SET007 Axioms: SET007+880.ax


%------------------------------------------------------------------------------
% File     : SET007+880 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Construction of Gr"obner Bases: Avoiding S-Polynomials
% Version  : [Urb08] axioms.
% English  : Buchberger's First Criterium

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : groeb_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   78 (   0 unit)
%            Number of atoms       : 1737 (  53 equality)
%            Maximal formula depth :   24 (  16 average)
%            Number of connectives : 1747 (  88 ~  ;   7  |;1257  &)
%                                         (   4 <=>; 391 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   55 (   0 propositional; 1-6 arity)
%            Number of functors    :   46 (   5 constant; 0-5 arity)
%            Number of variables   :  393 (   0 singleton; 392 !;   1 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_groeb_3,axiom,(
    ! [A,B,C] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_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_finset_1(k12_polynom1(k14_polynom1(A),B,C)) ) )).

fof(fc2_groeb_3,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & l2_struct_0(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))
        & m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A))) )
     => ( v1_relat_1(k2_groeb_3(A,B,C,D))
        & v1_funct_1(k2_groeb_3(A,B,C,D))
        & v1_funct_2(k2_groeb_3(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k2_groeb_3(A,B,C,D),k14_polynom1(A),B) ) ) )).

fof(fc3_groeb_3,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))
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & ~ v3_realset2(C)
        & l1_rlvect_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(A),C)
        & v1_polynom7(D,A,C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_relat_1(k5_groeb_3(A,B,C,D,np__0))
        & v1_funct_1(k5_groeb_3(A,B,C,D,np__0))
        & v1_funct_2(k5_groeb_3(A,B,C,D,np__0),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k5_groeb_3(A,B,C,D,np__0),k14_polynom1(A),C)
        & v3_polynom7(k5_groeb_3(A,B,C,D,np__0),A,C) ) ) )).

fof(fc4_groeb_3,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))
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_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)
        & v1_polynom7(D,A,C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_relat_1(k5_groeb_3(A,B,C,D,np__1))
        & v1_funct_1(k5_groeb_3(A,B,C,D,np__1))
        & v1_funct_2(k5_groeb_3(A,B,C,D,np__1),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k5_groeb_3(A,B,C,D,np__1),k14_polynom1(A),C)
        & v1_polynom7(k5_groeb_3(A,B,C,D,np__1),A,C)
        & v3_polynom7(k5_groeb_3(A,B,C,D,np__1),A,C) ) ) )).

fof(fc5_groeb_3,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))
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_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)
        & v1_polynom7(D,A,C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_relat_1(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))))
        & v1_funct_1(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))))
        & v1_funct_2(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))),k14_polynom1(A),C)
        & v3_polynom7(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))),A,C) ) ) )).

fof(t1_groeb_3,axiom,(
    ! [A,B] :
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) )
         => k1_groeb_2(A,k9_polynom1(A,B,C),C) = B ) ) )).

fof(t2_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_relat_2(B)
            & v4_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] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ( r1_termord(A,B,C,D)
                       => r1_termord(A,B,k9_polynom1(A,C,E),k9_polynom1(A,D,E)) ) ) ) ) ) ) )).

fof(t3_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_relat_2(B)
            & v4_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] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ( ( r1_termord(A,B,C,D)
                          & r2_termord(A,B,D,E) )
                       => r2_termord(A,B,C,E) ) ) ) ) ) ) )).

fof(t4_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_relat_2(B)
            & v4_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] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ( r2_termord(A,B,C,D)
                       => r2_termord(A,B,k9_polynom1(A,C,E),k9_polynom1(A,D,E)) ) ) ) ) ) ) )).

fof(t5_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_relat_2(B)
            & v4_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] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ! [F] :
                          ( ( v7_seqm_3(F)
                            & v1_polynom1(F)
                            & m1_pboole(F,A) )
                         => ( ( r2_termord(A,B,C,D)
                              & r1_termord(A,B,E,F) )
                           => r2_termord(A,B,k9_polynom1(A,C,E),k9_polynom1(A,D,F)) ) ) ) ) ) ) ) )).

fof(t6_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_relat_2(B)
            & v4_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] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ! [F] :
                          ( ( v7_seqm_3(F)
                            & v1_polynom1(F)
                            & m1_pboole(F,A) )
                         => ( ( r1_termord(A,B,C,D)
                              & r2_termord(A,B,E,F) )
                           => r2_termord(A,B,k9_polynom1(A,C,E),k9_polynom1(A,D,F)) ) ) ) ) ) ) ) )).

