SET007 Axioms: SET007+717.ax


%------------------------------------------------------------------------------
% File     : SET007+717 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On Ordering of Bags
% 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    : bagorder [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   93 (   4 unit)
%            Number of atoms       :  807 (  76 equality)
%            Maximal formula depth :   22 (   9 average)
%            Number of connectives :  807 (  93 ~  ;   2  |; 467  &)
%                                         (  27 <=>; 218 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   44 (   1 propositional; 0-3 arity)
%            Number of functors    :   66 (   6 constant; 0-4 arity)
%            Number of variables   :  236 (   0 singleton; 226 !;  10 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_bagorder,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v7_seqm_3(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B))
        & v1_seq_1(k7_relat_1(A,B))
        & v7_seqm_3(k7_relat_1(A,B)) ) ) )).

fof(fc2_bagorder,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_polynom1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B))
        & v1_polynom1(k7_relat_1(A,B)) ) ) )).

fof(fc3_bagorder,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers)
        & v7_seqm_3(D)
        & m1_pboole(D,A) )
     => ( v1_relat_1(k1_bagorder(A,B,C,D))
        & v1_funct_1(k1_bagorder(A,B,C,D))
        & v1_seq_1(k1_bagorder(A,B,C,D))
        & v7_seqm_3(k1_bagorder(A,B,C,D))
        & v1_polynom1(k1_bagorder(A,B,C,D)) ) ) )).

fof(fc4_bagorder,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers)
        & v1_polynom1(D)
        & m1_pboole(D,A) )
     => ( v1_relat_1(k1_bagorder(A,B,C,D))
        & v1_funct_1(k1_bagorder(A,B,C,D))
        & v1_polynom1(k1_bagorder(A,B,C,D)) ) ) )).

fof(fc5_bagorder,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k5_numbers) )
     => ~ v1_xboole_0(k2_bagorder(A,B)) ) )).

fof(rc1_bagorder,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)
          & v8_relat_2(B)
          & v2_bagorder(B,A) ) ) )).

fof(fc6_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ( v1_relat_1(k17_polynom1(A))
        & v1_partfun1(k17_polynom1(A),k14_polynom1(A),k14_polynom1(A))
        & v3_orders_1(k17_polynom1(A))
        & v1_relat_2(k17_polynom1(A))
        & v4_relat_2(k17_polynom1(A))
        & v8_relat_2(k17_polynom1(A))
        & v2_bagorder(k17_polynom1(A),A) ) ) )).

fof(fc7_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ( v1_relat_1(k4_bagorder(A))
        & v1_partfun1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(k4_bagorder(A))
        & v4_relat_2(k4_bagorder(A))
        & v8_relat_2(k4_bagorder(A))
        & v2_bagorder(k4_bagorder(A),A) ) ) )).

fof(fc8_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ( v1_relat_1(k6_bagorder(A))
        & v1_partfun1(k6_bagorder(A),k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(k6_bagorder(A))
        & v4_relat_2(k6_bagorder(A))
        & v8_relat_2(k6_bagorder(A))
        & v2_bagorder(k6_bagorder(A),A) ) ) )).

fof(fc9_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ( v1_relat_1(k7_bagorder(A))
        & v1_partfun1(k7_bagorder(A),k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(k7_bagorder(A))
        & v4_relat_2(k7_bagorder(A))
        & v8_relat_2(k7_bagorder(A))
        & v2_bagorder(k7_bagorder(A),A) ) ) )).

fof(fc10_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k14_bagorder(A))
        & v2_orders_2(k14_bagorder(A))
        & v3_orders_2(k14_bagorder(A))
        & v4_orders_2(k14_bagorder(A)) ) ) )).

fof(fc11_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k14_bagorder(A))
        & v2_orders_2(k14_bagorder(A))
        & v3_orders_2(k14_bagorder(A))
        & v4_orders_2(k14_bagorder(A))
        & v16_waybel_0(k14_bagorder(A)) ) ) )).

fof(t1_bagorder,axiom,(
    ! [A,B,C] :
      ( ( r2_hidden(C,A)
        & r2_hidden(C,B) )
     => ( k4_xboole_0(A,k1_tarski(C)) = k4_xboole_0(B,k1_tarski(C))
      <=> A = B ) ) )).

