% Mizar problem: t20_clopban2,clopban2,1327,60 
fof(t20_clopban2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => ( v5_clvect_1(k9_clopban2(A))
        & v3_rlvect_1(k9_clopban2(A))
        & v4_rlvect_1(k9_clopban2(A))
        & v5_rlvect_1(k9_clopban2(A))
        & v6_rlvect_1(k9_clopban2(A))
        & v4_group_1(k9_clopban2(A))
        & v2_cfuncdom(k9_clopban2(A))
        & v2_clvect_1(k9_clopban2(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_clopban2,abstractness_v1_clvect_1,abstractness_v4_clvect_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_funct_2,cc1_membered,cc1_relset_1,cc1_xcmplx_0,cc1_xreal_0,cc20_membered,cc2_clopban1,cc2_funct_1,cc2_membered,cc2_xcmplx_0,cc2_xreal_0,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_funct_2,cc5_membered,cc5_xreal_0,cc6_funct_2,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,commutativity_k8_complex1,commutativity_k9_complex1,connectedness_r1_xreal_0,d10_clvect_1,d13_clopban1,d1_binop_1,d1_clvect_1,d1_group_1,d2_clopban1,d2_clvect_1,d2_rlvect_1,d4_group_1,d5_clopban2,d5_rlvect_1,d6_clopban1,d6_rlvect_1,d7_rlvect_1,d8_clopban2,d8_rlvect_1,d9_cfuncdom,d9_clvect_1,dt_g1_clopban2,dt_g1_clvect_1,dt_g2_clvect_1,dt_k10_csspace,dt_k13_clopban1,dt_k14_clopban1,dt_k16_complex1,dt_k17_complex1,dt_k1_binop_1,dt_k1_clvect_1,dt_k1_domain_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_group_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_clopban1,dt_k2_group_1,dt_k2_lopban_1,dt_k2_numbers,dt_k2_rlvect_1,dt_k2_seq_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_clopban1,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_lopban_1,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_tarski,dt_k5_clopban1,dt_k5_clopban2,dt_k5_clvect_1,dt_k6_clopban1,dt_k6_clopban2,dt_k6_complex1,dt_k6_partfun1,dt_k6_relat_1,dt_k8_clopban1,dt_k8_complex1,dt_k8_csspace,dt_k8_funct_2,dt_k9_clopban2,dt_k9_complex1,dt_k9_csspace,dt_l1_cfuncdom,dt_l1_clopban2,dt_l1_clvect_1,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_clvect_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_u1_clvect_1,dt_u1_group_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u1_vectsp_1,dt_u2_clvect_1,dt_u2_struct_0,existence_l1_cfuncdom,existence_l1_clopban2,existence_l1_clvect_1,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_clvect_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,fc10_clopban1,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_clopban1,fc1_funct_2,fc1_membered,fc1_nat_1,fc1_struct_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_clopban1,fc2_funct_1,fc2_funct_2,fc2_membered,fc2_nat_1,fc2_xcmplx_0,fc3_clopban1,fc3_nat_1,fc3_xcmplx_0,fc3_xreal_0,fc4_clopban1,fc4_csspace3,fc4_nat_1,fc4_xreal_0,fc5_clopban1,fc6_clopban1,fc6_membered,fc7_clopban1,fc7_xreal_0,fc8_clopban1,fc8_clopban2,fc8_xcmplx_0,fc8_xreal_0,fc9_clopban2,fc9_xreal_0,free_g1_clopban2,free_g1_clvect_1,free_g2_clvect_1,projectivity_k16_complex1,projectivity_k17_complex1,rc1_funct_1,rc1_funct_2,rc1_membered,rc1_nat_1,rc1_xcmplx_0,rc1_xreal_0,rc2_cfuncdom,rc2_clopban2,rc2_funct_1,rc2_xcmplx_0,rc2_xreal_0,rc3_clopban2,rc3_funct_1,rc3_struct_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,rc5_struct_0,redefinition_k17_complex1,redefinition_k1_domain_1,redefinition_k1_fraenkel,redefinition_k2_binop_1,redefinition_k2_seq_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,redefinition_k6_partfun1,redefinition_k8_complex1,redefinition_k8_funct_2,redefinition_k9_complex1,redefinition_m1_struct_0,redefinition_m2_fraenkel,redefinition_m2_relset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,t19_clopban2,t1_arithm,t1_real,t1_subset,t2_arithm,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_rlvect_1,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(clopban2,t20_clopban2)]).

