% Mizar problem: t12_scm_comp,scm_comp,816,46 
fof(t12_scm_comp,conjecture,(
    ! [A] : 
      ( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp))
     => ! [B] : 
          ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
         => ! [C] : 
              ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
             => k17_scm_comp(k2_scm_comp(A,B,C)) = k1_limfunc1(k17_scm_comp(B),k17_scm_comp(C)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,antisymmetry_r2_hidden,cc10_membered,cc10_trees_3,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_funct_1,cc1_funct_2,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_bintree1,cc2_dtconstr,cc2_funct_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_membered,cc4_trees_3,cc5_funct_2,cc5_trees_3,cc6_funct_2,cc6_membered,cc9_membered,commutativity_k1_limfunc1,commutativity_k2_square_1,d13_scm_comp,d1_scm_comp,dt_c11__scm_comp,dt_g1_lang1,dt_k10_finseq_1,dt_k13_finseq_1,dt_k16_scm_comp,dt_k17_scm_comp,dt_k1_bintree1,dt_k1_funct_1,dt_k1_limfunc1,dt_k1_numbers,dt_k1_scm_comp,dt_k1_trees_4,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ami_2,dt_k2_scm_comp,dt_k2_square_1,dt_k2_zfmisc_1,dt_k3_finseq_2,dt_k3_scm_comp,dt_k4_dtconstr,dt_k4_lang1,dt_k5_lang1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_trees_3,dt_k6_dtconstr,dt_k6_lang1,dt_k6_trees_4,dt_k7_dtconstr,dt_k8_funct_2,dt_l1_lang1,dt_l1_struct_0,dt_m1_dtconstr,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_m3_trees_2,dt_m4_trees_3,dt_m5_trees_3,dt_u1_lang1,dt_u1_struct_0,existence_l1_lang1,existence_l1_struct_0,existence_m1_dtconstr,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,existence_m3_trees_2,existence_m4_trees_3,existence_m5_trees_3,fc17_trees_3,fc1_ami_2,fc1_dtconstr,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_dtconstr,fc2_membered,fc3_dtconstr,fc4_subset_1,fc5_membered,fc6_membered,fc6_trees_3,free_g1_lang1,idempotence_k1_limfunc1,idempotence_k2_square_1,l35_scm_comp,l37_scm_comp,rc1_dtconstr,rc1_funct_1,rc1_funct_2,rc1_int_1,rc1_membered,rc1_nat_1,rc1_subset_1,rc1_xboole_0,rc2_bintree1,rc2_funct_1,rc2_int_1,rc2_nat_1,rc2_subset_1,rc2_trees_3,rc2_xboole_0,rc3_bintree1,rc3_funct_1,rc3_nat_1,rc3_struct_0,rc4_bintree1,rc4_trees_3,rc5_struct_0,rc6_trees_3,rc8_trees_3,redefinition_k1_limfunc1,redefinition_k2_scm_comp,redefinition_k3_finseq_2,redefinition_k3_scm_comp,redefinition_k4_lang1,redefinition_k5_numbers,redefinition_k6_dtconstr,redefinition_k7_dtconstr,redefinition_k8_funct_2,redefinition_m1_dtconstr,redefinition_m1_struct_0,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m5_trees_3,reflexivity_r1_tarski,spc1_boole,spc1_numerals,spc5_boole,spc5_numerals,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(scm_comp,t12_scm_comp)]).

fof(abstractness_v1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => ( v1_lang1(A)
       => A = g1_lang1(u1_struct_0(A),u1_lang1(A)) ) ) ),
    file(lang1,v1_lang1),
    []).

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(cc10_trees_3,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v3_trees_3(A) )
     => ! [B] : 
          ( m1_finseq_1(B,A)
         => v6_trees_3(B) ) ) ),
    file(trees_3,cc10_trees_3),
    []).

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_dtconstr,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k3_finseq_2(A))
     => v1_finseq_1(B) ) ),
    file(dtconstr,cc1_dtconstr),
    []).

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

fof(cc1_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_bintree1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_dtconstr(A)
        & v2_dtconstr(A)
        & v3_bintree1(A)
        & l1_lang1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k4_dtconstr(A))
         => v2_bintree1(B) ) ) ),
    file(bintree1,cc2_bintree1),
    []).

fof(cc2_dtconstr,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m4_trees_3(B,A) )
     => ! [C] : 
          ( m1_finseq_1(C,B)
         => v6_trees_3(C) ) ) ),
    file(dtconstr,cc2_dtconstr),
    []).