fof(t2_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k2_finseq_1(A))
          <=> ( m2_subset_1(k5_real_1(B,np__1),k1_numbers,k5_numbers)
              & ~ r1_xreal_0(A,k5_real_1(B,np__1)) ) ) ) ) )).

fof(t3_bagorder,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(A))
         => k5_relat_1(k9_finseq_1(B),A) = k9_finseq_1(k1_funct_1(A,B)) ) ) )).

fof(t4_bagorder,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( k1_relat_1(A) = k1_relat_1(B)
                  & r1_tarski(k2_relat_1(A),k1_relat_1(C))
                  & r1_tarski(k2_relat_1(B),k1_relat_1(C))
                  & r1_rfinseq(A,B) )
               => r1_rfinseq(k5_relat_1(A,C),k5_relat_1(B,C)) ) ) ) ) )).

fof(t5_bagorder,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ( k9_wsierp_1(A) = np__0
      <=> A = k4_finseqop(k5_numbers,k3_finseq_1(A),np__0) ) ) )).

fof(d1_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_pboole(D,A)
                 => ! [E] :
                      ( m1_pboole(E,k5_binarith(C,B))
                     => ( E = k1_bagorder(A,B,C,D)
                      <=> ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( r2_hidden(F,k5_binarith(C,B))
                             => k1_funct_1(E,F) = k1_funct_1(D,k1_nat_1(B,F)) ) ) ) ) ) ) ) ) )).

fof(t6_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_pboole(C,A)
             => ! [D] :
                  ( m1_pboole(D,A)
                 => ( r6_pboole(A,C,D)
                  <=> ( r6_pboole(k5_binarith(k1_nat_1(B,np__1),np__0),k1_bagorder(A,np__0,k1_nat_1(B,np__1),C),k1_bagorder(A,np__0,k1_nat_1(B,np__1),D))
                      & r6_pboole(k5_binarith(A,k1_nat_1(B,np__1)),k1_bagorder(A,k1_nat_1(B,np__1),A,C),k1_bagorder(A,k1_nat_1(B,np__1),A,D)) ) ) ) ) ) ) )).

fof(t7_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ~ ( B != k1_xboole_0
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( r2_hidden(C,B)
                      & r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) )).

fof(t8_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ~ ( B != k1_xboole_0
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( r2_hidden(C,B)
                      & r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) )).

fof(t9_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v3_wellfnd1(B,A)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(C,D)
                     => ( k8_funct_2(k5_numbers,u1_struct_0(A),B,D) != k8_funct_2(k5_numbers,u1_struct_0(A),B,C)
                        & r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,C),k8_funct_2(k5_numbers,u1_struct_0(A),B,D)),u1_orders_2(A)) ) ) ) ) ) ) ) )).

fof(d3_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v1_bagorder(B,A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,np__1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,C)),u1_orders_2(A)) ) ) ) ) )).

fof(t10_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v1_bagorder(B,A)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(C,D)
                     => r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,C),k8_funct_2(k5_numbers,u1_struct_0(A),B,D)),u1_orders_2(A)) ) ) ) ) ) ) )).

fof(t11_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ~ ( v1_wellfnd1(A)
              & v1_bagorder(B,A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ? [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                      & r1_xreal_0(C,D)
                      & k8_funct_2(k5_numbers,u1_struct_0(A),B,C) != k8_funct_2(k5_numbers,u1_struct_0(A),B,D) ) ) ) ) ) )).

fof(t12_bagorder,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,A)
     => ! [C] :
          ( ( v1_finset_1(C)
            & m1_subset_1(C,k1_zfmisc_1(A)) )
         => ! [D] :
              ( ( v1_partfun1(D,A,A)
                & v1_relat_2(D)
                & v4_relat_2(D)
                & v8_relat_2(D)
                & m2_relset_1(D,A,A) )
             => ( ( C = k1_tarski(B)
                  & r3_orders_1(D,C) )
               => k2_triang_1(A,C,D) = k9_finseq_1(B) ) ) ) ) )).

fof(d4_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v7_seqm_3(B)
            & v1_polynom1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( C = k3_bagorder(A,B)
              <=> ? [D] :
                    ( m2_finseq_1(D,k5_numbers)
                    & C = k9_wsierp_1(D)
                    & D = k2_polynom2(A,k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)),B) ) ) ) ) ) )).