fof(abstractness_v1_clopban2,axiom,(
    ! [A] : 
      ( l1_clopban2(A)
     => ( v1_clopban2(A)
       => A = g1_clopban2(u1_struct_0(A),u1_group_1(A),u1_rlvect_1(A),u1_clvect_1(A),u1_vectsp_1(A),u2_struct_0(A),u2_clvect_1(A)) ) ) ),
    file(clopban2,v1_clopban2),
    []).

fof(abstractness_v1_clvect_1,axiom,(
    ! [A] : 
      ( l1_clvect_1(A)
     => ( v1_clvect_1(A)
       => A = g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)) ) ) ),
    file(clvect_1,v1_clvect_1),
    []).

fof(abstractness_v4_clvect_1,axiom,(
    ! [A] : 
      ( l2_clvect_1(A)
     => ( v4_clvect_1(A)
       => A = g2_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A),u2_clvect_1(A)) ) ) ),
    file(clvect_1,v4_clvect_1),
    []).

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

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

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

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

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

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

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

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

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

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

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

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

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

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_xcmplx_0,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc1_xcmplx_0),
    []).

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

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

fof(cc2_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B)))
         => ( v1_relat_1(C)
            & v1_funct_1(C) ) ) ) ),
    file(clopban1,cc2_clopban1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

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

fof(cc2_xcmplx_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc2_xcmplx_0),
    []).

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

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

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

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

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

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

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc5_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k2_numbers))
     => v1_membered(A) ) ),
    file(membered,cc5_membered),
    []).

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

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

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

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

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

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

fof(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_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k3_real_1(B,A) ) ),
    file(real_1,k3_real_1),
    []).

fof(commutativity_k3_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(commutativity_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k4_real_1(B,A) ) ),
    file(real_1,k4_real_1),
    []).

fof(commutativity_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(commutativity_k8_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k8_complex1(A,B) = k8_complex1(B,A) ) ),
    file(complex1,k8_complex1),
    []).

fof(commutativity_k9_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k9_complex1(A,B) = k9_complex1(B,A) ) ),
    file(complex1,k9_complex1),
    []).

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_clvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_clvect_1(A) )
     => ( v5_clvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,k2_numbers)
                   => ( ( k5_clvect_1(A,B) = 0
                       => B = k1_rlvect_1(A) )
                      & ( B = k1_rlvect_1(A)
                       => k5_clvect_1(A,B) = 0 )
                      & k5_clvect_1(A,k1_clvect_1(A,B,D)) = k4_real_1(k17_complex1(D),k5_clvect_1(A,B))
                      & r1_xreal_0(k5_clvect_1(A,k2_rlvect_1(A,B,C)),k3_real_1(k5_clvect_1(A,B),k5_clvect_1(A,C))) ) ) ) ) ) ) ),
    file(clvect_1,d10_clvect_1),
    []).

fof(d13_clopban1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => k14_clopban1(A,B) = g2_clvect_1(k8_clopban1(A,B),k10_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k8_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k9_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k13_clopban1(A,B)) ) ) ),
    file(clopban1,d13_clopban1),
    []).

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_clvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_clvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k2_numbers)
             => k1_clvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k2_numbers,u1_struct_0(A)),u1_struct_0(A),u1_clvect_1(A),k1_domain_1(k2_numbers,u1_struct_0(A),C,B)) ) ) ) ),
    file(clvect_1,d1_clvect_1),
    []).

fof(d1_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C) ) ) ) ),
    file(group_1,d1_group_1),
    []).

fof(d2_clopban1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_clvect_1(B)
            & l1_clvect_1(B) )
         => k3_clopban1(A,B) = g1_clvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k2_clopban1(A,B)) ) ) ),
    file(clopban1,d2_clopban1),
    []).

fof(d2_clvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_clvect_1(A) )
     => ( v2_clvect_1(A)
      <=> ( ! [B] : 
              ( m1_subset_1(B,k2_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k1_clvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_clvect_1(A,C,B),k1_clvect_1(A,D,B)) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,k2_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,k2_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k1_clvect_1(A,D,k8_complex1(B,C)) = k2_rlvect_1(A,k1_clvect_1(A,D,B),k1_clvect_1(A,D,C)) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,k2_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,k2_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k1_clvect_1(A,D,k9_complex1(B,C)) = k1_clvect_1(A,k1_clvect_1(A,D,C),B) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => k1_clvect_1(A,B,k6_complex1) = B ) ) ) ) ),
    file(clvect_1,d2_clvect_1),
    []).

fof(d2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => k1_rlvect_1(A) = u2_struct_0(A) ) ),
    file(rlvect_1,d2_rlvect_1),
    []).

fof(d4_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v4_group_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)) ) ) ) ) ) ),
    file(group_1,d4_group_1),
    []).

