SET007 Axioms: SET007+752.ax


%------------------------------------------------------------------------------
% File     : SET007+752 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Polynomial Reduction
% Version  : [Urb08] axioms.
% English  :

% 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    : polyred [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   85 (   0 unit)
%            Number of atoms       : 1854 (  41 equality)
%            Maximal formula depth :   27 (  15 average)
%            Number of connectives : 1887 ( 118 ~  ;   2  |;1333  &)
%                                         (  20 <=>; 414 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   83 (   0 propositional; 1-7 arity)
%            Number of functors    :   45 (   2 constant; 0-4 arity)
%            Number of variables   :  432 (   0 singleton; 420 !;  12 ?)
%            Maximal term depth    :    5 (   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(rc1_polyred,axiom,(
    ! [A,B] :
      ( ( v3_ordinal1(A)
        & ~ v3_realset2(B)
        & l2_struct_0(B) )
     => ? [C] :
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
          & v2_polynom1(C,k14_polynom1(A),B)
          & v1_polynom7(C,A,B)
          & v3_polynom7(C,A,B) ) ) )).

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

fof(fc1_polyred,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v2_group_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_vectsp_1(B)
        & v2_vectsp_2(B)
        & v1_algstr_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)
        & v1_polynom7(C,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)
        & v1_polynom7(D,A,B)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_relat_1(k28_polynom1(A,B,C,D))
        & v1_funct_1(k28_polynom1(A,B,C,D))
        & v1_funct_2(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k28_polynom1(A,B,C,D),k14_polynom1(A),B)
        & v1_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) )).

fof(fc2_polyred,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & ~ v3_struct_0(C)
        & l2_struct_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(A),C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_relat_1(k1_polyred(A,B,C,D))
        & v1_funct_1(k1_polyred(A,B,C,D))
        & v1_funct_2(k1_polyred(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k1_polyred(A,B,C,D),k14_polynom1(A),C) ) ) )).

fof(fc3_polyred,axiom,(
    ! [A,B] :
      ( ( 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(g1_orders_2(k14_polynom1(A),B))
        & v1_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v2_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v3_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v4_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v16_waybel_0(g1_orders_2(k14_polynom1(A),B)) ) ) )).

fof(fc4_polyred,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & 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)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
     => ( ~ v3_struct_0(g1_orders_2(k14_polynom1(A),B))
        & v1_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v2_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v3_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v4_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v1_wellfnd1(g1_orders_2(k14_polynom1(A),B)) ) ) )).

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

fof(t1_polyred,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(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)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
             => k24_polynom1(A,B,k23_polynom1(A,B,C,D)) = k23_polynom1(A,B,k24_polynom1(A,B,C),k24_polynom1(A,B,D)) ) ) ) )).

fof(t2_polyred,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v1_algstr_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)) )
         => k22_polynom1(A,B,k26_polynom1(A,B),C) = C ) ) )).

fof(t3_polyred,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)) )
         => ( k22_polynom1(A,B,k24_polynom1(A,B,C),C) = k26_polynom1(A,B)
            & k22_polynom1(A,B,C,k24_polynom1(A,B,C)) = k26_polynom1(A,B) ) ) ) )).

fof(t4_polyred,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,C,k26_polynom1(A,B)) = C ) ) )).

fof(t5_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v5_vectsp_1(B)
            & v2_algstr_1(B)
            & l3_vectsp_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)) )
             => k28_polynom1(A,B,k26_polynom1(A,B),C) = k26_polynom1(A,B) ) ) ) )).

fof(t6_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v2_group_1(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_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)) )
                 => ( k24_polynom1(A,B,k29_polynom1(A,B,C,D)) = k29_polynom1(A,B,k24_polynom1(A,B,C),D)
                    & k24_polynom1(A,B,k29_polynom1(A,B,C,D)) = k29_polynom1(A,B,C,k24_polynom1(A,B,D)) ) ) ) ) ) )).

fof(t7_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_vectsp_1(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))
                    & 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) )
                     => k15_polynom1(A,B,k28_polynom1(A,B,D,C),k9_polynom1(A,k2_polynom7(A,B,D),E)) = k1_group_1(B,k15_polynom1(A,B,D,k2_polynom7(A,B,D)),k15_polynom1(A,B,C,E)) ) ) ) ) ) )).

fof(t8_polyred,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v5_rlvect_1(B)
        & v5_vectsp_1(B)
        & v2_algstr_1(B)
        & l3_vectsp_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)) )
         => k5_polynom7(A,B,C,k1_rlvect_1(B)) = k26_polynom1(A,B) ) ) )).

