% Mizar problem: t59_groeb_3,groeb_3,3324,31 
fof(t59_groeb_3,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v6_vectsp_1(C)
                & v7_vectsp_1(C)
                & v8_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                 => ( ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                          & v2_polynom1(E,k14_polynom1(A),C)
                          & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                       => ! [F] : 
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
                              & v2_polynom1(F,k14_polynom1(A),C)
                              & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
                           => ! [G] : 
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,k14_polynom1(A),u1_struct_0(C))
                                  & v2_polynom1(G,k14_polynom1(A),C)
                                  & m2_relset_1(G,k14_polynom1(A),u1_struct_0(C)) )
                               => ( ( r2_hidden(E,D)
                                    & r2_hidden(F,D)
                                    & r4_rewrite1(k3_polyred(A,B,C,D),k3_groeb_2(A,B,C,E,F),G) )
                                 => ( r1_groeb_2(A,k3_termord(A,B,C,E),k3_termord(A,B,C,F))
                                    | G = k26_polynom1(A,C) ) ) ) ) )
                   => ( r2_hidden(k26_polynom1(A,C),D)
                      | r1_groeb_1(A,B,C,D) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc1_algstr_1,cc1_binom,cc1_card_1,cc1_finset_1,cc1_polynom4,cc1_polynom7,cc1_relset_1,cc1_termord,cc1_vectsp_1,cc1_xreal_0,cc2_algstr_1,cc2_binom,cc2_card_1,cc2_finset_1,cc2_int_1,cc2_polynom1,cc2_vectsp_1,cc2_xreal_0,cc3_algstr_1,cc3_binom,cc3_card_1,cc3_int_1,cc3_polynom1,cc3_polynom7,cc3_vectsp_1,cc3_xreal_0,cc4_algstr_1,cc4_binom,cc4_int_1,cc4_polynom1,cc4_polynom7,cc4_vectsp_1,cc4_xreal_0,cc5_binom,cc5_polynom1,cc5_vectsp_1,cc5_xreal_0,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_groeb_3,commutativity_k2_tarski,d11_rewrite1,d14_rewrite1,d2_tarski,d3_tarski,d6_rewrite1,dt_g3_vectsp_1,dt_k13_polynom1,dt_k14_polynom1,dt_k1_groeb_3,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k26_polynom1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k30_polynom1,dt_k3_groeb_2,dt_k3_polyred,dt_k3_relat_1,dt_k3_termord,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_pboole,dt_m1_polynom1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_group_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u1_vectsp_1,dt_u2_struct_0,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_pboole,existence_m1_polynom1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc12_finset_1,fc14_finset_1,fc14_polynom1,fc1_finset_1,fc1_polynom1,fc1_polynom7,fc1_struct_0,fc20_polynom1,fc25_polynom1,fc2_finset_1,fc35_polynom1,fc38_polynom1,fc39_polynom1,fc3_polynom1,fc3_polynom2,fc40_polynom1,fc41_polynom1,fc42_polynom1,fc43_polynom1,fc44_polynom1,fc5_polyred,free_g3_vectsp_1,l11_groeb_3,rc10_polynom1,rc10_vectsp_1,rc11_polynom1,rc12_polynom1,rc13_polynom1,rc14_polynom1,rc1_binom,rc1_card_1,rc1_finset_1,rc1_int_1,rc1_polynom2,rc1_polynom4,rc1_polynom7,rc1_termord,rc1_xreal_0,rc2_binom,rc2_card_1,rc2_finset_1,rc2_int_1,rc2_polynom1,rc2_polynom7,rc2_polyred,rc2_termord,rc2_xreal_0,rc3_binom,rc3_finset_1,rc3_struct_0,rc3_termord,rc3_xreal_0,rc4_binom,rc4_finset_1,rc4_struct_0,rc4_xreal_0,rc5_struct_0,rc6_polynom1,rc6_vectsp_1,rc7_polynom1,rc7_polynom7,rc7_vectsp_1,rc8_polynom1,rc8_polynom7,rc8_vectsp_1,rc9_polynom1,rc9_vectsp_1,redefinition_k14_polynom1,redefinition_k1_groeb_3,redefinition_k5_numbers,redefinition_m1_polynom1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,t1_subset,t23_rewrite1,t2_subset,t30_groeb_2,t3_boole,t3_subset,t47_rewrite1,t4_boole,t4_groeb_1,t4_subset,t56_groeb_3,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(groeb_3,t59_groeb_3)]).

fof(abstractness_v3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( v3_vectsp_1(A)
       => A = g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) ) ) ),
    file(vectsp_1,v3_vectsp_1),
    []).