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_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    []).

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

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

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

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

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

fof(cc4_trees_3,axiom,(
    ! [A] : 
      ( v3_trees_3(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v3_trees_3(B) ) ) ),
    file(trees_3,cc4_trees_3),
    []).

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_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m4_trees_3(B,A)
         => v3_trees_3(B) ) ) ),
    file(trees_3,cc5_trees_3),
    []).

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(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_k1_limfunc1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_limfunc1(A,B) = k1_limfunc1(B,A) ) ),
    file(limfunc1,k1_limfunc1),
    []).

fof(commutativity_k2_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => k2_square_1(A,B) = k2_square_1(B,A) ) ),
    file(square_1,k2_square_1),
    []).

fof(d13_scm_comp,axiom,(
    ! [A] : 
      ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k17_scm_comp(A)
          <=> ? [C] : 
                ( v1_funct_1(C)
                & v1_funct_2(C,k4_dtconstr(k1_scm_comp),k5_numbers)
                & m2_relset_1(C,k4_dtconstr(k1_scm_comp),k5_numbers)
                & B = k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,A)
                & ! [D] : 
                    ( m1_struct_0(D,k1_scm_comp,k6_dtconstr(k1_scm_comp))
                   => k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,k3_scm_comp(D)) = k16_scm_comp(D) )
                & ! [D] : 
                    ( m1_struct_0(D,k1_scm_comp,k7_dtconstr(k1_scm_comp))
                   => ! [E] : 
                        ( m1_dtconstr(E,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
                       => ! [F] : 
                            ( m1_dtconstr(F,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(k1_scm_comp))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(k1_scm_comp))
                                   => ( ( G = k1_bintree1(u1_struct_0(k1_scm_comp),E)
                                        & H = k1_bintree1(u1_struct_0(k1_scm_comp),F)
                                        & r1_lang1(k1_scm_comp,D,k4_lang1(u1_struct_0(k1_scm_comp),G,H)) )
                                     => ! [I] : 
                                          ( m2_subset_1(I,k1_numbers,k5_numbers)
                                         => ! [J] : 
                                              ( m2_subset_1(J,k1_numbers,k5_numbers)
                                             => ( ( I = k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,E)
                                                  & J = k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,F) )
                                               => k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,k2_scm_comp(D,E,F)) = k1_limfunc1(I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(scm_comp,d13_scm_comp),
    []).

fof(d1_scm_comp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_lang1(A)
        & v3_bintree1(A)
        & v1_dtconstr(A)
        & v2_dtconstr(A)
        & v3_dtconstr(A)
        & l1_lang1(A) )
     => ( A = k1_scm_comp
      <=> ( k6_dtconstr(A) = k2_ami_2
          & k7_dtconstr(A) = k2_zfmisc_1(1,5)
          & ! [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))
                     => ( r1_lang1(A,B,k4_lang1(u1_struct_0(A),C,D))
                      <=> r2_hidden(B,k2_zfmisc_1(1,5)) ) ) ) ) ) ) ) ),
    file(scm_comp,d1_scm_comp),
    []).

fof(dt_c11__scm_comp,axiom,
    ( v1_funct_1(c11__scm_comp)
    & v1_funct_2(c11__scm_comp,k4_dtconstr(k1_scm_comp),k5_numbers)
    & m2_relset_1(c11__scm_comp,k4_dtconstr(k1_scm_comp),k5_numbers) ),
    file(scm_comp,c11__scm_comp),
    []).

fof(dt_g1_lang1,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,k3_finseq_2(A))
     => ( v1_lang1(g1_lang1(A,B))
        & l1_lang1(g1_lang1(A,B)) ) ) ),
    file(lang1,g1_lang1),
    []).

fof(dt_k10_finseq_1,axiom,(
    $true ),
    file(finseq_1,k10_finseq_1),
    []).

fof(dt_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    []).

fof(dt_k16_scm_comp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_dtconstr(k1_scm_comp))
     => m2_subset_1(k16_scm_comp(A),k1_numbers,k5_numbers) ) ),
    file(scm_comp,k16_scm_comp),
    []).

fof(dt_k17_scm_comp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k4_dtconstr(k1_scm_comp))
     => m2_subset_1(k17_scm_comp(A),k1_numbers,k5_numbers) ) ),
    file(scm_comp,k17_scm_comp),
    []).

fof(dt_k1_bintree1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & m3_trees_2(B,A) )
     => m1_subset_1(k1_bintree1(A,B),A) ) ),
    file(bintree1,k1_bintree1),
    []).

