SET007 Axioms: SET007+649.ax


%------------------------------------------------------------------------------
% File     : SET007+649 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Evaluation of Multivariate Polynomials
% 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    : polynom2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   55 (   2 unit)
%            Number of atoms       :  761 (  70 equality)
%            Maximal formula depth :   23 (  13 average)
%            Number of connectives :  773 (  67 ~  ;  11  |; 484  &)
%                                         (   4 <=>; 207 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   63 (   1 propositional; 0-3 arity)
%            Number of functors    :   69 (  20 constant; 0-6 arity)
%            Number of variables   :  199 (   0 singleton; 191 !;   8 ?)
%            Maximal term depth    :    8 (   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_polynom2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A)
      & ~ v3_realset2(A) ) )).

fof(rc2_polynom2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_seq_1(B)
          & v7_seqm_3(B)
          & v1_polynom1(B)
          & ~ v1_polynom2(B,A) ) ) )).

fof(fc1_polynom2,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(D,k14_polynom1(A),B)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_relat_1(k25_polynom1(A,B,C,D))
        & v1_funct_1(k25_polynom1(A,B,C,D))
        & v1_funct_2(k25_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k25_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) )).

fof(fc2_polynom2,axiom,(
    ! [A,B,C] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
     => v1_finset_1(k12_polynom1(k14_polynom1(A),B,C)) ) )).

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

fof(fc4_polynom2,axiom,(
    ! [A,B,C] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v4_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_relat_1(k6_polynom2(A,B,C))
        & v1_funct_1(k6_polynom2(A,B,C))
        & v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
        & v1_endalg(k6_polynom2(A,B,C),k30_polynom1(A,B),B) ) ) )).

fof(fc5_polynom2,axiom,(
    ! [A,B,C] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_relat_1(k6_polynom2(A,B,C))
        & v1_funct_1(k6_polynom2(A,B,C))
        & v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
        & v1_grcat_1(k6_polynom2(A,B,C),k30_polynom1(A,B),B) ) ) )).

fof(fc6_polynom2,axiom,(
    ! [A,B,C] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_relat_1(k6_polynom2(A,B,C))
        & v1_funct_1(k6_polynom2(A,B,C))
        & v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
        & v1_grcat_1(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
        & v1_endalg(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
        & v1_group_6(k6_polynom2(A,B,C),k30_polynom1(A,B),B) ) ) )).

fof(fc7_polynom2,axiom,(
    ! [A,B,C] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_relat_1(k6_polynom2(A,B,C))
        & v1_funct_1(k6_polynom2(A,B,C))
        & v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
        & v1_quofield(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
        & v1_grcat_1(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
        & v1_endalg(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
        & v1_group_6(k6_polynom2(A,B,C),k30_polynom1(A,B),B) ) ) )).

fof(t1_polynom2,axiom,(
    $true )).

fof(t2_polynom2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),B,k1_nat_1(C,D)) = k1_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),B,C),k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),B,D)) ) ) ) ) )).

fof(t3_polynom2,axiom,(
    $true )).

fof(t4_polynom2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k4_finseq_1(A))
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r1_xreal_0(np__1,C)
                    & r1_xreal_0(C,B) )
                 => r2_hidden(C,k4_finseq_1(A)) ) ) ) ) ) )).

fof(t5_polynom2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & v1_algstr_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(C,k4_finseq_1(B))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(B))
                       => ( D = C
                          | k4_finseq_4(k5_numbers,u1_struct_0(A),B,D) = k1_rlvect_1(A) ) ) ) )
               => k9_rlvect_1(A,B) = k4_finseq_4(k5_numbers,u1_struct_0(A),B,C) ) ) ) ) )).

fof(t6_polynom2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_group_1(A)
        & v7_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ( ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & r2_hidden(C,k4_finseq_1(B))
                & k4_finseq_4(k5_numbers,u1_struct_0(A),B,C) = k1_rlvect_1(A) )
           => k3_group_4(A,B) = k1_rlvect_1(A) ) ) ) )).

fof(t7_polynom2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( k3_finseq_1(C) = k3_finseq_1(D)
                   => ( ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(E,k4_finseq_1(C))
                              & k4_finseq_4(k5_numbers,u1_struct_0(A),D,E) = k4_rlvect_1(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E))
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ( r2_hidden(F,k4_finseq_1(C))
                                   => ( F = E
                                      | k4_finseq_4(k5_numbers,u1_struct_0(A),D,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),C,F) ) ) ) ) )
                      | k9_rlvect_1(A,D) = k4_rlvect_1(A,B,k9_rlvect_1(A,C)) ) ) ) ) ) ) )).