fof(t9_polyred,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_vectsp_1(B)
        & l3_vectsp_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)) )
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ( k24_polynom1(A,B,k5_polynom7(A,B,C,D)) = k5_polynom7(A,B,C,k5_rlvect_1(B,D))
                & k24_polynom1(A,B,k5_polynom7(A,B,C,D)) = k5_polynom7(A,B,k24_polynom1(A,B,C),D) ) ) ) ) )).

fof(t10_polyred,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v5_vectsp_1(B)
        & l3_vectsp_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)) )
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_struct_0(B))
                 => k22_polynom1(A,B,k5_polynom7(A,B,C,D),k5_polynom7(A,B,C,E)) = k5_polynom7(A,B,C,k2_rlvect_1(B,D,E)) ) ) ) ) )).

fof(t11_polyred,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v4_group_1(B)
        & l2_vectsp_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)) )
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_struct_0(B))
                 => k5_polynom7(A,B,C,k1_group_1(B,D,E)) = k5_polynom7(A,B,k5_polynom7(A,B,C,E),D) ) ) ) ) )).

fof(t12_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_group_1(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_vectsp_1(B)
            & l3_vectsp_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)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => k5_polynom7(A,B,k28_polynom1(A,B,C,D),E) = k28_polynom1(A,B,C,k5_polynom7(A,B,D,E)) ) ) ) ) ) )).

fof(d1_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v7_seqm_3(B)
            & v1_polynom1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_struct_0(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(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))
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ( E = k1_polyred(A,B,C,D)
                      <=> ! [F] :
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,A) )
                           => ( r3_polynom1(A,B,F)
                             => ( k15_polynom1(A,C,E,F) = k15_polynom1(A,C,D,k10_polynom1(A,F,B))
                                & ! [G] :
                                    ( ( v7_seqm_3(G)
                                      & v1_polynom1(G)
                                      & m1_pboole(G,A) )
                                   => ( ~ r3_polynom1(A,B,G)
                                     => k15_polynom1(A,C,E,G) = k1_rlvect_1(C) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(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) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_struct_0(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(D))
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(D)) )
                     => k15_polynom1(A,D,k1_polyred(A,B,D,E),k9_polynom1(A,C,B)) = k15_polynom1(A,D,E,C) ) ) ) ) ) )).

fof(t15_polyred,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_realset2(C)
                & l2_struct_0(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] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => k3_termord(A,B,C,k1_polyred(A,E,C,D)) = k9_polynom1(A,E,k3_termord(A,B,C,D)) ) ) ) ) ) )).

fof(t16_polyred,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)
                & l2_struct_0(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] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ! [F] :
                          ( ( v7_seqm_3(F)
                            & v1_polynom1(F)
                            & m1_pboole(F,A) )
                         => ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k1_polyred(A,E,C,D)))
                           => r1_termord(A,B,F,k9_polynom1(A,E,k3_termord(A,B,C,D))) ) ) ) ) ) ) ) )).

fof(t17_polyred,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)
                & l2_struct_0(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => k1_polyred(A,k16_polynom1(A),C,D) = D ) ) ) ) )).

fof(t18_polyred,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)
                & l2_struct_0(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ! [F] :
                          ( ( v7_seqm_3(F)
                            & v1_polynom1(F)
                            & m1_pboole(F,A) )
                         => k1_polyred(A,k9_polynom1(A,E,F),C,D) = k1_polyred(A,E,C,k1_polyred(A,F,C,D)) ) ) ) ) ) ) )).

fof(t19_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_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] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => r1_tarski(k12_polynom1(k14_polynom1(A),B,k5_polynom7(A,B,C,D)),k12_polynom1(k14_polynom1(A),B,C)) ) ) ) ) )).

fof(t20_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v2_vectsp_2(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] :
                  ( ( v8_rlvect_1(D,B)
                    & m1_subset_1(D,u1_struct_0(B)) )
                 => r1_tarski(k12_polynom1(k14_polynom1(A),B,C),k12_polynom1(k14_polynom1(A),B,k5_polynom7(A,B,C,D))) ) ) ) ) )).

fof(t21_polyred,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)
                & v7_vectsp_1(C)
                & v2_vectsp_2(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] :
                      ( ( v8_rlvect_1(E,C)
                        & m1_subset_1(E,u1_struct_0(C)) )
                     => k3_termord(A,B,C,k5_polynom7(A,C,D,E)) = k3_termord(A,B,C,D) ) ) ) ) ) )).

