TSTP Solution File: SWV708-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV708-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 16:27:57 EDT 2022
% Result : Timeout 300.04s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV708-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Tue Jun 14 14:46:55 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.18/1.58 *** allocated 10000 integers for termspace/termends
% 1.18/1.58 *** allocated 10000 integers for clauses
% 1.18/1.58 *** allocated 10000 integers for justifications
% 1.18/1.58 *** allocated 15000 integers for termspace/termends
% 1.18/1.58 *** allocated 22500 integers for termspace/termends
% 1.18/1.58 *** allocated 33750 integers for termspace/termends
% 1.18/1.58 Bliksem 1.12
% 1.18/1.58
% 1.18/1.58
% 1.18/1.58 Automatic Strategy Selection
% 1.18/1.58
% 1.18/1.58 Clauses:
% 1.18/1.58 [
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.18/1.58 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.58 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.18/1.58 , X ) ) ), =( Y, Z ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.18/1.58 , X ) ) ), =( Y, Z ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( T, X ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ),
% 1.18/1.58 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.18/1.58 , 'tc_Int_Oint' ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.18/1.58 , X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.18/1.58 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.18/1.58 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.18/1.58 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.18/1.58 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.58 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.18/1.58 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.18/1.58 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.18/1.58 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.18/1.58 Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.18/1.58 ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.18/1.58 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.18/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.58 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.58 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.58 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.18/1.58 ), X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.18/1.58 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.18/1.58 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.58 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.18/1.58 ), =( Z, Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.18/1.58 'c_lessequals'( Z, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.18/1.58 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.18/1.58 'c_lessequals'( Z, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.18/1.58 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.18/1.58 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.18/1.58 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.18/1.58 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.18/1.58 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.18/1.58 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.18/1.58 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.18/1.58 V1 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.18/1.58 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.18/1.58 V1 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.18/1.58 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.18/1.58 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.58 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.58 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.58 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.58 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.58 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.58 ), X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.58 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.58 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.58 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.58 ), X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.18/1.58 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.18/1.58 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.18/1.58 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.18/1.58 , Z ) ), Z ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.58 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.18/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.18/1.58 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.18/1.58 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.18/1.58 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.18/1.58 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.58 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.18/1.58 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 T, X ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.58 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.18/1.58 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.18/1.58 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.58 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), Z ), T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.58 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.18/1.58 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.18/1.58 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.58 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.18/1.58 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.18/1.58 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.58 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.18/1.58 , X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.18/1.58 , X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.18/1.58 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.18/1.58 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.58 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.18/1.58 'tc_nat' ) ), Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.58 Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.18/1.58 Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.18/1.58 Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.18/1.58 Y ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.58 Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.18/1.58 Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.58 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.18/1.58 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.18/1.58 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.18/1.58 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.18/1.58 ), X ), Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.18/1.58 ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.18/1.58 ), Z ) ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.58 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.18/1.58 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.58 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.58 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.18/1.58 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.58 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.58 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.18/1.58 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.58 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.58 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.18/1.58 , X ) ), T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.18/1.58 ), Z ), T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.18/1.58 ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.58 ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.18/1.58 ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.58 ), X ) ) ],
% 1.18/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.18/1.58 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.18/1.58 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.18/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.58 , X ) ), T ) ) ) ],