fof(t8_polynom2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( k3_finseq_1(C) = k3_finseq_1(D)
                   => ( ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(E,k4_finseq_1(C))
                              & k4_finseq_4(k5_numbers,u1_struct_0(A),D,E) = k10_group_1(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E))
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ( r2_hidden(F,k4_finseq_1(C))
                                   => ( F = E
                                      | k4_finseq_4(k5_numbers,u1_struct_0(A),D,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),C,F) ) ) ) ) )
                      | k3_group_4(A,D) = k10_group_1(A,B,k3_group_4(A,C)) ) ) ) ) ) ) )).

fof(t9_polynom2,axiom,(
    ! [A,B] :
      ( ( v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_relat_2(C)
            & v4_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( r3_orders_1(C,B)
           => k2_triang_1(A,B,C) = k1_xboole_0 ) ) ) )).

fof(t10_polynom2,axiom,(
    ! [A,B] :
      ( ( v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_relat_2(C)
            & v4_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( r3_orders_1(C,B)
           => ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => ( ( r2_hidden(D,k4_finseq_1(k2_triang_1(A,B,C)))
                        & r2_hidden(E,k4_finseq_1(k2_triang_1(A,B,C)))
                        & k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,C),D) = k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,C),E) )
                     => D = E ) ) ) ) ) ) )).

fof(t11_polynom2,axiom,(
    ! [A,B] :
      ( ( v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,A)
         => ( ~ r2_hidden(C,B)
           => ! [D] :
                ( ( v1_finset_1(D)
                  & m1_subset_1(D,k1_zfmisc_1(A)) )
               => ( D = k2_xboole_0(k1_tarski(C),B)
                 => ! [E] :
                      ( ( v1_relat_2(E)
                        & v4_relat_2(E)
                        & v8_relat_2(E)
                        & v1_partfun1(E,A,A)
                        & m2_relset_1(E,A,A) )
                     => ( r3_orders_1(E,D)
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( ( r2_hidden(F,k4_finseq_1(k2_triang_1(A,D,E)))
                                & k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),F) = C )
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( ( r1_xreal_0(np__1,G)
                                      & r1_xreal_0(G,k5_real_1(F,np__1)) )
                                   => k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),G) = k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,E),G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_polynom2,axiom,(
    ! [A,B] :
      ( ( v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,A)
         => ( ~ r2_hidden(C,B)
           => ! [D] :
                ( ( v1_finset_1(D)
                  & m1_subset_1(D,k1_zfmisc_1(A)) )
               => ( D = k2_xboole_0(k1_tarski(C),B)
                 => ! [E] :
                      ( ( v1_relat_2(E)
                        & v4_relat_2(E)
                        & v8_relat_2(E)
                        & v1_partfun1(E,A,A)
                        & m2_relset_1(E,A,A) )
                     => ( r3_orders_1(E,D)
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( ( r2_hidden(F,k4_finseq_1(k2_triang_1(A,D,E)))
                                & k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),F) = C )
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( ( r1_xreal_0(F,G)
                                      & r1_xreal_0(G,k3_finseq_1(k2_triang_1(A,B,E))) )
                                   => k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),k1_nat_1(G,np__1)) = k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,E),G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_polynom2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ( ~ r2_hidden(C,B)
               => ! [D] :
                    ( ( v1_finset_1(D)
                      & m1_subset_1(D,k1_zfmisc_1(A)) )
                   => ( D = k2_xboole_0(k1_tarski(C),B)
                     => ! [E] :
                          ( ( v1_relat_2(E)
                            & v4_relat_2(E)
                            & v8_relat_2(E)
                            & v1_partfun1(E,A,A)
                            & m2_relset_1(E,A,A) )
                         => ( r3_orders_1(E,D)
                           => ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ( ( r2_hidden(k1_nat_1(F,np__1),k4_finseq_1(k2_triang_1(A,D,E)))
                                    & k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),k1_nat_1(F,np__1)) = C )
                                 => k2_triang_1(A,D,E) = k5_finseq_5(A,k2_triang_1(A,B,E),C,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_polynom2,axiom,(
    ! [A,B] :
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ( k11_polynom1(B) = k1_xboole_0
       => B = k16_polynom1(A) ) ) )).

fof(d1_polynom2,axiom,(
    ! [A,B] :
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ( v1_polynom2(B,A)
      <=> B = k16_polynom1(A) ) ) )).

fof(t15_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v7_seqm_3(B)
            & v1_polynom1(B)
            & m1_pboole(B,A) )
         => r3_orders_1(k1_yellow_1(A),k1_polynom2(A,B)) ) ) )).