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

fof(dt_k1_limfunc1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_limfunc1(A,B),k1_numbers,k5_numbers) ) ),
    file(limfunc1,k1_limfunc1),
    []).

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

fof(dt_k1_scm_comp,axiom,
    ( ~ v3_struct_0(k1_scm_comp)
    & v1_lang1(k1_scm_comp)
    & v3_bintree1(k1_scm_comp)
    & v1_dtconstr(k1_scm_comp)
    & v2_dtconstr(k1_scm_comp)
    & v3_dtconstr(k1_scm_comp)
    & l1_lang1(k1_scm_comp) ),
    file(scm_comp,k1_scm_comp),
    []).

fof(dt_k1_trees_4,axiom,(
    ! [A] : 
      ( v1_relat_1(k1_trees_4(A))
      & v1_funct_1(k1_trees_4(A))
      & v3_trees_2(k1_trees_4(A)) ) ),
    file(trees_4,k1_trees_4),
    []).

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_ami_2,axiom,(
    m1_subset_1(k2_ami_2,k1_zfmisc_1(k5_numbers)) ),
    file(ami_2,k2_ami_2),
    []).

fof(dt_k2_scm_comp,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp))
        & m1_subset_1(B,k4_dtconstr(k1_scm_comp))
        & m1_subset_1(C,k4_dtconstr(k1_scm_comp)) )
     => m1_dtconstr(k2_scm_comp(A,B,C),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ),
    file(scm_comp,k2_scm_comp),
    []).

fof(dt_k2_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => v1_xreal_0(k2_square_1(A,B)) ) ),
    file(square_1,k2_square_1),
    []).

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

fof(dt_k3_finseq_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k3_finseq_2(A))
      & m1_finseq_2(k3_finseq_2(A),A) ) ),
    file(finseq_2,k3_finseq_2),
    []).

fof(dt_k3_scm_comp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_dtconstr(k1_scm_comp))
     => m1_dtconstr(k3_scm_comp(A),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ),
    file(scm_comp,k3_scm_comp),
    []).

fof(dt_k4_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => m1_subset_1(k4_dtconstr(A),k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) ) ),
    file(dtconstr,k4_dtconstr),
    []).

fof(dt_k4_lang1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m2_finseq_2(k4_lang1(A,B,C),A,k3_finseq_2(A)) ) ),
    file(lang1,k4_lang1),
    []).

fof(dt_k5_lang1,axiom,(
    $true ),
    file(lang1,k5_lang1),
    []).

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

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

fof(dt_k5_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m4_trees_3(k5_trees_3(A),A) ) ),
    file(trees_3,k5_trees_3),
    []).

fof(dt_k6_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_dtconstr(A)
        & l1_lang1(A) )
     => ( ~ v1_xboole_0(k6_dtconstr(A))
        & m1_subset_1(k6_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(dtconstr,k6_dtconstr),
    []).

fof(dt_k6_lang1,axiom,(
    $true ),
    file(lang1,k6_lang1),
    []).

fof(dt_k6_trees_4,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v3_trees_2(C) )
     => ( v1_relat_1(k6_trees_4(A,B,C))
        & v1_funct_1(k6_trees_4(A,B,C))
        & v3_trees_2(k6_trees_4(A,B,C)) ) ) ),
    file(trees_4,k6_trees_4),
    []).

fof(dt_k7_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_dtconstr(A)
        & l1_lang1(A) )
     => ( ~ v1_xboole_0(k7_dtconstr(A))
        & m1_subset_1(k7_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(dtconstr,k7_dtconstr),
    []).

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_l1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => l1_struct_0(A) ) ),
    file(lang1,l1_lang1),
    []).

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

fof(dt_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ! [D] : 
          ( m1_dtconstr(D,A,B,C)
         => m5_trees_3(D,A,B) ) ) ),
    file(dtconstr,m1_dtconstr),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    []).