fof(d5_clopban2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => k6_clopban2(A) = k6_partfun1(u1_struct_0(A)) ) ),
    file(clopban2,d5_clopban2),
    []).

fof(d5_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v3_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) ) ) ) ) ),
    file(rlvect_1,d5_rlvect_1),
    []).

fof(d6_clopban1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_clvect_1(B)
            & l1_clvect_1(B) )
         => k6_clopban1(A,B) = g1_clvect_1(k5_clopban1(A,B),k10_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k8_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k9_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B))) ) ) ),
    file(clopban1,d6_clopban1),
    []).

fof(d6_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ),
    file(rlvect_1,d6_rlvect_1),
    []).

fof(d7_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v5_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => k2_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ) ),
    file(rlvect_1,d7_rlvect_1),
    []).

fof(d8_clopban2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => k9_clopban2(A) = g1_clopban2(k8_clopban1(A,A),k5_clopban2(A),k8_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k9_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k6_clopban2(A),k10_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k13_clopban1(A,A)) ) ),
    file(clopban2,d8_clopban2),
    []).

fof(d8_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v6_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ),
    file(rlvect_1,d8_rlvect_1),
    []).

fof(d9_cfuncdom,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_cfuncdom(A) )
     => ( v2_cfuncdom(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,k2_numbers)
                       => ! [F] : 
                            ( m1_subset_1(F,k2_numbers)
                           => ( k1_group_1(A,B,k2_group_1(A)) = B
                              & k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D))
                              & k1_clvect_1(A,k1_group_1(A,B,C),E) = k1_group_1(A,k1_clvect_1(A,B,E),C)
                              & k1_clvect_1(A,k2_rlvect_1(A,B,C),E) = k2_rlvect_1(A,k1_clvect_1(A,B,E),k1_clvect_1(A,C,E))
                              & k1_clvect_1(A,B,k8_complex1(E,F)) = k2_rlvect_1(A,k1_clvect_1(A,B,E),k1_clvect_1(A,B,F))
                              & k1_clvect_1(A,B,k9_complex1(E,F)) = k1_clvect_1(A,k1_clvect_1(A,B,F),E) ) ) ) ) ) ) ) ) ),
    file(cfuncdom,d9_cfuncdom),
    []).

fof(d9_clvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_clvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_clvect_1(A,B) = k2_seq_1(u1_struct_0(A),k1_numbers,u2_clvect_1(A),B) ) ) ),
    file(clvect_1,d9_clvect_1),
    []).

fof(dt_g1_clopban2,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( ( 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)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_subset_1(E,A)
        & m1_subset_1(F,A)
        & v1_funct_1(G)
        & v1_funct_2(G,A,k1_numbers)
        & m1_relset_1(G,A,k1_numbers) )
     => ( v1_clopban2(g1_clopban2(A,B,C,D,E,F,G))
        & l1_clopban2(g1_clopban2(A,B,C,D,E,F,G)) ) ) ),
    file(clopban2,g1_clopban2),
    []).

fof(dt_g1_clvect_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(B,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)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A) )
     => ( v1_clvect_1(g1_clvect_1(A,B,C,D))
        & l1_clvect_1(g1_clvect_1(A,B,C,D)) ) ) ),
    file(clvect_1,g1_clvect_1),
    []).

fof(dt_g2_clvect_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m1_subset_1(B,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)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k1_numbers)
        & m1_relset_1(E,A,k1_numbers) )
     => ( v4_clvect_1(g2_clvect_1(A,B,C,D,E))
        & l2_clvect_1(g2_clvect_1(A,B,C,D,E)) ) ) ),
    file(clvect_1,g2_clvect_1),
    []).

fof(dt_k10_csspace,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k10_csspace(A,B),B) ) ),
    file(csspace,k10_csspace),
    []).

fof(dt_k13_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( v1_funct_1(k13_clopban1(A,B))
        & v1_funct_2(k13_clopban1(A,B),k8_clopban1(A,B),k1_numbers)
        & m2_relset_1(k13_clopban1(A,B),k8_clopban1(A,B),k1_numbers) ) ) ),
    file(clopban1,k13_clopban1),
    []).

fof(dt_k14_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(k14_clopban1(A,B))
        & l2_clvect_1(k14_clopban1(A,B)) ) ) ),
    file(clopban1,k14_clopban1),
    []).

fof(dt_k16_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k16_complex1(A)) ) ),
    file(complex1,k16_complex1),
    []).

fof(dt_k17_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => m1_subset_1(k17_complex1(A),k1_numbers) ) ),
    file(complex1,k17_complex1),
    []).

