% Mizar problem: t7_freealg,freealg,1282,32 
fof(t7_freealg,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_relat_1(A)
        & m1_trees_4(A,k1_numbers,k5_numbers) )
     => ! [B] : 
          ( v1_freealg(B)
         => k3_unialg_1(k15_freealg(A,B)) = A ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,abstractness_v3_unialg_1,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_arytm_3,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_dtconstr,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc4_trees_3,cc5_trees_3,cc6_membered,cc9_membered,commutativity_k2_xboole_0,d11_unialg_1,d17_freealg,d18_freealg,d19_freealg,d3_finseq_1,d4_finseq_4,d9_freealg,dt_g1_lang1,dt_g1_unialg_1,dt_k12_trees_4,dt_k13_finseq_1,dt_k13_freealg,dt_k14_freealg,dt_k15_freealg,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finseq_1,dt_k2_freealg,dt_k2_unialg_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_freealg,dt_k3_unialg_1,dt_k4_dtconstr,dt_k4_finseq_1,dt_k4_finseq_2,dt_k4_finseq_4,dt_k4_freealg,dt_k4_partfun1,dt_k4_relset_1,dt_k4_trees_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_trees_3,dt_l1_lang1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m1_trees_4,dt_m2_finseq_1,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,dt_u1_unialg_1,existence_l1_lang1,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m1_trees_4,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_trees_2,existence_m4_trees_3,existence_m5_trees_3,fc16_finseq_1,fc17_finseq_1,fc1_dtconstr,fc1_finseq_1,fc1_finseq_2,fc1_freealg,fc1_ordinal2,fc1_partfun1,fc1_struct_0,fc1_subset_1,fc1_unialg_1,fc1_xboole_0,fc22_membered,fc22_trees_3,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc26_trees_3,fc2_dtconstr,fc2_finseq_1,fc2_freealg,fc2_membered,fc2_unialg_1,fc2_xboole_0,fc3_dtconstr,fc3_freealg,fc3_unialg_1,fc3_xboole_0,fc4_freealg,fc4_prvect_1,fc4_subset_1,fc4_unialg_1,fc5_membered,fc5_prvect_1,fc6_membered,fc6_trees_3,fc9_finseq_1,free_g1_lang1,free_g1_unialg_1,idempotence_k2_xboole_0,rc1_arytm_3,rc1_dtconstr,rc1_finseq_1,rc1_finseq_2,rc1_freealg,rc1_membered,rc1_partfun1,rc1_prvect_1,rc1_subset_1,rc1_unialg_1,rc1_xboole_0,rc2_finseq_1,rc2_freealg,rc2_partfun1,rc2_subset_1,rc2_trees_3,rc2_unialg_1,rc2_xboole_0,rc3_finseq_1,rc3_freealg,rc3_struct_0,rc3_unialg_1,rc4_finseq_1,rc4_trees_3,rc4_unialg_1,rc5_struct_0,rc5_unialg_1,rc6_finseq_1,rc6_trees_3,rc7_finseq_1,rc8_finseq_1,rc8_trees_3,redefinition_k12_trees_4,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_m1_trees_4,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m5_trees_3,reflexivity_r1_tarski,t10_finseq_2,t1_boole,t1_pralg_1,t1_subset,t2_subset,t2_unialg_2,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(freealg,t7_freealg)]).

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(abstractness_v3_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => ( v3_unialg_1(A)
       => A = g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) ) ) ),
    file(unialg_1,v3_unialg_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(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_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

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

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

fof(cc1_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_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc2_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_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

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

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

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_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_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_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d11_unialg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( B = k3_unialg_1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(u1_unialg_1(A))
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => ! [D] : 
                        ( ( ~ v1_xboole_0(D)
                          & v1_funct_1(D)
                          & v1_unialg_1(D,u1_struct_0(A))
                          & m2_relset_1(D,k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) )
                       => ( D = k1_funct_1(u1_unialg_1(A),C)
                         => k1_funct_1(B,C) = k2_unialg_1(u1_struct_0(A),D) ) ) ) ) ) ) ) ) ),
    file(unialg_1,d11_unialg_1),
    []).

