Bliksem---1.12.TMO-Non.f

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SWV574-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Wed Jul 20 16:26:49 EDT 2022

% Result   : Timeout 300.07s 300.47s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV574-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12  % Command  : bliksem %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % DateTime : Thu Jun 16 05:02:56 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.10/1.48  *** allocated 10000 integers for termspace/termends
% 1.10/1.48  *** allocated 10000 integers for clauses
% 1.10/1.48  *** allocated 10000 integers for justifications
% 1.10/1.48  *** allocated 15000 integers for termspace/termends
% 1.10/1.48  *** allocated 22500 integers for termspace/termends
% 1.10/1.48  *** allocated 33750 integers for termspace/termends
% 1.10/1.48  Bliksem 1.12
% 1.10/1.48  
% 1.10/1.48  
% 1.10/1.48  Automatic Strategy Selection
% 1.10/1.48  
% 1.10/1.48  Clauses:
% 1.10/1.48  [
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), 
% 1.10/1.48    Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.10/1.48     [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z, 
% 1.10/1.48    'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( X, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z, 
% 1.10/1.48    'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.10/1.48     [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T, 
% 1.10/1.48    'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T, 
% 1.10/1.48    'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olattice'( X ) ), =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olattice'( X ) ), =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.48     [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.48    , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.48    , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.10/1.48    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), 
% 1.10/1.48    Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.10/1.48     ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~( 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.10/1.48    , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.10/1.48     ), X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), 
% 1.10/1.48    ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.10/1.48    ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 
% 1.10/1.48    'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 
% 1.10/1.48    'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.10/1.48     ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48     ],
% 1.10/1.48     [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.48    'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.10/1.48    , 'tc_Int_Oint' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ), 
% 1.10/1.48    ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.48     [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.48    Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48    , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.10/1.48     [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 
% 1.10/1.48    'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.10/1.48     [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~( 
% 1.10/1.48    'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48    , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.48     ), =( Z, Y ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.48     [ =( 'c_SetInterval_Oord__class_OlessThan'( 'c_Suc'( X ), 'tc_nat' ), 
% 1.10/1.48    'c_SetInterval_Oord__class_OatMost'( X, 'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Z, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48    , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48    , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Z, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48    , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48    , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.10/1.48    , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ), 
% 1.10/1.48    'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0, 
% 1.10/1.48    V1 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ), 
% 1.10/1.48    'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0, 
% 1.10/1.48    V1 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP( 
% 1.10/1.48    X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP( 
% 1.10/1.48    X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48     ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48     ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.10/1.48     ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.48    Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48     ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.48    , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48     ), X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.48    Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48     ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.48     ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48     ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48     ), X ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.10/1.48    , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( 
% 1.10/1.48    Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.48     ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 
% 1.10/1.48    hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.48     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.10/1.48    hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, 
% 1.10/1.48    X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.10/1.48     ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.10/1.48     ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.48     ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.10/1.48    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.48    'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48     [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.10/1.48     [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.10/1.48     ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, 
% 1.10/1.48    X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, 
% 1.10/1.48    X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 
% 1.10/1.48    'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 
% 1.10/1.48    'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48    , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48    , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.10/1.48    'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.48    'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'tc_nat' ), 
% 1.10/1.48    'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.48    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.48    'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.10/1.48    , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.10/1.48    , X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ), 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.48    , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.10/1.48     ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.10/1.48     ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.10/1.48     ],
% 1.10/1.48     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP( 
% 1.10/1.48    hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.48    'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.10/1.48     [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.48    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.10/1.48     [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.10/1.48     ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.10/1.48    X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.10/1.48    X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.48     [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.48     ), X ), Y ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.10/1.48     [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.48     ), Z ) ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.48     ), Z ) ), Y ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.10/1.48    =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.10/1.48     ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.48    , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48     ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.10/1.48    'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48    , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.10/1.48    , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.48    , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48    , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.10/1.48    , X ) ), T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.10/1.48     ), Z ), T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.10/1.48     ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.48     ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.10/1.48     ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.48     ), X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48    , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.10/1.48    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.48     ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'( 
% 1.10/1.48    X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.48    , X ) ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.48     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 
% 1.10/1.48    'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.48    , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~( 
% 1.10/1.48    'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ), 
% 1.10/1.48    'c_lessequals'( Y, Z, X ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~( 
% 1.10/1.48    'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.48    'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.48    'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.10/1.48     [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z, 
% 1.10/1.48    'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X, 
% 1.10/1.48    'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olattice'( X ) ), =( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( 
% 1.10/1.48    'c_SetInterval_Oord__class_OlessThan'( Y, X ), 
% 1.10/1.48    'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 
% 1.10/1.48    'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.48    , Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.48    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    T, X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.48    , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.48    , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.48     [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 
% 1.10/1.48    'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL( 
% 1.10/1.48    hAPP( X, T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ), 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), Z ), T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ), 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.48    'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.48    'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48     ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48     ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48     ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.10/1.48    , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48     ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.10/1.48     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48     ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.48     ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.10/1.48    , X ) ), Z ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.48    , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.48     ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48     ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.10/1.48    , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.10/1.48    , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.10/1.48    , 'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.10/1.48    , 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.48    X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Z ), Y ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Z ), Y ), X ) ) ],
