% Mizar problem: t50_funcsdom,funcsdom,1115,24 
fof(t50_funcsdom,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k13_funcsdom(A))
        & v3_rlvect_1(k13_funcsdom(A))
        & v4_rlvect_1(k13_funcsdom(A))
        & v5_rlvect_1(k13_funcsdom(A))
        & v6_rlvect_1(k13_funcsdom(A))
        & v4_group_1(k13_funcsdom(A))
        & v7_group_1(k13_funcsdom(A))
        & v2_funcsdom(k13_funcsdom(A))
        & l1_funcsdom(k13_funcsdom(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_funcsdom,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc3_vectsp_1,cc4_membered,cc4_vectsp_1,cc5_vectsp_1,cc6_membered,cc9_membered,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,d16_group_1,d19_funcsdom,d1_binop_1,d1_group_1,d20_funcsdom,d2_rlvect_1,d3_rlvect_1,d4_group_1,d4_rlvect_1,d5_funcsdom,d5_rlvect_1,d6_funcsdom,d6_rlvect_1,d7_rlvect_1,d8_rlvect_1,dt_g1_funcsdom,dt_k10_funcsdom,dt_k13_funcsdom,dt_k1_binop_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_funcop_1,dt_k2_group_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k6_funcsdom,dt_k7_funcsdom,dt_k8_funcsdom,dt_k8_funct_2,dt_k9_funcsdom,dt_l1_funcsdom,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_rlvect_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_u1_group_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u1_vectsp_1,dt_u2_rlvect_1,dt_u2_struct_0,existence_l1_funcsdom,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_rlvect_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,fc1_funcop_1,fc1_subset_1,fc2_funcop_1,fc2_membered,fc3_funcop_1,fc3_funcsdom,fc4_funcsdom,fc4_subset_1,fc5_membered,fc6_membered,fc9_funcop_1,free_g1_funcsdom,rc1_membered,rc1_subset_1,rc2_funcsdom,rc2_subset_1,rc3_funcsdom,rc3_rlvect_1,rc4_funcsdom,rc8_vectsp_1,rc9_vectsp_1,redefinition_k1_domain_1,redefinition_k1_fraenkel,redefinition_k2_binop_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_fraenkel,redefinition_m2_relset_1,reflexivity_r1_tarski,spc0_boole,spc1_boole,spc1_numerals,t1_arithm,t1_numerals,t1_subset,t2_arithm,t2_subset,t3_arithm,t3_subset,t49_funcsdom,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(funcsdom,t50_funcsdom)]).

fof(abstractness_v1_funcsdom,axiom,(
    ! [A] : 
      ( l1_funcsdom(A)
     => ( v1_funcsdom(A)
       => A = g1_funcsdom(u1_struct_0(A),u1_group_1(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_vectsp_1(A),u2_struct_0(A)) ) ) ),
    file(funcsdom,v1_funcsdom),
    []).

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

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

fof(cc3_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc3_vectsp_1),
    []).

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

fof(cc4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(vectsp_1,cc4_vectsp_1),
    []).

fof(cc5_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc5_vectsp_1),
    []).

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

fof(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(d16_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v7_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) = k1_group_1(A,C,B) ) ) ) ) ),
    file(group_1,d16_group_1),
    []).

fof(d19_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k13_funcsdom(A) = g1_funcsdom(k1_fraenkel(A,k1_numbers),k7_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A),k10_funcsdom(A),k9_funcsdom(A)) ) ),
    file(funcsdom,d19_funcsdom),
    []).

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_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(d20_funcsdom,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_funcsdom(A) )
     => ( v2_funcsdom(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,k1_numbers)
                       => ! [F] : 
                            ( m1_subset_1(F,k1_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))
                              & k3_rlvect_1(A,k1_group_1(A,B,C),E) = k1_group_1(A,k3_rlvect_1(A,B,E),C)
                              & k3_rlvect_1(A,k2_rlvect_1(A,B,C),E) = k2_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,E))
                              & k3_rlvect_1(A,B,k3_real_1(E,F)) = k2_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,B,F))
                              & k3_rlvect_1(A,B,k4_real_1(E,F)) = k3_rlvect_1(A,k3_rlvect_1(A,B,F),E) ) ) ) ) ) ) ) ) ),
    file(funcsdom,d20_funcsdom),
    []).

