% Mizar problem: t44_lattice5,lattice5,4260,23 
fof(t44_lattice5,conjecture,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_lattice5(B,u1_struct_0(A),A,k17_lattice5(A))
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ( C = k3_tarski(a_2_5_lattice5(A,B))
               => ( v1_funct_1(k3_tarski(a_2_6_lattice5(A,B)))
                  & v1_funct_2(k3_tarski(a_2_6_lattice5(A,B)),k2_zfmisc_1(C,C),u1_struct_0(A))
                  & v1_lattice5(k3_tarski(a_2_6_lattice5(A,B)),C,A)
                  & v2_lattice5(k3_tarski(a_2_6_lattice5(A,B)),C,A)
                  & v3_lattice5(k3_tarski(a_2_6_lattice5(A,B)),C,A)
                  & m2_relset_1(k3_tarski(a_2_6_lattice5(A,B)),k2_zfmisc_1(C,C),u1_struct_0(A)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_abian,cc1_arytm_3,cc1_card_1,cc1_finseq_1,cc1_lattice3,cc1_ordinal1,cc1_relset_1,cc2_arytm_3,cc2_card_1,cc2_int_1,cc2_lattice3,cc2_ordinal1,cc3_arytm_3,cc3_card_1,cc3_int_1,cc3_ordinal1,cc4_int_1,commutativity_k13_lattice3,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d10_xboole_0,d1_binop_1,d1_funct_2,d1_mcart_1,d21_lattice5,d2_mcart_1,d3_tarski,d4_tarski,d5_funct_1,d5_partfun1,d5_tarski,d6_funcop_1,d6_lattice5,d7_lattice5,d8_lattice5,d9_ordinal1,d9_xboole_0,dt_k10_lattice3,dt_k13_lattice3,dt_k17_lattice5,dt_k1_binop_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funct_6,dt_k2_mcart_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_funct_6,dt_k3_tarski,dt_k3_yellow_0,dt_k4_lattice5,dt_k4_partfun1,dt_k4_relset_1,dt_k4_rfunct_3,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k7_yellow_2,dt_k8_yellow_2,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_lattice5,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_rfunct_3,existence_m1_subset_1,existence_m2_lattice5,existence_m2_relset_1,existence_m2_subset_1,fc11_finseq_1,fc17_abian,fc17_finseq_1,fc1_int_1,fc1_numbers,fc1_ordinal2,fc1_partfun1,fc1_struct_0,fc1_subset_1,fc2_finseq_1,fc2_ordinal1,fc2_subset_1,fc3_subset_1,fc4_ordinal1,fc4_subset_1,fc6_int_1,fc7_funcop_1,fraenkel_a_1_0_lattice5,fraenkel_a_2_5_lattice5,fraenkel_a_2_6_lattice5,fraenkel_a_2_7_lattice5,rc1_arytm_3,rc1_card_1,rc1_finseq_1,rc1_funcop_1,rc1_int_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_card_1,rc2_finseq_1,rc2_int_1,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc3_finseq_1,rc3_lattice5,rc3_ordinal1,rc3_struct_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k13_lattice3,redefinition_k1_domain_1,redefinition_k1_nat_1,redefinition_k4_lattice5,redefinition_k4_relset_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_k7_yellow_2,redefinition_k8_yellow_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r3_xboole_0,s2_funct_1__e16_80__lattice5,spc0_boole,spc1_boole,spc1_numerals,symmetry_r3_xboole_0,t119_zfmisc_1,t11_relset_1,t13_hahnban,t1_arithm,t1_lattice5,t1_numerals,t1_real,t1_subset,t1_xboole_1,t2_real,t2_subset,t2_tarski,t31_funct_6,t3_lattice5,t3_real,t3_subset,t41_lattice5,t42_lattice5,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t89_funct_6,t8_boole,t8_grfunc_1,t8_real,t92_zfmisc_1]),
    [file(lattice5,t44_lattice5)]).

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

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

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

fof(commutativity_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k13_lattice3(A,B,C) = k13_lattice3(A,C,B) ) ),
    file(lattice3,k13_lattice3),
    []).