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

fof(dt_k1_clvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_clvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k2_numbers) )
     => m1_subset_1(k1_clvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(clvect_1,k1_clvect_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_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

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

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

fof(dt_k1_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k1_group_1),
    []).

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

fof(dt_k1_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ),
    file(rlvect_1,k1_rlvect_1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(dt_k2_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( v1_funct_1(k2_clopban1(A,B))
        & v1_funct_2(k2_clopban1(A,B),k2_zfmisc_1(k2_numbers,k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
        & m2_relset_1(k2_clopban1(A,B),k2_zfmisc_1(k2_numbers,k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B))) ) ) ),
    file(clopban1,k2_clopban1),
    []).

fof(dt_k2_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => m1_subset_1(k2_group_1(A),u1_struct_0(A)) ) ),
    file(group_1,k2_group_1),
    []).

fof(dt_k2_lopban_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B) )
     => ( v1_funct_1(k2_lopban_1(A,B))
        & v1_funct_2(k2_lopban_1(A,B),k2_zfmisc_1(k1_fraenkel(A,u1_struct_0(B)),k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
        & m2_relset_1(k2_lopban_1(A,B),k2_zfmisc_1(k1_fraenkel(A,u1_struct_0(B)),k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B))) ) ) ),
    file(lopban_1,k2_lopban_1),
    []).

fof(dt_k2_numbers,axiom,(
    $true ),
    file(numbers,k2_numbers),
    []).

fof(dt_k2_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k2_rlvect_1),
    []).

fof(dt_k2_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ),
    file(seq_1,k2_seq_1),
    []).

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_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( ~ v3_struct_0(k3_clopban1(A,B))
        & v3_rlvect_1(k3_clopban1(A,B))
        & v4_rlvect_1(k3_clopban1(A,B))
        & v5_rlvect_1(k3_clopban1(A,B))
        & v6_rlvect_1(k3_clopban1(A,B))
        & v2_clvect_1(k3_clopban1(A,B))
        & l1_clvect_1(k3_clopban1(A,B)) ) ) ),
    file(clopban1,k3_clopban1),
    []).

fof(dt_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ),
    file(real_1,k3_real_1),
    []).

fof(dt_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(dt_k4_lopban_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => m2_fraenkel(k4_lopban_1(A,B),A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B))) ) ),
    file(lopban_1,k4_lopban_1),
    []).

fof(dt_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ),
    file(real_1,k4_real_1),
    []).

fof(dt_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

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

fof(dt_k5_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => m1_subset_1(k5_clopban1(A,B),k1_zfmisc_1(u1_struct_0(k3_clopban1(u1_struct_0(A),B)))) ) ),
    file(clopban1,k5_clopban1),
    []).

fof(dt_k5_clopban2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => ( v1_funct_1(k5_clopban2(A))
        & v1_funct_2(k5_clopban2(A),k2_zfmisc_1(k8_clopban1(A,A),k8_clopban1(A,A)),k8_clopban1(A,A))
        & m2_relset_1(k5_clopban2(A),k2_zfmisc_1(k8_clopban1(A,A),k8_clopban1(A,A)),k8_clopban1(A,A)) ) ) ),
    file(clopban2,k5_clopban2),
    []).

fof(dt_k5_clvect_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_clvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k5_clvect_1(A,B),k1_numbers) ) ),
    file(clvect_1,k5_clvect_1),
    []).

fof(dt_k6_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( ~ v3_struct_0(k6_clopban1(A,B))
        & v3_rlvect_1(k6_clopban1(A,B))
        & v4_rlvect_1(k6_clopban1(A,B))
        & v5_rlvect_1(k6_clopban1(A,B))
        & v6_rlvect_1(k6_clopban1(A,B))
        & v2_clvect_1(k6_clopban1(A,B))
        & l1_clvect_1(k6_clopban1(A,B)) ) ) ),
    file(clopban1,k6_clopban1),
    []).

fof(dt_k6_clopban2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => m1_struct_0(k6_clopban2(A),k6_clopban1(A,A),k8_clopban1(A,A)) ) ),
    file(clopban2,k6_clopban2),
    []).

fof(dt_k6_complex1,axiom,(
    m1_subset_1(k6_complex1,k2_numbers) ),
    file(complex1,k6_complex1),
    []).

fof(dt_k6_partfun1,axiom,(
    ! [A] : 
      ( v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) ),
    file(partfun1,k6_partfun1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_k8_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => m1_subset_1(k8_clopban1(A,B),k1_zfmisc_1(u1_struct_0(k6_clopban1(A,B)))) ) ),
    file(clopban1,k8_clopban1),
    []).