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

fof(cc1_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) ) ) ) ),
    file(algstr_1,cc1_algstr_1),
    []).

fof(cc1_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_binom(A) ) ) ) ),
    file(binom,cc1_binom),
    []).

fof(cc1_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_polynom4,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & v4_vectsp_1(A)
          & v8_vectsp_1(A)
          & v9_vectsp_1(A)
          & v1_algstr_1(A)
          & v3_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & v4_vectsp_1(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A)
          & v2_vectsp_2(A)
          & v1_algstr_1(A)
          & v3_algstr_1(A) ) ) ) ),
    file(polynom4,cc1_polynom4),
    []).

fof(cc1_polynom7,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => ( ~ v3_realset2(A)
       => ~ v3_struct_0(A) ) ) ),
    file(polynom7,cc1_polynom7),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc1_termord,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ! [B] : 
          ( m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
         => ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
              & v1_relat_2(B)
              & v4_relat_2(B)
              & v8_relat_2(B)
              & v2_bagorder(B,A) )
           => ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
              & v1_relat_2(B)
              & v4_relat_2(B)
              & v8_relat_2(B)
              & v2_bagorder(B,A)
              & v1_wellord1(B) ) ) ) ) ),
    file(termord,cc1_termord),
    []).

fof(cc1_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc1_vectsp_1),
    []).

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

fof(cc2_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc2_algstr_1),
    []).

fof(cc2_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_binom(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A) ) ) ) ),
    file(binom,cc2_binom),
    []).

fof(cc2_card_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc2_card_1),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_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_polynom1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v10_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A) ) ) ) ),
    file(polynom1,cc2_polynom1),
    []).

fof(cc2_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc2_vectsp_1),
    []).

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

fof(cc3_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_rlvect_1(A) ) ) ) ),
    file(algstr_1,cc3_algstr_1),
    []).

fof(cc3_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v3_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A) ) ) ) ),
    file(binom,cc3_binom),
    []).

fof(cc3_card_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_finset_1(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc3_card_1),
    []).

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

fof(cc3_polynom1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v7_seqm_3(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) ) ) ),
    file(polynom1,cc3_polynom1),
    []).

fof(cc3_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
              & v3_polynom7(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
              & v2_polynom1(C,k14_polynom1(A),B) ) ) ) ) ),
    file(polynom7,cc3_polynom7),
    []).

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

fof(cc4_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_algstr_1(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc4_algstr_1),
    []).

fof(cc4_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v2_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v3_algstr_1(A) ) ) ) ),
    file(binom,cc4_binom),
    []).

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_polynom1,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,k5_numbers)
     => ( ( v1_funct_1(B)
          & v1_funct_2(B,A,k5_numbers) )
       => ( v1_funct_1(B)
          & v1_funct_2(B,A,k5_numbers)
          & v7_seqm_3(B) ) ) ) ),
    file(polynom1,cc4_polynom1),
    []).

fof(cc4_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
              & v4_polynom7(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
              & v2_polynom1(C,k14_polynom1(A),B)
              & v3_polynom7(C,A,B) ) ) ) ) ),
    file(polynom7,cc4_polynom7),
    []).

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

fof(cc5_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A) )
       => ( ~ v3_struct_0(A)
          & v3_algstr_1(A) ) ) ) ),
    file(binom,cc5_binom),
    []).

fof(cc5_polynom1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_polynom1(A) ) ) ),
    file(polynom1,cc5_polynom1),
    []).

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

fof(cc6_polynom1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => v1_polynom1(B) ) ) ),
    file(polynom1,cc6_polynom1),
    []).

