SET007 Axioms: SET007+751.ax


%------------------------------------------------------------------------------
% File     : SET007+751 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Term Orders
% 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    : termord [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   64 (   0 unit)
%            Number of atoms       : 1021 (  37 equality)
%            Maximal formula depth :   22 (  13 average)
%            Number of connectives : 1007 (  50 ~  ;   5  |; 718  &)
%                                         (   9 <=>; 225 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   48 (   0 propositional; 1-4 arity)
%            Number of functors    :   28 (   2 constant; 0-4 arity)
%            Number of variables   :  256 (   0 singleton; 250 !;   6 ?)
%            Maximal term depth    :    4 (   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_termord,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A) ) )).

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

fof(fc1_termord,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)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v3_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))
        & v3_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)
        & v3_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) )).

fof(fc2_termord,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_vectsp_1(B)
        & l3_vectsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v4_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))
        & v4_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)
        & v3_polynom7(k28_polynom1(A,B,C,D),A,B)
        & v4_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) )).

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

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

fof(fc3_termord,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & ~ v3_realset2(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)
        & v1_polynom7(D,A,C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_relat_1(k5_termord(A,B,C,D))
        & v1_funct_1(k5_termord(A,B,C,D))
        & v1_funct_2(k5_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k5_termord(A,B,C,D),k14_polynom1(A),C)
        & v1_polynom7(k5_termord(A,B,C,D),A,C)
        & v3_polynom7(k5_termord(A,B,C,D),A,C) ) ) )).

fof(fc4_termord,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & ~ v3_realset2(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)
        & v1_polynom7(D,A,C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => v8_rlvect_1(k4_termord(A,B,C,D),C) ) )).

fof(d1_termord,axiom,(
    ! [A,B] :
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ( v1_termord(B,A)
      <=> B != k16_polynom1(A) ) ) )).

fof(t1_termord,axiom,(
    ! [A,B] :
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) )
         => ( r3_polynom1(A,B,C)
          <=> ? [D] :
                ( v7_seqm_3(D)
                & v1_polynom1(D)
                & m1_pboole(D,A)
                & r6_pboole(A,C,k9_polynom1(A,B,D)) ) ) ) ) )).

fof(t2_termord,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)
            & 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(t3_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & v2_vectsp_2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( ( v8_rlvect_1(E,B)
                        & m1_subset_1(E,u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v8_rlvect_1(F,B)
                            & m1_subset_1(F,u1_struct_0(B)) )
                         => k1_polynom7(A,B,k1_group_1(B,E,F),k9_polynom1(A,C,D)) = k28_polynom1(A,B,k1_polynom7(A,B,E,C),k1_polynom7(A,B,F,D)) ) ) ) ) ) ) )).

fof(t4_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & v2_vectsp_2(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k4_polynom7(A,B,k1_group_1(B,C,D)) = k28_polynom1(A,B,k4_polynom7(A,B,C),k4_polynom7(A,B,D)) ) ) ) ) )).

fof(d2_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r1_termord(A,B,C,D)
                  <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ) )).

fof(d3_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r2_termord(A,B,C,D)
                  <=> ( r1_termord(A,B,C,D)
                      & C != D ) ) ) ) ) ) )).

fof(d4_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( ( r1_termord(A,B,C,D)
                     => k1_termord(A,B,C,D) = C )
                    & ( ~ r1_termord(A,B,C,D)
                     => k1_termord(A,B,C,D) = D ) ) ) ) ) ) )).

fof(d5_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( ( r1_termord(A,B,D,C)
                     => k2_termord(A,B,C,D) = C )
                    & ( ~ r1_termord(A,B,D,C)
                     => k2_termord(A,B,C,D) = D ) ) ) ) ) ) )).

fof(t5_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r1_termord(A,B,C,D)
                  <=> ~ r2_termord(A,B,D,C) ) ) ) ) ) )).

fof(t6_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => r1_termord(A,B,C,C) ) ) ) )).