fof(t22_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_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))
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => k5_polynom7(A,B,k1_polyred(A,D,B,C),E) = k28_polynom1(A,B,k1_polynom7(A,B,E,D),C) ) ) ) ) ) )).

fof(t23_polyred,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] :
              ( ( v2_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v2_vectsp_2(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)
                        & 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))
                            & v1_polynom7(F,A,C)
                            & v3_polynom7(F,A,C)
                            & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
                         => ( r2_hidden(k3_termord(A,B,C,D),k12_polynom1(k14_polynom1(A),C,E))
                           => r2_hidden(k3_termord(A,B,C,k28_polynom1(A,C,F,D)),k12_polynom1(k14_polynom1(A),C,k28_polynom1(A,C,F,E))) ) ) ) ) ) ) ) )).

fof(d2_polyred,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)
                & l2_struct_0(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_polyred(A,B,C,D,E)
                      <=> r2_hidden(k4_tarski(k12_polynom1(k14_polynom1(A),C,D),k12_polynom1(k14_polynom1(A),C,E)),k13_bagorder(g1_orders_2(k14_polynom1(A),B))) ) ) ) ) ) ) )).

fof(d3_polyred,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)
                & l2_struct_0(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)) )
                     => ( r2_polyred(A,B,C,D,E)
                      <=> ( r1_polyred(A,B,C,D,E)
                          & k12_polynom1(k14_polynom1(A),C,D) != k12_polynom1(k14_polynom1(A),C,E) ) ) ) ) ) ) ) )).

fof(d4_polyred,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)
                & l2_struct_0(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)) )
                 => k2_polyred(A,B,C,D) = k12_polynom1(k14_polynom1(A),C,D) ) ) ) ) )).

fof(t24_polyred,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_realset2(C)
                & l2_struct_0(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)) )
                 => k11_bagorder(g1_orders_2(k14_polynom1(A),B),k2_polyred(A,B,C,D)) = k3_termord(A,B,C,D) ) ) ) ) )).

fof(t25_polyred,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)
                & 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)) )
                 => r1_polyred(A,B,C,D,D) ) ) ) ) )).

fof(t26_polyred,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)
                & 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] :
                      ( ( 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_polyred(A,B,C,D,E)
                          & r1_polyred(A,B,C,E,D) )
                      <=> k12_polynom1(k14_polynom1(A),C,D) = k12_polynom1(k14_polynom1(A),C,E) ) ) ) ) ) ) )).

fof(t27_polyred,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)
                & 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] :
                      ( ( 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_polyred(A,B,C,D,E)
                              & r1_polyred(A,B,C,E,F) )
                           => r1_polyred(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(t28_polyred,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)
                & 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] :
                      ( ( 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_polyred(A,B,C,D,E)
                        | r1_polyred(A,B,C,E,D) ) ) ) ) ) ) )).

fof(t29_polyred,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)
                & 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] :
                      ( ( 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_polyred(A,B,C,D,E)
                      <=> ~ r2_polyred(A,B,C,E,D) ) ) ) ) ) ) )).

fof(t30_polyred,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)
                & l2_struct_0(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)) )
                 => r1_polyred(A,B,C,k26_polynom1(A,C),D) ) ) ) ) )).

fof(t31_polyred,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] :
              ( ( v2_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(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))
                      & r2_hidden(E,D)
                      & ! [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(F,D)
                           => r1_polyred(A,B,C,E,F) ) ) ) ) ) ) ) )).

fof(t32_polyred,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] :
                      ( ( 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)) )
                     => ( r2_polyred(A,B,C,D,E)
                      <=> ~ ( ~ ( D = k26_polynom1(A,C)
                                & E != k26_polynom1(A,C) )
                            & ~ r2_termord(A,B,k3_termord(A,B,C,D),k3_termord(A,B,C,E))
                            & ~ ( k3_termord(A,B,C,D) = k3_termord(A,B,C,E)
                                & r2_polyred(A,B,C,k6_termord(A,B,C,D),k6_termord(A,B,C,E)) ) ) ) ) ) ) ) ) )).

fof(t33_polyred,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)
                    & v1_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => r2_polyred(A,B,C,k6_termord(A,B,C,D),k5_termord(A,B,C,D)) ) ) ) ) )).