% 1.10/1.48     [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.48     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.10/1.48     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.10/1.48     [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T, 
% 1.10/1.48    'tc_bool' ) ), Y ) ) ) ],
% 1.10/1.48     [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T, 
% 1.10/1.48    'tc_bool' ) ), Y ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.10/1.48    , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.10/1.48    , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.10/1.48     ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.10/1.48     ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ), 
% 1.10/1.48    ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, 
% 1.10/1.48    Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ), 
% 1.10/1.48    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ), 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.10/1.48    , X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, 
% 1.10/1.48    X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48    , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, 
% 1.10/1.48    X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.10/1.48    , X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48    , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48    , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.48     [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( 
% 1.10/1.48    hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.48     ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.48     ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.48     ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ), 
% 1.10/1.48    X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.48    , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.10/1.48    , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.10/1.48     ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.10/1.48     ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.10/1.48     ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), 
% 1.10/1.48    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.48    'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.10/1.48     [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.10/1.48    , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48     ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, 
% 1.10/1.48    T, X ) ), T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.10/1.48     ) ), Z ), T, X ) ) ],
% 1.10/1.48     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.48    'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.48    'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48     [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.48    , Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.10/1.48     ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.10/1.48     ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 
% 1.10/1.48    'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.10/1.48     ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.10/1.48     ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.10/1.48     ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48     ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), Z, X ) ) ],
% 1.10/1.48     [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.48    , 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.10/1.48    , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.48    , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.10/1.48    , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.48    , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.10/1.48    , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 
% 1.10/1.48    'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.48     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.48     ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~( 
% 1.10/1.48    =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.48     ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.10/1.48    X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.10/1.48    , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.48    'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.48     ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.48     ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.48     ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.10/1.48    'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.10/1.48    'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    Y, Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.48     ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.10/1.48    , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.48    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.10/1.48    , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z, 
% 1.10/1.48    X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    Z, T, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z, 
% 1.10/1.48    X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    T, Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~( 
% 1.10/1.48    'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~( 
% 1.10/1.48    'c_lessequals'( Z, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z, 
% 1.10/1.48    X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    Z, T, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z, 
% 1.10/1.48    X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.48    T, Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.10/1.48    , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~( 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP( 
% 1.10/1.48    hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.10/1.48    , V0, U, V1 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP( 
% 1.10/1.48    hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.10/1.48    , V0, U, V1 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ), 
% 1.10/1.48    Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    X, T, U, Y, W, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    X, T, U, Z, W, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~( 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP( 
% 1.10/1.48    hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~( 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    T, X, U, Y, W, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    T, X, U, Z, W, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    T, X, U, W, Y, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    T, X, U, W, Z, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.10/1.48    , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ), 
% 1.10/1.48    ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.10/1.48    , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ), 
% 1.10/1.48    ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.10/1.48    , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ), 
% 1.10/1.48    ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP( 
% 1.10/1.48    hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.10/1.48    , V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ), 
% 1.10/1.48    hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, 
% 1.10/1.48    W, V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP( 
% 1.10/1.48    hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.10/1.48    , V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ), 
% 1.10/1.48    hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, 
% 1.10/1.48    W, V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.10/1.48    , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ), 
% 1.10/1.48    ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ), 
% 1.10/1.48    hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, 
% 1.10/1.48    W, V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ), 
% 1.10/1.48    hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, 
% 1.10/1.48    W, V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP( 
% 1.10/1.48    hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.10/1.48    , V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~( 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP( 
% 1.10/1.48    hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.10/1.48    , V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    X, T, U, Y, W, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP( 
% 1.10/1.48    hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.10/1.48    , V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~( 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    T, X, U, Y, W, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.10/1.48    T, X, U, W, Y, V0 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP( 
% 1.10/1.48    hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.10/1.48    , V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~( 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP( 
% 1.10/1.48    hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~( 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP( 
% 1.10/1.48    hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~( 
% 1.10/1.48    'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.48     ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.48     ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48    , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.10/1.48    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.48    , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.48     ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.10/1.48     ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.48     ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 
% 1.10/1.48    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.48    X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 
% 1.10/1.48    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.10/1.48     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.10/1.48    , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( 
% 1.10/1.48    Y ) ) ) ],
% 1.10/1.48     [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48     [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.48    'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =( 
% 1.10/1.48    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ), 
% 1.10/1.48    'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.10/1.48     [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y, 
% 1.10/1.48    'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48     ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.10/1.48    , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Z ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48     ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.48    Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48     ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.48    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.48    , X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.48     ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48    ,
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Z, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.48    'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.48    'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( 