fof(d17_freealg,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_relat_1(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( v1_freealg(B)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(C,k4_finseq_1(A))
               => ! [D] : 
                    ( ( ~ v1_xboole_0(D)
                      & v1_funct_1(D)
                      & v1_unialg_1(D,k4_dtconstr(k3_freealg(A,B)))
                      & v2_unialg_1(D,k4_dtconstr(k3_freealg(A,B)))
                      & m2_relset_1(D,k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))) )
                   => ( D = k13_freealg(A,B,C)
                    <=> ( k4_relset_1(k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)),D) = k4_finseq_2(k4_finseq_4(k5_numbers,k5_numbers,A,C),k4_dtconstr(k3_freealg(A,B)))
                        & ! [E] : 
                            ( m1_trees_4(E,k5_trees_3(u1_struct_0(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)))
                           => ( r2_hidden(E,k4_relset_1(k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)),D))
                             => k1_funct_1(D,E) = k12_trees_4(u1_struct_0(k3_freealg(A,B)),k4_freealg(A,B,C),E) ) ) ) ) ) ) ) ) ) ),
    file(freealg,d17_freealg),
    []).

fof(d18_freealg,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_relat_1(A)
        & m1_trees_4(A,k1_numbers,k5_numbers) )
     => ! [B] : 
          ( v1_freealg(B)
         => ! [C] : 
              ( m2_finseq_1(C,k4_partfun1(k13_finseq_1(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))))
             => ( C = k14_freealg(A,B)
              <=> ( k3_finseq_1(C) = k3_finseq_1(A)
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(C))
                       => k1_funct_1(C,D) = k13_freealg(A,B,D) ) ) ) ) ) ) ) ),
    file(freealg,d18_freealg),
    []).

fof(d19_freealg,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_relat_1(A)
        & m1_trees_4(A,k1_numbers,k5_numbers) )
     => ! [B] : 
          ( v1_freealg(B)
         => k15_freealg(A,B) = g1_unialg_1(k4_dtconstr(k3_freealg(A,B)),k14_freealg(A,B)) ) ) ),
    file(freealg,d19_freealg),
    []).

fof(d3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    []).

fof(d4_finseq_4,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( r2_hidden(D,k1_relat_1(C))
         => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ),
    file(finseq_4,d4_finseq_4),
    []).

fof(d9_freealg,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_trees_4(A,k1_numbers,k5_numbers) )
     => ! [B] : k3_freealg(A,B) = g1_lang1(k2_xboole_0(k4_finseq_1(A),B),k2_freealg(A,B)) ) ),
    file(freealg,d9_freealg),
    []).

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_g1_unialg_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
     => ( v3_unialg_1(g1_unialg_1(A,B))
        & l1_unialg_1(g1_unialg_1(A,B)) ) ) ),
    file(unialg_1,g1_unialg_1),
    []).

fof(dt_k12_trees_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_finseq_1(C,k5_trees_3(A)) )
     => m5_trees_3(k12_trees_4(A,B,C),A,k5_trees_3(A)) ) ),
    file(trees_4,k12_trees_4),
    []).

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

fof(dt_k13_freealg,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_relat_1(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_freealg(B)
        & m1_subset_1(C,k5_numbers) )
     => ( ~ v1_xboole_0(k13_freealg(A,B,C))
        & v1_funct_1(k13_freealg(A,B,C))
        & v1_unialg_1(k13_freealg(A,B,C),k4_dtconstr(k3_freealg(A,B)))
        & v2_unialg_1(k13_freealg(A,B,C),k4_dtconstr(k3_freealg(A,B)))
        & m2_relset_1(k13_freealg(A,B,C),k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))) ) ) ),
    file(freealg,k13_freealg),
    []).

fof(dt_k14_freealg,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_relat_1(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_freealg(B) )
     => m2_finseq_1(k14_freealg(A,B),k4_partfun1(k13_finseq_1(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)))) ) ),
    file(freealg,k14_freealg),
    []).

fof(dt_k15_freealg,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_relat_1(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_freealg(B) )
     => ( ~ v3_struct_0(k15_freealg(A,B))
        & v3_unialg_1(k15_freealg(A,B))
        & v6_unialg_1(k15_freealg(A,B))
        & v7_unialg_1(k15_freealg(A,B))
        & v8_unialg_1(k15_freealg(A,B))
        & l1_unialg_1(k15_freealg(A,B)) ) ) ),
    file(freealg,k15_freealg),
    []).

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

fof(dt_k1_finseq_1,axiom,(
    $true ),
    file(finseq_1,k1_finseq_1),
    []).