fof(t7_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & v2_vectsp_2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
                & v1_polynom7(C,A,B)
                & v3_polynom7(C,A,B)
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                    & v1_polynom7(D,A,B)
                    & v3_polynom7(D,A,B)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
                 => k2_polynom7(A,B,k28_polynom1(A,B,C,D)) = k9_polynom1(A,k2_polynom7(A,B,C),k2_polynom7(A,B,D)) ) ) ) ) )).

fof(t8_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & v2_vectsp_2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
                & v2_polynom1(C,k14_polynom1(A),B)
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                    & v1_polynom7(D,A,B)
                    & v3_polynom7(D,A,B)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ( r2_hidden(E,k12_polynom1(k14_polynom1(A),B,C))
                      <=> r2_hidden(k9_polynom1(A,k2_polynom7(A,B,D),E),k12_polynom1(k14_polynom1(A),B,k28_polynom1(A,B,D,C))) ) ) ) ) ) ) )).

fof(t10_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & v1_algstr_1(B)
            & v2_vectsp_2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
                & v2_polynom1(C,k14_polynom1(A),B)
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                    & v1_polynom7(D,A,B)
                    & v3_polynom7(D,A,B)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
                 => k4_card_1(k12_polynom1(k14_polynom1(A),B,C)) = k4_card_1(k12_polynom1(k14_polynom1(A),B,k28_polynom1(A,B,D,C))) ) ) ) ) )).

fof(t11_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)
                & ~ v3_realset2(C)
                & l1_rlvect_1(C) )
             => k6_termord(A,B,C,k26_polynom1(A,C)) = k26_polynom1(A,C) ) ) ) )).

fof(t12_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [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) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
                & v2_polynom1(C,k14_polynom1(A),B)
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                    & v2_polynom1(D,k14_polynom1(A),B)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
                 => ( k25_polynom1(A,B,C,D) = k26_polynom1(A,B)
                   => C = D ) ) ) ) ) )).

fof(t13_groeb_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => k24_polynom1(A,B,k26_polynom1(A,B)) = k26_polynom1(A,B) ) )).

fof(t14_groeb_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => k25_polynom1(A,B,k26_polynom1(A,B),C) = k24_polynom1(A,B,C) ) ) )).

fof(t15_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)
                & ~ 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)) )
                 => k25_polynom1(A,C,D,k6_termord(A,B,C,D)) = k5_termord(A,B,C,D) ) ) ) ) )).

fof(d1_groeb_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A)))
             => k2_groeb_3(A,B,C,D) = k1_funct_4(C,k2_pre_circ(k4_xboole_0(k12_polynom1(k14_polynom1(A),B,C),D),k1_rlvect_1(B))) ) ) ) )).

fof(t16_groeb_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A)))
             => ( k12_polynom1(k14_polynom1(A),B,k2_groeb_3(A,B,C,D)) = k3_xboole_0(k12_polynom1(k14_polynom1(A),B,C),D)
                & ! [E] :
                    ( ( v7_seqm_3(E)
                      & v1_polynom1(E)
                      & m1_pboole(E,A) )
                   => ( r2_hidden(E,k12_polynom1(k14_polynom1(A),B,k2_groeb_3(A,B,C,D)))
                     => k15_polynom1(A,B,k2_groeb_3(A,B,C,D),E) = k15_polynom1(A,B,C,E) ) ) ) ) ) ) )).

fof(t17_groeb_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A)))
             => r1_tarski(k12_polynom1(k14_polynom1(A),B,k2_groeb_3(A,B,C,D)),k12_polynom1(k14_polynom1(A),B,C)) ) ) ) )).

fof(t18_groeb_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => ( k2_groeb_3(A,B,C,k12_polynom1(k14_polynom1(A),B,C)) = C
            & k2_groeb_3(A,B,C,k1_subset_1(k14_polynom1(A))) = k26_polynom1(A,B) ) ) ) )).