% 1.18/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.58 'tc_nat' ) ), =( Y, Z ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.58 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.58 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.58 X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.18/1.58 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.58 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.58 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.18/1.58 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.58 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.58 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.58 Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.58 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.18/1.58 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.58 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.58 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.58 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.18/1.58 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.18/1.58 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.58 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.58 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.58 Y, X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.58 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Z ), Y ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Z ), Y ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.58 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.18/1.58 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.18/1.58 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.18/1.58 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.18/1.58 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.58 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.18/1.58 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.18/1.58 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.58 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.58 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.58 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.58 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.58 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.18/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.58 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.58 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.18/1.58 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.58 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.18/1.58 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.18/1.58 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.18/1.58 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.18/1.58 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.18/1.58 , V0, U, V1 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.18/1.58 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.18/1.58 , V0, U, V1 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.18/1.58 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 X, T, U, Y, W, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 X, T, U, Z, W, V0 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.18/1.58 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.18/1.58 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.58 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 Y, Z, X ), X ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.58 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.58 'c_Suc'( X ), 'tc_nat' ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.18/1.58 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.58 , Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.18/1.58 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.18/1.58 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.18/1.58 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.18/1.58 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.58 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.18/1.58 ), 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.58 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.18/1.58 ), 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.18/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.18/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.18/1.58 ), Z ) ), T ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Y, Z, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.18/1.58 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.18/1.58 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.18/1.58 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.18/1.58 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.18/1.58 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.18/1.58 T, X ) ), T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.18/1.58 ) ), Z ), T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.18/1.58 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.18/1.58 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.18/1.58 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.18/1.58 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.58 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.18/1.58 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.58 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.18/1.58 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), X ), Z ), 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.58 , X, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.58 , X, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.18/1.58 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.58 , Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.18/1.58 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.18/1.58 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.58 ), Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.58 ), Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.18/1.58 ), Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.18/1.58 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.18/1.58 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 T, X, U, Y, W, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 T, X, U, Z, W, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 T, X, U, W, Y, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 T, X, U, W, Z, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.18/1.58 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.18/1.58 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.18/1.58 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.18/1.58 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.18/1.58 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.18/1.58 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.18/1.58 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.18/1.58 , V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.18/1.58 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.18/1.58 W, V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.18/1.58 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.18/1.58 , V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.18/1.58 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.18/1.58 W, V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.18/1.58 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.18/1.58 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.18/1.58 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.18/1.58 W, V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.18/1.58 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.18/1.58 W, V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.18/1.58 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.18/1.58 , V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.18/1.58 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.18/1.58 , V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 X, T, U, Y, W, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.18/1.58 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.18/1.58 , V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 T, X, U, Y, W, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.58 T, X, U, W, Y, V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.18/1.58 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.18/1.58 , V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.18/1.58 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.18/1.58 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.18/1.58 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.18/1.58 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.58 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.18/1.58 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.18/1.58 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.58 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.18/1.58 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.58 ) ), Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.18/1.58 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.18/1.58 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.18/1.58 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.18/1.58 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.58 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.18/1.58 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.18/1.58 ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.18/1.58 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.18/1.58 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.58 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.18/1.58 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.58 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.18/1.58 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.58 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.18/1.58 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.18/1.58 X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.18/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.58 , X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.18/1.58 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.18/1.58 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.58 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.18/1.58 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.58 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.58 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.18/1.58 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.58 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.18/1.59 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.18/1.59 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.18/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.59 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.59 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.18/1.59 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.59 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.59 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.59 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.59 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.18/1.59 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.59 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.59 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.18/1.59 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Suc'( T ) ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.18/1.59 Z ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.18/1.59 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), U ), X ) ), Z ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.59 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.18/1.59 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.18/1.59 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.18/1.