% 1.10/1.48    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.48    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.48    Y ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 
% 1.10/1.48    Y ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.48    Y ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.10/1.48    X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.10/1.48    'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 
% 1.10/1.48    Y ) ],
% 1.10/1.48     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 
% 1.10/1.48    Y ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.48    Y ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 
% 1.10/1.48    Y ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z, 
% 1.10/1.48    X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP( 
% 1.10/1.48    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48    , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.48    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.48    'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP( 
% 1.10/1.48    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48     ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49     ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), 
% 1.10/1.49    ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49    , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49    , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49    , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.49     ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49     ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), 
% 1.10/1.49    ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 
% 1.10/1.49    X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49    , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.10/1.49     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.49     ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49     ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49     ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~( 
% 1.10/1.49    'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~( 
% 1.10/1.49    'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'( 
% 1.10/1.49    Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.49     ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.49     ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.49    , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49     ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.49    , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.49    X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.49    X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'( 
% 1.10/1.49    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49    , X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ) ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.10/1.49     ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.10/1.49     ), =( 'c_HOL_Oinverse__class_Oinverse'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.49     ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.10/1.49    , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.10/1.49     ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.10/1.49    Y ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 
% 1.10/1.49    Y ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 
% 1.10/1.49    Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 
% 1.10/1.49    Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.10/1.49    Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 
% 1.10/1.49    Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.49     ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.10/1.49     ],
% 1.10/1.49     [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.10/1.49    , Y ) ) ],
% 1.10/1.49     [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X, 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'tc_nat' ) ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.10/1.49     [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.10/1.49    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL( 
% 1.10/1.49    hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.10/1.49     [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.10/1.49    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.10/1.49    'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.49     ), 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.49     ), 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ), 
% 1.10/1.49    ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.10/1.49     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.10/1.49     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.10/1.49     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.10/1.49     [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.10/1.49     [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( Y, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    X ) ) ],
% 1.10/1.49     [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( X ), Y, X ), 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.49     ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.49     ), T ) ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.49     ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.10/1.49     ), T ) ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), 
% 1.10/1.49    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 
% 1.10/1.49    'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.49    , X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.49    , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, 
% 1.10/1.49    Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.10/1.49    , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49    , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.49    , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~( 
% 1.10/1.49    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.10/1.49    X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, 
% 1.10/1.49    X ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.10/1.49    , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 
% 1.10/1.49    Y ) ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.10/1.49     ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.10/1.49     ) ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'( 
% 1.10/1.49    Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.10/1.49     ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.49     ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49     ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.49     ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), 
% 1.10/1.49    X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.10/1.49     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.49     ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49    , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49    , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.49     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    X, T, 'tc_nat' ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.10/1.49    , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.10/1.49    , U ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.49    , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.49    'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.49    , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.10/1.49    , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.10/1.49     ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.10/1.49    , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.49    , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.49    , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.10/1.49    , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.49    , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.10/1.49    , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.49    , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.49    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, 
% 1.10/1.49    X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.49    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, 
% 1.10/1.49    X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49    , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.10/1.49    , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.49    , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.49    , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.49    , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49    , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), Y ), T ), Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.49    X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), 
% 1.10/1.49    Y ) ) ],
% 1.10/1.49     [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.10/1.49     [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.49     [ =( 'c_SetInterval_Oord__class_OatMost'( 'c_Suc'( X ), 'tc_nat' ), 
% 1.10/1.49    'c_Set_Oinsert'( 'c_Suc'( X ), 'c_SetInterval_Oord__class_OatMost'( X, 
% 1.10/1.49    'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49     ), Y ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.10/1.49    , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ), 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.49    , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.10/1.49     [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.10/1.49    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.10/1.49     ) ) ), =( Z, U ), =( Y, T ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.10/1.49    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.10/1.49     ) ) ), =( Z, U ), =( Y, T ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.10/1.49    , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49    , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49     [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.10/1.49    , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.10/1.49     [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.10/1.49    , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.10/1.49     [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.10/1.49    , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ), 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49    , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.49     ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49     ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.10/1.49    , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.10/1.49    , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49     ) ), Z ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'( 
% 1.10/1.49    X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.49    X ) ) ],
% 1.10/1.49     [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ) ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.49    , Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.10/1.49    , X ) ) ],
% 1.10/1.49     [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.49    , Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49    , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'( 
% 1.10/1.49    X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.10/1.49     ) ) ) ],
% 1.10/1.49     [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 
% 1.10/1.49    'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.10/1.49     ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.10/1.49    'tc_nat' ) ), Y ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.49     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.49     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.10/1.49     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.10/1.49     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.10/1.49    , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.10/1.49    , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.10/1.49    , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.10/1.49    , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y, 