fof(t13_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v7_seqm_3(B)
            & v1_polynom1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(A)) )
             => ! [D] :
                  ( m2_finseq_1(D,k5_numbers)
                 => ! [E] :
                      ( m2_finseq_1(E,k5_numbers)
                     => ( ( D = k2_polynom2(A,k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)),B)
                          & E = k2_polynom2(A,k2_triang_1(A,k1_finsub_1(k1_zfmisc_1(A),k1_polynom2(A,B),C),k1_yellow_1(A)),B) )
                       => k9_wsierp_1(D) = k9_wsierp_1(E) ) ) ) ) ) ) )).

fof(t14_bagorder,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) )
             => k3_bagorder(A,k9_polynom1(A,B,C)) = k1_nat_1(k3_bagorder(A,B),k3_bagorder(A,C)) ) ) ) )).

fof(t15_bagorder,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) )
             => ( r3_polynom1(A,C,B)
               => k3_bagorder(A,k10_polynom1(A,B,C)) = k5_real_1(k3_bagorder(A,B),k3_bagorder(A,C)) ) ) ) ) )).

fof(t16_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( v7_seqm_3(B)
            & v1_polynom1(B)
            & m1_pboole(B,A) )
         => ( k3_bagorder(A,B) = np__0
          <=> r6_pboole(A,B,k16_polynom1(A)) ) ) ) )).

fof(t17_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => r6_pboole(k5_binarith(B,A),k1_bagorder(C,A,B,k16_polynom1(C)),k16_polynom1(k5_binarith(B,A))) ) ) ) )).

fof(t18_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v7_seqm_3(D)
                    & v1_polynom1(D)
                    & m1_pboole(D,C) )
                 => ! [E] :
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,C) )
                     => r6_pboole(k5_binarith(B,A),k1_bagorder(C,A,B,k9_polynom1(C,D,E)),k9_polynom1(k5_binarith(B,A),k1_bagorder(C,A,B,D),k1_bagorder(C,A,B,E))) ) ) ) ) ) )).

fof(t19_bagorder,axiom,(
    ! [A] : k1_polynom2(A,k16_polynom1(A)) = k1_xboole_0 )).

fof(t20_bagorder,axiom,(
    ! [A,B] :
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ( k1_polynom2(A,B) = k1_xboole_0
       => r6_pboole(A,B,k16_polynom1(A)) ) ) )).

fof(t21_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( v3_ordinal1(B)
         => ! [C] :
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ( r2_hidden(B,A)
               => ( v7_seqm_3(k7_relat_1(C,B))
                  & v1_polynom1(k7_relat_1(C,B))
                  & m1_pboole(k7_relat_1(C,B),B) ) ) ) ) ) )).

fof(t22_bagorder,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) )
             => ( r3_polynom1(A,C,B)
               => r1_tarski(k1_polynom2(A,C),k1_polynom2(A,B)) ) ) ) ) )).

fof(d5_bagorder,axiom,(
    $true )).

fof(d6_bagorder,axiom,(
    $true )).

fof(d7_bagorder,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)) )
         => ( v2_bagorder(B,A)
          <=> ( r7_relat_2(B,k14_polynom1(A))
              & ! [C] :
                  ( ( v7_seqm_3(C)
                    & v1_polynom1(C)
                    & m1_pboole(C,A) )
                 => r2_hidden(k4_tarski(k16_polynom1(A),C),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] :
                          ( ( v7_seqm_3(E)
                            & v1_polynom1(E)
                            & m1_pboole(E,A) )
                         => ( r2_hidden(k4_tarski(C,D),B)
                           => r2_hidden(k4_tarski(k9_polynom1(A,C,E),k9_polynom1(A,D,E)),B) ) ) ) ) ) ) ) ) )).

fof(t23_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => v2_bagorder(k17_polynom1(A),A) ) )).

fof(t24_bagorder,axiom,(
    ! [A] :
      ( ( v3_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ~ v2_wellord1(k17_polynom1(A)) ) )).

fof(d8_bagorder,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)) )
         => ( B = k4_bagorder(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_hidden(k4_tarski(C,D),B)
                    <=> ~ ( ~ r6_pboole(A,C,D)
                          & ! [E] :
                              ( v3_ordinal1(E)
                             => ~ ( r2_hidden(E,A)
                                  & ~ r1_xreal_0(k8_polynom1(D,E),k8_polynom1(C,E))
                                  & ! [F] :
                                      ( v3_ordinal1(F)
                                     => ( ( r2_hidden(E,F)
                                          & r2_hidden(F,A) )
                                       => k8_polynom1(C,F) = k8_polynom1(D,F) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => v2_bagorder(k4_bagorder(A),A) ) )).