fof(t7_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( ( r1_termord(A,B,C,D)
                      & r1_termord(A,B,D,C) )
                   => r6_pboole(A,C,D) ) ) ) ) ) )).

fof(t8_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ( ( r1_termord(A,B,C,D)
                          & r1_termord(A,B,D,E) )
                       => r1_termord(A,B,C,E) ) ) ) ) ) ) )).

fof(t9_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => r1_termord(A,B,k16_polynom1(A),C) ) ) ) )).

fof(t10_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r3_polynom1(A,C,D)
                   => r1_termord(A,B,C,D) ) ) ) ) ) )).

fof(t11_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r6_pboole(A,k1_termord(A,B,C,D),C)
                    | r6_pboole(A,k1_termord(A,B,C,D),D) ) ) ) ) ) )).

fof(t12_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r6_pboole(A,k2_termord(A,B,C,D),C)
                    | r6_pboole(A,k2_termord(A,B,C,D),D) ) ) ) ) ) )).

fof(t13_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r1_termord(A,B,k1_termord(A,B,C,D),C)
                    & r1_termord(A,B,k1_termord(A,B,C,D),D) ) ) ) ) ) )).

fof(t14_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r1_termord(A,B,C,k2_termord(A,B,C,D))
                    & r1_termord(A,B,D,k2_termord(A,B,C,D)) ) ) ) ) ) )).

fof(t15_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r6_pboole(A,k1_termord(A,B,C,D),k1_termord(A,B,D,C))
                    & r6_pboole(A,k2_termord(A,B,C,D),k2_termord(A,B,D,C)) ) ) ) ) ) )).

fof(t16_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,A) )
                 => ( r6_pboole(A,k1_termord(A,B,C,D),C)
                  <=> r6_pboole(A,k2_termord(A,B,C,D),D) ) ) ) ) ) )).

fof(d6_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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] :
                      ( m1_polynom1(E,A,k14_polynom1(A))
                     => ( E = k3_termord(A,B,C,D)
                      <=> ( ( k12_polynom1(k14_polynom1(A),C,D) = k1_xboole_0
                            & r6_pboole(A,E,k16_polynom1(A)) )
                          | ( r2_hidden(E,k12_polynom1(k14_polynom1(A),C,D))
                            & ! [F] :
                                ( ( v7_seqm_3(F)
                                  & v1_polynom1(F)
                                  & m1_pboole(F,A) )
                               => ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,D))
                                 => r1_termord(A,B,F,E) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)) )
                 => k4_termord(A,B,C,D) = k15_polynom1(A,C,D,k3_termord(A,B,C,D)) ) ) ) ) )).

fof(d8_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)) )
                 => k5_termord(A,B,C,D) = k1_polynom7(A,C,k4_termord(A,B,C,D),k3_termord(A,B,C,D)) ) ) ) ) )).

fof(t17_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)) )
                 => ( k4_termord(A,B,C,D) = k1_rlvect_1(C)
                  <=> D = k26_polynom1(A,C) ) ) ) ) ) )).

fof(t18_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => k15_polynom1(A,C,k5_termord(A,B,C,D),k3_termord(A,B,C,D)) = k15_polynom1(A,C,D,k3_termord(A,B,C,D)) ) ) ) ) )).

fof(t19_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ( E != k3_termord(A,B,C,D)
                       => k15_polynom1(A,C,k5_termord(A,B,C,D),E) = k1_rlvect_1(C) ) ) ) ) ) ) )).

fof(t20_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => r1_tarski(k12_polynom1(k14_polynom1(A),C,k5_termord(A,B,C,D)),k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) )).

fof(t21_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ( k12_polynom1(k14_polynom1(A),C,k5_termord(A,B,C,D)) = k1_xboole_0
                    | k12_polynom1(k14_polynom1(A),C,k5_termord(A,B,C,D)) = k1_tarski(k3_termord(A,B,C,D)) ) ) ) ) ) )).