% 1.10/1.49    'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y, 
% 1.10/1.49    'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 
% 1.10/1.49    'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), X ), Y ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.10/1.49     ],
% 1.10/1.49     [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.10/1.49    , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ), 
% 1.10/1.49    'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 
% 1.10/1.49    'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), =( 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.49    'c_SetInterval_Oord__class_OlessThan'( Y, X ), 
% 1.10/1.49    'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ), 'tc_fun'( X, 
% 1.10/1.49    'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.10/1.49     ) ],
% 1.10/1.49     [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ), 
% 1.10/1.49    ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.10/1.49    'tc_nat' ) ), Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.10/1.49    'tc_nat' ) ), Y ) ],
% 1.10/1.49     [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 
% 1.10/1.49    'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls', 
% 1.10/1.49    'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49    , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.49     ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y, 
% 1.10/1.49    'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.10/1.49     [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.49     ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.49     ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.10/1.49    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.49     ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.49     ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49    , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 
% 1.10/1.49    X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49    , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49     ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    X ), 'c_HOL_Oinverse__class_Odivide'( Z, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.49    , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49     ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.10/1.49    , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49     ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49     ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.10/1.49    'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.10/1.49     ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49     ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.49    , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49     ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49     ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.49     ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OPls', X ) ), Y ) ],
% 1.10/1.49     [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.49     ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), 
% 1.10/1.49    ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.10/1.49     ), X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.49     ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 
% 1.10/1.49    Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49    , X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49    , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49    , X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49    , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49    , X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.49     ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.10/1.49    , Y ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.49     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.49     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~( 
% 1.10/1.49    'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.10/1.49     ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), Y ), Y ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.10/1.49    'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.49    , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.10/1.49    , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.49     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.10/1.49    T, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.49     ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), 
% 1.10/1.49    ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.49     ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.10/1.49    ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.10/1.49    , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.10/1.49    , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), 
% 1.10/1.49    ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Suc'( T ) ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.49    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.49    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.10/1.49    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.10/1.49    'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.10/1.49    , T ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ), 
% 1.10/1.49    ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ), 
% 1.10/1.49    'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'( 
% 1.10/1.49    Z, X ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.10/1.49    , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.10/1.49    'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Lattices_Olattice'( X ) ), =( 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( Y, 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.10/1.49     [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z, 
% 1.10/1.49    'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z, 
% 1.10/1.49    'tc_bool' ) ) ) ],
% 1.10/1.49     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( Y, 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.10/1.49    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.10/1.49    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.10/1.49    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.49     ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), 
% 1.10/1.49    X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.10/1.49     ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.49     ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), 
% 1.10/1.49    X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49    , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.10/1.49     ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49     ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), 
% 1.10/1.49    ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.49     [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.10/1.49    'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), 
% 1.10/1.49    Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, 
% 1.10/1.49    X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 
% 1.10/1.49    'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.10/1.49     ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.49    , X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49    , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.49    , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49    , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49     ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.10/1.49    , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y, 
% 1.10/1.49    'tc_bool' ) ), X ) ],
% 1.10/1.49     [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.49    , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.10/1.49     ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.49    , Z ), Y ), 'tc_nat' ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.49    , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.10/1.49     ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49    , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49    , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.49    , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), 
% 1.10/1.49    ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.49     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49    , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49    , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.49    , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), 
% 1.10/1.49    ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.49     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.10/1.49     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y, 
% 1.10/1.49    'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49    , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.10/1.49    , X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49    , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.10/1.49    , X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.10/1.49    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.10/1.49    , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 
% 1.10/1.49    'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.10/1.49    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.49     ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.49     ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 
% 1.10/1.49    'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49     ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49    , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49     ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( 
% 1.10/1.49    'c_SetInterval_Oord__class_OatMost'( Y, X ), 
% 1.10/1.49    'c_SetInterval_Oord__class_OatMost'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49    , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.49    , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 
% 1.10/1.49    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49    , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49     ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.49    , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 
% 1.10/1.49    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.10/1.49     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.10/1.49     [ =( 'c_SetInterval_Oord__class_OlessThan'( 'c_Suc'( X ), 'tc_nat' ), 
% 1.10/1.49    'c_Set_Oinsert'( X, 'c_SetInterval_Oord__class_OlessThan'( X, 'tc_nat' )
% 1.10/1.49    , 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49     ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( 
% 1.10/1.49    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49     ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ), 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.10/1.49     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.10/1.49     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.10/1.49     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.10/1.49    'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.49    , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.49    , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), 
% 1.10/1.49    'c_lessequals'( Z, Y, X ) ],
% 1.10/1.49     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X, 
% 1.10/1.49    'tc_Int_Oint' ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.49    , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49    , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.49     [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.49    , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), =( 
% 1.10/1.49    'c_Lattices_Olower__semilattice__class_Oinf'( 
% 1.10/1.49    'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ), 