fof(d2_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v7_seqm_3(B)
            & v1_polynom1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_group_1(C)
                & ~ v3_realset2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( E = k3_polynom2(A,B,C,D)
                      <=> ? [F] :
                            ( m2_finseq_1(F,u1_struct_0(C))
                            & k3_finseq_1(F) = k3_finseq_1(k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)))
                            & E = k3_group_4(C,F)
                            & ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ( ( r1_xreal_0(np__1,G)
                                    & r1_xreal_0(G,k3_finseq_1(F)) )
                                 => k4_finseq_4(k5_numbers,u1_struct_0(C),F,G) = k2_binop_1(u1_struct_0(C),k5_numbers,u1_struct_0(C),k5_group_1(C),k4_finseq_4(k5_numbers,u1_struct_0(C),k1_partfun1(k5_numbers,A,A,u1_struct_0(C),k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)),D),G),k4_finseq_4(k5_numbers,k5_numbers,k2_polynom2(A,k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)),B),G)) ) ) ) ) ) ) ) ) ) )).

fof(t16_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_group_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k3_polynom2(A,k16_polynom1(A),B,C) = k2_group_1(B) ) ) ) )).

fof(t17_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_group_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [C,D] :
              ( ( v7_seqm_3(D)
                & v1_polynom1(D)
                & m1_pboole(D,A) )
             => ( k1_polynom2(A,D) = k1_tarski(C)
               => ! [E] :
                    ( ( v1_funct_1(E)
                      & v1_funct_2(E,A,u1_struct_0(B))
                      & m2_relset_1(E,A,u1_struct_0(B)) )
                   => k3_polynom2(A,D,B,E) = k1_binop_1(k5_group_1(B),k1_funct_1(E,C),k8_polynom1(D,C)) ) ) ) ) ) )).

fof(t18_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(B))
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k3_polynom2(A,k9_polynom1(A,C,D),B,E) = k10_group_1(B,k3_polynom2(A,C,B,E),k3_polynom2(A,D,B,E)) ) ) ) ) ) )).

fof(t19_polynom2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v2_group_1(A)
        & v7_vectsp_1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( v3_ordinal1(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k14_polynom1(B),u1_struct_0(A))
                & v2_polynom1(C,k14_polynom1(B),A)
                & m2_relset_1(C,k14_polynom1(B),u1_struct_0(A)) )
             => ( k12_polynom1(k14_polynom1(B),A,C) = k1_xboole_0
               => C = k26_polynom1(B,A) ) ) ) ) )).

fof(t20_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [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)) )
             => r3_orders_1(k17_polynom1(A),k12_polynom1(k14_polynom1(A),B,C)) ) ) ) )).

fof(d3_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( m1_polynom1(B,A,k14_polynom1(A))
         => k4_polynom2(A,B) = B ) ) )).

fof(d4_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [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,A,u1_struct_0(B))
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( E = k5_polynom2(A,B,C,D)
                      <=> ? [F] :
                            ( m2_finseq_1(F,u1_struct_0(B))
                            & k3_finseq_1(F) = k3_finseq_1(k2_triang_1(k14_polynom1(A),k12_polynom1(k14_polynom1(A),B,C),k17_polynom1(A)))
                            & E = k9_rlvect_1(B,F)
                            & ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ( ( r1_xreal_0(np__1,G)
                                    & r1_xreal_0(G,k3_finseq_1(F)) )
                                 => k4_finseq_4(k5_numbers,u1_struct_0(B),F,G) = k1_group_1(B,k4_finseq_4(k5_numbers,u1_struct_0(B),k1_partfun1(k5_numbers,k14_polynom1(A),k14_polynom1(A),u1_struct_0(B),k2_triang_1(k14_polynom1(A),k12_polynom1(k14_polynom1(A),B,C),k17_polynom1(A)),C),G),k3_polynom2(A,k4_polynom2(A,k4_finseq_4(k5_numbers,k14_polynom1(A),k2_triang_1(k14_polynom1(A),k12_polynom1(k14_polynom1(A),B,C),k17_polynom1(A)),G)),B,D)) ) ) ) ) ) ) ) ) ) )).

fof(t21_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [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) )
                 => ( k12_polynom1(k14_polynom1(A),B,C) = k1_tarski(D)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,u1_struct_0(B))
                          & m2_relset_1(E,A,u1_struct_0(B)) )
                       => k5_polynom2(A,B,C,E) = k1_group_1(B,k15_polynom1(A,B,C,D),k3_polynom2(A,D,B,E)) ) ) ) ) ) ) )).

fof(t22_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k5_polynom2(A,B,k26_polynom1(A,B),C) = k1_rlvect_1(B) ) ) ) )).