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(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(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_mcart_1,axiom,(
    ! [A] : 
      ( ? [B,C] : A = k4_tarski(B,C)
     => ! [B] : 
          ( B = k1_mcart_1(A)
        <=> ! [C,D] : 
              ( A = k4_tarski(C,D)
             => B = C ) ) ) ),
    file(mcart_1,d1_mcart_1),
    []).

fof(d21_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( m2_lattice5(D,A,B,C)
                  <=> ( k1_relat_1(D) = k5_numbers
                      & k1_funct_1(D,0) = k4_tarski(A,C)
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ? [F] : 
                              ( ~ v1_xboole_0(F)
                              & ? [G] : 
                                  ( v1_funct_1(G)
                                  & v1_funct_2(G,k2_zfmisc_1(F,F),u1_struct_0(B))
                                  & v1_lattice5(G,F,B)
                                  & v2_lattice5(G,F,B)
                                  & v3_lattice5(G,F,B)
                                  & m2_relset_1(G,k2_zfmisc_1(F,F),u1_struct_0(B))
                                  & ? [H] : 
                                      ( ~ v1_xboole_0(H)
                                      & ? [I] : 
                                          ( v1_funct_1(I)
                                          & v1_funct_2(I,k2_zfmisc_1(H,H),u1_struct_0(B))
                                          & v1_lattice5(I,H,B)
                                          & v2_lattice5(I,H,B)
                                          & v3_lattice5(I,H,B)
                                          & m2_relset_1(I,k2_zfmisc_1(H,H),u1_struct_0(B))
                                          & r2_lattice5(F,B,G,H,I)
                                          & k1_funct_1(D,E) = k4_tarski(F,G)
                                          & k1_funct_1(D,k1_nat_1(E,1)) = k4_tarski(H,I) ) ) ) ) ) ) ) ) ) ) ) ),
    file(lattice5,d21_lattice5),
    []).

fof(d2_mcart_1,axiom,(
    ! [A] : 
      ( ? [B,C] : A = k4_tarski(B,C)
     => ! [B] : 
          ( B = k2_mcart_1(A)
        <=> ! [C,D] : 
              ( A = k4_tarski(C,D)
             => B = D ) ) ) ),
    file(mcart_1,d2_mcart_1),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d4_tarski,axiom,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    []).

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(d5_partfun1,axiom,(
    ! [A,B,C] : 
      ( C = k4_partfun1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & r1_tarski(k1_relat_1(E),A)
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(partfun1,d5_partfun1),
    []).

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

fof(d6_funcop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funcop_1(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => ( v1_relat_1(k1_funct_1(A,B))
              & v1_funct_1(k1_funct_1(A,B)) ) ) ) ) ),
    file(funcop_1,d6_funcop_1),
    []).

fof(d6_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v1_lattice5(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => k4_lattice5(A,B,C,D,E) = k4_lattice5(A,B,C,E,D) ) ) ) ) ) ) ),
    file(lattice5,d6_lattice5),
    []).

fof(d7_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v2_lattice5(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => k4_lattice5(A,B,C,D,D) = k3_yellow_0(B) ) ) ) ) ) ),
    file(lattice5,d7_lattice5),
    []).

fof(d8_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v3_lattice5(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => ! [F] : 
                            ( m1_subset_1(F,A)
                           => r1_orders_2(B,k4_lattice5(A,B,C,D,F),k13_lattice3(B,k4_lattice5(A,B,C,D,E),k4_lattice5(A,B,C,E,F))) ) ) ) ) ) ) ) ),
    file(lattice5,d8_lattice5),
    []).

fof(d9_ordinal1,axiom,(
    ! [A] : 
      ( v6_ordinal1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => r3_xboole_0(B,C) ) ) ),
    file(ordinal1,d9_ordinal1),
    []).

fof(d9_xboole_0,axiom,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        | r1_tarski(B,A) ) ) ),
    file(xboole_0,d9_xboole_0),
    []).

fof(dt_k10_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k10_lattice3),
    []).

fof(dt_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k13_lattice3),
    []).

fof(dt_k17_lattice5,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k17_lattice5(A))
        & v1_funct_2(k17_lattice5(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & v1_lattice5(k17_lattice5(A),u1_struct_0(A),A)
        & v2_lattice5(k17_lattice5(A),u1_struct_0(A),A)
        & v3_lattice5(k17_lattice5(A),u1_struct_0(A),A)
        & m2_relset_1(k17_lattice5(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattice5,k17_lattice5),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

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

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

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_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_6(A))
        & v1_funct_1(k2_funct_6(A)) ) ) ),
    file(funct_6,k2_funct_6),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

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_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_6(A))
        & v1_funct_1(k3_funct_6(A)) ) ) ),
    file(funct_6,k3_funct_6),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k3_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) ),
    file(yellow_0,k3_yellow_0),
    []).

fof(dt_k4_lattice5,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => m1_subset_1(k4_lattice5(A,B,C,D,E),u1_struct_0(B)) ) ),
    file(lattice5,k4_lattice5),
    []).