fof(t22_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ( r6_pboole(A,k2_polynom7(A,C,k5_termord(A,B,C,D)),k3_termord(A,B,C,D))
                    & k3_polynom7(A,C,k5_termord(A,B,C,D)) = k4_termord(A,B,C,D) ) ) ) ) ) )).

fof(t23_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_struct_0(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v3_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ( r6_pboole(A,k3_termord(A,B,C,D),k2_polynom7(A,C,D))
                    & k4_termord(A,B,C,D) = k3_polynom7(A,C,D)
                    & k5_termord(A,B,C,D) = D ) ) ) ) ) )).

fof(t24_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_struct_0(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v4_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ( r6_pboole(A,k3_termord(A,B,C,D),k16_polynom1(A))
                    & k4_termord(A,B,C,D) = k15_polynom1(A,C,D,k16_polynom1(A)) ) ) ) ) ) )).

fof(t25_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_struct_0(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( r6_pboole(A,k3_termord(A,B,C,k4_polynom7(A,C,D)),k16_polynom1(A))
                    & k4_termord(A,B,C,k4_polynom7(A,C,D)) = D ) ) ) ) ) )).

fof(t26_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => r6_pboole(A,k3_termord(A,B,C,k5_termord(A,B,C,D)),k3_termord(A,B,C,D)) ) ) ) ) )).

fof(t27_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => k4_termord(A,B,C,k5_termord(A,B,C,D)) = k4_termord(A,B,C,D) ) ) ) ) )).

fof(t28_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ 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)) )
                 => k5_termord(A,B,C,k5_termord(A,B,C,D)) = k5_termord(A,B,C,D) ) ) ) ) )).

fof(t29_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v2_group_1(C)
                & v7_vectsp_1(C)
                & v1_algstr_1(C)
                & ~ v3_realset2(C)
                & v2_vectsp_2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & v1_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & v1_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => r2_hidden(k9_polynom1(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E)),k12_polynom1(k14_polynom1(A),C,k28_polynom1(A,C,D,E))) ) ) ) ) ) )).

fof(t31_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v2_group_1(C)
                & v7_vectsp_1(C)
                & ~ v3_realset2(C)
                & v2_vectsp_2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & v1_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & v1_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => r6_pboole(A,k3_termord(A,B,C,k28_polynom1(A,C,D,E)),k9_polynom1(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))) ) ) ) ) ) )).

fof(t32_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v2_group_1(C)
                & v7_vectsp_1(C)
                & ~ v3_realset2(C)
                & v2_vectsp_2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & v1_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & v1_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => k4_termord(A,B,C,k28_polynom1(A,C,D,E)) = k1_group_1(C,k4_termord(A,B,C,D),k4_termord(A,B,C,E)) ) ) ) ) ) )).

fof(t33_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v2_group_1(C)
                & v7_vectsp_1(C)
                & ~ v3_realset2(C)
                & v2_vectsp_2(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & v1_polynom7(D,A,C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & v1_polynom7(E,A,C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => k5_termord(A,B,C,k28_polynom1(A,C,D,E)) = k28_polynom1(A,C,k5_termord(A,B,C,D),k5_termord(A,B,C,E)) ) ) ) ) ) )).

fof(t34_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v2_bagorder(B,A)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v5_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( 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_termord(A,B,k3_termord(A,B,C,k22_polynom1(A,C,D,E)),k2_termord(A,B,k3_termord(A,B,C,D),k3_termord(A,B,C,E))) ) ) ) ) ) )).

fof(d9_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => k6_termord(A,B,C,D) = k25_polynom1(A,C,D,k5_termord(A,B,C,D)) ) ) ) ) )).

fof(t35_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( 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_tarski(k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D)),k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) )).

fof(t36_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( 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)) )
                 => k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D)) = k4_xboole_0(k12_polynom1(k14_polynom1(A),C,D),k1_tarski(k3_termord(A,B,C,D))) ) ) ) ) )).