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.18/1.59 , Y ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'tc_nat' ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.18/1.59 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.59 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.18/1.59 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.18/1.59 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.59 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.59 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.18/1.59 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.59 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.18/1.59 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.18/1.59 , U ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.18/1.59 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.18/1.59 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.18/1.59 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.18/1.59 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.18/1.59 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.18/1.59 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.18/1.59 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), T ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.18/1.59 Y ) ) ],
% 1.18/1.59 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.18/1.59 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ), Y ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.18/1.59 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.59 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.59 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.59 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.59 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.59 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.18/1.59 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.18/1.59 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.18/1.59 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.18/1.59 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.18/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.18/1.59 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.59 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.18/1.59 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.18/1.59 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.18/1.59 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.18/1.59 , Y ), Z ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.59 ) ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.18/1.59 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z
% 1.18/1.59 ), 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), Y ), Z ), X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.59 , Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.59 , Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.59 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.18/1.59 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.18/1.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.18/1.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.59 ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.59 ), 'tc_nat' ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.18/1.59 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ), Y ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.59 , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.59 , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.18/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.18/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.18/1.59 'tc_nat' ) ), Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.18/1.59 'tc_nat' ) ), Y ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.18/1.59 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.18/1.59 , X ) ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.18/1.59 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.18/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.18/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Suc'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.18/1.59 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.18/1.59 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls',
% 1.18/1.59 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y,
% 1.18/1.59 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.18/1.59 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.18/1.59 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.18/1.59 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.18/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.18/1.59 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.18/1.59 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.59 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.59 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.18/1.59 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OPls', X ) ), Y ) ],
% 1.18/1.59 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.18/1.59 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.59 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.18/1.59 ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.18/1.59 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.18/1.59 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.59 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.59 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.18/1.59 , Y ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.18/1.59 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.18/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.18/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.18/1.59 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.18/1.59 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.18/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.18/1.59 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.18/1.59 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y )
% 1.18/1.59 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.18/1.59 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.18/1.59 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.18/1.59 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.18/1.59 X ), 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.59 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.18/1.59 hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) )
% 1.18/1.59 ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.18/1.59 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.18/1.59 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.18/1.59 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.18/1.59 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.59 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.18/1.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.18/1.59 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.18/1.59 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.18/1.59 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.18/1.59 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.18/1.59 , T ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.18/1.59 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.18/1.59 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.59 ) ), X, 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.59 ) ), X, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.59 Z, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.18/1.59 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.18/1.59 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.59 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.18/1.59 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.59 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.18/1.59 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.59 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.18/1.59 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.18/1.59 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.59 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.18/1.59 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.18/1.59 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.18/1.59 X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.18/1.59 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.18/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.59 , X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.59 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.59 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.59 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.18/1.59 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.18/1.59 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.18/1.59 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y,