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

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

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_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_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k2_finseq_1),
    []).

fof(dt_k2_freealg,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k5_numbers) )
     => m2_relset_1(k2_freealg(A,B),k2_xboole_0(k4_finseq_1(A),B),k3_finseq_2(k2_xboole_0(k4_finseq_1(A),B))) ) ),
    file(freealg,k2_freealg),
    []).

fof(dt_k2_unialg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(B)
        & v1_unialg_1(B,A)
        & m1_relset_1(B,k13_finseq_1(A),A) )
     => m2_subset_1(k2_unialg_1(A,B),k1_numbers,k5_numbers) ) ),
    file(unialg_1,k2_unialg_1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

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

fof(dt_k3_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_freealg,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_lang1(k3_freealg(A,B))
        & l1_lang1(k3_freealg(A,B)) ) ) ),
    file(freealg,k3_freealg),
    []).

fof(dt_k3_unialg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m2_finseq_1(k3_unialg_1(A),k5_numbers) ) ),
    file(unialg_1,k3_unialg_1),
    []).

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_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    []).

fof(dt_k4_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) ),
    file(finseq_2,k4_finseq_2),
    []).

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    []).

fof(dt_k4_freealg,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k4_freealg(A,B,C),u1_struct_0(k3_freealg(A,B))) ) ),
    file(freealg,k4_freealg),
    []).

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

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

fof(dt_k4_trees_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k4_trees_4(A,B))
        & v1_funct_1(k4_trees_4(A,B))
        & v3_trees_2(k4_trees_4(A,B)) ) ) ),
    file(trees_4,k4_trees_4),
    []).

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_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_l1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => l1_struct_0(A) ) ),
    file(unialg_1,l1_unialg_1),
    []).

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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m1_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m1_trees_4(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(trees_4,m1_trees_4),
    []).

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_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(dt_u1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => m2_finseq_1(u1_unialg_1(A),k4_partfun1(k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))) ) ),
    file(unialg_1,u1_unialg_1),
    []).

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_l1_unialg_1,axiom,(
    ? [A] : l1_unialg_1(A) ),
    file(unialg_1,l1_unialg_1),
    []).

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_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m1_trees_4(C,A,B) ) ),
    file(trees_4,m1_trees_4),
    []).

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

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(fc16_finseq_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k13_finseq_1(A))
      & v1_fraenkel(k13_finseq_1(A)) ) ),
    file(finseq_1,fc16_finseq_1),
    []).

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

fof(fc1_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_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    []).

fof(fc1_finseq_2,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k4_finseq_2(A,B)) ) ),
    file(finseq_2,fc1_finseq_2),
    []).

fof(fc1_freealg,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( ~ v3_struct_0(k3_freealg(A,B))
        & v1_lang1(k3_freealg(A,B)) ) ) ),
    file(freealg,fc1_freealg),
    []).

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

fof(fc1_partfun1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ),
    file(partfun1,fc1_partfun1),
    []).

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

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

fof(fc1_unialg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) )
     => ( ~ v3_struct_0(g1_unialg_1(A,B))
        & v3_unialg_1(g1_unialg_1(A,B)) ) ) ),
    file(unialg_1,fc1_unialg_1),
    []).

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

fof(fc22_membered,axiom,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    []).

fof(fc22_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_trees_1(B) )
     => ( ~ v1_xboole_0(k2_xboole_0(A,B))
        & v1_trees_1(k2_xboole_0(A,B)) ) ) ),
    file(trees_3,fc22_trees_3),
    []).

fof(fc23_membered,axiom,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    []).

fof(fc24_membered,axiom,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    []).

fof(fc25_membered,axiom,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    []).

fof(fc26_membered,axiom,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    []).

fof(fc26_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_trees_3(A)) )
     => ( ~ v1_xboole_0(k1_relat_1(B))
        & v1_finset_1(k1_relat_1(B))
        & v1_trees_1(k1_relat_1(B)) ) ) ),
    file(trees_3,fc26_trees_3),
    []).

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_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_freealg,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( ~ v3_struct_0(k3_freealg(A,B))
        & v1_lang1(k3_freealg(A,B))
        & v2_dtconstr(k3_freealg(A,B)) ) ) ),
    file(freealg,fc2_freealg),
    []).

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

fof(fc2_unialg_1,axiom,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A))
        & v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) ) ) ),
    file(unialg_1,fc2_unialg_1),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

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(fc3_freealg,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v2_relat_1(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( ~ v3_struct_0(k3_freealg(A,B))
        & v1_lang1(k3_freealg(A,B))
        & v2_dtconstr(k3_freealg(A,B))
        & v3_dtconstr(k3_freealg(A,B)) ) ) ),
    file(freealg,fc3_freealg),
    []).

fof(fc3_unialg_1,axiom,(
    ! [A] : 
      ( ( v7_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A))
        & v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) ) ) ),
    file(unialg_1,fc3_unialg_1),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc4_freealg,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k5_numbers)
        & ~ v1_xboole_0(B)
        & v1_freealg(B) )
     => ( ~ v3_struct_0(k3_freealg(A,B))
        & v1_lang1(k3_freealg(A,B))
        & v1_dtconstr(k3_freealg(A,B))
        & v2_dtconstr(k3_freealg(A,B))
        & v3_dtconstr(k3_freealg(A,B)) ) ) ),
    file(freealg,fc4_freealg),
    []).

fof(fc4_prvect_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(prvect_1,fc4_prvect_1),
    []).