fof(t26_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => v2_wellord1(k4_bagorder(A)) ) )).

fof(d9_bagorder,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) )
                       => ( r2_hidden(k4_tarski(C,D),B)
                         => r2_hidden(k4_tarski(k9_polynom1(A,C,E),k9_polynom1(A,D,E)),B) ) ) ) )
           => ! [C] :
                ( ( v1_partfun1(C,k14_polynom1(A),k14_polynom1(A))
                  & v1_relat_2(C)
                  & v4_relat_2(C)
                  & v8_relat_2(C)
                  & m2_relset_1(C,k14_polynom1(A),k14_polynom1(A)) )
               => ( C = k5_bagorder(A,B)
                <=> ! [D] :
                      ( ( v7_seqm_3(D)
                        & v1_polynom1(D)
                        & m1_pboole(D,A) )
                     => ! [E] :
                          ( ( v7_seqm_3(E)
                            & v1_polynom1(E)
                            & m1_pboole(E,A) )
                         => ( r2_hidden(k4_tarski(D,E),C)
                          <=> ~ ( r1_xreal_0(k3_bagorder(A,E),k3_bagorder(A,D))
                                & ~ ( k3_bagorder(A,D) = k3_bagorder(A,E)
                                    & r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ) ) ) ) ) )).

fof(t27_bagorder,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) )
                         => ( r2_hidden(k4_tarski(C,D),B)
                           => r2_hidden(k4_tarski(k9_polynom1(A,C,E),k9_polynom1(A,D,E)),B) ) ) ) )
              & r7_relat_2(B,k14_polynom1(A)) )
           => v2_bagorder(k5_bagorder(A,B),A) ) ) ) )).

fof(d10_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => k6_bagorder(A) = k5_bagorder(A,k17_polynom1(A)) ) )).

fof(d11_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => k7_bagorder(A) = k5_bagorder(A,k4_bagorder(A)) ) )).

fof(t28_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => v2_bagorder(k6_bagorder(A),A) ) )).

fof(t29_bagorder,axiom,(
    ! [A] :
      ( ( v3_ordinal1(A)
        & ~ v1_finset_1(A) )
     => ~ v2_wellord1(k6_bagorder(A)) ) )).

fof(t30_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => v2_bagorder(k7_bagorder(A),A) ) )).

fof(t31_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => v2_wellord1(k7_bagorder(A)) ) )).

fof(d12_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_partfun1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1)))
                & v1_relat_2(C)
                & v4_relat_2(C)
                & v8_relat_2(C)
                & m2_relset_1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1))) )
             => ! [D] :
                  ( ( v1_partfun1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))))
                    & v1_relat_2(D)
                    & v4_relat_2(D)
                    & v8_relat_2(D)
                    & m2_relset_1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1)))) )
                 => ! [E] :
                      ( ( v1_partfun1(E,k14_polynom1(B),k14_polynom1(B))
                        & v1_relat_2(E)
                        & v4_relat_2(E)
                        & v8_relat_2(E)
                        & m2_relset_1(E,k14_polynom1(B),k14_polynom1(B)) )
                     => ( E = k8_bagorder(A,B,C,D)
                      <=> ! [F] :
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,B) )
                           => ! [G] :
                                ( ( v7_seqm_3(G)
                                  & v1_polynom1(G)
                                  & m1_pboole(G,B) )
                               => ( r2_hidden(k4_tarski(F,G),E)
                                <=> ( ( k1_bagorder(B,np__0,k1_nat_1(A,np__1),F) != k1_bagorder(B,np__0,k1_nat_1(A,np__1),G)
                                      & r2_hidden(k4_tarski(k1_bagorder(B,np__0,k1_nat_1(A,np__1),F),k1_bagorder(B,np__0,k1_nat_1(A,np__1),G)),C) )
                                    | ( r6_pboole(k5_binarith(k1_nat_1(A,np__1),np__0),k1_bagorder(B,np__0,k1_nat_1(A,np__1),F),k1_bagorder(B,np__0,k1_nat_1(A,np__1),G))
                                      & r2_hidden(k4_tarski(k1_bagorder(B,k1_nat_1(A,np__1),B,F),k1_bagorder(B,k1_nat_1(A,np__1),B,G)),D) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t32_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_partfun1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1)))
                & v1_relat_2(C)
                & v4_relat_2(C)
                & v8_relat_2(C)
                & m2_relset_1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1))) )
             => ! [D] :
                  ( ( v1_partfun1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))))
                    & v1_relat_2(D)
                    & v4_relat_2(D)
                    & v8_relat_2(D)
                    & m2_relset_1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1)))) )
                 => ( ( v2_bagorder(C,k1_nat_1(A,np__1))
                      & v2_bagorder(D,k5_binarith(B,k1_nat_1(A,np__1))) )
                   => v2_bagorder(k8_bagorder(A,B,C,D),B) ) ) ) ) ) )).