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_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(dt_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

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

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_m3_trees_2,axiom,(
    ! [A,B] : 
      ( m3_trees_2(B,A)
     => v1_relat_1(B) ) ),
    file(trees_2,m3_trees_2),
    []).

fof(dt_m4_trees_3,axiom,(
    $true ),
    file(trees_3,m4_trees_3),
    []).

fof(dt_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ! [C] : 
          ( m5_trees_3(C,A,B)
         => ( v1_funct_1(C)
            & v3_trees_2(C)
            & m3_trees_2(C,A) ) ) ) ),
    file(trees_3,m5_trees_3),
    []).

fof(dt_u1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => m2_relset_1(u1_lang1(A),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ),
    file(lang1,u1_lang1),
    []).

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

fof(existence_l1_lang1,axiom,(
    ? [A] : l1_lang1(A) ),
    file(lang1,l1_lang1),
    []).

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

fof(existence_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ? [D] : m1_dtconstr(D,A,B,C) ) ),
    file(dtconstr,m1_dtconstr),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    []).

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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) ),
    file(finseq_2,m2_finseq_2),
    []).

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

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

fof(existence_m3_trees_2,axiom,(
    ! [A] : 
    ? [B] : m3_trees_2(B,A) ),
    file(trees_2,m3_trees_2),
    []).

fof(existence_m4_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m4_trees_3(B,A) ) ),
    file(trees_3,m4_trees_3),
    []).

fof(existence_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ? [C] : m5_trees_3(C,A,B) ) ),
    file(trees_3,m5_trees_3),
    []).

fof(fc17_trees_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) )
     => ( v1_relat_1(k10_finseq_1(A,B))
        & v1_funct_1(k10_finseq_1(A,B))
        & ~ v1_xboole_0(k10_finseq_1(A,B))
        & v1_finset_1(k10_finseq_1(A,B))
        & v1_finseq_1(k10_finseq_1(A,B))
        & v6_trees_3(k10_finseq_1(A,B)) ) ) ),
    file(trees_3,fc17_trees_3),
    []).

fof(fc1_ami_2,axiom,
    ( ~ v1_xboole_0(k2_ami_2)
    & v1_membered(k2_ami_2)
    & v2_membered(k2_ami_2)
    & v3_membered(k2_ami_2)
    & v4_membered(k2_ami_2)
    & v5_membered(k2_ami_2) ),
    file(ami_2,fc1_ami_2),
    []).

fof(fc1_dtconstr,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,k3_finseq_2(A)) )
     => ( ~ v3_struct_0(g1_lang1(A,B))
        & v1_lang1(g1_lang1(A,B)) ) ) ),
    file(dtconstr,fc1_dtconstr),
    []).

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

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_dtconstr(A)
        & l1_lang1(A) )
     => ( ~ v1_xboole_0(k4_dtconstr(A))
        & v3_trees_3(k4_dtconstr(A)) ) ) ),
    file(dtconstr,fc2_dtconstr),
    []).

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

fof(fc3_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_dtconstr(A)
        & l1_lang1(A) )
     => ( ~ v1_xboole_0(k4_dtconstr(A))
        & v3_trees_3(k4_dtconstr(A)) ) ) ),
    file(dtconstr,fc3_dtconstr),
    []).

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(fc6_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k5_trees_3(A))
        & v3_trees_3(k5_trees_3(A)) ) ) ),
    file(trees_3,fc6_trees_3),
    []).

fof(free_g1_lang1,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,k3_finseq_2(A))
     => ! [C,D] : 
          ( g1_lang1(A,B) = g1_lang1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(lang1,g1_lang1),
    []).

fof(idempotence_k1_limfunc1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_limfunc1(A,A) = A ) ),
    file(limfunc1,k1_limfunc1),
    []).

fof(idempotence_k2_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => k2_square_1(A,A) = A ) ),
    file(square_1,k2_square_1),
    []).

fof(l35_scm_comp,axiom,
    ( ! [A] : 
        ( m1_struct_0(A,k1_scm_comp,k6_dtconstr(k1_scm_comp))
       => k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,c11__scm_comp,k3_scm_comp(A)) = k16_scm_comp(A) )
    & ! [A] : 
        ( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp))
       => ! [B] : 
            ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
           => ! [C] : 
                ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(k1_scm_comp))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(k1_scm_comp))
                       => ( ( D = k1_bintree1(u1_struct_0(k1_scm_comp),B)
                            & E = k1_bintree1(u1_struct_0(k1_scm_comp),C)
                            & r1_lang1(k1_scm_comp,A,k4_lang1(u1_struct_0(k1_scm_comp),D,E)) )
                         => ! [F] : 
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( ( F = k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,c11__scm_comp,B)
                                      & G = k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,c11__scm_comp,C) )
                                   => k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,c11__scm_comp,k2_scm_comp(A,B,C)) = k1_limfunc1(F,G) ) ) ) ) ) ) ) ) ) ),
    file(scm_comp,l35_scm_comp),
    []).