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

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

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

fof(commutativity_k1_groeb_3,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(D,k14_polynom1(A),B)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => k1_groeb_3(A,B,C,D) = k1_groeb_3(A,B,D,C) ) ),
    file(groeb_3,k1_groeb_3),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d11_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r9_rewrite1(A,B)
        <=> ? [C] : r4_rewrite1(A,B,C) ) ) ),
    file(rewrite1,d11_rewrite1),
    []).

fof(d14_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_rewrite1(A)
      <=> ! [B] : 
            ( r2_hidden(B,k3_relat_1(A))
           => r9_rewrite1(A,B) ) ) ) ),
    file(rewrite1,d14_rewrite1),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

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

fof(d6_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r4_rewrite1(A,B,C)
        <=> ( r3_rewrite1(A,C)
            & r1_rewrite1(A,B,C) ) ) ) ),
    file(rewrite1,d6_rewrite1),
    []).

fof(dt_g3_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( 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)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ( v3_vectsp_1(g3_vectsp_1(A,B,C,D,E))
        & l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ),
    file(vectsp_1,g3_vectsp_1),
    []).

fof(dt_k13_polynom1,axiom,(
    $true ),
    file(polynom1,k13_polynom1),
    []).

fof(dt_k14_polynom1,axiom,(
    ! [A] : m1_subset_1(k14_polynom1(A),k1_zfmisc_1(k13_polynom1(A))) ),
    file(polynom1,k14_polynom1),
    []).

fof(dt_k1_groeb_3,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(D,k14_polynom1(A),B)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => ( ~ v1_xboole_0(k1_groeb_3(A,B,C,D))
        & v1_finset_1(k1_groeb_3(A,B,C,D))
        & m1_subset_1(k1_groeb_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k30_polynom1(A,B)))) ) ) ),
    file(groeb_3,k1_groeb_3),
    []).

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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

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

fof(dt_k26_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ( v1_funct_1(k26_polynom1(A,B))
        & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
        & m2_relset_1(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) ) ) ),
    file(polynom1,k26_polynom1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k30_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B))
        & l3_vectsp_1(k30_polynom1(A,B)) ) ) ),
    file(polynom1,k30_polynom1),
    []).

fof(dt_k3_groeb_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & v2_group_1(C)
        & v4_group_1(C)
        & v7_group_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v7_vectsp_1(C)
        & v9_vectsp_1(C)
        & ~ v3_realset2(C)
        & l3_vectsp_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(A),C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C))
        & v1_funct_1(E)
        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(E,k14_polynom1(A),C)
        & m1_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_funct_1(k3_groeb_2(A,B,C,D,E))
        & v1_funct_2(k3_groeb_2(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k3_groeb_2(A,B,C,D,E),k14_polynom1(A),C)
        & m2_relset_1(k3_groeb_2(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C)) ) ) ),
    file(groeb_2,k3_groeb_2),
    []).

fof(dt_k3_polyred,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & v2_group_1(C)
        & v4_group_1(C)
        & v7_group_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v7_vectsp_1(C)
        & v9_vectsp_1(C)
        & ~ v3_realset2(C)
        & l3_vectsp_1(C)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) )
     => m2_relset_1(k3_polyred(A,B,C,D),k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C))) ) ),
    file(polyred,k3_polyred),
    []).

fof(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    []).

fof(dt_k3_termord,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & ~ v3_struct_0(C)
        & l2_struct_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(A),C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => m1_polynom1(k3_termord(A,B,C,D),A,k14_polynom1(A)) ) ),
    file(termord,k3_termord),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

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_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_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_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

fof(dt_m1_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) )
     => ! [C] : 
          ( m1_polynom1(C,A,B)
         => ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) ) ) ) ),
    file(polynom1,m1_polynom1),
    []).

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_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(dt_u1_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_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_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_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_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

fof(existence_m1_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) )
     => ? [C] : m1_polynom1(C,A,B) ) ),
    file(polynom1,m1_polynom1),
    []).

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_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(fc12_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc14_polynom1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(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)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0) ),
    file(polynom1,fc14_polynom1),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_polynom1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & 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)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ( ~ v3_struct_0(g3_vectsp_1(A,B,C,D,E))
        & v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ),
    file(polynom1,fc1_polynom1),
    []).

fof(fc1_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ( v1_relat_1(k26_polynom1(A,B))
        & v1_funct_1(k26_polynom1(A,B))
        & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k26_polynom1(A,B),k14_polynom1(A),B)
        & v3_polynom7(k26_polynom1(A,B),A,B)
        & v4_polynom7(k26_polynom1(A,B),A,B) ) ) ),
    file(polynom7,fc1_polynom7),
    []).