fof(t34_polyred,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)) )
                 => r1_polyred(A,B,C,k5_termord(A,B,C,D),D) ) ) ) ) )).

fof(t35_polyred,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)
                    & v1_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => r2_polyred(A,B,C,k6_termord(A,B,C,D),D) ) ) ) ) )).

fof(d5_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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] :
                              ( ( v7_seqm_3(G)
                                & v1_polynom1(G)
                                & m1_pboole(G,A) )
                             => ( r3_polyred(A,B,C,D,E,F,G)
                              <=> ( D != k26_polynom1(A,C)
                                  & E != k26_polynom1(A,C)
                                  & r2_hidden(G,k12_polynom1(k14_polynom1(A),C,D))
                                  & ? [H] :
                                      ( v7_seqm_3(H)
                                      & v1_polynom1(H)
                                      & m1_pboole(H,A)
                                      & k9_polynom1(A,H,k3_termord(A,B,C,E)) = G
                                      & F = k25_polynom1(A,C,D,k5_polynom7(A,C,k1_polyred(A,H,C,E),k5_vectsp_1(C,k15_polynom1(A,C,D,G),k4_termord(A,B,C,E)))) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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,E,F)
                          <=> ? [G] :
                                ( v7_seqm_3(G)
                                & v1_polynom1(G)
                                & m1_pboole(G,A)
                                & r3_polyred(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(d7_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                         => ( r5_polyred(A,B,C,D,E,F)
                          <=> ? [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(G,F)
                                & r4_polyred(A,B,C,D,G,E) ) ) ) ) ) ) ) ) )).

fof(d8_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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)) )
                     => ( r6_polyred(A,B,C,D,E)
                      <=> ? [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,E,F) ) ) ) ) ) ) ) )).

fof(d9_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                     => ( r7_polyred(A,B,C,D,E)
                      <=> ? [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))
                            & r5_polyred(A,B,C,D,F,E) ) ) ) ) ) ) ) )).

fof(d10_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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)) )
                         => ( r8_polyred(A,B,C,D,E,F)
                          <=> r3_polyred(A,B,C,D,E,F,k3_termord(A,B,C,D)) ) ) ) ) ) ) ) )).

fof(d11_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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)) )
                     => ( r9_polyred(A,B,C,D,E)
                      <=> ? [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))
                            & r8_polyred(A,B,C,D,E,F) ) ) ) ) ) ) ) )).

fof(d12_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                     => ( r10_polyred(A,B,C,D,E)
                      <=> ? [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(F,E)
                            & r9_polyred(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(t36_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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)
                        & v1_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ( r6_polyred(A,B,C,D,E)
                      <=> ? [F] :
                            ( v7_seqm_3(F)
                            & v1_polynom1(F)
                            & m1_pboole(F,A)
                            & r2_hidden(F,k12_polynom1(k14_polynom1(A),C,D))
                            & r3_polynom1(A,k3_termord(A,B,C,E),F) ) ) ) ) ) ) ) )).

fof(t37_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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)) )
                 => ~ r6_polyred(A,B,C,k26_polynom1(A,C),D) ) ) ) ) )).

fof(t38_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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))
                            & v1_polynom7(F,A,C)
                            & v3_polynom7(F,A,C)
                            & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
                         => ( r4_polyred(A,B,C,D,E,k25_polynom1(A,C,D,k29_polynom1(A,C,F,E)))
                           => r2_hidden(k3_termord(A,B,C,k29_polynom1(A,C,F,E)),k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) ) ) ) )).

fof(t39_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_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)) )
                 => ! [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] :
                              ( ( v7_seqm_3(G)
                                & v1_polynom1(G)
                                & m1_pboole(G,A) )
                             => ~ ( r3_polyred(A,B,C,D,E,F,G)
                                  & r2_hidden(G,k12_polynom1(k14_polynom1(A),C,F)) ) ) ) ) ) ) ) ) )).

fof(t40_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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] :
                              ( ( v7_seqm_3(G)
                                & v1_polynom1(G)
                                & m1_pboole(G,A) )
                             => ! [H] :
                                  ( ( v7_seqm_3(H)
                                    & v1_polynom1(H)
                                    & m1_pboole(H,A) )
                                 => ( ( r2_termord(A,B,G,H)
                                      & r3_polyred(A,B,C,D,E,F,G) )
                                   => ( r2_hidden(H,k12_polynom1(k14_polynom1(A),C,F))
                                    <=> r2_hidden(H,k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) ) ) ) ) ) ) )).