fof(t23_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k5_polynom2(A,B,k27_polynom1(A,B),C) = k2_group_1(B) ) ) ) )).

fof(t24_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [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,A,u1_struct_0(B))
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k5_polynom2(A,B,k24_polynom1(A,B,C),D) = k5_rlvect_1(B,k5_polynom2(A,B,C,D)) ) ) ) ) )).

fof(t25_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [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)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(B))
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k5_polynom2(A,B,k23_polynom1(A,B,C,D),E) = k4_rlvect_1(B,k5_polynom2(A,B,C,E),k5_polynom2(A,B,D,E)) ) ) ) ) ) )).

fof(t26_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [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)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(B))
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k5_polynom2(A,B,k25_polynom1(A,B,C,D),E) = k6_rlvect_1(B,k5_polynom2(A,B,C,E),k5_polynom2(A,B,D,E)) ) ) ) ) ) )).

fof(t27_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
                & v2_polynom1(C,k14_polynom1(A),B)
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                    & v2_polynom1(D,k14_polynom1(A),B)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(B))
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k5_polynom2(A,B,k29_polynom1(A,B,C,D),E) = k10_group_1(B,k5_polynom2(A,B,C,E),k5_polynom2(A,B,D,E)) ) ) ) ) ) )).

fof(d5_polynom2,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B)) )
                 => ( D = k6_polynom2(A,B,C)
                  <=> ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k14_polynom1(A),u1_struct_0(B))
                          & v2_polynom1(E,k14_polynom1(A),B)
                          & m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) )
                       => k1_funct_1(D,E) = k5_polynom2(A,B,E,C) ) ) ) ) ) ) )).

fof(s1_polynom2,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ~ ( r2_hidden(A,k2_finseq_1(f2_s1_polynom2))
            & ! [B] :
                ( m1_subset_1(B,f1_s1_polynom2)
               => ~ p1_s1_polynom2(A,B) ) ) )
   => ? [A] :
        ( m2_finseq_1(A,f1_s1_polynom2)
        & k4_finseq_1(A) = k2_finseq_1(f2_s1_polynom2)
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(f2_s1_polynom2))
             => p1_s1_polynom2(B,k4_finseq_4(k5_numbers,f1_s1_polynom2,A,B)) ) ) ) )).

fof(s2_polynom2,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ( r1_xreal_0(np__1,A)
            & r1_xreal_0(A,k5_real_1(f3_s2_polynom2,np__1)) )
         => ! [B] :
              ( m1_subset_1(B,f1_s2_polynom2)
             => ? [C] :
                  ( m1_subset_1(C,f1_s2_polynom2)
                  & p1_s2_polynom2(A,B,C) ) ) ) )
   => ? [A] :
        ( m2_finseq_1(A,f1_s2_polynom2)
        & k3_finseq_1(A) = f3_s2_polynom2
        & ( k4_finseq_4(k5_numbers,f1_s2_polynom2,A,np__1) = f2_s2_polynom2
          | f3_s2_polynom2 = np__0 )
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( ( r1_xreal_0(np__1,B)
                & r1_xreal_0(B,k5_real_1(f3_s2_polynom2,np__1)) )
             => p1_s2_polynom2(B,k4_finseq_4(k5_numbers,f1_s2_polynom2,A,B),k4_finseq_4(k5_numbers,f1_s2_polynom2,A,k1_nat_1(B,np__1))) ) ) ) )).

fof(s3_polynom2,axiom,
    ( ( ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,A)
              & r1_xreal_0(A,k5_real_1(f3_s3_polynom2,np__1)) )
           => ! [B] :
                ( m1_subset_1(B,f1_s3_polynom2)
               => ! [C] :
                    ( m1_subset_1(C,f1_s3_polynom2)
                   => ! [D] :
                        ( m1_subset_1(D,f1_s3_polynom2)
                       => ( ( p1_s3_polynom2(A,B,C)
                            & p1_s3_polynom2(A,B,D) )
                         => C = D ) ) ) ) ) )
      & k3_finseq_1(f4_s3_polynom2) = f3_s3_polynom2
      & ( k4_finseq_4(k5_numbers,f1_s3_polynom2,f4_s3_polynom2,np__1) = f2_s3_polynom2
        | f3_s3_polynom2 = np__0 )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,A)
              & r1_xreal_0(A,k5_real_1(f3_s3_polynom2,np__1)) )
           => p1_s3_polynom2(A,k4_finseq_4(k5_numbers,f1_s3_polynom2,f4_s3_polynom2,A),k4_finseq_4(k5_numbers,f1_s3_polynom2,f4_s3_polynom2,k1_nat_1(A,np__1))) ) )
      & k3_finseq_1(f5_s3_polynom2) = f3_s3_polynom2
      & ( k4_finseq_4(k5_numbers,f1_s3_polynom2,f5_s3_polynom2,np__1) = f2_s3_polynom2
        | f3_s3_polynom2 = np__0 )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,A)
              & r1_xreal_0(A,k5_real_1(f3_s3_polynom2,np__1)) )
           => p1_s3_polynom2(A,k4_finseq_4(k5_numbers,f1_s3_polynom2,f5_s3_polynom2,A),k4_finseq_4(k5_numbers,f1_s3_polynom2,f5_s3_polynom2,k1_nat_1(A,np__1))) ) ) )
   => f4_s3_polynom2 = f5_s3_polynom2 )).