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(fc20_polynom1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(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)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0)
    & v1_polynom1(k1_xboole_0) ),
    file(polynom1,fc20_polynom1),
    []).

fof(fc25_polynom1,axiom,(
    ! [A] : ~ v1_xboole_0(k13_polynom1(A)) ),
    file(polynom1,fc25_polynom1),
    []).

fof(fc2_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    []).

fof(fc35_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ( v1_relat_1(k26_polynom1(A,B))
        & v1_funct_1(k26_polynom1(A,B))
        & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k26_polynom1(A,B),k14_polynom1(A),B) ) ) ),
    file(polynom1,fc35_polynom1),
    []).

fof(fc38_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v3_rlvect_1(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B)) ) ) ),
    file(polynom1,fc38_polynom1),
    []).

fof(fc39_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v4_rlvect_1(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B)) ) ) ),
    file(polynom1,fc39_polynom1),
    []).

fof(fc3_polynom1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(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)
    & v1_matrlin(k1_xboole_0) ),
    file(polynom1,fc3_polynom1),
    []).

fof(fc3_polynom2,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v4_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v3_rlvect_1(k30_polynom1(A,B))
        & v4_rlvect_1(k30_polynom1(A,B))
        & v5_rlvect_1(k30_polynom1(A,B))
        & v6_rlvect_1(k30_polynom1(A,B))
        & v2_group_1(k30_polynom1(A,B))
        & v4_group_1(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B))
        & v4_vectsp_1(k30_polynom1(A,B))
        & v6_vectsp_1(k30_polynom1(A,B))
        & v8_vectsp_1(k30_polynom1(A,B))
        & v1_algstr_1(k30_polynom1(A,B))
        & v2_algstr_1(k30_polynom1(A,B))
        & v3_algstr_1(k30_polynom1(A,B))
        & v4_algstr_1(k30_polynom1(A,B))
        & v5_algstr_1(k30_polynom1(A,B))
        & v6_algstr_1(k30_polynom1(A,B)) ) ) ),
    file(polynom2,fc3_polynom2),
    []).

fof(fc40_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v4_rlvect_1(k30_polynom1(A,B))
        & v5_rlvect_1(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B)) ) ) ),
    file(polynom1,fc40_polynom1),
    []).

fof(fc41_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v4_rlvect_1(k30_polynom1(A,B))
        & v5_rlvect_1(k30_polynom1(A,B))
        & v6_rlvect_1(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B))
        & v1_algstr_1(k30_polynom1(A,B))
        & v2_algstr_1(k30_polynom1(A,B))
        & v3_algstr_1(k30_polynom1(A,B))
        & v4_algstr_1(k30_polynom1(A,B))
        & v5_algstr_1(k30_polynom1(A,B))
        & v6_algstr_1(k30_polynom1(A,B)) ) ) ),
    file(polynom1,fc41_polynom1),
    []).

fof(fc42_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v3_rlvect_1(k30_polynom1(A,B))
        & v4_rlvect_1(k30_polynom1(A,B))
        & v5_rlvect_1(k30_polynom1(A,B))
        & v6_rlvect_1(k30_polynom1(A,B))
        & v7_group_1(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B))
        & v1_algstr_1(k30_polynom1(A,B))
        & v2_algstr_1(k30_polynom1(A,B))
        & v3_algstr_1(k30_polynom1(A,B))
        & v4_algstr_1(k30_polynom1(A,B))
        & v5_algstr_1(k30_polynom1(A,B))
        & v6_algstr_1(k30_polynom1(A,B)) ) ) ),
    file(polynom1,fc42_polynom1),
    []).

fof(fc43_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v4_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v3_rlvect_1(k30_polynom1(A,B))
        & v4_rlvect_1(k30_polynom1(A,B))
        & v5_rlvect_1(k30_polynom1(A,B))
        & v6_rlvect_1(k30_polynom1(A,B))
        & v4_group_1(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B))
        & v1_algstr_1(k30_polynom1(A,B))
        & v2_algstr_1(k30_polynom1(A,B))
        & v3_algstr_1(k30_polynom1(A,B))
        & v4_algstr_1(k30_polynom1(A,B))
        & v5_algstr_1(k30_polynom1(A,B))
        & v6_algstr_1(k30_polynom1(A,B)) ) ) ),
    file(polynom1,fc43_polynom1),
    []).