fof(t41_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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] :
                              ( ( v7_seqm_3(G)
                                & v1_polynom1(G)
                                & m1_pboole(G,A) )
                             => ! [H] :
                                  ( ( v7_seqm_3(H)
                                    & v1_polynom1(H)
                                    & m1_pboole(H,A) )
                                 => ( ( r2_termord(A,B,G,H)
                                      & r3_polyred(A,B,C,D,E,F,G) )
                                   => k15_polynom1(A,C,D,H) = k15_polynom1(A,C,F,H) ) ) ) ) ) ) ) ) ) )).

fof(t42_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_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)) )
                 => ! [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,E,F)
                           => ! [G] :
                                ( ( v7_seqm_3(G)
                                  & v1_polynom1(G)
                                  & m1_pboole(G,A) )
                               => ( r2_hidden(G,k12_polynom1(k14_polynom1(A),C,F))
                                 => r1_termord(A,B,G,k3_termord(A,B,C,D)) ) ) ) ) ) ) ) ) ) )).

fof(t43_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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,E,F)
                           => r2_polyred(A,B,C,F,D) ) ) ) ) ) ) ) )).

fof(d13_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                 => ! [E] :
                      ( m2_relset_1(E,k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)))
                     => ( E = k3_polyred(A,B,C,D)
                      <=> ! [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(k4_tarski(F,G),E)
                                <=> r5_polyred(A,B,C,F,G,D) ) ) ) ) ) ) ) ) ) )).

fof(t44_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( 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] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                         => ( r1_rewrite1(k3_polyred(A,B,C,F),D,E)
                           => ( r1_polyred(A,B,C,E,D)
                              & ( E = k26_polynom1(A,C)
                                | r1_termord(A,B,k3_termord(A,B,C,E),k3_termord(A,B,C,D)) ) ) ) ) ) ) ) ) ) )).

fof(t45_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & v1_algstr_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)
                           => r1_rewrite1(k3_polyred(A,B,C,D),k29_polynom1(A,C,F,E),k26_polynom1(A,C)) ) ) ) ) ) ) ) )).

fof(t46_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
                            & v2_polynom1(F,k14_polynom1(A),C)
                            & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k14_polynom1(A),u1_struct_0(C))
                                & v1_polynom7(G,A,C)
                                & v3_polynom7(G,A,C)
                                & m2_relset_1(G,k14_polynom1(A),u1_struct_0(C)) )
                             => ( r5_polyred(A,B,C,E,F,D)
                               => r5_polyred(A,B,C,k29_polynom1(A,C,G,E),k29_polynom1(A,C,G,F),D) ) ) ) ) ) ) ) ) )).

fof(t47_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
                            & v2_polynom1(F,k14_polynom1(A),C)
                            & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k14_polynom1(A),u1_struct_0(C))
                                & v3_polynom7(G,A,C)
                                & m2_relset_1(G,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),k29_polynom1(A,C,G,E),k29_polynom1(A,C,G,F)) ) ) ) ) ) ) ) ) )).

fof(t48_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
                            & v3_polynom7(F,A,C)
                            & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
                         => ( r1_rewrite1(k3_polyred(A,B,C,D),E,k26_polynom1(A,C))
                           => r1_rewrite1(k3_polyred(A,B,C,D),k29_polynom1(A,C,F,E),k26_polynom1(A,C)) ) ) ) ) ) ) ) )).

fof(t49_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ 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)) )
                         => ! [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)) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k14_polynom1(A),u1_struct_0(C))
                                    & v2_polynom1(H,k14_polynom1(A),C)
                                    & m2_relset_1(H,k14_polynom1(A),u1_struct_0(C)) )
                                 => ~ ( k25_polynom1(A,C,E,F) = G
                                      & r1_rewrite1(k3_polyred(A,B,C,D),G,H)
                                      & ! [I] :
                                          ( ( v1_funct_1(I)
                                            & v1_funct_2(I,k14_polynom1(A),u1_struct_0(C))
                                            & v2_polynom1(I,k14_polynom1(A),C)
                                            & m2_relset_1(I,k14_polynom1(A),u1_struct_0(C)) )
                                         => ! [J] :
                                              ( ( v1_funct_1(J)
                                                & v1_funct_2(J,k14_polynom1(A),u1_struct_0(C))
                                                & v2_polynom1(J,k14_polynom1(A),C)
                                                & m2_relset_1(J,k14_polynom1(A),u1_struct_0(C)) )
                                             => ~ ( k25_polynom1(A,C,I,J) = H
                                                  & r1_rewrite1(k3_polyred(A,B,C,D),E,I)
                                                  & r1_rewrite1(k3_polyred(A,B,C,D),F,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t50_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ 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),k25_polynom1(A,C,E,F),k26_polynom1(A,C))
                           => r5_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) )).