fof(dt_k8_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k8_complex1(A,B),k2_numbers) ) ),
    file(complex1,k8_complex1),
    []).

fof(dt_k8_csspace,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_funct_1(k8_csspace(A,B))
        & v1_funct_2(k8_csspace(A,B),k2_zfmisc_1(B,B),B)
        & m2_relset_1(k8_csspace(A,B),k2_zfmisc_1(B,B),B) ) ) ),
    file(csspace,k8_csspace),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_k9_clopban2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => l1_clopban2(k9_clopban2(A)) ) ),
    file(clopban2,k9_clopban2),
    []).

fof(dt_k9_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k9_complex1(A,B),k2_numbers) ) ),
    file(complex1,k9_complex1),
    []).

fof(dt_k9_csspace,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_funct_1(k9_csspace(A,B))
        & v1_funct_2(k9_csspace(A,B),k2_zfmisc_1(k2_numbers,B),B)
        & m2_relset_1(k9_csspace(A,B),k2_zfmisc_1(k2_numbers,B),B) ) ) ),
    file(csspace,k9_csspace),
    []).

fof(dt_l1_cfuncdom,axiom,(
    ! [A] : 
      ( l1_cfuncdom(A)
     => ( l3_vectsp_1(A)
        & l1_clvect_1(A) ) ) ),
    file(cfuncdom,l1_cfuncdom),
    []).

fof(dt_l1_clopban2,axiom,(
    ! [A] : 
      ( l1_clopban2(A)
     => ( l1_cfuncdom(A)
        & l2_clvect_1(A) ) ) ),
    file(clopban2,l1_clopban2),
    []).

fof(dt_l1_clvect_1,axiom,(
    ! [A] : 
      ( l1_clvect_1(A)
     => l1_rlvect_1(A) ) ),
    file(clvect_1,l1_clvect_1),
    []).

fof(dt_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

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

fof(dt_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(dt_l2_clvect_1,axiom,(
    ! [A] : 
      ( l2_clvect_1(A)
     => l1_clvect_1(A) ) ),
    file(clvect_1,l2_clvect_1),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_l2_vectsp_1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(dt_l3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ) ),
    file(vectsp_1,l3_vectsp_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_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [C] : 
          ( m1_struct_0(C,A,B)
         => m1_subset_1(C,u1_struct_0(A)) ) ) ),
    file(struct_0,m1_struct_0),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_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_u1_clvect_1,axiom,(
    ! [A] : 
      ( l1_clvect_1(A)
     => ( v1_funct_1(u1_clvect_1(A))
        & v1_funct_2(u1_clvect_1(A),k2_zfmisc_1(k2_numbers,u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_clvect_1(A),k2_zfmisc_1(k2_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(clvect_1,u1_clvect_1),
    []).

fof(dt_u1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_funct_1(u1_group_1(A))
        & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(group_1,u1_group_1),
    []).

fof(dt_u1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_funct_1(u1_rlvect_1(A))
        & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u1_rlvect_1),
    []).

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

fof(dt_u1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)) ) ),
    file(vectsp_1,u1_vectsp_1),
    []).

fof(dt_u2_clvect_1,axiom,(
    ! [A] : 
      ( l2_clvect_1(A)
     => ( v1_funct_1(u2_clvect_1(A))
        & v1_funct_2(u2_clvect_1(A),u1_struct_0(A),k1_numbers)
        & m2_relset_1(u2_clvect_1(A),u1_struct_0(A),k1_numbers) ) ) ),
    file(clvect_1,u2_clvect_1),
    []).

fof(dt_u2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ),
    file(struct_0,u2_struct_0),
    []).

fof(existence_l1_cfuncdom,axiom,(
    ? [A] : l1_cfuncdom(A) ),
    file(cfuncdom,l1_cfuncdom),
    []).

fof(existence_l1_clopban2,axiom,(
    ? [A] : l1_clopban2(A) ),
    file(clopban2,l1_clopban2),
    []).

fof(existence_l1_clvect_1,axiom,(
    ? [A] : l1_clvect_1(A) ),
    file(clvect_1,l1_clvect_1),
    []).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

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

fof(existence_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(existence_l2_clvect_1,axiom,(
    ? [A] : l2_clvect_1(A) ),
    file(clvect_1,l2_clvect_1),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_l2_vectsp_1,axiom,(
    ? [A] : l2_vectsp_1(A) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(existence_l3_vectsp_1,axiom,(
    ? [A] : l3_vectsp_1(A) ),
    file(vectsp_1,l3_vectsp_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_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ? [C] : m1_struct_0(C,A,B) ) ),
    file(struct_0,m1_struct_0),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_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(fc10_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(k14_clopban1(A,B))
        & v3_rlvect_1(k14_clopban1(A,B))
        & v4_rlvect_1(k14_clopban1(A,B))
        & v5_rlvect_1(k14_clopban1(A,B))
        & v6_rlvect_1(k14_clopban1(A,B))
        & v2_clvect_1(k14_clopban1(A,B))
        & v5_clvect_1(k14_clopban1(A,B)) ) ) ),
    file(clopban1,fc10_clopban1),
    []).