fof(fc44_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v4_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B) )
     => ( ~ v3_struct_0(k30_polynom1(A,B))
        & v3_rlvect_1(k30_polynom1(A,B))
        & v4_rlvect_1(k30_polynom1(A,B))
        & v5_rlvect_1(k30_polynom1(A,B))
        & v6_rlvect_1(k30_polynom1(A,B))
        & v2_group_1(k30_polynom1(A,B))
        & v4_group_1(k30_polynom1(A,B))
        & v3_vectsp_1(k30_polynom1(A,B))
        & v4_vectsp_1(k30_polynom1(A,B))
        & v6_vectsp_1(k30_polynom1(A,B))
        & v8_vectsp_1(k30_polynom1(A,B))
        & v1_algstr_1(k30_polynom1(A,B))
        & v2_algstr_1(k30_polynom1(A,B))
        & v3_algstr_1(k30_polynom1(A,B))
        & v4_algstr_1(k30_polynom1(A,B))
        & v5_algstr_1(k30_polynom1(A,B))
        & v6_algstr_1(k30_polynom1(A,B)) ) ) ),
    file(polynom1,fc44_polynom1),
    []).

fof(fc5_polyred,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v2_bagorder(B,A)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & ~ v3_struct_0(C)
        & v2_group_1(C)
        & v4_group_1(C)
        & v7_group_1(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v7_vectsp_1(C)
        & v9_vectsp_1(C)
        & ~ v10_vectsp_1(C)
        & l3_vectsp_1(C)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) )
     => ( v1_relat_1(k3_polyred(A,B,C,D))
        & v2_relat_2(k3_polyred(A,B,C,D))
        & v1_rewrite1(k3_polyred(A,B,C,D))
        & v2_rewrite1(k3_polyred(A,B,C,D))
        & v3_rewrite1(k3_polyred(A,B,C,D)) ) ) ),
    file(polyred,fc5_polyred),
    []).

fof(free_g3_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( 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)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ! [F,G,H,I,J] : 
          ( g3_vectsp_1(A,B,C,D,E) = g3_vectsp_1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) ),
    file(vectsp_1,g3_vectsp_1),
    []).

fof(l11_groeb_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] : 
              ( ( v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v6_vectsp_1(C)
                & v7_vectsp_1(C)
                & v8_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E,F] : 
                      ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                     => ( r1_rewrite1(k3_polyred(A,B,C,F),D,E)
                       => ( v1_funct_1(E)
                          & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                          & v2_polynom1(E,k14_polynom1(A),C)
                          & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) ) ) ) ) ) ) ) ),
    file(groeb_3,l11_groeb_3),
    []).

fof(rc10_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B) ) ),
    file(polynom1,rc10_polynom1),
    []).

fof(rc10_vectsp_1,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A) ) ),
    file(vectsp_1,rc10_vectsp_1),
    []).

fof(rc11_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_seq_1(A)
      & v7_seqm_3(A)
      & v1_polynom1(A) ) ),
    file(polynom1,rc11_polynom1),
    []).

fof(rc12_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,k5_numbers)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funct_2(B,A,k5_numbers)
      & v1_seq_1(B)
      & v7_seqm_3(B)
      & v1_polynom1(B) ) ),
    file(polynom1,rc12_polynom1),
    []).

fof(rc13_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B)
      & v7_seqm_3(B)
      & v1_polynom1(B) ) ),
    file(polynom1,rc13_polynom1),
    []).

fof(rc14_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
          & v2_polynom1(C,k14_polynom1(A),B) ) ) ),
    file(polynom1,rc14_polynom1),
    []).

fof(rc1_binom,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v2_algstr_1(A) ) ),
    file(binom,rc1_binom),
    []).

fof(rc1_card_1,axiom,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

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

fof(rc1_polynom2,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A)
      & ~ v3_realset2(A) ) ),
    file(polynom2,rc1_polynom2),
    []).

fof(rc1_polynom4,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A)
      & v2_vectsp_2(A)
      & ~ v3_realset2(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A) ) ),
    file(polynom4,rc1_polynom4),
    []).

fof(rc1_polynom7,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A) ) ),
    file(polynom7,rc1_polynom7),
    []).

fof(rc1_termord,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A) ) ),
    file(termord,rc1_termord),
    []).

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

fof(rc2_binom,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v3_algstr_1(A) ) ),
    file(binom,rc2_binom),
    []).

fof(rc2_card_1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    []).

fof(rc2_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

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

fof(rc2_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_funcop_1(A)
      & v1_matrlin(A) ) ),
    file(polynom1,rc2_polynom1),
    []).

fof(rc2_polynom7,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A)
      & v2_vectsp_2(A)
      & v1_binom(A)
      & ~ v3_realset2(A) ) ),
    file(polynom7,rc2_polynom7),
    []).

fof(rc2_polyred,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A)
      & v2_vectsp_2(A)
      & v1_binom(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A)
      & ~ v3_realset2(A) ) ),
    file(polyred,rc2_polyred),
    []).

fof(rc2_termord,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A)
      & ~ v3_realset2(A) ) ),
    file(termord,rc2_termord),
    []).