fof(d2_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ! [F] :
                            ( ( v1_finset_1(F)
                              & m1_subset_1(F,k1_zfmisc_1(k14_polynom1(A))) )
                           => ( F = k3_groeb_3(A,B,C,D,E)
                            <=> ( r1_tarski(F,k12_polynom1(k14_polynom1(A),C,D))
                                & k4_card_1(F) = E
                                & ! [G] :
                                    ( ( v7_seqm_3(G)
                                      & v1_polynom1(G)
                                      & m1_pboole(G,A) )
                                   => ! [H] :
                                        ( ( v7_seqm_3(H)
                                          & v1_polynom1(H)
                                          & m1_pboole(H,A) )
                                       => ( ( r2_hidden(G,F)
                                            & r2_hidden(H,k12_polynom1(k14_polynom1(A),C,D))
                                            & r1_termord(A,B,G,H) )
                                         => r2_hidden(H,F) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => k4_groeb_3(A,B,C,D,E) = k4_xboole_0(k12_polynom1(k14_polynom1(A),C,D),k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) )).

fof(t19_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ( k2_xboole_0(k3_groeb_3(A,B,C,D,E),k4_groeb_3(A,B,C,D,E)) = k12_polynom1(k14_polynom1(A),C,D)
                          & k3_xboole_0(k3_groeb_3(A,B,C,D,E),k4_groeb_3(A,B,C,D,E)) = k1_xboole_0 ) ) ) ) ) ) ) )).

fof(t20_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ! [F] :
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,A) )
                           => ! [G] :
                                ( ( v7_seqm_3(G)
                                  & v1_polynom1(G)
                                  & m1_pboole(G,A) )
                               => ( ( r2_hidden(F,k3_groeb_3(A,B,C,D,E))
                                    & r2_hidden(G,k4_groeb_3(A,B,C,D,E)) )
                                 => r2_termord(A,B,G,F) ) ) ) ) ) ) ) ) ) )).

fof(t21_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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)) )
                 => ( k3_groeb_3(A,B,C,D,np__0) = k1_xboole_0
                    & k4_groeb_3(A,B,C,D,np__0) = k12_polynom1(k14_polynom1(A),C,D) ) ) ) ) ) )).

fof(t22_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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)) )
                 => ( k3_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) = k12_polynom1(k14_polynom1(A),C,D)
                    & k4_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) = k1_xboole_0 ) ) ) ) ) )).

fof(t23_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)
                & ~ v3_realset2(C)
                & l1_rlvect_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)
                    & v1_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,E)
                          & r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) )
                       => r2_hidden(k3_termord(A,B,C,D),k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) ) )).

fof(t24_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ( r1_tarski(k4_groeb_3(A,B,C,D,E),k12_polynom1(k14_polynom1(A),C,D))
                          & k4_card_1(k4_groeb_3(A,B,C,D,E)) = k5_real_1(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
                          & ! [F] :
                              ( ( v7_seqm_3(F)
                                & v1_polynom1(F)
                                & m1_pboole(F,A) )
                             => ! [G] :
                                  ( ( v7_seqm_3(G)
                                    & v1_polynom1(G)
                                    & m1_pboole(G,A) )
                                 => ( ( r2_hidden(F,k4_groeb_3(A,B,C,D,E))
                                      & r2_hidden(G,k12_polynom1(k14_polynom1(A),C,D))
                                      & r1_termord(A,B,G,F) )
                                   => r2_hidden(G,k4_groeb_3(A,B,C,D,E)) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => k5_groeb_3(A,B,C,D,E) = k2_groeb_3(A,C,D,k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) )).

fof(d5_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => k6_groeb_3(A,B,C,D,E) = k2_groeb_3(A,C,D,k4_groeb_3(A,B,C,D,E)) ) ) ) ) ) )).

fof(t25_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ( k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)) = k3_groeb_3(A,B,C,D,E)
                          & k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)) = k4_groeb_3(A,B,C,D,E) ) ) ) ) ) ) ) )).

fof(t26_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ( r1_tarski(k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,D))
                          & r1_tarski(k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) ) ) ) )).

fof(t27_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)
                & ~ v3_realset2(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,E)
                          & r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) )
                       => r1_tarski(k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D))) ) ) ) ) ) ) )).

fof(t28_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ! [F] :
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,A) )
                           => ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,D))
                             => ( ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)))
                                  | r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E))) )
                                & ~ r2_hidden(F,k3_xboole_0(k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)))) ) ) ) ) ) ) ) ) ) )).