% 1.10/1.49    'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X, 
% 1.10/1.49    'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.10/1.49     ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), =( 
% 1.10/1.49    'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ), 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), ~( =( 
% 1.10/1.49    'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ), 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), =( 
% 1.10/1.49    'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ), 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( 
% 1.10/1.49    'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.10/1.49    Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.10/1.49     [ ~( 'class_Orderings_Oorder'( X ) ), ~( =( 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 
% 1.10/1.49    'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ) ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.49     [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), 
% 1.10/1.49    'c_SetInterval_Oord__class_OlessThan'( X, 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_GCD_Ogcd__class_OGCD'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 
% 1.10/1.49    'tc_nat', 'tc_bool' ) ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ =( 'c_SetInterval_Oord__class_OlessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ), 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 
% 1.10/1.49    'tc_nat', 'tc_bool' ) ) ) ],
% 1.10/1.49     [ =( 'c_GCD_Ogcd__class_OLCM'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 
% 1.10/1.49    'tc_nat', 'tc_bool' ) ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.10/1.49     ) ],
% 1.10/1.49     [ =( 'c_GCD_Ogcd__class_OGCD'( 'c_Set_Oinsert'( X, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ), 
% 1.10/1.49    'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.49     [ =( 'c_GCD_Ogcd__class_OLCM'( 'c_Set_Oinsert'( X, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ), 
% 1.10/1.49    'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.49     ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), 
% 1.10/1.49    ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), 
% 1.10/1.49    =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), 
% 1.10/1.49    =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.49     ), Y ), Y ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.10/1.49    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'( 
% 1.10/1.49    X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.10/1.49    X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.49     [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.10/1.49    'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.49     ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49     ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49    , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.10/1.49    'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49     ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.10/1.49    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.10/1.49    X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.49     ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.49     ), Y ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.10/1.49    'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.49     ), Y ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.10/1.49    , Y ) ],
% 1.10/1.49     [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, 
% 1.10/1.49    'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.10/1.49     [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, 
% 1.10/1.49    'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.10/1.49    , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.10/1.49     [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.10/1.49    , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 
% 1.10/1.49    'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 
% 1.10/1.49    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 
% 1.10/1.49    'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_SetInterval_Oord__class_OatMost'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ), 'tc_nat' ), 'c_Set_Oinsert'( 'c_HOL_Ozero__class_Ozero'( 
% 1.10/1.49    'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool'
% 1.10/1.49     ) ), 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'c_Suc'( X ), 
% 1.10/1.49    'tc_nat' ), 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 
% 1.10/1.49    'tc_nat', 'tc_bool' ) ), 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.10/1.49    'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49    , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), 
% 1.10/1.49    'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49     [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.10/1.49    , X, Z, U, W, V0 ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.10/1.49    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP( 
% 1.10/1.49    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.10/1.49     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.49     [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.10/1.49     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 
% 1.10/1.49    'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 
% 1.10/1.49    'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.10/1.49     [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.49     ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.49     ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 
% 1.10/1.49    'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.49     ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =( 
% 1.10/1.49    'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'( 
% 1.10/1.49    'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.49     ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49     ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.10/1.49     [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.10/1.49     [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.10/1.49     [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ) ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 
% 1.10/1.49    'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.10/1.49     [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.10/1.49     [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49     [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.10/1.49     [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z, 
% 1.10/1.49    X, T ), Y ) ) ) ],
% 1.10/1.49     [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ), 
% 1.10/1.49    'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.10/1.49     [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.10/1.49     [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.10/1.49     [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ), 
% 1.10/1.49    'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.10/1.49     [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), 
% 1.10/1.49    'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.49     [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.10/1.49     [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49    , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.10/1.49     ) ],
% 1.10/1.49     [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), 
% 1.10/1.49    'tc_nat' ) ) ],
% 1.10/1.49     [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ), 
% 1.10/1.49    'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.10/1.49     [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ), 
% 1.10/1.49    'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.10/1.49     [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ), 
% 1.10/1.49    'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.10/1.49     [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, 
% 1.10/1.49    'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ), 
% 1.10/1.49    'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.10/1.49     [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.10/1.49     ) ), Y ) ) ) ],
% 1.10/1.49     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.49     [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.10/1.49     [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.10/1.49    ,
% 1.10/1.49     [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.10/1.49     [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ), 
% 1.10/1.49    'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.10/1.49     [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.49     ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.49     [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.10/1.49    , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 
% 1.10/1.49    'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.10/1.49     [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.10/1.49     ) ) ],
% 1.10/1.49     [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.10/1.49     [ ~( =( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.10/1.49    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'( 
% 1.10/1.49    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 
% 1.10/1.49    'c_Set_Oinsert'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Set_Oinsert'( 
% 1.10/1.49    'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Set_Oinsert'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'c_Set_Oinsert'( 
% 1.10/1.49    'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'( 
% 1.10/1.49    'c_Int_OPls' ) ), 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 
% 1.10/1.49    'tc_nat', 'tc_bool' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) )
% 1.10/1.49     ) ],
% 1.10/1.49     [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~( 
% 1.10/1.49    'class_Lattices_Olattice'( Y ) ) ],
% 1.10/1.49     [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~( 
% 1.10/1.49    'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.10/1.49     [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~( 
% 1.10/1.49    'class_Orderings_Opreorder'( Y ) ) ],
% 1.10/1.49     [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~( 
% 1.10/1.49    'class_Lattices_Olattice'( Y ) ) ],
% 1.10/1.49     [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~( 
% 1.10/1.49    'class_Orderings_Oorder'( Y ) ) ],
% 1.10/1.49     [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'( 
% 1.10/1.49    Y ) ) ],
% 1.10/1.49     [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.10/1.49     ],
% 1.10/1.49     [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.10/1.50     ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.10/1.50     ],
% 1.10/1.50     [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.10/1.50    ,
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.10/1.50     [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.10/1.50     [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.10/1.50     [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.10/1.50     [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.10/1.50     [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.10/1.50     [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 
% 1.10/1.50    'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 
% 1.10/1.50    'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 
% 1.10/1.50    'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.10/1.50     ],
% 1.10/1.50     [ 'class_OrderedGroup_Olordered__ab__group__add__meet'( 'tc_Int_Oint' )
% 1.10/1.50     ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.10/1.50     ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.10/1.50    ,
% 1.10/1.50     [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.10/1.50    ,
% 1.10/1.50     [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.10/1.50    ,
% 1.10/1.50     [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.10/1.50    ,