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(fc4_unialg_1,axiom,(
    ! [A] : 
      ( ( v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( ~ v1_xboole_0(u1_unialg_1(A))
        & v1_relat_1(u1_unialg_1(A))
        & v2_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A)) ) ) ),
    file(unialg_1,fc4_unialg_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(fc5_prvect_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_relat_1(A)) )
     => ~ v1_xboole_0(k1_funct_1(A,B)) ) ),
    file(prvect_1,fc5_prvect_1),
    []).

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(fc9_finseq_1,axiom,(
    ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ),
    file(finseq_1,fc9_finseq_1),
    []).

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(free_g1_unialg_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
     => ! [C,D] : 
          ( g1_unialg_1(A,B) = g1_unialg_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(unialg_1,g1_unialg_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(rc1_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_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_2(B,A)
      & ~ v1_xboole_0(B) ) ),
    file(finseq_2,rc1_finseq_2),
    []).

fof(rc1_freealg,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_freealg(A) ) ),
    file(freealg,rc1_freealg),
    []).

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_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_prvect_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(prvect_1,rc1_prvect_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_unialg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_relset_1(B,k13_finseq_1(A),A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_unialg_1(B,A)
          & v2_unialg_1(B,A) ) ) ),
    file(unialg_1,rc1_unialg_1),
    []).

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

fof(rc2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    []).

fof(rc2_freealg,axiom,(
    ? [A] : 
      ( m1_finseq_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & ~ v2_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(freealg,rc2_freealg),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

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

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

fof(rc2_unialg_1,axiom,(
    ? [A] : 
      ( l1_unialg_1(A)
      & v3_unialg_1(A) ) ),
    file(unialg_1,rc2_unialg_1),
    []).

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

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc3_freealg,axiom,(
    ? [A] : 
      ( m1_finseq_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(freealg,rc3_freealg),
    []).

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

fof(rc3_unialg_1,axiom,(
    ? [A] : 
      ( l1_unialg_1(A)
      & ~ v3_struct_0(A)
      & v3_unialg_1(A) ) ),
    file(unialg_1,rc3_unialg_1),
    []).

fof(rc4_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_1),
    []).

fof(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(rc4_unialg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
          & v1_relat_1(B)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B)
          & v4_unialg_1(B,A)
          & v5_unialg_1(B,A) ) ) ),
    file(unialg_1,rc4_unialg_1),
    []).

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

fof(rc5_unialg_1,axiom,(
    ? [A] : 
      ( l1_unialg_1(A)
      & ~ v3_struct_0(A)
      & v3_unialg_1(A)
      & v6_unialg_1(A)
      & v7_unialg_1(A)
      & v8_unialg_1(A) ) ),
    file(unialg_1,rc5_unialg_1),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc6_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(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(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_k12_trees_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_finseq_1(C,k5_trees_3(A)) )
     => k12_trees_4(A,B,C) = k4_trees_4(B,C) ) ),
    file(trees_4,k12_trees_4),
    []).

fof(redefinition_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k1_finseq_1(A) ) ),
    file(finseq_1,k2_finseq_1),
    []).

fof(redefinition_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    []).

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

fof(redefinition_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k4_finseq_1(A) = k1_relat_1(A) ) ),
    file(finseq_1,k4_finseq_1),
    []).

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

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

fof(redefinition_m1_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m1_trees_4(C,A,B)
        <=> m1_finseq_1(C,B) ) ) ),
    file(trees_4,m1_trees_4),
    []).

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_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(t10_finseq_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k3_finseq_1(B) = A
                  & k3_finseq_1(C) = A
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k2_finseq_1(A))
                       => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) )
               => B = C ) ) ) ) ),
    file(finseq_2,t10_finseq_2),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_pralg_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( k4_finseq_2(C,A) = k4_finseq_2(D,B)
                   => C = D ) ) ) ) ) ),
    file(pralg_1,t1_pralg_1),
    []).

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(t2_unialg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_funct_1(B)
            & v1_unialg_1(B,A)
            & v2_unialg_1(B,A)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => k1_relat_1(B) = k4_finseq_2(k2_unialg_1(A,B),A) ) ) ),
    file(unialg_2,t2_unialg_2),
    []).

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),
    []).