% 1.18/1.59 'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.59 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.18/1.59 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.18/1.59 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.18/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.18/1.59 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.18/1.59 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.18/1.59 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.18/1.59 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.18/1.59 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.18/1.59 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.18/1.59 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.59 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.18/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.18/1.59 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.59 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.18/1.59 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.18/1.59 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.18/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.18/1.59 Y, X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.18/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.18/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.18/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.59 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 Y, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.59 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.59 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.18/1.59 Z, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.59 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.18/1.59 'c_lessequals'( Z, Y, X ) ],
% 1.18/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X,
% 1.18/1.59 'tc_Int_Oint' ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.59 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.18/1.59 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.18/1.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.59 ), Y ), Y ) ) ],
% 1.18/1.59 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.18/1.59 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.18/1.59 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.18/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.18/1.59 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.18/1.59 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.18/1.59 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.18/1.59 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 , X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.59 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.18/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.59 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.18/1.59 ), Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.18/1.59 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.18/1.59 ), Y ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.59 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.18/1.59 , Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.59 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X,
% 1.18/1.59 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.18/1.59 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.18/1.59 , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.18/1.59 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.18/1.59 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.18/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.18/1.59 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.18/1.59 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.59 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.18/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.18/1.59 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.18/1.59 , X, Z, U, W, V0 ) ) ],
% 1.18/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.18/1.59 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.18/1.59 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.18/1.59 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.18/1.59 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.59 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.18/1.59 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.18/1.59 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.59 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.59 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.18/1.59 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.18/1.59 , 'tc_nat' ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ =( 'c_FFT__Mirabelle_OIFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.18/1.59 ), X ) ],
% 1.18/1.59 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.18/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.59 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.18/1.59 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.59 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.18/1.59 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.18/1.59 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.18/1.59 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.18/1.59 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.59 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.18/1.59 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.59 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.18/1.59 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.59 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.59 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.59 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.18/1.59 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.18/1.59 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.18/1.59 , 'tc_nat' ) ],
% 1.18/1.59 [ ~( =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP(
% 1.18/1.59 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.18/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.18/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.18/1.59 , 'v_a____', 'v_i____' ), hAPP( 'c_FFT__Mirabelle_OIFFT'(
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_a____' ), 'v_i____' ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.59 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.18/1.59 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.59 'class_Orderings_Opreorder'( Y ) ) ],
% 1.18/1.59 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.59 'class_Orderings_Oorder'( Y ) ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.18/1.59 ],
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.18/1.59 ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.18/1.59 ],
% 1.18/1.59 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.18/1.59 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.18/1.59 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.18/1.59 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.18/1.59 ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.18/1.59 ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.18/1.59 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.18/1.59 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.18/1.59 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.18/1.59 ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.18/1.59 ],
% 1.18/1.59 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.18/1.59 ],
% 1.18/1.59 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.59 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.18/1.60 [ 'c_fequal'( X, X, Y ) ],
% 1.18/1.60 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.18/1.60 ] .
% 1.18/1.60
% 1.18/1.60
% 1.18/1.60 percentage equality = 0.197239, percentage horn = 0.837051
% 1.18/1.60 This is a problem with some equality
% 1.18/1.60
% 1.18/1.60
% 1.18/1.60
% 1.18/1.60 Options Used:
% 1.18/1.60
% 1.18/1.60 useres = 1
% 1.18/1.60 useparamod = 1
% 1.18/1.60 useeqrefl = 1
% 1.18/1.60 useeqfact = 1
% 1.18/1.60 usefactor = 1
% 1.18/1.60 usesimpsplitting = 0
% 1.18/1.60 usesimpdemod = 5
% 1.18/1.60 usesimpres = 3
% 1.18/1.60
% 1.18/1.60 resimpinuse = 1000
% 1.18/1.60 resimpclauses = 20000
% 1.18/1.60 substype = eqrewr
% 1.18/1.60 backwardsubs = 1
% 1.18/1.60 selectoldest = 5
% 1.18/1.60
% 1.18/1.60 litorderings [0] = split
% 1.18/1.60 litorderings [1] = extend the termordering, first sorting on arguments
% 1.18/1.60
% 1.18/1.60 termordering = kbo
% 1.18/1.60
% 1.18/1.60 litapriori = 0
% 1.18/1.60 termapriori = 1
% 1.18/1.60 litaposteriori = 0
% 1.18/1.60 termaposteriori = 0
% 1.18/1.60 demodaposteriori = 0
% 1.18/1.60 ordereqreflfact = 0
% 1.18/1.60
% 1.18/1.60 litselect = negord
% 1.18/1.60
% 1.18/1.60 maxweight = 15
% 1.18/1.60 maxdepth = 30000
% 1.18/1.60 maxlength = 115
% 1.18/1.60 maxnrvars = 195
% 1.18/1.60 excuselevel = 1
% 1.18/1.60 increasemaxweight = 1
% 1.18/1.60
% 1.18/1.60 maxselected = 10000000
% 1.18/1.60 maxnrclauses = 10000000
% 1.18/1.60
% 1.18/1.60 showgenerated = 0
% 1.18/1.60 showkept = 0