% 1.10/1.50     [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.10/1.50    ,
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.10/1.50    ,
% 1.10/1.50     [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Lattices_Olower__semilattice'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Lattices_Olattice'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.10/1.50     [ 'c_fequal'( X, X, Y ) ],
% 1.10/1.50     [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.10/1.50  ] .
% 1.10/1.50  
% 1.10/1.50  
% 1.10/1.50  percentage equality = 0.214136, percentage horn = 0.820774
% 1.10/1.50  This is a problem with some equality
% 1.10/1.50  
% 1.10/1.50  
% 1.10/1.50  
% 1.10/1.50  Options Used:
% 1.10/1.50  
% 1.10/1.50  useres =            1
% 1.10/1.50  useparamod =        1
% 1.10/1.50  useeqrefl =         1
% 1.10/1.50  useeqfact =         1
% 1.10/1.50  usefactor =         1
% 1.10/1.50  usesimpsplitting =  0
% 1.10/1.50  usesimpdemod =      5
% 1.10/1.50  usesimpres =        3
% 1.10/1.50  
% 1.10/1.50  resimpinuse      =  1000
% 1.10/1.50  resimpclauses =     20000
% 1.10/1.50  substype =          eqrewr
% 1.10/1.50  backwardsubs =      1
% 1.10/1.50  selectoldest =      5
% 1.10/1.50  
% 1.10/1.50  litorderings [0] =  split
% 1.10/1.50  litorderings [1] =  extend the termordering, first sorting on arguments
% 1.10/1.50  
% 1.10/1.50  termordering =      kbo
% 1.10/1.50  
% 1.10/1.50  litapriori =        0
% 1.10/1.50  termapriori =       1
% 1.10/1.50  litaposteriori =    0
% 1.10/1.50  termaposteriori =   0
% 1.10/1.50  demodaposteriori =  0
% 1.10/1.50  ordereqreflfact =   0
% 1.10/1.50  
% 1.10/1.50  litselect =         negord
% 1.10/1.50  
% 1.10/1.50  maxweight =         15
% 1.10/1.50  maxdepth =          30000
% 1.10/1.50  maxlength =         115
% 1.10/1.50  maxnrvars =         195
% 1.10/1.50  excuselevel =       1
% 1.10/1.50  increasemaxweight = 1
% 1.10/1.50  
% 1.10/1.50  maxselected =       10000000
% 1.10/1.50  maxnrclauses =      10000000
% 1.10/1.50  
% 1.10/1.50  showgenerated =    0
% 1.10/1.50  showkept =         0
% 1.10/1.50  showselected =     0
% 1.10/1.50  showdeleted =      0
% 1.10/1.50  showresimp =       1
% 1.10/1.50  showstatus =       2000
% 1.10/1.50  
% 1.10/1.50  prologoutput =     1
% 1.10/1.50  nrgoals =          5000000
% 1.10/1.50  totalproof =       1
% 1.10/1.50  
% 1.10/1.50  Symbols occurring in the translation:
% 1.10/1.50  
% 1.10/1.50  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.10/1.50  .  [1, 2]      (w:1, o:134, a:1, s:1, b:0), 
% 1.10/1.50  !  [4, 1]      (w:0, o:62, a:1, s:1, b:0), 
% 1.10/1.50  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.10/1.50  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.10/1.50  'class_Ring__and__Field_Oordered__field'  [40, 1]      (w:1, o:68, a:1, s:1
% 1.10/1.50    , b:0), 
% 1.10/1.50  'class_Ring__and__Field_Odivision__by__zero'  [41, 1]      (w:1, o:71, a:1
% 1.10/1.50    , s:1, b:0), 
% 1.10/1.50  'c_HOL_Oinverse__class_Odivide'  [44, 3]      (w:1, o:169, a:1, s:1, b:0), 
% 1.10/1.50    
% 1.10/1.50  'c_lessequals'  [46, 3]      (w:1, o:170, a:1, s:1, b:0), 
% 1.10/1.50  'c_HOL_Ozero__class_Ozero'  [47, 1]      (w:1, o:72, a:1, s:1, b:0), 
% 1.10/1.50  'c_HOL_Oord__class_Oless'  [48, 3]      (w:1, o:171, a:1, s:1, b:0), 
% 1.10/1.50  'c_HOL_Otimes__class_Otimes'  [49, 1]      (w:1, o:73, a:1, s:1, b:0), 
% 1.10/1.50  hAPP  [50, 2]      (w:1, o:159, a:1, s:1, b:0), 
% 1.10/1.50  'class_Ring__and__Field_Oordered__ring__strict'  [51, 1]      (w:1, o:74
% 1.10/1.50    , a:1, s:1, b:0), 
% 1.10/1.50  'c_HOL_Oplus__class_Oplus'  [52, 1]      (w:1, o:76, a:1, s:1, b:0), 
% 1.10/1.50  'class_Lattices_Olower__semilattice'  [55, 1]      (w:1, o:77, a:1, s:1, b:
% 1.10/1.50    0), 
% 1.10/1.50  'c_Lattices_Olower__semilattice__class_Oinf'  [57, 3]      (w:1, o:172, a:1
% 1.10/1.50    , s:1, b:0), 
% 1.10/1.50  'tc_bool'  [60, 0]      (w:1, o:27, a:1, s:1, b:0), 
% 1.10/1.50  'tc_fun'  [61, 2]      (w:1, o:160, a:1, s:1, b:0), 
% 1.10/1.50  'class_Lattices_Olattice'  [63, 1]      (w:1, o:78, a:1, s:1, b:0), 
% 1.10/1.50  'class_Ring__and__Field_Oordered__semidom'  [64, 1]      (w:1, o:79, a:1
% 2.74/3.13    , s:1, b:0), 
% 2.74/3.13  'c_Power_Opower__class_Opower'  [65, 1]      (w:1, o:81, a:1, s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Oordered__semiring__strict'  [67, 1]      (w:1, o:
% 2.74/3.13    82, a:1, s:1, b:0), 
% 2.74/3.13  'class_OrderedGroup_Olordered__ab__group__add'  [68, 1]      (w:1, o:83, a:
% 2.74/3.13    1, s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Oordered__idom'  [69, 1]      (w:1, o:84, a:1, s:1
% 2.74/3.13    , b:0), 
% 2.74/3.13  'class_OrderedGroup_Opordered__comm__monoid__add'  [70, 1]      (w:1, o:85
% 2.74/3.13    , a:1, s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Ocomm__semiring__1'  [71, 1]      (w:1, o:69, a:1
% 2.74/3.13    , s:1, b:0), 
% 2.74/3.13  'tc_nat'  [74, 0]      (w:1, o:45, a:1, s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Oordered__semiring'  [75, 1]      (w:1, o:86, a:1
% 2.74/3.13    , s:1, b:0), 
% 2.74/3.13  'c_Divides_Odiv__class_Odiv'  [77, 3]      (w:1, o:173, a:1, s:1, b:0), 
% 2.74/3.13  'class_Int_Onumber'  [78, 1]      (w:1, o:87, a:1, s:1, b:0), 
% 2.74/3.13  'c_Int_Onumber__class_Onumber__of'  [80, 2]      (w:1, o:164, a:1, s:1, b:0
% 2.74/3.13    ), 
% 2.74/3.13  'class_Power_Opower'  [81, 1]      (w:1, o:107, a:1, s:1, b:0), 
% 2.74/3.13  'c_HOL_Oone__class_Oone'  [82, 1]      (w:1, o:75, a:1, s:1, b:0), 
% 2.74/3.13  'c_Power_Opower_Opower'  [83, 3]      (w:1, o:174, a:1, s:1, b:0), 
% 2.74/3.13  'class_Divides_Osemiring__div'  [84, 1]      (w:1, o:108, a:1, s:1, b:0), 
% 2.74/3.13  'c_Suc'  [85, 1]      (w:1, o:109, a:1, s:1, b:0), 
% 2.74/3.13  'c_Fact_Ofact__class_Ofact'  [86, 2]      (w:1, o:165, a:1, s:1, b:0), 
% 2.74/3.13  'c_HOL_Oinverse__class_Oinverse'  [91, 2]      (w:1, o:163, a:1, s:1, b:0)
% 2.74/3.13    , 
% 2.74/3.13  'class_Int_Onumber__ring'  [92, 1]      (w:1, o:110, a:1, s:1, b:0), 
% 2.74/3.13  'tc_Int_Oint'  [93, 0]      (w:1, o:48, a:1, s:1, b:0), 
% 2.74/3.13  'c_Divides_Odiv__class_Omod'  [94, 3]      (w:1, o:175, a:1, s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Ofield'  [95, 1]      (w:1, o:111, a:1, s:1, b:0), 
% 2.74/3.13    
% 2.74/3.13  'class_Orderings_Oorder'  [96, 1]      (w:1, o:88, a:1, s:1, b:0), 
% 2.74/3.13  'class_Orderings_Olinorder'  [97, 1]      (w:1, o:89, a:1, s:1, b:0), 
% 2.74/3.13  hBOOL  [99, 1]      (w:1, o:112, a:1, s:1, b:0), 
% 2.74/3.13  'c_SetInterval_Oord__class_OlessThan'  [101, 2]      (w:1, o:166, a:1, s:1
% 2.74/3.13    , b:0), 
% 2.74/3.13  'c_SetInterval_Oord__class_OatMost'  [102, 2]      (w:1, o:167, a:1, s:1
% 2.74/3.13    , b:0), 
% 2.74/3.13  'class_OrderedGroup_Opordered__ab__semigroup__add'  [105, 1]      (w:1, o:
% 2.74/3.13    90, a:1, s:1, b:0), 
% 2.74/3.13  'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'  [106, 1]      
% 2.74/3.13    (w:1, o:91, a:1, s:1, b:0), 
% 2.74/3.13  'c_Groebner__Basis_Ogb__semiring'  [112, 6]      (w:1, o:179, a:1, s:1, b:0
% 2.74/3.13    ), 
% 2.74/3.13  'class_OrderedGroup_Oab__semigroup__idem__mult'  [113, 1]      (w:1, o:92
% 2.74/3.13    , a:1, s:1, b:0), 
% 2.74/3.13  'class_OrderedGroup_Ocomm__monoid__add'  [114, 1]      (w:1, o:93, a:1, s:1
% 2.74/3.13    , b:0), 
% 2.74/3.13  'class_Ring__and__Field_Omult__mono1'  [115, 1]      (w:1, o:113, a:1, s:1
% 2.74/3.13    , b:0), 
% 2.74/3.13  'class_Ring__and__Field_Omult__mono'  [116, 1]      (w:1, o:114, a:1, s:1
% 2.74/3.13    , b:0), 
% 2.74/3.13  'class_Ring__and__Field_Opordered__ring'  [117, 1]      (w:1, o:116, a:1
% 2.74/3.13    , s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Oidom'  [118, 1]      (w:1, o:117, a:1, s:1, b:0), 
% 2.74/3.13    
% 2.74/3.13  'class_Ring__and__Field_Odivision__ring'  [121, 1]      (w:1, o:118, a:1
% 2.74/3.13    , s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Osemiring__0'  [122, 1]      (w:1, o:121, a:1, s:1
% 2.74/3.13    , b:0), 
% 2.74/3.13  'class_OrderedGroup_Omonoid__mult'  [123, 1]      (w:1, o:95, a:1, s:1, b:0
% 2.74/3.13    ), 
% 2.74/3.13  'class_Orderings_Opreorder'  [124, 1]      (w:1, o:96, a:1, s:1, b:0), 
% 2.74/3.13  'class_OrderedGroup_Oab__group__add'  [125, 1]      (w:1, o:97, a:1, s:1
% 2.74/3.13    , b:0), 
% 2.74/3.13  'class_OrderedGroup_Oab__semigroup__add'  [126, 1]      (w:1, o:98, a:1, s:
% 2.74/3.13    1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Osemiring'  [127, 1]      (w:1, o:122, a:1, s:1, b:
% 2.74/3.13    0), 
% 2.74/3.13  'class_OrderedGroup_Ocomm__monoid__mult'  [130, 1]      (w:1, o:99, a:1, s:
% 2.74/3.13    1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Opordered__cancel__semiring'  [131, 1]      (w:1
% 2.74/3.13    , o:123, a:1, s:1, b:0), 
% 2.74/3.13  'class_OrderedGroup_Oab__semigroup__mult'  [132, 1]      (w:1, o:100, a:1
% 2.74/3.13    , s:1, b:0), 
% 2.74/3.13  'class_RealVector_Oreal__normed__algebra'  [133, 1]      (w:1, o:124, a:1
% 2.74/3.13    , s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Ocomm__semiring'  [138, 1]      (w:1, o:70, a:1, s:
% 2.74/3.13    1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Opordered__semiring'  [139, 1]      (w:1, o:125, a:
% 2.74/3.13    1, s:1, b:0), 
% 2.74/3.13  'class_Ring__and__Field_Oordered__comm__semiring__strict'  [140, 1]      
% 2.74/3.13    (w:1, o:115, a:1, s:1, b:0), 
% 2.74/3.13  'class_RealVector_Oreal__normed__field'  [141, 1]      (w:1, o:126, a:1, s:
% 11.86/12.27    1, b:0), 
% 11.86/12.27  'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'  [142, 1]      
% 11.86/12.27    (w:1, o:101, a:1, s:1, b:0), 
% 11.86/12.27  'class_Ring__and__Field_Osemiring__1'  [143, 1]      (w:1, o:127, a:1, s:1
% 11.86/12.27    , b:0), 
% 11.86/12.27  'c_Int_Oiszero'  [144, 2]      (w:1, o:168, a:1, s:1, b:0), 
% 11.86/12.27  'class_Ring__and__Field_Oring__no__zero__divisors'  [145, 1]      (w:1, o:
% 11.86/12.27    119, a:1, s:1, b:0), 
% 11.86/12.27  'class_Ring__and__Field_Omult__zero'  [146, 1]      (w:1, o:128, a:1, s:1
% 11.86/12.27    , b:0), 
% 11.86/12.27  'class_Ring__and__Field_Oring__1__no__zero__divisors'  [147, 1]      (w:1
% 11.86/12.27    , o:120, a:1, s:1, b:0), 
% 11.86/12.27  'class_Ring__and__Field_Ozero__neq__one'  [148, 1]      (w:1, o:129, a:1
% 11.86/12.27    , s:1, b:0), 
% 11.86/12.27  'class_Ring__and__Field_Ono__zero__divisors'  [149, 1]      (w:1, o:67, a:1
% 11.86/12.27    , s:1, b:0), 
% 11.86/12.27  'class_OrderedGroup_Ocancel__ab__semigroup__add'  [150, 1]      (w:1, o:102
% 11.86/12.27    , a:1, s:1, b:0), 
% 11.86/12.27  'class_OrderedGroup_Ocancel__semigroup__add'  [151, 1]      (w:1, o:103, a:
% 11.86/12.27    1, s:1, b:0), 
% 11.86/12.27  'class_OrderedGroup_Olordered__ab__group__add__meet'  [152, 1]      (w:1
% 11.86/12.27    , o:94, a:1, s:1, b:0), 
% 11.86/12.27  'class_OrderedGroup_Omonoid__add'  [154, 1]      (w:1, o:104, a:1, s:1, b:0
% 11.86/12.27    ), 
% 11.86/12.27  'class_Lattices_Obounded__lattice'  [158, 1]      (w:1, o:130, a:1, s:1, b:
% 11.86/12.27    0), 
% 11.86/12.27  'c_Orderings_Obot__class_Obot'  [159, 1]      (w:1, o:80, a:1, s:1, b:0), 
% 11.86/12.27  'class_Orderings_Obot'  [160, 1]      (w:1, o:105, a:1, s:1, b:0), 
% 11.86/12.27  'c_Set_Oinsert'  [164, 3]      (w:1, o:176, a:1, s:1, b:0), 
% 11.86/12.27  'c_Int_OBit1'  [166, 1]      (w:1, o:132, a:1, s:1, b:0), 
% 11.86/12.27  'c_Int_OPls'  [168, 0]      (w:1, o:57, a:1, s:1, b:0), 
% 11.86/12.27  'c_Int_OBit0'  [169, 1]      (w:1, o:131, a:1, s:1, b:0), 
% 11.86/12.27  'c_SetInterval_Oord__class_OatLeastLessThan'  [170, 3]      (w:1, o:177, a:
% 11.86/12.27    1, s:1, b:0), 
% 11.86/12.27  'class_Int_Oring__char__0'  [171, 1]      (w:1, o:133, a:1, s:1, b:0), 
% 11.86/12.27  'class_OrderedGroup_Opordered__ab__group__add'  [172, 1]      (w:1, o:106
% 11.86/12.27    , a:1, s:1, b:0), 
% 11.86/12.27  'c_GCD_Ogcd__class_OGCD'  [173, 2]      (w:1, o:161, a:1, s:1, b:0), 
% 11.86/12.27  'c_GCD_Ogcd__class_OLCM'  [174, 2]      (w:1, o:162, a:1, s:1, b:0), 
% 11.86/12.27  'c_fequal'  [177, 3]      (w:1, o:178, a:1, s:1, b:0).