fof(t29_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ! [F] :
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,A) )
                           => ! [G] :
                                ( ( v7_seqm_3(G)
                                  & v1_polynom1(G)
                                  & m1_pboole(G,A) )
                               => ( ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)))
                                    & r2_hidden(G,k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E))) )
                                 => r2_termord(A,B,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t30_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,E)
                          & r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) )
                       => r2_hidden(k3_termord(A,B,C,D),k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).

fof(t31_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ! [F] :
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,A) )
                           => ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)))
                             => ( k15_polynom1(A,C,k6_groeb_3(A,B,C,D,E),F) = k15_polynom1(A,C,D,F)
                                & k15_polynom1(A,C,k5_groeb_3(A,B,C,D,E),F) = k1_rlvect_1(C) ) ) ) ) ) ) ) ) ) )).

fof(t32_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => ! [F] :
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,A) )
                           => ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)))
                             => ( k15_polynom1(A,C,k5_groeb_3(A,B,C,D,E),F) = k15_polynom1(A,C,D,F)
                                & k15_polynom1(A,C,k6_groeb_3(A,B,C,D,E),F) = k1_rlvect_1(C) ) ) ) ) ) ) ) ) ) )).

fof(t33_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                       => k22_polynom1(A,C,k5_groeb_3(A,B,C,D,E),k6_groeb_3(A,B,C,D,E)) = D ) ) ) ) ) ) )).

fof(t34_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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)) )
                 => ( k5_groeb_3(A,B,C,D,np__0) = k26_polynom1(A,C)
                    & k6_groeb_3(A,B,C,D,np__0) = D ) ) ) ) ) )).

fof(t35_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] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(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)) )
                 => ( k5_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) = D
                    & k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) = k26_polynom1(A,C) ) ) ) ) ) )).

fof(t36_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] :
              ( ( v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_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)
                    & v1_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ( k5_groeb_3(A,B,C,D,np__1) = k5_termord(A,B,C,D)
                    & k6_groeb_3(A,B,C,D,np__1) = k6_termord(A,B,C,D) ) ) ) ) ) )).

fof(t37_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)
                & ~ v3_realset2(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( E = k5_real_1(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),np__1)
                       => ( v1_funct_1(k6_groeb_3(A,B,C,D,E))
                          & v1_funct_2(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C))
                          & v1_polynom7(k6_groeb_3(A,B,C,D,E),A,C)
                          & v3_polynom7(k6_groeb_3(A,B,C,D,E),A,C)
                          & m2_relset_1(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C)) ) ) ) ) ) ) ) )).

fof(t38_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_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
                       => r1_termord(A,B,k3_termord(A,B,C,k6_groeb_3(A,B,C,D,k1_nat_1(E,np__1))),k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).

fof(t39_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] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( ~ r1_xreal_0(E,np__0)
                          & ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
                          & ~ r2_termord(A,B,k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E)),k3_termord(A,B,C,D)) ) ) ) ) ) ) )).

fof(t40_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] :
              ( ( v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v2_group_1(C)
                & v7_vectsp_1(C)
                & ~ v3_realset2(C)
                & v2_vectsp_2(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))
                        & v1_polynom7(E,A,C)
                        & v3_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(F,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                           => ! [G] :
                                ( ( v7_seqm_3(G)
                                  & v1_polynom1(G)
                                  & m1_pboole(G,A) )
                               => ( r2_hidden(k9_polynom1(A,k2_polynom7(A,C,E),G),k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,k28_polynom1(A,C,E,D),F)))
                                <=> r2_hidden(G,k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,F))) ) ) ) ) ) ) ) ) ) )).

fof(t41_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_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
                       => r1_tarski(k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,k1_nat_1(E,np__1))),k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).

fof(t42_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_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
                       => k4_xboole_0(k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,k1_nat_1(E,np__1)))) = k1_tarski(k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).

fof(t43_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] :
              ( ( v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & ~ v3_realset2(C)
                & l1_rlvect_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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
                       => k6_groeb_3(A,B,C,D,k1_nat_1(E,np__1)) = k6_termord(A,B,C,k6_groeb_3(A,B,C,D,E)) ) ) ) ) ) ) )).

fof(t44_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] :
              ( ( v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v2_group_1(C)
                & v7_vectsp_1(C)
                & ~ v3_realset2(C)
                & v2_vectsp_2(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))
                        & v1_polynom7(E,A,C)
                        & v3_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(F,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
                           => k6_groeb_3(A,B,C,k28_polynom1(A,C,E,D),F) = k28_polynom1(A,C,E,k6_groeb_3(A,B,C,D,F)) ) ) ) ) ) ) ) )).