fof(d13_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_orders_2(B)
            & l1_orders_2(B) )
         => ( B = k9_bagorder(A)
          <=> ( u1_struct_0(B) = 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_hidden(k4_tarski(C,D),u1_orders_2(B))
                      <=> r3_polynom1(A,C,D) ) ) ) ) ) ) ) )).

fof(t33_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k11_dickson))) = k14_polynom1(A) ) )).

fof(t34_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k9_bagorder(A) = k5_yellow_1(A,k2_pre_circ(A,k11_dickson)) ) )).

fof(t35_bagorder,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & v1_relat_2(B)
            & v4_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ( v2_bagorder(B,A)
           => ( r1_tarski(u1_orders_2(k9_bagorder(A)),B)
              & v2_wellord1(B) ) ) ) ) )).

fof(d14_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ( ~ v1_xboole_0(B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k10_bagorder(A,B)
                <=> ( r2_hidden(C,B)
                    & r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ) )).

fof(d15_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ( ~ v1_xboole_0(B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k11_bagorder(A,B)
                <=> ( r2_hidden(C,B)
                    & r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ) )).

fof(t36_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(u1_struct_0(A)))
             => ( r2_hidden(k1_domain_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)),B,C),k3_tarski(k2_relat_1(k12_bagorder(A))))
              <=> ~ ( B != k1_xboole_0
                    & ~ ( B != k1_xboole_0
                        & C != k1_xboole_0
                        & k11_bagorder(A,B) != k11_bagorder(A,C)
                        & r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k11_bagorder(A,B),k11_bagorder(A,C)),u1_orders_2(A)) )
                    & ~ ( B != k1_xboole_0
                        & C != k1_xboole_0
                        & k11_bagorder(A,B) = k11_bagorder(A,C)
                        & r2_hidden(k4_tarski(k4_xboole_0(B,k6_domain_1(u1_struct_0(A),k11_bagorder(A,B))),k4_xboole_0(C,k6_domain_1(u1_struct_0(A),k11_bagorder(A,C)))),k3_tarski(k2_relat_1(k12_bagorder(A)))) ) ) ) ) ) ) )).

fof(t37_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ~ ( B != k1_xboole_0
              & r2_hidden(k4_tarski(B,k1_xboole_0),k3_tarski(k2_relat_1(k12_bagorder(A)))) ) ) ) )).

fof(t38_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => m1_subset_1(k4_xboole_0(B,k6_domain_1(u1_struct_0(A),k11_bagorder(A,B))),k5_finsub_1(u1_struct_0(A))) ) ) )).

fof(t39_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( v1_partfun1(k3_tarski(k2_relat_1(k12_bagorder(A))),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))
        & v1_relat_2(k3_tarski(k2_relat_1(k12_bagorder(A))))
        & v4_relat_2(k3_tarski(k2_relat_1(k12_bagorder(A))))
        & v8_relat_2(k3_tarski(k2_relat_1(k12_bagorder(A))))
        & m2_relset_1(k3_tarski(k2_relat_1(k12_bagorder(A))),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))) ) ) )).

fof(d17_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => k13_bagorder(A) = k3_tarski(k2_relat_1(k12_bagorder(A))) ) )).

fof(d18_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => k14_bagorder(A) = g1_orders_2(k5_finsub_1(u1_struct_0(A)),k13_bagorder(A)) ) )).