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Starting Search:
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    4513
% 11.86/12.27  Kept:         2000
% 11.86/12.27  Inuse:        147
% 11.86/12.27  Deleted:      5
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    10761
% 11.86/12.27  Kept:         4038
% 11.86/12.27  Inuse:        264
% 11.86/12.27  Deleted:      12
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    19037
% 11.86/12.27  Kept:         6064
% 11.86/12.27  Inuse:        289
% 11.86/12.27  Deleted:      12
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    24305
% 11.86/12.27  Kept:         8078
% 11.86/12.27  Inuse:        343
% 11.86/12.27  Deleted:      13
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    32196
% 11.86/12.27  Kept:         10478
% 11.86/12.27  Inuse:        470
% 11.86/12.27  Deleted:      21
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    43250
% 11.86/12.27  Kept:         12586
% 11.86/12.27  Inuse:        510
% 11.86/12.27  Deleted:      21
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    49327
% 11.86/12.27  Kept:         14612
% 11.86/12.27  Inuse:        530
% 11.86/12.27  Deleted:      21
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    58184
% 11.86/12.27  Kept:         16695
% 11.86/12.27  Inuse:        598
% 11.86/12.27  Deleted:      23
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    64906
% 11.86/12.27  Kept:         18716
% 11.86/12.27  Inuse:        637
% 11.86/12.27  Deleted:      28
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying clauses:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    73582
% 11.86/12.27  Kept:         20721
% 11.86/12.27  Inuse:        684
% 11.86/12.27  Deleted:      250
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    81277
% 11.86/12.27  Kept:         22743
% 11.86/12.27  Inuse:        735
% 11.86/12.27  Deleted:      250
% 11.86/12.27  Deletedinuse: 0
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  Resimplifying inuse:
% 11.86/12.27  Done
% 11.86/12.27  
% 11.86/12.27  
% 11.86/12.27  Intermediate Status:
% 11.86/12.27  Generated:    92348
% 11.86/12.27  Kept:         24828
% 11.86/12.27  Inuse:        796
% 11.86/12.27  Deleted:      251
% 11.86/12.27  Deletedinuse: 1
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    104355
% 49.62/50.03  Kept:         27687
% 49.62/50.03  Inuse:        846
% 49.62/50.03  Deleted:      251
% 49.62/50.03  Deletedinuse: 1
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    111681
% 49.62/50.03  Kept:         29690
% 49.62/50.03  Inuse:        885
% 49.62/50.03  Deleted:      251
% 49.62/50.03  Deletedinuse: 1
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    122431
% 49.62/50.03  Kept:         32056
% 49.62/50.03  Inuse:        911
% 49.62/50.03  Deleted:      251
% 49.62/50.03  Deletedinuse: 1
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    131461
% 49.62/50.03  Kept:         34063
% 49.62/50.03  Inuse:        952
% 49.62/50.03  Deleted:      252
% 49.62/50.03  Deletedinuse: 2
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    143427
% 49.62/50.03  Kept:         36075
% 49.62/50.03  Inuse:        981
% 49.62/50.03  Deleted:      252
% 49.62/50.03  Deletedinuse: 2
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    153099
% 49.62/50.03  Kept:         38649
% 49.62/50.03  Inuse:        996
% 49.62/50.03  Deleted:      252
% 49.62/50.03  Deletedinuse: 2
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    160899
% 49.62/50.03  Kept:         40649
% 49.62/50.03  Inuse:        1001
% 49.62/50.03  Deleted:      252
% 49.62/50.03  Deletedinuse: 2
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying clauses:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    170094
% 49.62/50.03  Kept:         42844
% 49.62/50.03  Inuse:        1036
% 49.62/50.03  Deleted:      625
% 49.62/50.03  Deletedinuse: 2
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    179633
% 49.62/50.03  Kept:         44901
% 49.62/50.03  Inuse:        1071
% 49.62/50.03  Deleted:      625
% 49.62/50.03  Deletedinuse: 2
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    187779
% 49.62/50.03  Kept:         46947
% 49.62/50.03  Inuse:        1101
% 49.62/50.03  Deleted:      625
% 49.62/50.03  Deletedinuse: 2
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    196473
% 49.62/50.03  Kept:         49041
% 49.62/50.03  Inuse:        1140
% 49.62/50.03  Deleted:      629
% 49.62/50.03  Deletedinuse: 5
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    210853
% 49.62/50.03  Kept:         51160
% 49.62/50.03  Inuse:        1155
% 49.62/50.03  Deleted:      629
% 49.62/50.03  Deletedinuse: 5
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    229252
% 49.62/50.03  Kept:         53690
% 49.62/50.03  Inuse:        1165
% 49.62/50.03  Deleted:      629
% 49.62/50.03  Deletedinuse: 5
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    239187
% 49.62/50.03  Kept:         55722
% 49.62/50.03  Inuse:        1195
% 49.62/50.03  Deleted:      629
% 49.62/50.03  Deletedinuse: 5
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    249308
% 49.62/50.03  Kept:         57908
% 49.62/50.03  Inuse:        1228
% 49.62/50.03  Deleted:      631
% 49.62/50.03  Deletedinuse: 5
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    257929
% 49.62/50.03  Kept:         60098
% 49.62/50.03  Inuse:        1258
% 49.62/50.03  Deleted:      639
% 49.62/50.03  Deletedinuse: 13
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying clauses:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    266544
% 49.62/50.03  Kept:         62102
% 49.62/50.03  Inuse:        1270
% 49.62/50.03  Deleted:      1306
% 49.62/50.03  Deletedinuse: 14
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    280300
% 49.62/50.03  Kept:         65441
% 49.62/50.03  Inuse:        1288
% 49.62/50.03  Deleted:      1306
% 49.62/50.03  Deletedinuse: 14
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    293129
% 49.62/50.03  Kept:         68393
% 49.62/50.03  Inuse:        1323
% 49.62/50.03  Deleted:      1306
% 49.62/50.03  Deletedinuse: 14
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    302017
% 49.62/50.03  Kept:         70526
% 49.62/50.03  Inuse:        1338
% 49.62/50.03  Deleted:      1306
% 49.62/50.03  Deletedinuse: 14
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    319353
% 49.62/50.03  Kept:         72650
% 49.62/50.03  Inuse:        1358
% 49.62/50.03  Deleted:      1307
% 49.62/50.03  Deletedinuse: 15
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    326833
% 49.62/50.03  Kept:         74716
% 49.62/50.03  Inuse:        1383
% 49.62/50.03  Deleted:      1307
% 49.62/50.03  Deletedinuse: 15
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    335500
% 49.62/50.03  Kept:         76953
% 49.62/50.03  Inuse:        1408
% 49.62/50.03  Deleted:      1307
% 49.62/50.03  Deletedinuse: 15
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  Resimplifying inuse:
% 49.62/50.03  Done
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    346624
% 49.62/50.03  Kept:         79218
% 49.62/50.03  Inuse:        1438
% 49.62/50.03  Deleted:      1308
% 49.62/50.03  Deletedinuse: 16
% 49.62/50.03  
% 49.62/50.03  
% 49.62/50.03  Intermediate Status:
% 49.62/50.03  Generated:    354542
% 49.62/50.03  Kept:         81373
% 49.62/50.03  Inuse:        1446
% 110.05/110.55  Deleted:      1308
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying clauses:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    361562
% 110.05/110.55  Kept:         83500
% 110.05/110.55  Inuse:        1448
% 110.05/110.55  Deleted:      1616
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    370434
% 110.05/110.55  Kept:         85542
% 110.05/110.55  Inuse:        1478
% 110.05/110.55  Deleted:      1616
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    386537
% 110.05/110.55  Kept:         89930
% 110.05/110.55  Inuse:        1484
% 110.05/110.55  Deleted:      1616
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    393777
% 110.05/110.55  Kept:         92360
% 110.05/110.55  Inuse:        1493
% 110.05/110.55  Deleted:      1616
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    400696
% 110.05/110.55  Kept:         96296
% 110.05/110.55  Inuse:        1498
% 110.05/110.55  Deleted:      1616
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    407993
% 110.05/110.55  Kept:         99126
% 110.05/110.55  Inuse:        1507