fof(t45_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)) )
                     => ! [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)) )
                         => ( r4_polyred(A,B,C,D,F,E)
                           => r4_polyred(A,B,C,k24_polynom1(A,C,D),F,k24_polynom1(A,C,E)) ) ) ) ) ) ) ) )).

fof(t46_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)) )
                     => ! [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)) )
                             => ( ( r5_polyred(A,B,C,D,E,k1_groeb_1(A,C,G))
                                  & ! [H] :
                                      ( ( v7_seqm_3(H)
                                        & v1_polynom1(H)
                                        & m1_pboole(H,A) )
                                     => ~ ( r2_hidden(H,k12_polynom1(k14_polynom1(A),C,F))
                                          & r3_polynom1(A,k3_termord(A,B,C,G),H) ) ) )
                               => r5_polyred(A,B,C,k23_polynom1(A,C,D,F),k23_polynom1(A,C,E,F),k1_groeb_1(A,C,G)) ) ) ) ) ) ) ) ) )).

fof(t47_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)
                    & v1_polynom7(D,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)
                        & v1_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => r5_polyred(A,B,C,k29_polynom1(A,C,D,E),k29_polynom1(A,C,k6_termord(A,B,C,D),E),k1_groeb_1(A,C,E)) ) ) ) ) ) )).

fof(t48_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)
                    & v1_polynom7(D,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)
                        & v1_polynom7(E,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)) )
                         => ( k15_polynom1(A,C,F,k3_termord(A,B,C,k29_polynom1(A,C,D,E))) = k1_rlvect_1(C)
                           => r5_polyred(A,B,C,k23_polynom1(A,C,k29_polynom1(A,C,D,E),F),k23_polynom1(A,C,k29_polynom1(A,C,k6_termord(A,B,C,D),E),F),k1_groeb_1(A,C,E)) ) ) ) ) ) ) ) )).

fof(t49_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] :
                  ( 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)) )
                         => ( r1_rewrite1(k3_polyred(A,B,C,D),E,F)
                           => r1_rewrite1(k3_polyred(A,B,C,D),k24_polynom1(A,C,E),k24_polynom1(A,C,F)) ) ) ) ) ) ) ) )).

fof(t50_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)) )
                     => ! [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)) )
                             => ( ( r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,G)),D,E)
                                  & ! [H] :
                                      ( ( v7_seqm_3(H)
                                        & v1_polynom1(H)
                                        & m1_pboole(H,A) )
                                     => ~ ( r2_hidden(H,k12_polynom1(k14_polynom1(A),C,F))
                                          & r3_polynom1(A,k3_termord(A,B,C,G),H) ) ) )
                               => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,G)),k23_polynom1(A,C,D,F),k23_polynom1(A,C,E,F)) ) ) ) ) ) ) ) ) )).

fof(t51_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)
                    & v1_polynom7(D,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)
                        & v1_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,E)),k29_polynom1(A,C,D,E),k26_polynom1(A,C)) ) ) ) ) ) )).

fof(t52_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] :
              ( ( 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))
                       => ! [F] :
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,A) )
                           => ! [G] :
                                ( ( v7_seqm_3(G)
                                  & v1_polynom1(G)
                                  & m1_pboole(G,A) )
                               => ~ ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D)))
                                    & r2_hidden(G,k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,E)))
                                    & k9_polynom1(A,k3_termord(A,B,C,D),G) = k9_polynom1(A,k3_termord(A,B,C,E),F) ) ) ) ) ) ) ) ) ) )).

fof(t53_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] :
              ( ( 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))
                       => k3_groeb_2(A,B,C,D,E) = k25_polynom1(A,C,k29_polynom1(A,C,k5_termord(A,B,C,E),k6_termord(A,B,C,D)),k29_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,E))) ) ) ) ) ) ) )).

fof(t54_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] :
              ( ( 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))
                       => k3_groeb_2(A,B,C,D,E) = k25_polynom1(A,C,k29_polynom1(A,C,k6_termord(A,B,C,D),E),k29_polynom1(A,C,k6_termord(A,B,C,E),D)) ) ) ) ) ) ) )).

fof(t55_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)
                    & v1_polynom7(D,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)
                        & v1_polynom7(E,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))
                          & v1_polynom7(k6_termord(A,B,C,D),A,C)
                          & v1_polynom7(k6_termord(A,B,C,E),A,C) )
                       => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,D)),k25_polynom1(A,C,k29_polynom1(A,C,k5_termord(A,B,C,E),k6_termord(A,B,C,D)),k29_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,E))),k29_polynom1(A,C,E,k6_termord(A,B,C,D))) ) ) ) ) ) ) )).