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

fof(rc3_binom,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_binom(A) ) ),
    file(binom,rc3_binom),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

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

fof(rc3_termord,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ? [B] : 
          ( m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
          & v1_relat_1(B)
          & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
          & v1_relat_2(B)
          & v4_relat_2(B)
          & v6_relat_2(B)
          & v8_relat_2(B)
          & v2_bagorder(B,A) ) ) ),
    file(termord,rc3_termord),
    []).

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

fof(rc4_binom,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v1_binom(A) ) ),
    file(binom,rc4_binom),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

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

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

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

fof(rc6_polynom1,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v9_vectsp_1(A)
      & ~ v3_realset2(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A) ) ),
    file(polynom1,rc6_polynom1),
    []).

fof(rc6_vectsp_1,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & v3_vectsp_1(A) ) ),
    file(vectsp_1,rc6_vectsp_1),
    []).

fof(rc7_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A)
      & v7_seqm_3(A) ) ),
    file(polynom1,rc7_polynom1),
    []).

fof(rc7_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
          & v3_polynom7(C,A,B) ) ) ),
    file(polynom7,rc7_polynom7),
    []).

fof(rc7_vectsp_1,axiom,(
    ? [A] : 
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_vectsp_1(A) ) ),
    file(vectsp_1,rc7_vectsp_1),
    []).

fof(rc8_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B)
      & v7_seqm_3(B) ) ),
    file(polynom1,rc8_polynom1),
    []).

fof(rc8_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
          & v4_polynom7(C,A,B) ) ) ),
    file(polynom7,rc8_polynom7),
    []).

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_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B) ) ),
    file(polynom1,rc9_polynom1),
    []).

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_k14_polynom1,axiom,(
    ! [A] : k14_polynom1(A) = k13_polynom1(A) ),
    file(polynom1,k14_polynom1),
    []).

fof(redefinition_k1_groeb_3,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(D,k14_polynom1(A),B)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => k1_groeb_3(A,B,C,D) = k2_tarski(C,D) ) ),
    file(groeb_3,k1_groeb_3),
    []).

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

fof(redefinition_m1_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) )
     => ! [C] : 
          ( m1_polynom1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(polynom1,m1_polynom1),
    []).

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

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

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

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

fof(t23_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ! [C,D] : 
                ( r1_rewrite1(A,C,D)
               => r1_rewrite1(B,C,D) ) ) ) ) ),
    file(rewrite1,t23_rewrite1),
    []).

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

fof(t30_groeb_2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                 => ( ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                          & v2_polynom1(E,k14_polynom1(A),C)
                          & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                       => ! [F] : 
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
                              & v2_polynom1(F,k14_polynom1(A),C)
                              & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
                           => ( ( r2_hidden(E,D)
                                & r2_hidden(F,D) )
                             => r1_rewrite1(k3_polyred(A,B,C,D),k3_groeb_2(A,B,C,E,F),k26_polynom1(A,C)) ) ) )
                   => ( r2_hidden(k26_polynom1(A,C),D)
                      | r1_groeb_1(A,B,C,D) ) ) ) ) ) ) ),
    file(groeb_2,t30_groeb_2),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t47_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ~ r2_hidden(B,k3_relat_1(A))
         => r9_rewrite1(A,B) ) ) ),
    file(rewrite1,t47_rewrite1),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t4_groeb_1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] : 
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                     => ( r1_tarski(D,E)
                       => r1_tarski(k3_polyred(A,B,C,D),k3_polyred(A,B,C,E)) ) ) ) ) ) ) ),
    file(groeb_1,t4_groeb_1),
    []).

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(t56_groeb_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] : 
              ( ( v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v6_vectsp_1(C)
                & v7_vectsp_1(C)
                & v8_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ( r1_groeb_2(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))
                       => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_3(A,C,D,E)),k3_groeb_2(A,B,C,D,E),k26_polynom1(A,C)) ) ) ) ) ) ) ),
    file(groeb_3,t56_groeb_3),
    []).

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),
    []).