% 110.05/110.55  Deleted:      1616
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    419376
% 110.05/110.55  Kept:         101127
% 110.05/110.55  Inuse:        1545
% 110.05/110.55  Deleted:      1616
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    428648
% 110.05/110.55  Kept:         103137
% 110.05/110.55  Inuse:        1557
% 110.05/110.55  Deleted:      1616
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying clauses:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    481583
% 110.05/110.55  Kept:         105978
% 110.05/110.55  Inuse:        1563
% 110.05/110.55  Deleted:      1816
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    496997
% 110.05/110.55  Kept:         109366
% 110.05/110.55  Inuse:        1573
% 110.05/110.55  Deleted:      1816
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    518264
% 110.05/110.55  Kept:         112463
% 110.05/110.55  Inuse:        1578
% 110.05/110.55  Deleted:      1816
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    540046
% 110.05/110.55  Kept:         115571
% 110.05/110.55  Inuse:        1583
% 110.05/110.55  Deleted:      1816
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    551292
% 110.05/110.55  Kept:         117785
% 110.05/110.55  Inuse:        1598
% 110.05/110.55  Deleted:      1816
% 110.05/110.55  Deletedinuse: 16
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    561494
% 110.05/110.55  Kept:         119815
% 110.05/110.55  Inuse:        1609
% 110.05/110.55  Deleted:      1817
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    595466
% 110.05/110.55  Kept:         124064
% 110.05/110.55  Inuse:        1623
% 110.05/110.55  Deleted:      1817
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying clauses:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    601742
% 110.05/110.55  Kept:         126974
% 110.05/110.55  Inuse:        1625
% 110.05/110.55  Deleted:      2057
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    618601
% 110.05/110.55  Kept:         129068
% 110.05/110.55  Inuse:        1648
% 110.05/110.55  Deleted:      2057
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    629141
% 110.05/110.55  Kept:         131321
% 110.05/110.55  Inuse:        1673
% 110.05/110.55  Deleted:      2057
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    636272
% 110.05/110.55  Kept:         133545
% 110.05/110.55  Inuse:        1683
% 110.05/110.55  Deleted:      2057
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    644114
% 110.05/110.55  Kept:         135956
% 110.05/110.55  Inuse:        1693
% 110.05/110.55  Deleted:      2057
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    654425
% 110.05/110.55  Kept:         137978
% 110.05/110.55  Inuse:        1713
% 110.05/110.55  Deleted:      2057
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    665994
% 110.05/110.55  Kept:         140389
% 110.05/110.55  Inuse:        1733
% 110.05/110.55  Deleted:      2057
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    675930
% 110.05/110.55  Kept:         142433
% 110.05/110.55  Inuse:        1748
% 110.05/110.55  Deleted:      2057
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying clauses:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    686308
% 110.05/110.55  Kept:         144767
% 110.05/110.55  Inuse:        1763
% 110.05/110.55  Deleted:      2488
% 110.05/110.55  Deletedinuse: 17
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  Resimplifying inuse:
% 110.05/110.55  Done
% 110.05/110.55  
% 110.05/110.55  
% 110.05/110.55  Intermediate Status:
% 110.05/110.55  Generated:    696000
% 110.05/110.55  Kept:         146844
% 110.05/110.55  Inuse:        1778
% 110.05/110.55  Deleted:      2488
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    703837
% 232.71/233.16  Kept:         148866
% 232.71/233.16  Inuse:        1796
% 232.71/233.16  Deleted:      2488
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    735561
% 232.71/233.16  Kept:         152477
% 232.71/233.16  Inuse:        1803
% 232.71/233.16  Deleted:      2488
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    768032
% 232.71/233.16  Kept:         155909
% 232.71/233.16  Inuse:        1813
% 232.71/233.16  Deleted:      2488
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    800766
% 232.71/233.16  Kept:         159371
% 232.71/233.16  Inuse:        1823
% 232.71/233.16  Deleted:      2488
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    811078
% 232.71/233.16  Kept:         161426
% 232.71/233.16  Inuse:        1843
% 232.71/233.16  Deleted:      2488
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    846803
% 232.71/233.16  Kept:         165730
% 232.71/233.16  Inuse:        1853
% 232.71/233.16  Deleted:      2488
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying clauses:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    858026
% 232.71/233.16  Kept:         168303
% 232.71/233.16  Inuse:        1873
% 232.71/233.16  Deleted:      2777
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    868586
% 232.71/233.16  Kept:         170589
% 232.71/233.16  Inuse:        1893
% 232.71/233.16  Deleted:      2777
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    885733
% 232.71/233.16  Kept:         173537
% 232.71/233.16  Inuse:        1913
% 232.71/233.16  Deleted:      2777
% 232.71/233.16  Deletedinuse: 17
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    897552
% 232.71/233.16  Kept:         175797
% 232.71/233.16  Inuse:        1918
% 232.71/233.16  Deleted:      2778
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    907051
% 232.71/233.16  Kept:         177967
% 232.71/233.16  Inuse:        1938
% 232.71/233.16  Deleted:      2778
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    919074
% 232.71/233.16  Kept:         180081
% 232.71/233.16  Inuse:        1968
% 232.71/233.16  Deleted:      2778
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    953116
% 232.71/233.16  Kept:         185177
% 232.71/233.16  Inuse:        1988
% 232.71/233.16  Deleted:      2778
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying clauses:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    963440
% 232.71/233.16  Kept:         187194
% 232.71/233.16  Inuse:        2014
% 232.71/233.16  Deleted:      2960
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    984482
% 232.71/233.16  Kept:         191236
% 232.71/233.16  Inuse:        2032
% 232.71/233.16  Deleted:      2960
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    996594
% 232.71/233.16  Kept:         193535
% 232.71/233.16  Inuse:        2037
% 232.71/233.16  Deleted:      2960
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    1008668
% 232.71/233.16  Kept:         195880
% 232.71/233.16  Inuse:        2042
% 232.71/233.16  Deleted:      2960
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    1026192
% 232.71/233.16  Kept:         199010
% 232.71/233.16  Inuse:        2052
% 232.71/233.16  Deleted:      2960
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    1041660
% 232.71/233.16  Kept:         201525
% 232.71/233.16  Inuse:        2057
% 232.71/233.16  Deleted:      2960
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    1051889
% 232.71/233.16  Kept:         203626
% 232.71/233.16  Inuse:        2082
% 232.71/233.16  Deleted:      2960
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    1060130
% 232.71/233.16  Kept:         205825
% 232.71/233.16  Inuse:        2102
% 232.71/233.16  Deleted:      2960
% 232.71/233.16  Deletedinuse: 18
% 232.71/233.16  
% 232.71/233.16  Resimplifying clauses:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    1073090
% 232.71/233.16  Kept:         208030
% 232.71/233.16  Inuse:        2137
% 232.71/233.16  Deleted:      3031
% 232.71/233.16  Deletedinuse: 19
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    1087278
% 232.71/233.16  Kept:         210800
% 232.71/233.16  Inuse:        2152
% 232.71/233.16  Deleted:      3031
% 232.71/233.16  Deletedinuse: 19
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    1102771
% 232.71/233.16  Kept:         216593
% 232.71/233.16  Inuse:        2167
% 232.71/233.16  Deleted:      3031
% 232.71/233.16  Deletedinuse: 19
% 232.71/233.16  
% 232.71/233.16  Resimplifying inuse:
% 232.71/233.16  Done
% 232.71/233.16  
% 232.71/233.16  
% 232.71/233.16  Intermediate Status:
% 232.71/233.16  Generated:    111Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------