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)) ) ) ) ) ) ) )).

fof(t57_groeb_3,axiom,(
    ! [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))))
                 => ( r1_groeb_1(A,B,C,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)) )
                       => ! [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_groeb_2(A,k3_termord(A,B,C,E),k3_termord(A,B,C,F))
                                | r1_rewrite1(k3_polyred(A,B,C,D),k3_groeb_2(A,B,C,E,F),k26_polynom1(A,C)) ) ) ) ) ) ) ) ) ) )).

fof(t58_groeb_3,axiom,(
    ! [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_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)
                & ~ v3_realset2(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_groeb_2(A,k3_termord(A,B,C,E),k3_termord(A,B,C,F))
                                | 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)
                      | ! [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) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t59_groeb_3,axiom,(
    ! [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) ) ) ) ) ) ) )).

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)))) ) ) )).

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) ) )).

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) ) )).

fof(dt_k2_groeb_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A))) )
     => ( v1_funct_1(k2_groeb_3(A,B,C,D))
        & v1_funct_2(k2_groeb_3(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & m2_relset_1(k2_groeb_3(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) )).

fof(dt_k3_groeb_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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))
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & l1_rlvect_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))
        & m1_subset_1(E,k5_numbers) )
     => ( v1_finset_1(k3_groeb_3(A,B,C,D,E))
        & m1_subset_1(k3_groeb_3(A,B,C,D,E),k1_zfmisc_1(k14_polynom1(A))) ) ) )).

fof(dt_k4_groeb_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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))
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & l1_rlvect_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))
        & m1_subset_1(E,k5_numbers) )
     => ( v1_finset_1(k4_groeb_3(A,B,C,D,E))
        & m1_subset_1(k4_groeb_3(A,B,C,D,E),k1_zfmisc_1(k14_polynom1(A))) ) ) )).

fof(dt_k5_groeb_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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))
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & l1_rlvect_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))
        & m1_subset_1(E,k5_numbers) )
     => ( v1_funct_1(k5_groeb_3(A,B,C,D,E))
        & v1_funct_2(k5_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k5_groeb_3(A,B,C,D,E),k14_polynom1(A),C)
        & m2_relset_1(k5_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C)) ) ) )).

fof(dt_k6_groeb_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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))
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & l1_rlvect_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))
        & m1_subset_1(E,k5_numbers) )
     => ( v1_funct_1(k6_groeb_3(A,B,C,D,E))
        & v1_funct_2(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),C)
        & m2_relset_1(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C)) ) ) )).

fof(t9_groeb_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & v2_vectsp_2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
                & v2_polynom1(C,k14_polynom1(A),B)
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                    & v1_polynom7(D,A,B)
                    & v3_polynom7(D,A,B)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
                 => k12_polynom1(k14_polynom1(A),B,k28_polynom1(A,B,D,C)) = a_4_0_groeb_3(A,B,C,D) ) ) ) ) )).

fof(fraenkel_a_4_0_groeb_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( v3_ordinal1(B)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v2_group_1(C)
        & v7_vectsp_1(C)
        & ~ v3_realset2(C)
        & v2_vectsp_2(C)
        & l3_vectsp_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(B),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(B),C)
        & m2_relset_1(D,k14_polynom1(B),u1_struct_0(C))
        & v1_funct_1(E)
        & v1_funct_2(E,k14_polynom1(B),u1_struct_0(C))
        & v1_polynom7(E,B,C)
        & v3_polynom7(E,B,C)
        & m2_relset_1(E,k14_polynom1(B),u1_struct_0(C)) )
     => ( r2_hidden(A,a_4_0_groeb_3(B,C,D,E))
      <=> ? [F] :
            ( m1_polynom1(F,B,k14_polynom1(B))
            & A = k9_polynom1(B,k2_polynom7(B,C,E),F)
            & r2_hidden(F,k12_polynom1(k14_polynom1(B),C,D)) ) ) ) )).
%------------------------------------------------------------------------------