% 1.18/1.60 showselected = 0
% 1.18/1.60 showdeleted = 0
% 1.18/1.60 showresimp = 1
% 1.18/1.60 showstatus = 2000
% 1.18/1.60
% 1.18/1.60 prologoutput = 1
% 1.18/1.60 nrgoals = 5000000
% 1.18/1.60 totalproof = 1
% 1.18/1.60
% 1.18/1.60 Symbols occurring in the translation:
% 1.18/1.60
% 1.18/1.60 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.18/1.60 . [1, 2] (w:1, o:139, a:1, s:1, b:0),
% 1.18/1.60 ! [4, 1] (w:0, o:61, a:1, s:1, b:0),
% 1.18/1.60 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.18/1.60 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.18/1.60 'tc_nat' [41, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.18/1.60 'c_HOL_Oord__class_Oless' [42, 3] (w:1, o:172, a:1, s:1, b:0),
% 1.56/1.95 hAPP [44, 2] (w:1, o:164, a:1, s:1, b:0),
% 1.56/1.95 hBOOL [45, 1] (w:1, o:66, a:1, s:1, b:0),
% 1.56/1.95 'class_Orderings_Oorder' [49, 1] (w:1, o:67, a:1, s:1, b:0),
% 1.56/1.95 'c_lessequals' [50, 3] (w:1, o:173, a:1, s:1, b:0),
% 1.56/1.95 'class_Orderings_Olinorder' [51, 1] (w:1, o:68, a:1, s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Oordered__semidom' [52, 1] (w:1, o:71, a:1
% 1.56/1.95 , s:1, b:0),
% 1.56/1.95 'c_HOL_Oone__class_Oone' [53, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.56/1.95 'c_HOL_Otimes__class_Otimes' [54, 1] (w:1, o:73, a:1, s:1, b:0),
% 1.56/1.95 'c_Power_Opower__class_Opower' [56, 1] (w:1, o:74, a:1, s:1, b:0),
% 1.56/1.95 'class_Lattices_Oboolean__algebra' [57, 1] (w:1, o:75, a:1, s:1, b:0)
% 1.56/1.95 ,
% 1.56/1.95 'c_HOL_Ouminus__class_Ouminus' [58, 2] (w:1, o:165, a:1, s:1, b:0),
% 1.56/1.95 'class_OrderedGroup_Ogroup__add' [59, 1] (w:1, o:76, a:1, s:1, b:0),
% 1.56/1.95
% 1.56/1.95 'class_Ring__and__Field_Ofield' [61, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.56/1.95 'c_HOL_Ozero__class_Ozero' [63, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.56/1.95 'c_HOL_Oinverse__class_Odivide' [64, 3] (w:1, o:174, a:1, s:1, b:0),
% 1.56/1.95
% 1.56/1.95 'class_OrderedGroup_Olordered__ab__group__add__abs' [65, 1] (w:1, o:
% 1.56/1.95 79, a:1, s:1, b:0),
% 1.56/1.95 'c_HOL_Oplus__class_Oplus' [66, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.56/1.95 'c_HOL_Oabs__class_Oabs' [67, 2] (w:1, o:166, a:1, s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Odivision__by__zero' [68, 1] (w:1, o:84, a:1
% 1.56/1.95 , s:1, b:0),
% 1.56/1.95 'c_Divides_Odiv__class_Omod' [69, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Oordered__field' [70, 1] (w:1, o:85, a:1, s:1
% 1.56/1.95 , b:0),
% 1.56/1.95 'class_Ring__and__Field_Oordered__idom' [71, 1] (w:1, o:86, a:1, s:1
% 1.56/1.95 , b:0),
% 1.56/1.95 'class_Int_Onumber__ring' [72, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.56/1.95 'tc_Int_Oint' [73, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.56/1.95 'c_Int_Onumber__class_Onumber__of' [74, 2] (w:1, o:168, a:1, s:1, b:0
% 1.56/1.95 ),
% 1.56/1.95 'class_OrderedGroup_Opordered__ab__group__add__abs' [75, 1] (w:1, o:
% 1.56/1.95 89, a:1, s:1, b:0),
% 1.56/1.95 'c_HOL_Oinverse__class_Oinverse' [76, 2] (w:1, o:167, a:1, s:1, b:0)
% 1.56/1.95 ,
% 1.56/1.95 'class_Ring__and__Field_Ocomm__semiring__1' [77, 1] (w:1, o:82, a:1
% 1.56/1.95 , s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Oordered__ring__strict' [82, 1] (w:1, o:70
% 1.56/1.95 , a:1, s:1, b:0),
% 1.56/1.95 'class_OrderedGroup_Opordered__comm__monoid__add' [83, 1] (w:1, o:90
% 1.56/1.95 , a:1, s:1, b:0),
% 1.56/1.95 'class_OrderedGroup_Opordered__ab__group__add' [84, 1] (w:1, o:91, a:
% 1.56/1.95 1, s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Oordered__semiring__strict' [85, 1] (w:1, o:
% 1.56/1.95 92, a:1, s:1, b:0),
% 1.56/1.95 'class_OrderedGroup_Olordered__ab__group__add' [86, 1] (w:1, o:93, a:
% 1.56/1.95 1, s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Oabs__if' [87, 1] (w:1, o:94, a:1, s:1, b:0)
% 1.56/1.95 ,
% 1.56/1.95 'class_Ring__and__Field_Oidom' [88, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Oordered__semiring' [89, 1] (w:1, o:96, a:1
% 1.56/1.95 , s:1, b:0),
% 1.56/1.95 'class_Int_Onumber' [91, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.56/1.95 'class_Power_Opower' [93, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.56/1.95 'c_Power_Opower_Opower' [94, 3] (w:1, o:176, a:1, s:1, b:0),
% 1.56/1.95 'c_Suc' [95, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.56/1.95 'class_OrderedGroup_Opordered__ab__semigroup__add' [99, 1] (w:1, o:98
% 1.56/1.95 , a:1, s:1, b:0),
% 1.56/1.95 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [100, 1]
% 1.56/1.95 (w:1, o:99, a:1, s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Opordered__ring__abs' [101, 1] (w:1, o:115
% 1.56/1.95 , a:1, s:1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Oring' [102, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.56/1.95
% 1.56/1.95 'c_Groebner__Basis_Ogb__semiring' [109, 6] (w:1, o:179, a:1, s:1, b:0
% 1.56/1.95 ),
% 1.56/1.95 'class_OrderedGroup_Oab__semigroup__idem__mult' [110, 1] (w:1, o:100
% 1.56/1.95 , a:1, s:1, b:0),
% 1.56/1.95 'class_Divides_Osemiring__div' [111, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.56/1.95
% 1.56/1.95 'class_OrderedGroup_Ocomm__monoid__add' [112, 1] (w:1, o:101, a:1, s:
% 1.56/1.95 1, b:0),
% 1.56/1.95 'class_Ring__and__Field_Omult__mono1' [113, 1] (w:1, o:120, a:1, s:1
% 1.56/1.95 , b:0),
% 1.56/1.95 'class_Ring__and__Field_Omult__mono' [114, 1] (w:1, o:121, a:1, s:1
% 1.56/1.95 , b:0),
% 1.56/1.95 'class_Ring__and__Field_Opordered__ring' [115, 1] (w:1, o:122, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Odivision__ring' [118, 1] (w:1, o:123, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Olordered__ring' [119, 1] (w:1, o:119, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'c_Int_OBit0' [120, 1] (w:1, o:124, a:1, s:1, b:0),
% 9.58/9.96 'class_OrderedGroup_Omonoid__mult' [121, 1] (w:1, o:102, a:1, s:1, b:
% 9.58/9.96 0),
% 9.58/9.96 'class_OrderedGroup_Ocomm__monoid__mult' [122, 1] (w:1, o:103, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'class_Orderings_Opreorder' [123, 1] (w:1, o:104, a:1, s:1, b:0),
% 9.58/9.96 'class_OrderedGroup_Oab__group__add' [124, 1] (w:1, o:105, a:1, s:1
% 9.58/9.96 , b:0),
% 9.58/9.96 'class_OrderedGroup_Oab__semigroup__add' [125, 1] (w:1, o:106, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Osemiring' [126, 1] (w:1, o:128, a:1, s:1, b:
% 9.58/9.96 0),
% 9.58/9.96 'class_Ring__and__Field_Opordered__cancel__semiring' [128, 1] (w:1
% 9.58/9.96 , o:129, a:1, s:1, b:0),
% 9.58/9.96 'class_OrderedGroup_Oab__semigroup__mult' [129, 1] (w:1, o:107, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'class_RealVector_Oreal__normed__algebra' [130, 1] (w:1, o:130, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Ocomm__semiring' [135, 1] (w:1, o:83, a:1, s:
% 9.58/9.96 1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Opordered__semiring' [136, 1] (w:1, o:131, a:
% 9.58/9.96 1, s:1, b:0),
% 9.58/9.96 'class_Divides_Oring__div' [137, 1] (w:1, o:117, a:1, s:1, b:0),
% 9.58/9.96 'class_RealVector_Oreal__normed__field' [138, 1] (w:1, o:132, a:1, s:
% 9.58/9.96 1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Oordered__comm__semiring__strict' [140, 1]
% 9.58/9.96 (w:1, o:114, a:1, s:1, b:0),
% 9.58/9.96 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [141, 1]
% 9.58/9.96 (w:1, o:108, a:1, s:1, b:0),
% 9.58/9.96 'class_OrderedGroup_Ocancel__ab__semigroup__add' [142, 1] (w:1, o:109
% 9.58/9.96 , a:1, s:1, b:0),
% 9.58/9.96 'class_OrderedGroup_Ocancel__semigroup__add' [143, 1] (w:1, o:110, a:
% 9.58/9.96 1, s:1, b:0),
% 9.58/9.96 'class_OrderedGroup_Oordered__ab__group__add' [145, 1] (w:1, o:88, a:
% 9.58/9.96 1, s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Osemiring__1' [146, 1] (w:1, o:134, a:1, s:1
% 9.58/9.96 , b:0),
% 9.58/9.96 'c_Int_Oiszero' [147, 2] (w:1, o:169, a:1, s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Oring__no__zero__divisors' [148, 1] (w:1, o:
% 9.58/9.96 125, a:1, s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Omult__zero' [149, 1] (w:1, o:135, a:1, s:1
% 9.58/9.96 , b:0),
% 9.58/9.96 'class_Ring__and__Field_Ozero__neq__one' [150, 1] (w:1, o:136, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Ono__zero__divisors' [151, 1] (w:1, o:69, a:1
% 9.58/9.96 , s:1, b:0),
% 9.58/9.96 'class_OrderedGroup_Omonoid__add' [152, 1] (w:1, o:111, a:1, s:1, b:0
% 9.58/9.96 ),
% 9.58/9.96 'class_Ring__and__Field_Oring__1' [158, 1] (w:1, o:126, a:1, s:1, b:0
% 9.58/9.96 ),
% 9.58/9.96 'c_Int_OBit1' [160, 1] (w:1, o:137, a:1, s:1, b:0),
% 9.58/9.96 'c_Int_OPls' [161, 0] (w:1, o:53, a:1, s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Ocomm__ring__1' [165, 1] (w:1, o:81, a:1, s:1
% 9.58/9.96 , b:0),
% 9.58/9.96 'class_Ring__and__Field_Osemiring__0' [166, 1] (w:1, o:133, a:1, s:1
% 9.58/9.96 , b:0),
% 9.58/9.96 'class_Int_Oring__char__0' [167, 1] (w:1, o:138, a:1, s:1, b:0),
% 9.58/9.96 'v_i____' [168, 0] (w:1, o:54, a:1, s:1, b:0),
% 9.58/9.96 'c_FFT__Mirabelle_OIFFT' [169, 2] (w:1, o:170, a:1, s:1, b:0),
% 9.58/9.96 'class_Ring__and__Field_Oring__1__no__zero__divisors' [170, 1] (w:1
% 9.58/9.96 , o:127, a:1, s:1, b:0),
% 9.58/9.96 'v_a____' [171, 0] (w:1, o:55, a:1, s:1, b:0),
% 9.58/9.96 'c_FFT__Mirabelle_OIDFT' [172, 3] (w:1, o:177, a:1, s:1, b:0),
% 9.58/9.96 'tc_fun' [175, 2] (w:1, o:171, a:1, s:1, b:0),
% 9.58/9.96 'tc_Complex_Ocomplex' [176, 0] (w:1, o:58, a:1, s:1, b:0),
% 9.58/9.96 'c_fequal' [177, 3] (w:1, o:178, a:1, s:1, b:0).