fof(t37_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( 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)) )
                 => k12_polynom1(k14_polynom1(A),C,k22_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,D))) = k12_polynom1(k14_polynom1(A),C,D) ) ) ) ) )).

fof(t38_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( 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)) )
                 => k22_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,D)) = D ) ) ) ) )).

fof(t39_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( 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)) )
                 => k15_polynom1(A,C,k6_termord(A,B,C,D),k3_termord(A,B,C,D)) = k1_rlvect_1(C) ) ) ) ) )).

fof(t40_termord,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] :
              ( ( 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] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ( r2_hidden(E,k12_polynom1(k14_polynom1(A),C,D))
                       => ( E = k3_termord(A,B,C,D)
                          | k15_polynom1(A,C,k6_termord(A,B,C,D),E) = k15_polynom1(A,C,D,E) ) ) ) ) ) ) ) )).

fof(dt_k1_termord,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A)
        & v7_seqm_3(D)
        & v1_polynom1(D)
        & m1_pboole(D,A) )
     => ( v7_seqm_3(k1_termord(A,B,C,D))
        & v1_polynom1(k1_termord(A,B,C,D))
        & m1_pboole(k1_termord(A,B,C,D),A) ) ) )).

fof(dt_k2_termord,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A)
        & v7_seqm_3(D)
        & v1_polynom1(D)
        & m1_pboole(D,A) )
     => ( v7_seqm_3(k2_termord(A,B,C,D))
        & v1_polynom1(k2_termord(A,B,C,D))
        & m1_pboole(k2_termord(A,B,C,D),A) ) ) )).

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

fof(dt_k4_termord,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & ~ v3_struct_0(C)
        & l2_struct_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(A),C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => m1_subset_1(k4_termord(A,B,C,D),u1_struct_0(C)) ) )).

fof(dt_k5_termord,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & ~ v3_struct_0(C)
        & l2_struct_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(A),C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_funct_1(k5_termord(A,B,C,D))
        & v1_funct_2(k5_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
        & v3_polynom7(k5_termord(A,B,C,D),A,C)
        & m2_relset_1(k5_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) ) ) )).

fof(dt_k6_termord,axiom,(
    ! [A,B,C,D] :
      ( ( v3_ordinal1(A)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & l1_rlvect_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(A),C)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_funct_1(k6_termord(A,B,C,D))
        & v1_funct_2(k6_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
        & v2_polynom1(k6_termord(A,B,C,D),k14_polynom1(A),C)
        & m2_relset_1(k6_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) ) ) )).

fof(t30_termord,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)
            & 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)) )
                 => r1_tarski(k12_polynom1(k14_polynom1(A),B,k28_polynom1(A,B,C,D)),a_4_0_termord(A,B,C,D)) ) ) ) ) )).

fof(fraenkel_a_4_0_termord,axiom,(
    ! [A,B,C,D,E] :
      ( ( v3_ordinal1(B)
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v2_group_1(C)
        & v7_vectsp_1(C)
        & l3_vectsp_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(B),u1_struct_0(C))
        & v2_polynom1(D,k14_polynom1(B),C)
        & m2_relset_1(D,k14_polynom1(B),u1_struct_0(C))
        & v1_funct_1(E)
        & v1_funct_2(E,k14_polynom1(B),u1_struct_0(C))
        & v2_polynom1(E,k14_polynom1(B),C)
        & m2_relset_1(E,k14_polynom1(B),u1_struct_0(C)) )
     => ( r2_hidden(A,a_4_0_termord(B,C,D,E))
      <=> ? [F,G] :
            ( m1_polynom1(F,B,k14_polynom1(B))
            & m1_polynom1(G,B,k14_polynom1(B))
            & A = k9_polynom1(B,F,G)
            & r2_hidden(F,k12_polynom1(k14_polynom1(B),C,D))
            & r2_hidden(G,k12_polynom1(k14_polynom1(B),C,E)) ) ) ) )).
%------------------------------------------------------------------------------