fof(t40_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_bagorder(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k14_bagorder(A)))
             => ( r2_hidden(k1_domain_1(u1_struct_0(k14_bagorder(A)),u1_struct_0(k14_bagorder(A)),B,C),u1_orders_2(k14_bagorder(A)))
              <=> ? [D] :
                    ( m1_subset_1(D,k5_finsub_1(u1_struct_0(A)))
                    & ? [E] :
                        ( m1_subset_1(E,k5_finsub_1(u1_struct_0(A)))
                        & B = D
                        & C = E
                        & ~ ( D != k1_xboole_0
                            & ~ ( D != k1_xboole_0
                                & E != k1_xboole_0
                                & k11_bagorder(A,D) != k11_bagorder(A,E)
                                & r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k11_bagorder(A,D),k11_bagorder(A,E)),u1_orders_2(A)) )
                            & ~ ( D != k1_xboole_0
                                & E != k1_xboole_0
                                & k11_bagorder(A,D) = k11_bagorder(A,E)
                                & r2_hidden(k4_tarski(k4_xboole_0(D,k6_domain_1(u1_struct_0(A),k11_bagorder(A,D))),k4_xboole_0(E,k6_domain_1(u1_struct_0(A),k11_bagorder(A,E)))),k13_bagorder(A)) ) ) ) ) ) ) ) ) )).

fof(d19_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( ( v1_wellfnd1(A)
              & r1_tarski(B,u1_struct_0(A)) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k15_bagorder(A,B)
                <=> ( r2_hidden(C,B)
                    & r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ) )).

fof(d20_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(A))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
                 => ( D = k16_bagorder(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k8_funct_2(k5_numbers,u1_struct_0(A),D,E) = k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(E,C)) ) ) ) ) ) ) )).

fof(t41_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( v3_wellfnd1(B,A)
               => v3_wellfnd1(k16_bagorder(A,B,C),A) ) ) ) ) )).

fof(t42_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( v1_wellfnd1(A)
       => v1_wellfnd1(k14_bagorder(A)) ) ) )).

fof(dt_k1_bagorder,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers)
        & m1_pboole(D,A) )
     => m1_pboole(k1_bagorder(A,B,C,D),k5_binarith(C,B)) ) )).

fof(dt_k2_bagorder,axiom,(
    $true )).

fof(dt_k3_bagorder,axiom,(
    ! [A,B] :
      ( ( v3_ordinal1(A)
        & v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => m2_subset_1(k3_bagorder(A,B),k1_numbers,k5_numbers) ) )).

fof(dt_k4_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ( v1_partfun1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(k4_bagorder(A))
        & v4_relat_2(k4_bagorder(A))
        & v8_relat_2(k4_bagorder(A))
        & m2_relset_1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A)) ) ) )).

fof(dt_k5_bagorder,axiom,(
    ! [A,B] :
      ( ( 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)) )
     => ( v1_partfun1(k5_bagorder(A,B),k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(k5_bagorder(A,B))
        & v4_relat_2(k5_bagorder(A,B))
        & v8_relat_2(k5_bagorder(A,B))
        & m2_relset_1(k5_bagorder(A,B),k14_polynom1(A),k14_polynom1(A)) ) ) )).

fof(dt_k6_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ( v1_partfun1(k6_bagorder(A),k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(k6_bagorder(A))
        & v4_relat_2(k6_bagorder(A))
        & v8_relat_2(k6_bagorder(A))
        & m2_relset_1(k6_bagorder(A),k14_polynom1(A),k14_polynom1(A)) ) ) )).

fof(dt_k7_bagorder,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ( v1_partfun1(k7_bagorder(A),k14_polynom1(A),k14_polynom1(A))
        & v1_relat_2(k7_bagorder(A))
        & v4_relat_2(k7_bagorder(A))
        & v8_relat_2(k7_bagorder(A))
        & m2_relset_1(k7_bagorder(A),k14_polynom1(A),k14_polynom1(A)) ) ) )).

fof(dt_k8_bagorder,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & v1_partfun1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1)))
        & v1_relat_2(C)
        & v4_relat_2(C)
        & v8_relat_2(C)
        & m1_relset_1(C,k14_polynom1(k1_nat_1(A,np__1)),k14_polynom1(k1_nat_1(A,np__1)))
        & v1_partfun1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))))
        & v1_relat_2(D)
        & v4_relat_2(D)
        & v8_relat_2(D)
        & m1_relset_1(D,k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1))),k14_polynom1(k5_binarith(B,k1_nat_1(A,np__1)))) )
     => ( v1_partfun1(k8_bagorder(A,B,C,D),k14_polynom1(B),k14_polynom1(B))
        & v1_relat_2(k8_bagorder(A,B,C,D))
        & v4_relat_2(k8_bagorder(A,B,C,D))
        & v8_relat_2(k8_bagorder(A,B,C,D))
        & m2_relset_1(k8_bagorder(A,B,C,D),k14_polynom1(B),k14_polynom1(B)) ) ) )).