% 9.58/9.96
% 9.58/9.96
% 9.58/9.96 Starting Search:
% 9.58/9.96
% 9.58/9.96 Resimplifying inuse:
% 9.58/9.96 Done
% 9.58/9.96
% 9.58/9.96
% 9.58/9.96 Intermediate Status:
% 9.58/9.96 Generated: 4072
% 9.58/9.96 Kept: 2006
% 9.58/9.96 Inuse: 86
% 9.58/9.96 Deleted: 2
% 9.58/9.96 Deletedinuse: 0
% 9.58/9.96
% 9.58/9.96 Resimplifying inuse:
% 9.58/9.96 Done
% 9.58/9.96
% 9.58/9.96 Resimplifying inuse:
% 9.58/9.96 Done
% 9.58/9.96
% 9.58/9.96
% 9.58/9.96 Intermediate Status:
% 9.58/9.96 Generated: 10337
% 9.58/9.96 Kept: 4077
% 9.58/9.96 Inuse: 187
% 9.58/9.96 Deleted: 12
% 9.58/9.96 Deletedinuse: 3
% 9.58/9.96
% 9.58/9.96 Resimplifying inuse:
% 9.58/9.96 Done
% 9.58/9.96
% 9.58/9.96 Resimplifying inuse:
% 9.58/9.96 Done
% 9.58/9.96
% 9.58/9.96
% 9.58/9.96 Intermediate Status:
% 9.58/9.96 Generated: 16479
% 9.58/9.96 Kept: 6120
% 9.58/9.96 Inuse: 216
% 9.58/9.96 Deleted: 14
% 9.58/9.96 Deletedinuse: 3
% 9.58/9.96
% 9.58/9.96 Resimplifying inuse:
% 9.58/9.96 Done
% 9.58/9.96
% 9.58/9.96 Resimplifying inuse:
% 9.58/9.96 Done
% 9.58/9.96
% 9.58/9.96
% 9.58/9.96 Intermediate Status:
% 9.58/9.96 Generated: 23952
% 9.58/9.96 Kept: 8357
% 9.58/9.96 Inuse: 288
% 9.58/9.96 Deleted: 16
% 9.58/9.96 Deletedinuse: 3
% 9.58/9.96
% 9.58/9.96 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 31221
% 32.73/33.18 Kept: 10385
% 32.73/33.18 Inuse: 377
% 32.73/33.18 Deleted: 17
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 37817
% 32.73/33.18 Kept: 12405
% 32.73/33.18 Inuse: 480
% 32.73/33.18 Deleted: 24
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 45205
% 32.73/33.18 Kept: 14782
% 32.73/33.18 Inuse: 535
% 32.73/33.18 Deleted: 25
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 58718
% 32.73/33.18 Kept: 17070
% 32.73/33.18 Inuse: 559
% 32.73/33.18 Deleted: 25
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 66733
% 32.73/33.18 Kept: 19439
% 32.73/33.18 Inuse: 574
% 32.73/33.18 Deleted: 25
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying clauses:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 73979
% 32.73/33.18 Kept: 21462
% 32.73/33.18 Inuse: 608
% 32.73/33.18 Deleted: 337
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 84634
% 32.73/33.18 Kept: 23521
% 32.73/33.18 Inuse: 653
% 32.73/33.18 Deleted: 337
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 95393
% 32.73/33.18 Kept: 26267
% 32.73/33.18 Inuse: 673
% 32.73/33.18 Deleted: 337
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 102979
% 32.73/33.18 Kept: 28307
% 32.73/33.18 Inuse: 718
% 32.73/33.18 Deleted: 337
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 111585
% 32.73/33.18 Kept: 30365
% 32.73/33.18 Inuse: 753
% 32.73/33.18 Deleted: 337
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 124756
% 32.73/33.18 Kept: 33085
% 32.73/33.18 Inuse: 798
% 32.73/33.18 Deleted: 337
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 135408
% 32.73/33.18 Kept: 35089
% 32.73/33.18 Inuse: 846
% 32.73/33.18 Deleted: 338
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 145540
% 32.73/33.18 Kept: 37177
% 32.73/33.18 Inuse: 876
% 32.73/33.18 Deleted: 338
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 156559
% 32.73/33.18 Kept: 39249
% 32.73/33.18 Inuse: 917
% 32.73/33.18 Deleted: 338
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying clauses:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 165270
% 32.73/33.18 Kept: 41398
% 32.73/33.18 Inuse: 942
% 32.73/33.18 Deleted: 784
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 176232
% 32.73/33.18 Kept: 44083
% 32.73/33.18 Inuse: 962
% 32.73/33.18 Deleted: 784
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 183743
% 32.73/33.18 Kept: 46126
% 32.73/33.18 Inuse: 987
% 32.73/33.18 Deleted: 784
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 193103
% 32.73/33.18 Kept: 48776
% 32.73/33.18 Inuse: 997
% 32.73/33.18 Deleted: 784
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 203506
% 32.73/33.18 Kept: 50829
% 32.73/33.18 Inuse: 1032
% 32.73/33.18 Deleted: 784
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 221996
% 32.73/33.18 Kept: 54268
% 32.73/33.18 Inuse: 1047
% 32.73/33.18 Deleted: 784
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 237485
% 32.73/33.18 Kept: 58459
% 32.73/33.18 Inuse: 1086
% 32.73/33.18 Deleted: 784
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 245095
% 32.73/33.18 Kept: 60654
% 32.73/33.18 Inuse: 1107
% 32.73/33.18 Deleted: 784
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying clauses:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 252367