fof(fc10_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    []).

fof(fc11_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    []).

fof(fc12_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    []).

fof(fc1_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( ~ v3_struct_0(k3_clopban1(A,B))
        & v3_rlvect_1(k3_clopban1(A,B))
        & v4_rlvect_1(k3_clopban1(A,B))
        & v5_rlvect_1(k3_clopban1(A,B))
        & v6_rlvect_1(k3_clopban1(A,B))
        & v1_clvect_1(k3_clopban1(A,B))
        & v2_clvect_1(k3_clopban1(A,B)) ) ) ),
    file(clopban1,fc1_clopban1),
    []).

fof(fc1_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    []).

fof(fc1_membered,axiom,
    ( ~ v1_xboole_0(k2_numbers)
    & v1_membered(k2_numbers) ),
    file(membered,fc1_membered),
    []).

fof(fc1_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    []).

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(fc21_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc21_xreal_0),
    []).

fof(fc22_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc22_xreal_0),
    []).

fof(fc23_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc23_xreal_0),
    []).

fof(fc24_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc24_xreal_0),
    []).

fof(fc2_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( ~ v3_struct_0(k3_clopban1(A,B))
        & v3_rlvect_1(k3_clopban1(A,B))
        & v4_rlvect_1(k3_clopban1(A,B))
        & v5_rlvect_1(k3_clopban1(A,B))
        & v6_rlvect_1(k3_clopban1(A,B))
        & v1_clvect_1(k3_clopban1(A,B))
        & v2_clvect_1(k3_clopban1(A,B))
        & v1_monoid_0(k3_clopban1(A,B)) ) ) ),
    file(clopban1,fc2_clopban1),
    []).

fof(fc2_funct_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A)) ) ),
    file(funct_1,fc2_funct_1),
    []).

fof(fc2_funct_2,axiom,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    []).

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

fof(fc2_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc2_nat_1),
    []).

fof(fc2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k2_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc2_xcmplx_0),
    []).

fof(fc3_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( ~ v1_xboole_0(k5_clopban1(A,B))
        & v1_fraenkel(k5_clopban1(A,B)) ) ) ),
    file(clopban1,fc3_clopban1),
    []).

fof(fc3_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    []).

fof(fc3_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc3_xcmplx_0),
    []).

fof(fc3_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    []).

fof(fc4_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( ~ v3_struct_0(g1_clvect_1(k5_clopban1(A,B),k10_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k8_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k9_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B))))
        & v3_rlvect_1(g1_clvect_1(k5_clopban1(A,B),k10_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k8_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k9_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B))))
        & v4_rlvect_1(g1_clvect_1(k5_clopban1(A,B),k10_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k8_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k9_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B))))
        & v5_rlvect_1(g1_clvect_1(k5_clopban1(A,B),k10_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k8_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k9_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B))))
        & v6_rlvect_1(g1_clvect_1(k5_clopban1(A,B),k10_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k8_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k9_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B))))
        & v1_clvect_1(g1_clvect_1(k5_clopban1(A,B),k10_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k8_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k9_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B))))
        & v2_clvect_1(g1_clvect_1(k5_clopban1(A,B),k10_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k8_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)),k9_csspace(k3_clopban1(u1_struct_0(A),B),k5_clopban1(A,B)))) ) ) ),
    file(clopban1,fc4_clopban1),
    []).

fof(fc4_csspace3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,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)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k1_numbers)
        & m1_relset_1(E,A,k1_numbers) )
     => ( ~ v3_struct_0(g2_clvect_1(A,B,C,D,E))
        & v4_clvect_1(g2_clvect_1(A,B,C,D,E)) ) ) ),
    file(csspace3,fc4_csspace3),
    []).

fof(fc4_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    []).

fof(fc4_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc4_xreal_0),
    []).

fof(fc5_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( ~ v3_struct_0(k6_clopban1(A,B))
        & v3_rlvect_1(k6_clopban1(A,B))
        & v4_rlvect_1(k6_clopban1(A,B))
        & v5_rlvect_1(k6_clopban1(A,B))
        & v6_rlvect_1(k6_clopban1(A,B))
        & v1_clvect_1(k6_clopban1(A,B))
        & v2_clvect_1(k6_clopban1(A,B)) ) ) ),
    file(clopban1,fc5_clopban1),
    []).