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

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k4_rfunct_3,axiom,(
    ! [A,B] : m1_rfunct_3(k4_rfunct_3(A,B),A,B) ),
    file(rfunct_3,k4_rfunct_3),
    []).

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

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_k7_yellow_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B))
        & m1_subset_1(D,A) )
     => m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)) ) ),
    file(yellow_2,k7_yellow_2),
    []).

fof(dt_k8_yellow_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(yellow_2,k8_yellow_2),
    []).

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_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_rfunct_3,axiom,(
    $true ),
    file(rfunct_3,m1_rfunct_3),
    []).

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

fof(dt_m2_lattice5,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & v1_lattice5(C,A,B)
        & v2_lattice5(C,A,B)
        & v3_lattice5(C,A,B)
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ! [D] : 
          ( m2_lattice5(D,A,B,C)
         => ( v1_relat_1(D)
            & v1_funct_1(D) ) ) ) ),
    file(lattice5,m2_lattice5),
    []).

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_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

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_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_rfunct_3,axiom,(
    ! [A,B] : 
    ? [C] : m1_rfunct_3(C,A,B) ),
    file(rfunct_3,m1_rfunct_3),
    []).

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

fof(existence_m2_lattice5,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & v1_lattice5(C,A,B)
        & v2_lattice5(C,A,B)
        & v3_lattice5(C,A,B)
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ? [D] : m2_lattice5(D,A,B,C) ) ),
    file(lattice5,m2_lattice5),
    []).

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(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_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(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    []).

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_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_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(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_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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

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

fof(fc4_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_tarski(A))
        & v2_ordinal1(k3_tarski(A))
        & v3_ordinal1(k3_tarski(A)) ) ) ),
    file(ordinal1,fc4_ordinal1),
    []).

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(fc7_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    []).

fof(fraenkel_a_1_0_lattice5,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_0_lattice5(B))
      <=> ? [C] : 
            ( m1_subset_1(C,B)
            & A = k2_zfmisc_1(C,C)
            & r2_hidden(C,B) ) ) ) ),
    file(lattice5,a_1_0_lattice5),
    []).

fof(fraenkel_a_2_5_lattice5,axiom,(
    ! [A,B,C] : 
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & m2_lattice5(C,u1_struct_0(B),B,k17_lattice5(B)) )
     => ( r2_hidden(A,a_2_5_lattice5(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_mcart_1(k1_funct_1(C,D)) ) ) ) ),
    file(lattice5,a_2_5_lattice5),
    []).

fof(fraenkel_a_2_6_lattice5,axiom,(
    ! [A,B,C] : 
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & m2_lattice5(C,u1_struct_0(B),B,k17_lattice5(B)) )
     => ( r2_hidden(A,a_2_6_lattice5(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k2_mcart_1(k1_funct_1(C,D)) ) ) ) ),
    file(lattice5,a_2_6_lattice5),
    []).

fof(fraenkel_a_2_7_lattice5,axiom,(
    ! [A,B,C] : 
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & m2_lattice5(C,u1_struct_0(B),B,k17_lattice5(B)) )
     => ( r2_hidden(A,a_2_7_lattice5(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k2_zfmisc_1(k1_mcart_1(k1_funct_1(C,D)),k1_mcart_1(k1_funct_1(C,D))) ) ) ) ),
    file(lattice5,a_2_7_lattice5),
    []).

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_funcop_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_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_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_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc2_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_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(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_lattice5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B) )
     => ? [C] : 
          ( m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
          & v1_lattice5(C,A,B)
          & v2_lattice5(C,A,B)
          & v3_lattice5(C,A,B) ) ) ),
    file(lattice5,rc3_lattice5),
    []).

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

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_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(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(redefinition_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k13_lattice3(A,B,C) = k10_lattice3(A,B,C) ) ),
    file(lattice3,k13_lattice3),
    []).