fof(dt_k9_bagorder,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_orders_2(k9_bagorder(A))
        & l1_orders_2(k9_bagorder(A)) ) ) )).

fof(dt_k10_bagorder,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) )
     => m1_subset_1(k10_bagorder(A,B),u1_struct_0(A)) ) )).

fof(dt_k11_bagorder,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) )
     => m1_subset_1(k11_bagorder(A,B),u1_struct_0(A)) ) )).

fof(dt_k12_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k12_bagorder(A))
        & v1_funct_2(k12_bagorder(A),k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))))
        & m2_relset_1(k12_bagorder(A),k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))))) ) ) )).

fof(dt_k13_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( v1_partfun1(k13_bagorder(A),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))
        & v1_relat_2(k13_bagorder(A))
        & v4_relat_2(k13_bagorder(A))
        & v8_relat_2(k13_bagorder(A))
        & m2_relset_1(k13_bagorder(A),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))) ) ) )).

fof(dt_k14_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( v2_orders_2(k14_bagorder(A))
        & v3_orders_2(k14_bagorder(A))
        & v4_orders_2(k14_bagorder(A))
        & l1_orders_2(k14_bagorder(A)) ) ) )).

fof(dt_k15_bagorder,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v16_waybel_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B) )
     => m1_subset_1(k15_bagorder(A,B),u1_struct_0(A)) ) )).

fof(dt_k16_bagorder,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & m1_subset_1(C,k5_numbers) )
     => ( v1_funct_1(k16_bagorder(A,B,C))
        & v1_funct_2(k16_bagorder(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k16_bagorder(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(d2_bagorder,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_subset_1(B,k1_numbers,k5_numbers) )
         => k2_bagorder(A,B) = a_2_0_bagorder(A,B) ) ) )).

fof(d16_bagorder,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))))) )
         => ( B = k12_bagorder(A)
          <=> ( k4_relset_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))),B) = k5_numbers
              & k8_funct_2(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))),B,np__0) = a_1_0_bagorder(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k8_funct_2(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))),B,k1_nat_1(C,np__1)) = a_3_0_bagorder(A,B,C) ) ) ) ) ) )).

fof(fraenkel_a_2_0_bagorder,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_0_bagorder(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(B))
            & A = D
            & v1_finset_1(D)
            & ~ v1_xboole_0(D)
            & r1_tarski(k1_card_1(D),C) ) ) ) )).

fof(fraenkel_a_1_0_bagorder,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v16_waybel_0(B)
        & l1_orders_2(B) )
     => ( r2_hidden(A,a_1_0_bagorder(B))
      <=> ? [C,D] :
            ( m1_subset_1(C,k5_finsub_1(u1_struct_0(B)))
            & m1_subset_1(D,k5_finsub_1(u1_struct_0(B)))
            & A = k1_domain_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)),C,D)
            & ( C = k1_xboole_0
              | ( C != k1_xboole_0
                & D != k1_xboole_0
                & k11_bagorder(B,C) != k11_bagorder(B,D)
                & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),k11_bagorder(B,C),k11_bagorder(B,D)),u1_orders_2(B)) ) ) ) ) ) )).

fof(fraenkel_a_3_0_bagorder,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v16_waybel_0(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)))))
        & m2_relset_1(C,k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)))))
        & m2_subset_1(D,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_3_0_bagorder(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,k5_finsub_1(u1_struct_0(B)))
            & m1_subset_1(F,k5_finsub_1(u1_struct_0(B)))
            & A = k1_domain_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)),E,F)
            & E != k1_xboole_0
            & F != k1_xboole_0
            & k11_bagorder(B,E) = k11_bagorder(B,F)
            & r2_hidden(k4_tarski(k4_xboole_0(E,k6_domain_1(u1_struct_0(B),k11_bagorder(B,E))),k4_xboole_0(F,k6_domain_1(u1_struct_0(B),k11_bagorder(B,F)))),k8_funct_2(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)))),C,D)) ) ) ) )).
%------------------------------------------------------------------------------