fof(fc6_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & l1_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & l1_clvect_1(B) )
     => ( ~ v3_struct_0(k6_clopban1(A,B))
        & v3_rlvect_1(k6_clopban1(A,B))
        & v4_rlvect_1(k6_clopban1(A,B))
        & v5_rlvect_1(k6_clopban1(A,B))
        & v6_rlvect_1(k6_clopban1(A,B))
        & v1_clvect_1(k6_clopban1(A,B))
        & v2_clvect_1(k6_clopban1(A,B))
        & v1_monoid_0(k6_clopban1(A,B)) ) ) ),
    file(clopban1,fc6_clopban1),
    []).

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

fof(fc7_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ~ v1_xboole_0(k8_clopban1(A,B)) ) ),
    file(clopban1,fc7_clopban1),
    []).

fof(fc7_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    []).

fof(fc8_clopban1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(g1_clvect_1(k8_clopban1(A,B),k10_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k8_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k9_csspace(k6_clopban1(A,B),k8_clopban1(A,B))))
        & v3_rlvect_1(g1_clvect_1(k8_clopban1(A,B),k10_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k8_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k9_csspace(k6_clopban1(A,B),k8_clopban1(A,B))))
        & v4_rlvect_1(g1_clvect_1(k8_clopban1(A,B),k10_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k8_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k9_csspace(k6_clopban1(A,B),k8_clopban1(A,B))))
        & v5_rlvect_1(g1_clvect_1(k8_clopban1(A,B),k10_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k8_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k9_csspace(k6_clopban1(A,B),k8_clopban1(A,B))))
        & v6_rlvect_1(g1_clvect_1(k8_clopban1(A,B),k10_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k8_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k9_csspace(k6_clopban1(A,B),k8_clopban1(A,B))))
        & v1_clvect_1(g1_clvect_1(k8_clopban1(A,B),k10_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k8_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k9_csspace(k6_clopban1(A,B),k8_clopban1(A,B))))
        & v2_clvect_1(g1_clvect_1(k8_clopban1(A,B),k10_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k8_csspace(k6_clopban1(A,B),k8_clopban1(A,B)),k9_csspace(k6_clopban1(A,B),k8_clopban1(A,B)))) ) ) ),
    file(clopban1,fc8_clopban1),
    []).

fof(fc8_clopban2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => ( ~ v3_struct_0(k9_clopban2(A))
        & v1_clopban2(k9_clopban2(A)) ) ) ),
    file(clopban2,fc8_clopban2),
    []).

fof(fc8_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & ~ v1_xboole_0(B)
        & v1_xcmplx_0(B) )
     => ( ~ v1_xboole_0(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xcmplx_0,fc8_xcmplx_0),
    []).

fof(fc8_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    []).

fof(fc9_clopban2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => ( ~ v3_struct_0(k9_clopban2(A))
        & v2_group_1(k9_clopban2(A))
        & v1_clopban2(k9_clopban2(A)) ) ) ),
    file(clopban2,fc9_clopban2),
    []).

fof(fc9_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    []).

fof(free_g1_clopban2,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( ( 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)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_subset_1(E,A)
        & m1_subset_1(F,A)
        & v1_funct_1(G)
        & v1_funct_2(G,A,k1_numbers)
        & m1_relset_1(G,A,k1_numbers) )
     => ! [H,I,J,K,L,M,N] : 
          ( g1_clopban2(A,B,C,D,E,F,G) = g1_clopban2(H,I,J,K,L,M,N)
         => ( A = H
            & B = I
            & C = J
            & D = K
            & E = L
            & F = M
            & G = N ) ) ) ),
    file(clopban2,g1_clopban2),
    []).

fof(free_g1_clvect_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(B,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)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A) )
     => ! [E,F,G,H] : 
          ( g1_clvect_1(A,B,C,D) = g1_clvect_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(clvect_1,g1_clvect_1),
    []).

fof(free_g2_clvect_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m1_subset_1(B,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)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k1_numbers)
        & m1_relset_1(E,A,k1_numbers) )
     => ! [F,G,H,I,J] : 
          ( g2_clvect_1(A,B,C,D,E) = g2_clvect_1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) ),
    file(clvect_1,g2_clvect_1),
    []).

fof(projectivity_k16_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ),
    file(complex1,k16_complex1),
    []).

fof(projectivity_k17_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k17_complex1(k17_complex1(A)) = k17_complex1(A) ) ),
    file(complex1,k17_complex1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

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

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

fof(rc1_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    []).