fof(l37_scm_comp,axiom,(
    k7_dtconstr(k1_scm_comp) = k2_zfmisc_1(1,5) ),
    file(scm_comp,l37_scm_comp),
    []).

fof(rc1_dtconstr,axiom,(
    ? [A] : 
      ( l1_lang1(A)
      & ~ v3_struct_0(A)
      & v1_lang1(A)
      & v1_dtconstr(A)
      & v2_dtconstr(A)
      & v3_dtconstr(A) ) ),
    file(dtconstr,rc1_dtconstr),
    []).

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_int_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    []).

fof(rc1_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_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_bintree1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m3_trees_2(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v3_trees_2(B)
          & v2_bintree1(B) ) ) ),
    file(bintree1,rc2_bintree1),
    []).

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_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    []).

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

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_trees_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v3_trees_3(A) ) ),
    file(trees_3,rc2_trees_3),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_bintree1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v3_trees_2(A)
      & v2_bintree1(A) ) ),
    file(bintree1,rc3_bintree1),
    []).

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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

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

fof(rc4_bintree1,axiom,(
    ? [A] : 
      ( l1_lang1(A)
      & ~ v3_struct_0(A)
      & v1_lang1(A)
      & v1_dtconstr(A)
      & v2_dtconstr(A)
      & v3_dtconstr(A)
      & v3_bintree1(A) ) ),
    file(bintree1,rc4_bintree1),
    []).

fof(rc4_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m4_trees_3(B,A)
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v3_trees_3(B) ) ) ),
    file(trees_3,rc4_trees_3),
    []).

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

fof(rc6_trees_3,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v6_trees_3(A) ) ),
    file(trees_3,rc6_trees_3),
    []).

fof(rc8_trees_3,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v6_trees_3(A) ) ),
    file(trees_3,rc8_trees_3),
    []).

fof(redefinition_k1_limfunc1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_limfunc1(A,B) = k2_square_1(A,B) ) ),
    file(limfunc1,k1_limfunc1),
    []).

fof(redefinition_k2_scm_comp,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp))
        & m1_subset_1(B,k4_dtconstr(k1_scm_comp))
        & m1_subset_1(C,k4_dtconstr(k1_scm_comp)) )
     => k2_scm_comp(A,B,C) = k6_trees_4(A,B,C) ) ),
    file(scm_comp,k2_scm_comp),
    []).

fof(redefinition_k3_finseq_2,axiom,(
    ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ),
    file(finseq_2,k3_finseq_2),
    []).

fof(redefinition_k3_scm_comp,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_dtconstr(k1_scm_comp))
     => k3_scm_comp(A) = k1_trees_4(A) ) ),
    file(scm_comp,k3_scm_comp),
    []).

fof(redefinition_k4_lang1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k4_lang1(A,B,C) = k10_finseq_1(B,C) ) ),
    file(lang1,k4_lang1),
    []).

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

fof(redefinition_k6_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_dtconstr(A)
        & l1_lang1(A) )
     => k6_dtconstr(A) = k5_lang1(A) ) ),
    file(dtconstr,k6_dtconstr),
    []).

fof(redefinition_k7_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_dtconstr(A)
        & l1_lang1(A) )
     => k7_dtconstr(A) = k6_lang1(A) ) ),
    file(dtconstr,k7_dtconstr),
    []).

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_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ! [D] : 
          ( m1_dtconstr(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(dtconstr,m1_dtconstr),
    []).

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_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(redefinition_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(redefinition_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ! [C] : 
          ( m5_trees_3(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(trees_3,m5_trees_3),
    []).

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

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(spc5_boole,axiom,(
    ~ v1_xboole_0(5) ),
    file(boole,spc5_boole),
    []).

fof(spc5_numerals,axiom,
    ( v2_xreal_0(5)
    & m1_subset_1(5,k5_numbers) ),
    file(numerals,spc5_numerals),
    []).

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

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

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),
    []).