fof(s4_polynom2,axiom,
    ( ( p1_s4_polynom2(f1_s4_polynom2)
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(f1_s4_polynom2,A)
              & p1_s4_polynom2(A) )
           => ( r1_xreal_0(f2_s4_polynom2,A)
              | p1_s4_polynom2(k1_nat_1(A,np__1)) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ( r1_xreal_0(f1_s4_polynom2,A)
            & r1_xreal_0(A,f2_s4_polynom2) )
         => p1_s4_polynom2(A) ) ) )).

fof(s5_polynom2,axiom,
    ( ( p1_s5_polynom2(f1_s5_polynom2)
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(f1_s5_polynom2,A)
              & ! [B] :
                  ( m2_subset_1(B,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(f1_s5_polynom2,B)
                      & r1_xreal_0(B,A) )
                   => p1_s5_polynom2(B) ) ) )
           => ( r1_xreal_0(f2_s5_polynom2,A)
              | p1_s5_polynom2(k1_nat_1(A,np__1)) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ( r1_xreal_0(f1_s5_polynom2,A)
            & r1_xreal_0(A,f2_s5_polynom2) )
         => p1_s5_polynom2(A) ) ) )).

fof(s6_polynom2,axiom,
    ( ( p1_s6_polynom2(k1_funct_1(f2_s6_polynom2,np__1))
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,A)
              & p1_s6_polynom2(k1_funct_1(f2_s6_polynom2,A)) )
           => ( r1_xreal_0(k3_finseq_1(f2_s6_polynom2),A)
              | p1_s6_polynom2(k1_funct_1(f2_s6_polynom2,k1_nat_1(A,np__1))) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ( r1_xreal_0(np__1,A)
            & r1_xreal_0(A,k3_finseq_1(f2_s6_polynom2)) )
         => p1_s6_polynom2(k1_funct_1(f2_s6_polynom2,A)) ) ) )).

fof(dt_k1_polynom2,axiom,(
    ! [A,B] :
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ( v1_finset_1(k1_polynom2(A,B))
        & m1_subset_1(k1_polynom2(A,B),k1_zfmisc_1(A)) ) ) )).

fof(redefinition_k1_polynom2,axiom,(
    ! [A,B] :
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => k1_polynom2(A,B) = k11_polynom1(B) ) )).

fof(dt_k2_polynom2,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => ( v1_funct_1(k2_polynom2(A,B,C))
        & m2_relset_1(k2_polynom2(A,B,C),k5_numbers,k5_numbers) ) ) )).

fof(redefinition_k2_polynom2,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => k2_polynom2(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k3_polynom2,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & ~ v3_struct_0(C)
        & v2_group_1(C)
        & ~ v3_realset2(C)
        & l3_vectsp_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,u1_struct_0(C))
        & m1_relset_1(D,A,u1_struct_0(C)) )
     => m1_subset_1(k3_polynom2(A,B,C,D),u1_struct_0(C)) ) )).

fof(dt_k4_polynom2,axiom,(
    ! [A,B] :
      ( ( v3_ordinal1(A)
        & m1_subset_1(B,k14_polynom1(A)) )
     => ( v7_seqm_3(k4_polynom2(A,B))
        & v1_polynom1(k4_polynom2(A,B))
        & m1_pboole(k4_polynom2(A,B),A) ) ) )).

fof(dt_k5_polynom2,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,A,u1_struct_0(B))
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => m1_subset_1(k5_polynom2(A,B,C,D),u1_struct_0(B)) ) )).

fof(dt_k6_polynom2,axiom,(
    ! [A,B,C] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v2_group_1(B)
        & v7_vectsp_1(B)
        & ~ v3_realset2(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_funct_1(k6_polynom2(A,B,C))
        & v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
        & m2_relset_1(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B)) ) ) )).
%------------------------------------------------------------------------------