(B,k1_lattice5(A)) )
     => m2_subset_1(k3_lattice5(A,B),k1_numbers,k5_numbers) ) ),
    file(lattice5,k3_lattice5),
    []).

fof(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k5_eqrel_1,axiom,(
    ! [A,B,C] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A)
        & v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v3_relat_2(k5_eqrel_1(A,B,C))
        & v8_relat_2(k5_eqrel_1(A,B,C))
        & v1_partfun1(k5_eqrel_1(A,B,C),A,A)
        & m2_relset_1(k5_eqrel_1(A,B,C),A,A) ) ) ),
    file(eqrel_1,k5_eqrel_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_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_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_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

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_m1_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => l1_orders_2(B) ) ) ),
    file(yellow_0,m1_yellow_0),
    []).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(dt_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

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_m1_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ? [B] : m1_yellow_0(B,A) ) ),
    file(yellow_0,m1_yellow_0),
    []).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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(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_int_1,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v1_int_1(k2_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc1_int_1),
    []).

fof(fc1_lattice5,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k1_lattice5(A))
      & v2_orders_2(k1_lattice5(A))
      & v3_orders_2(k1_lattice5(A))
      & v4_orders_2(k1_lattice5(A))
      & v1_lattice3(k1_lattice5(A))
      & v2_lattice3(k1_lattice5(A)) ) ),
    file(lattice5,fc1_lattice5),
    []).

fof(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

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_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_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_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ( v1_ordinal1(k1_card_1(A))
        & v2_ordinal1(k1_card_1(A))
        & v3_ordinal1(k1_card_1(A))
        & v1_finset_1(k1_card_1(A))
        & v1_card_1(k1_card_1(A)) ) ) ),
    file(card_1,fc2_card_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_lattice5,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k1_lattice5(A))
      & v2_orders_2(k1_lattice5(A))
      & v3_orders_2(k1_lattice5(A))
      & v4_orders_2(k1_lattice5(A))
      & v1_yellow_0(k1_lattice5(A))
      & v2_yellow_0(k1_lattice5(A))
      & v3_yellow_0(k1_lattice5(A))
      & v1_lattice3(k1_lattice5(A))
      & v2_lattice3(k1_lattice5(A))
      & v3_lattice3(k1_lattice5(A)) ) ),
    file(lattice5,fc2_lattice5),
    []).

fof(fc2_ordinal1,axiom,
    ( 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_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(fc2_partfun1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A))
      & v1_relat_2(k6_relat_1(A))
      & v3_relat_2(k6_relat_1(A))
      & v4_relat_2(k6_relat_1(A))
      & v8_relat_2(k6_relat_1(A)) ) ),
    file(partfun1,fc2_partfun1),
    []).

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

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_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

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(fc6_int_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v1_int_1(k2_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc6_int_1),
    []).

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(idempotence_k5_eqrel_1,axiom,(
    ! [A,B,C] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A)
        & v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m1_relset_1(C,A,A) )
     => k5_eqrel_1(A,B,B) = B ) ),
    file(eqrel_1,k5_eqrel_1),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_card_1,axiom,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    []).

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_int_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_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_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

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_pralg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_finseq_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B) ) ) ),
    file(pralg_1,rc1_pralg_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_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(rc2_card_1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    []).

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_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_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_lattice5,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_yellow_0(B,A)
          & v1_orders_2(B)
          & v5_yellow_0(B,A)
          & v6_yellow_0(B,A) ) ) ),
    file(lattice5,rc2_lattice5),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

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

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(rc3_partfun1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_relat_2(B)
      & v3_relat_2(B)
      & v4_relat_2(B)
      & v8_relat_2(B)
      & v1_partfun1(B,A,A) ) ),
    file(partfun1,rc3_partfun1),
    []).

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

fof(rc4_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_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_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_k13_cqc_sim1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k13_cqc_sim1(A) = k6_relat_1(A) ) ),
    file(cqc_sim1,k13_cqc_sim1),
    []).

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

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_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    []).

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

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(spc2_boole,axiom,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    []).

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

fof(t14_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] : 
          ( v1_relat_1(D)
         => ! [E] : 
              ( v1_relat_1(E)
             => ! [F] : 
                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                 => ! [G] : 
                      ( m2_subset_1(G,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(F,G)
                          & r1_relat_2(D,A)
                          & r1_relat_2(E,A)
                          & ? [H] : 
                              ( ~ v1_xboole_0(H)
                              & m2_finseq_1(H,A)
                              & k3_finseq_1(H) = F
                              & r1_lattice5(A,H,B,C,D,E) )
                          & ! [H] : 
                              ( ( ~ v1_xboole_0(H)
                                & m2_finseq_1(H,A) )
                             => ~ ( k3_finseq_1(H) = G
                                  & r1_lattice5(A,H,B,C,D,E) ) ) ) ) ) ) ) ) ),
    file(lattice5,t14_lattice5),
    []).

fof(t16_eqrel_1,axiom,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => ( ( v3_relat_2(B)
          & v8_relat_2(B)
          & v1_partfun1(B,A,A)
          & m2_relset_1(B,A,A) )
      <=> ( v1_relat_2(B)
          & v3_relat_2(B)
          & v8_relat_2(B)
          & k3_relat_1(B) = A ) ) ) ),
    file(eqrel_1,t16_eqrel_1),
    []).

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(t28_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => B != k2_xcmplx_0(A,C) ) ) ) ) ),
    file(nat_1,t28_nat_1),
    []).

fof(t29_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_1),
    []).

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(t38_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    []).

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),
    []).