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

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_k4_lattice5,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => k4_lattice5(A,B,C,D,E) = k1_binop_1(C,D,E) ) ),
    file(lattice5,k4_lattice5),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k4_rfunct_3,axiom,(
    ! [A,B] : k4_rfunct_3(A,B) = k4_partfun1(A,B) ),
    file(rfunct_3,k4_rfunct_3),
    []).

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

fof(redefinition_k7_yellow_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B))
        & m1_subset_1(D,A) )
     => k7_yellow_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(yellow_2,k7_yellow_2),
    []).

fof(redefinition_k8_yellow_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => k8_yellow_2(A,B,C) = k2_relat_1(C) ) ),
    file(yellow_2,k8_yellow_2),
    []).

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(reflexivity_r3_xboole_0,axiom,(
    ! [A,B] : r3_xboole_0(A,A) ),
    file(xboole_0,r3_xboole_0),
    []).

fof(s2_funct_1__e16_80__lattice5,axiom,(
    ! [A,B] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m2_lattice5(B,u1_struct_0(A),A,k17_lattice5(A)) )
     => ( ( ! [C,D,E] : 
              ( ( r2_hidden(C,k5_numbers)
                & D = k2_mcart_1(k1_funct_1(B,C))
                & E = k2_mcart_1(k1_funct_1(B,C)) )
             => D = E )
          & ! [C] : ~ ( r2_hidden(C,k5_numbers)
              & ! [D] : D != k2_mcart_1(k1_funct_1(B,C)) ) )
       => ? [C] : 
            ( v1_relat_1(C)
            & v1_funct_1(C)
            & k1_relat_1(C) = k5_numbers
            & ! [D] : 
                ( r2_hidden(D,k5_numbers)
               => k1_funct_1(C,D) = k2_mcart_1(k1_funct_1(B,D)) ) ) ) ) ),
    file(lattice5,s2_funct_1__e16_80__lattice5),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

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(symmetry_r3_xboole_0,axiom,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
     => r3_xboole_0(B,A) ) ),
    file(xboole_0,r3_xboole_0),
    []).

fof(t119_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_1),
    []).

fof(t11_relset_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    []).

fof(t13_hahnban,axiom,(
    ! [A,B,C] : 
      ( ( v6_ordinal1(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_rfunct_3(A,B))) )
     => r2_hidden(k3_tarski(C),k4_rfunct_3(A,B)) ) ),
    file(hahnban,t13_hahnban),
    []).

fof(t1_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    []).

fof(t1_lattice5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ( A = k3_tarski(k2_relat_1(B))
           => k1_relat_1(A) = k3_tarski(k2_relat_1(k2_funct_6(B))) ) ) ) ),
    file(lattice5,t1_lattice5),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

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(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_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(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t31_funct_6,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r2_hidden(A,k1_relat_1(B))
              & C = k1_funct_1(B,A) )
           => ( r2_hidden(A,k1_relat_1(k2_funct_6(B)))
              & k1_funct_1(k2_funct_6(B),A) = k1_relat_1(C)
              & r2_hidden(A,k1_relat_1(k3_funct_6(B)))
              & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C) ) ) ) ) ),
    file(funct_6,t31_funct_6),
    []).

fof(t3_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v6_ordinal1(A)
       => k2_zfmisc_1(k3_tarski(A),k3_tarski(A)) = k3_tarski(a_1_0_lattice5(A)) ) ) ),
    file(lattice5,t3_lattice5),
    []).

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(t41_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] : 
                  ( m2_lattice5(D,A,B,C)
                 => ! [E] : 
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] : 
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(E,F)
                           => r1_tarski(k1_mcart_1(k1_funct_1(D,E)),k1_mcart_1(k1_funct_1(D,F))) ) ) ) ) ) ) ) ),
    file(lattice5,t41_lattice5),
    []).

fof(t42_lattice5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] : 
                  ( m2_lattice5(D,A,B,C)
                 => ! [E] : 
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] : 
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(E,F)
                           => r1_tarski(k2_mcart_1(k1_funct_1(D,E)),k2_mcart_1(k1_funct_1(D,F))) ) ) ) ) ) ) ) ),
    file(lattice5,t42_lattice5),
    []).

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(t89_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => k1_relat_1(k2_funct_6(A)) = k1_relat_1(A) ) ),
    file(funct_6,t89_funct_6),
    []).

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

fof(t8_grfunc_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    []).

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),
    []).

fof(t92_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    []).