fof(t51_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ 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),k25_polynom1(A,C,E,F),k26_polynom1(A,C))
                           => r2_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) )).

fof(d14_polyred,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r11_polyred(A,B,C,D)
                  <=> r2_hidden(k6_rlvect_1(A,C,D),B) ) ) ) ) ) )).

fof(t52_polyred,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_vectsp_1(A)
        & v1_algstr_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v3_ideal_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r11_polyred(A,B,C,C) ) ) ) )).

fof(t53_polyred,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_vectsp_1(A)
        & v6_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v3_ideal_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r11_polyred(A,B,C,D)
                   => r11_polyred(A,B,D,C) ) ) ) ) ) )).

fof(t54_polyred,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_ideal_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r11_polyred(A,B,C,D)
                          & r11_polyred(A,B,D,E) )
                       => r11_polyred(A,B,C,E) ) ) ) ) ) ) )).

fof(t55_polyred,axiom,(
    ! [A] :
      ( ( v2_group_1(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_vectsp_1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_ideal_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r11_polyred(A,B,C,D)
                              & r11_polyred(A,B,E,F) )
                           => r11_polyred(A,B,k4_rlvect_1(A,C,E),k4_rlvect_1(A,D,F)) ) ) ) ) ) ) ) )).

fof(t56_polyred,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_ideal_1(B,A)
            & v3_ideal_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r11_polyred(A,B,C,D)
                              & r11_polyred(A,B,E,F) )
                           => r11_polyred(A,B,k10_group_1(A,C,E),k10_group_1(A,D,F)) ) ) ) ) ) ) ) )).

fof(t57_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k30_polynom1(A,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k30_polynom1(A,C)))
                         => ( r2_rewrite1(k3_polyred(A,B,C,D),E,F)
                           => r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),E,F) ) ) ) ) ) ) ) )).

fof(t58_polyred,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)
                & v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k30_polynom1(A,C)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k30_polynom1(A,C)))
                         => ( r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),E,F)
                           => r2_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) )).

fof(t59_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ 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)
                           => r2_hidden(k25_polynom1(A,C,E,F),k7_ideal_1(k30_polynom1(A,C),D)) ) ) ) ) ) ) ) )).

fof(t60_polyred,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] :
              ( ( v2_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ 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)) )
                     => ( r1_rewrite1(k3_polyred(A,B,C,D),E,k26_polynom1(A,C))
                       => r2_hidden(E,k7_ideal_1(k30_polynom1(A,C),D)) ) ) ) ) ) ) )).

fof(dt_k1_polyred,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & ~ v3_struct_0(C)
        & l2_struct_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_funct_1(k1_polyred(A,B,C,D))
        & v1_funct_2(k1_polyred(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
        & m2_relset_1(k1_polyred(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) ) ) )).

fof(dt_k2_polyred,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & ~ v3_struct_0(C)
        & l2_struct_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(A),C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => m1_subset_1(k2_polyred(A,B,C,D),k5_finsub_1(u1_struct_0(g1_orders_2(k14_polynom1(A),B)))) ) )).

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

fof(t14_polyred,axiom,(
    ! [A] :
      ( v3_ordinal1(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))
                & v2_polynom1(C,k14_polynom1(A),B)
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => r1_tarski(k12_polynom1(k14_polynom1(A),B,k1_polyred(A,D,B,C)),a_4_0_polyred(A,B,C,D)) ) ) ) ) )).

fof(fraenkel_a_4_0_polyred,axiom,(
    ! [A,B,C,D,E] :
      ( ( v3_ordinal1(B)
        & ~ v3_struct_0(C)
        & l2_struct_0(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))
        & v7_seqm_3(E)
        & v1_polynom1(E)
        & m1_pboole(E,B) )
     => ( r2_hidden(A,a_4_0_polyred(B,C,D,E))
      <=> ? [F] :
            ( m1_polynom1(F,B,k14_polynom1(B))
            & A = k9_polynom1(B,E,F)
            & r2_hidden(F,k12_polynom1(k14_polynom1(B),C,D)) ) ) ) )).
%------------------------------------------------------------------------------