% 32.73/33.18 Kept: 62672
% 32.73/33.18 Inuse: 1139
% 32.73/33.18 Deleted: 1072
% 32.73/33.18 Deletedinuse: 3
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 32.73/33.18 Generated: 259251
% 32.73/33.18 Kept: 64701
% 32.73/33.18 Inuse: 1166
% 32.73/33.18 Deleted: 1076
% 32.73/33.18 Deletedinuse: 6
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18 Resimplifying inuse:
% 32.73/33.18 Done
% 32.73/33.18
% 32.73/33.18
% 32.73/33.18 Intermediate Status:
% 62.99/63.43 Generated: 267737
% 62.99/63.43 Kept: 66716
% 62.99/63.43 Inuse: 1183
% 62.99/63.43 Deleted: 1076
% 62.99/63.43 Deletedinuse: 6
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43
% 62.99/63.43 Intermediate Status:
% 62.99/63.43 Generated: 278987
% 62.99/63.43 Kept: 69492
% 62.99/63.43 Inuse: 1191
% 62.99/63.43 Deleted: 1076
% 62.99/63.43 Deletedinuse: 6
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43
% 62.99/63.43 Intermediate Status:
% 62.99/63.43 Generated: 293023
% 62.99/63.43 Kept: 71730
% 62.99/63.43 Inuse: 1211
% 62.99/63.43 Deleted: 1076
% 62.99/63.43 Deletedinuse: 6
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43
% 62.99/63.43 Intermediate Status:
% 62.99/63.43 Generated: 303340
% 62.99/63.43 Kept: 74091
% 62.99/63.43 Inuse: 1236
% 62.99/63.43 Deleted: 1076
% 62.99/63.43 Deletedinuse: 6
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43
% 62.99/63.43 Intermediate Status:
% 62.99/63.43 Generated: 312080
% 62.99/63.43 Kept: 76178
% 62.99/63.43 Inuse: 1261
% 62.99/63.43 Deleted: 1076
% 62.99/63.43 Deletedinuse: 6
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43
% 62.99/63.43 Intermediate Status:
% 62.99/63.43 Generated: 321155
% 62.99/63.43 Kept: 78197
% 62.99/63.43 Inuse: 1286
% 62.99/63.43 Deleted: 1076
% 62.99/63.43 Deletedinuse: 6
% 62.99/63.43
% 62.99/63.43 Resimplifying inuse:
% 62.99/63.43 Done
% 62.99/63.43
% 62.99/63.43
% 62.99/63.43 Intermediate Status:
% 62.99/63.43 Generated: 346648
% 62.99/63.43 Kept: 81676
% 62.99/63.44 Inuse: 1301
% 62.99/63.44 Deleted: 1076
% 62.99/63.44 Deletedinuse: 6
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying clauses:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 358262
% 62.99/63.44 Kept: 84382
% 62.99/63.44 Inuse: 1316
% 62.99/63.44 Deleted: 1494
% 62.99/63.44 Deletedinuse: 6
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 381068
% 62.99/63.44 Kept: 87195
% 62.99/63.44 Inuse: 1351
% 62.99/63.44 Deleted: 1495
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 387326
% 62.99/63.44 Kept: 89211
% 62.99/63.44 Inuse: 1362
% 62.99/63.44 Deleted: 1495
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 396806
% 62.99/63.44 Kept: 91670
% 62.99/63.44 Inuse: 1386
% 62.99/63.44 Deleted: 1495
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 406973
% 62.99/63.44 Kept: 93713
% 62.99/63.44 Inuse: 1421
% 62.99/63.44 Deleted: 1495
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 417413
% 62.99/63.44 Kept: 95946
% 62.99/63.44 Inuse: 1431
% 62.99/63.44 Deleted: 1495
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 427267
% 62.99/63.44 Kept: 98024
% 62.99/63.44 Inuse: 1441
% 62.99/63.44 Deleted: 1495
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 439907
% 62.99/63.44 Kept: 100769
% 62.99/63.44 Inuse: 1461
% 62.99/63.44 Deleted: 1495
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying clauses:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 450024
% 62.99/63.44 Kept: 102787
% 62.99/63.44 Inuse: 1478
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 465545
% 62.99/63.44 Kept: 106055
% 62.99/63.44 Inuse: 1506
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 475194
% 62.99/63.44 Kept: 108058
% 62.99/63.44 Inuse: 1514
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 490275
% 62.99/63.44 Kept: 111247
% 62.99/63.44 Inuse: 1536
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 512717
% 62.99/63.44 Kept: 113275
% 62.99/63.44 Inuse: 1572
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 522109
% 62.99/63.44 Kept: 115429
% 62.99/63.44 Inuse: 1586
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 531812
% 62.99/63.44 Kept: 117511
% 62.99/63.44 Inuse: 1601
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 541940
% 62.99/63.44 Kept: 119530
% 62.99/63.44 Inuse: 1620
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 552376
% 62.99/63.44 Kept: 121543
% 62.99/63.44 Inuse: 1639
% 62.99/63.44 Deleted: 1575
% 62.99/63.44 Deletedinuse: 7
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying clauses:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44 Resimplifying inuse:
% 62.99/63.44 Done
% 62.99/63.44
% 62.99/63.44
% 62.99/63.44 Intermediate Status:
% 62.99/63.44 Generated: 563199
% 62.99/63.44 Kept: 123653
% 62.99/63.44 Inuse: 1656
% 169.12/169.60 Deleted: 1915
% 169.12/169.60 Deletedinuse: 7
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 576084
% 169.12/169.60 Kept: 125955
% 169.12/169.60 Inuse: 1686
% 169.12/169.60 Deleted: 1916
% 169.12/169.60 Deletedinuse: 8
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 588617
% 169.12/169.60 Kept: 128375
% 169.12/169.60 Inuse: 1711
% 169.12/169.60 Deleted: 1916
% 169.12/169.60 Deletedinuse: 8
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 600400
% 169.12/169.60 Kept: 130863
% 169.12/169.60 Inuse: 1731
% 169.12/169.60 Deleted: 1916
% 169.12/169.60 Deletedinuse: 8
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 610639
% 169.12/169.60 Kept: 132903
% 169.12/169.60 Inuse: 1746
% 169.12/169.60 Deleted: 1916
% 169.12/169.60 Deletedinuse: 8
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 621726
% 169.12/169.60 Kept: 135115
% 169.12/169.60 Inuse: 1761
% 169.12/169.60 Deleted: 1916
% 169.12/169.60 Deletedinuse: 8
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 632274
% 169.12/169.60 Kept: 137177
% 169.12/169.60 Inuse: 1776
% 169.12/169.60 Deleted: 1916
% 169.12/169.60 Deletedinuse: 8
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 641368
% 169.12/169.60 Kept: 139178
% 169.12/169.60 Inuse: 1794
% 169.12/169.60 Deleted: 1916
% 169.12/169.60 Deletedinuse: 8
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 669497
% 169.12/169.60 Kept: 142671
% 169.12/169.60 Inuse: 1820
% 169.12/169.60 Deleted: 1918
% 169.12/169.60 Deletedinuse: 9
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying clauses:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 703143
% 169.12/169.60 Kept: 146216
% 169.12/169.60 Inuse: 1830
% 169.12/169.60 Deleted: 2664
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 722795
% 169.12/169.60 Kept: 148341
% 169.12/169.60 Inuse: 1840
% 169.12/169.60 Deleted: 2664
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 735699
% 169.12/169.60 Kept: 150357
% 169.12/169.60 Inuse: 1862
% 169.12/169.60 Deleted: 2664
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 766806
% 169.12/169.60 Kept: 154137
% 169.12/169.60 Inuse: 1865
% 169.12/169.60 Deleted: 2664
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 778723
% 169.12/169.60 Kept: 156689
% 169.12/169.60 Inuse: 1885
% 169.12/169.60 Deleted: 2664
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 789755
% 169.12/169.60 Kept: 158947
% 169.12/169.60 Inuse: 1905
% 169.12/169.60 Deleted: 2664
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 811543
% 169.12/169.60 Kept: 162654
% 169.12/169.60 Inuse: 1915
% 169.12/169.60 Deleted: 2664
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying clauses:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 824422
% 169.12/169.60 Kept: 164678
% 169.12/169.60 Inuse: 1924
% 169.12/169.60 Deleted: 3030
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 835091
% 169.12/169.60 Kept: 166883
% 169.12/169.60 Inuse: 1925
% 169.12/169.60 Deleted: 3030
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 843739
% 169.12/169.60 Kept: 168895
% 169.12/169.60 Inuse: 1943
% 169.12/169.60 Deleted: 3030
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 853787
% 169.12/169.60 Kept: 171313
% 169.12/169.60 Inuse: 1960
% 169.12/169.60 Deleted: 3030
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 863528
% 169.12/169.60 Kept: 173433
% 169.12/169.60 Inuse: 1980
% 169.12/169.60 Deleted: 3030
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 874037
% 169.12/169.60 Kept: 175864
% 169.12/169.60 Inuse: 2005
% 169.12/169.60 Deleted: 3030
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 883009
% 169.12/169.60 Kept: 177999
% 169.12/169.60 Inuse: 2029
% 169.12/169.60 Deleted: 3031
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 892954
% 169.12/169.60 Kept: 180028
% 169.12/169.60 Inuse: 2056
% 169.12/169.60 Deleted: 3032
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60
% 169.12/169.60 Intermediate Status:
% 169.12/169.60 Generated: 911589
% 169.12/169.60 Kept: 185078
% 169.12/169.60 Inuse: 2083
% 169.12/169.60 Deleted: 3032
% 169.12/169.60 Deletedinuse: 13
% 169.12/169.60
% 169.12/169.60 Resimplifying inuse:
% 169.12/169.60 Done
% 169.12/169.60
% 169.12/169.60 Resimplifying claCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------