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(d3_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) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ),
    file(rlvect_1,d3_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(d4_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)) ) ) ) ),
    file(rlvect_1,d4_rlvect_1),
    []).

fof(d5_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k9_funcsdom(A) = k2_funcop_1(A,0) ) ),
    file(funcsdom,d5_funcsdom),
    []).

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_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k10_funcsdom(A) = k2_funcop_1(A,1) ) ),
    file(funcsdom,d6_funcsdom),
    []).

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_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(dt_g1_funcsdom,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( 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(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_subset_1(E,A)
        & m1_subset_1(F,A) )
     => ( v1_funcsdom(g1_funcsdom(A,B,C,D,E,F))
        & l1_funcsdom(g1_funcsdom(A,B,C,D,E,F)) ) ) ),
    file(funcsdom,g1_funcsdom),
    []).

fof(dt_k10_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m2_fraenkel(k10_funcsdom(A),A,k1_numbers,k1_fraenkel(A,k1_numbers)) ) ),
    file(funcsdom,k10_funcsdom),
    []).

fof(dt_k13_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_funcsdom(k13_funcsdom(A))
        & l1_funcsdom(k13_funcsdom(A)) ) ) ),
    file(funcsdom,k13_funcsdom),
    []).

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_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_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

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_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_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_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_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_numbers) )
     => m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k3_rlvect_1),
    []).

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

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_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_k6_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k6_funcsdom(A))
        & v1_funct_2(k6_funcsdom(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
        & m2_relset_1(k6_funcsdom(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) ) ) ),
    file(funcsdom,k6_funcsdom),
    []).

fof(dt_k7_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k7_funcsdom(A))
        & v1_funct_2(k7_funcsdom(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
        & m2_relset_1(k7_funcsdom(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) ) ) ),
    file(funcsdom,k7_funcsdom),
    []).

fof(dt_k8_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k8_funcsdom(A))
        & v1_funct_2(k8_funcsdom(A),k2_zfmisc_1(k1_numbers,k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
        & m2_relset_1(k8_funcsdom(A),k2_zfmisc_1(k1_numbers,k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) ) ) ),
    file(funcsdom,k8_funcsdom),
    []).

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_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m2_fraenkel(k9_funcsdom(A),A,k1_numbers,k1_fraenkel(A,k1_numbers)) ) ),
    file(funcsdom,k9_funcsdom),
    []).

fof(dt_l1_funcsdom,axiom,(
    ! [A] : 
      ( l1_funcsdom(A)
     => ( l3_vectsp_1(A)
        & l2_rlvect_1(A) ) ) ),
    file(funcsdom,l1_funcsdom),
    []).

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_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => l1_rlvect_1(A) ) ),
    file(rlvect_1,l2_rlvect_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_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_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_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => ( v1_funct_1(u2_rlvect_1(A))
        & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u2_rlvect_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_funcsdom,axiom,(
    ? [A] : l1_funcsdom(A) ),
    file(funcsdom,l1_funcsdom),
    []).

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_rlvect_1,axiom,(
    ? [A] : l2_rlvect_1(A) ),
    file(rlvect_1,l2_rlvect_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_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(fc1_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc2_funcop_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    []).

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

fof(fc3_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    []).

fof(fc3_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k13_funcsdom(A))
        & v1_funcsdom(k13_funcsdom(A)) ) ) ),
    file(funcsdom,fc3_funcsdom),
    []).

fof(fc4_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k13_funcsdom(A))
        & v2_group_1(k13_funcsdom(A))
        & v6_vectsp_1(k13_funcsdom(A))
        & v8_vectsp_1(k13_funcsdom(A))
        & v1_funcsdom(k13_funcsdom(A)) ) ) ),
    file(funcsdom,fc4_funcsdom),
    []).

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

fof(fc6_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(fc9_funcop_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    []).

fof(free_g1_funcsdom,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( 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(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_subset_1(E,A)
        & m1_subset_1(F,A) )
     => ! [G,H,I,J,K,L] : 
          ( g1_funcsdom(A,B,C,D,E,F) = g1_funcsdom(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) ),
    file(funcsdom,g1_funcsdom),
    []).