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

fof(rc2_cfuncdom,axiom,(
    ? [A] : 
      ( l1_cfuncdom(A)
      & ~ v3_struct_0(A) ) ),
    file(cfuncdom,rc2_cfuncdom),
    []).

fof(rc2_clopban2,axiom,(
    ? [A] : 
      ( l1_clopban2(A)
      & v1_clopban2(A) ) ),
    file(clopban2,rc2_clopban2),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_xcmplx_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A) ) ),
    file(xcmplx_0,rc2_xcmplx_0),
    []).

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

fof(rc3_clopban2,axiom,(
    ? [A] : 
      ( l1_clopban2(A)
      & ~ v3_struct_0(A) ) ),
    file(clopban2,rc3_clopban2),
    []).

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

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

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

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

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

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

fof(redefinition_k17_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k17_complex1(A) = k16_complex1(A) ) ),
    file(complex1,k17_complex1),
    []).

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

fof(redefinition_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(redefinition_k2_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(seq_1,k2_seq_1),
    []).

fof(redefinition_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(real_1,k3_real_1),
    []).

fof(redefinition_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ),
    file(real_1,k4_real_1),
    []).

fof(redefinition_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(redefinition_k6_partfun1,axiom,(
    ! [A] : k6_partfun1(A) = k6_relat_1(A) ),
    file(partfun1,k6_partfun1),
    []).

fof(redefinition_k8_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k8_complex1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(complex1,k8_complex1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_k9_complex1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k9_complex1(A,B) = k3_xcmplx_0(A,B) ) ),
    file(complex1,k9_complex1),
    []).

fof(redefinition_m1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [C] : 
          ( m1_struct_0(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(struct_0,m1_struct_0),
    []).

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

fof(t19_clopban2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_clvect_1(A)
        & v5_clvect_1(A)
        & l2_clvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k9_clopban2(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k9_clopban2(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k9_clopban2(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k2_numbers)
                     => ! [F] : 
                          ( m1_subset_1(F,k2_numbers)
                         => ( k2_rlvect_1(k9_clopban2(A),B,C) = k2_rlvect_1(k9_clopban2(A),C,B)
                            & k2_rlvect_1(k9_clopban2(A),k2_rlvect_1(k9_clopban2(A),B,C),D) = k2_rlvect_1(k9_clopban2(A),B,k2_rlvect_1(k9_clopban2(A),C,D))
                            & k2_rlvect_1(k9_clopban2(A),B,k1_rlvect_1(k9_clopban2(A))) = B
                            & ? [G] : 
                                ( m1_subset_1(G,u1_struct_0(k9_clopban2(A)))
                                & k2_rlvect_1(k9_clopban2(A),B,G) = k1_rlvect_1(k9_clopban2(A)) )
                            & k1_group_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),B,C),D) = k1_group_1(k9_clopban2(A),B,k1_group_1(k9_clopban2(A),C,D))
                            & k1_group_1(k9_clopban2(A),B,k2_group_1(k9_clopban2(A))) = B
                            & k1_group_1(k9_clopban2(A),k2_group_1(k9_clopban2(A)),B) = B
                            & k1_group_1(k9_clopban2(A),B,k2_rlvect_1(k9_clopban2(A),C,D)) = k2_rlvect_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),B,C),k1_group_1(k9_clopban2(A),B,D))
                            & k1_group_1(k9_clopban2(A),k2_rlvect_1(k9_clopban2(A),C,D),B) = k2_rlvect_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),C,B),k1_group_1(k9_clopban2(A),D,B))
                            & k1_clvect_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),B,C),E) = k1_group_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,E),C)
                            & k1_clvect_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),B,C),k9_complex1(E,F)) = k1_group_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,E),k1_clvect_1(k9_clopban2(A),C,F))
                            & k1_clvect_1(k9_clopban2(A),k2_rlvect_1(k9_clopban2(A),B,C),E) = k2_rlvect_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,E),k1_clvect_1(k9_clopban2(A),C,E))
                            & k1_clvect_1(k9_clopban2(A),B,k8_complex1(E,F)) = k2_rlvect_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,E),k1_clvect_1(k9_clopban2(A),B,F))
                            & k1_clvect_1(k9_clopban2(A),B,k9_complex1(E,F)) = k1_clvect_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,F),E)
                            & k1_clvect_1(k9_clopban2(A),B,k6_complex1) = B ) ) ) ) ) ) ) ),
    file(clopban2,t19_clopban2),
    []).

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

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(t2_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,0) = 0 ) ),
    file(arithm,t2_arithm),
    []).

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(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_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) ) ) ) ),
    file(rlvect_1,t5_rlvect_1),
    []).

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),
    []).