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_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_funcsdom,axiom,(
    ? [A] : 
      ( l1_funcsdom(A)
      & v1_funcsdom(A) ) ),
    file(funcsdom,rc2_funcsdom),
    []).

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_funcsdom,axiom,(
    ? [A] : 
      ( l1_funcsdom(A)
      & ~ v3_struct_0(A) ) ),
    file(funcsdom,rc3_funcsdom),
    []).

fof(rc3_rlvect_1,axiom,(
    ? [A] : 
      ( l2_rlvect_1(A)
      & ~ v3_struct_0(A) ) ),
    file(rlvect_1,rc3_rlvect_1),
    []).

fof(rc4_funcsdom,axiom,(
    ? [A] : 
      ( l1_funcsdom(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v1_funcsdom(A)
      & v2_funcsdom(A) ) ),
    file(funcsdom,rc4_funcsdom),
    []).

fof(rc8_vectsp_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v4_group_1(A)
      & v7_group_1(A) ) ),
    file(vectsp_1,rc8_vectsp_1),
    []).

fof(rc9_vectsp_1,axiom,(
    ? [A] : 
      ( l1_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v6_vectsp_1(A)
      & v8_vectsp_1(A) ) ),
    file(vectsp_1,rc9_vectsp_1),
    []).

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_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_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

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

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

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_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t3_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(1,A) = A ) ),
    file(arithm,t3_arithm),
    []).

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

fof(t49_funcsdom,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k13_funcsdom(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k13_funcsdom(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k13_funcsdom(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ( k2_rlvect_1(k13_funcsdom(A),B,C) = k2_rlvect_1(k13_funcsdom(A),C,B)
                            & k2_rlvect_1(k13_funcsdom(A),k2_rlvect_1(k13_funcsdom(A),B,C),D) = k2_rlvect_1(k13_funcsdom(A),B,k2_rlvect_1(k13_funcsdom(A),C,D))
                            & k2_rlvect_1(k13_funcsdom(A),B,k1_rlvect_1(k13_funcsdom(A))) = B
                            & ? [G] : 
                                ( m1_subset_1(G,u1_struct_0(k13_funcsdom(A)))
                                & k2_rlvect_1(k13_funcsdom(A),B,G) = k1_rlvect_1(k13_funcsdom(A)) )
                            & k1_group_1(k13_funcsdom(A),B,C) = k1_group_1(k13_funcsdom(A),C,B)
                            & k1_group_1(k13_funcsdom(A),k1_group_1(k13_funcsdom(A),B,C),D) = k1_group_1(k13_funcsdom(A),B,k1_group_1(k13_funcsdom(A),C,D))
                            & k1_group_1(k13_funcsdom(A),B,k2_group_1(k13_funcsdom(A))) = B
                            & k1_group_1(k13_funcsdom(A),B,k2_rlvect_1(k13_funcsdom(A),C,D)) = k2_rlvect_1(k13_funcsdom(A),k1_group_1(k13_funcsdom(A),B,C),k1_group_1(k13_funcsdom(A),B,D))
                            & k3_rlvect_1(k13_funcsdom(A),k1_group_1(k13_funcsdom(A),B,C),E) = k1_group_1(k13_funcsdom(A),k3_rlvect_1(k13_funcsdom(A),B,E),C)
                            & k3_rlvect_1(k13_funcsdom(A),k2_rlvect_1(k13_funcsdom(A),B,C),E) = k2_rlvect_1(k13_funcsdom(A),k3_rlvect_1(k13_funcsdom(A),B,E),k3_rlvect_1(k13_funcsdom(A),C,E))
                            & k3_rlvect_1(k13_funcsdom(A),B,k3_real_1(E,F)) = k2_rlvect_1(k13_funcsdom(A),k3_rlvect_1(k13_funcsdom(A),B,E),k3_rlvect_1(k13_funcsdom(A),B,F))
                            & k3_rlvect_1(k13_funcsdom(A),B,k4_real_1(E,F)) = k3_rlvect_1(k13_funcsdom(A),k3_rlvect_1(k13_funcsdom(A),B,F),E) ) ) ) ) ) ) ) ),
    file(funcsdom,t49_funcsdom),
    []).

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

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

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

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

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