TSTP Solution File: SWV587-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV587-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:26:56 EDT 2022
% Result : Timeout 300.03s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV587-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n023.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 : Wed Jun 15 22:24:50 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.19/1.61 *** allocated 10000 integers for termspace/termends
% 1.19/1.61 *** allocated 10000 integers for clauses
% 1.19/1.61 *** allocated 10000 integers for justifications
% 1.19/1.61 *** allocated 15000 integers for termspace/termends
% 1.19/1.61 *** allocated 22500 integers for termspace/termends
% 1.19/1.61 *** allocated 33750 integers for termspace/termends
% 1.19/1.61 Bliksem 1.12
% 1.19/1.61
% 1.19/1.61
% 1.19/1.61 Automatic Strategy Selection
% 1.19/1.61
% 1.19/1.61 Clauses:
% 1.19/1.61 [
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.19/1.61 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.19/1.61 V0, V1 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.19/1.61 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.19/1.61 V0, V1 ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.19/1.61 U ), hAPP( 'c_Suc', W ) ) ), Y ) ), ~( hBOOL( hAPP( hAPP( X, U ), Y ) ) )
% 1.19/1.61 , ~( hBOOL( hAPP( hAPP( X, V0 ), U ) ) ), ~(
% 1.19/1.61 'c_Ring__and__Field_Oordered__semidom'( V1, V0, Y, Z, V2, X, T ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.61 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.19/1.61 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ) ) ],
% 1.19/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 'tc_nat' ), X, 'tc_nat' ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.19/1.61 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.19/1.61 , V0, V1 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.19/1.61 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.19/1.61 , V0, V1 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ), T ), X ), ~(
% 1.19/1.61 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), Z ), X ) ],
% 1.19/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.19/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.61 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 1.19/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.19/1.61 , 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.19/1.61 ), =( Z, Y ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.61 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.19/1.61 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.19/1.61 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.19/1.61 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.19/1.61 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.19/1.61 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.19/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.19/1.61 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.19/1.61 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.19/1.61 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.19/1.61 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.19/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.61 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.61 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.19/1.61 , X ) ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.19/1.61 , X ) ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ =( hAPP( 'c_NthRoot_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 'tc_nat' ), X ), Y ) ), Z ), hAPP( 'c_NthRoot_Oroot'( X ), hAPP(
% 1.19/1.61 'c_NthRoot_Oroot'( Y ), Z ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.61 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.61 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.61 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.19/1.61 , X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.19/1.61 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.19/1.61 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.19/1.61 ) ) ],
% 1.19/1.61 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( 'c_Suc',
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ), X ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.19/1.61 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.19/1.61 , ~( 'c_HOL_Oord__class_Oless'( W, V0, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.61 X, Y ), U ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, Y, Z
% 1.19/1.61 , V3, X, T ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP( Z,
% 1.19/1.61 hAPP( hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ), X ) ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower_Opower'( T, U, W ), V0 ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.61 Z, T ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, T, U
% 1.19/1.61 , V3, Z, W ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.19/1.61 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.19/1.61 , ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~( 'c_HOL_Oord__class_Oless'( W
% 1.19/1.61 , V0, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, Y
% 1.19/1.61 , Z, V3, X, T ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP( Z,
% 1.19/1.61 hAPP( hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ), X ) ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower_Opower'( T, U, W ), V0 ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.61 Z, T ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, T, U
% 1.19/1.61 , V3, Z, W ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.19/1.61 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.61 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.19/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.19/1.61 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.19/1.61 , V3, V4, V5, V6 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.19/1.61 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.19/1.61 , X, V4, V5 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.19/1.61 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.19/1.61 V5 ) ) ],
% 1.19/1.61 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.19/1.61 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.19/1.62 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.19/1.62 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.19/1.62 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.19/1.62 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.19/1.62 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.19/1.62 V5 ) ) ],
% 1.19/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.19/1.62 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.19/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.19/1.62 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.19/1.62 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.19/1.62 V5 ) ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.19/1.62 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.19/1.62 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.19/1.62 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.62 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.19/1.62 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.19/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ), X ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.62 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.19/1.62 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.62 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.19/1.62 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.19/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.19/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.19/1.62 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 X ) ), Y ), X ) ],
% 1.19/1.62 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.62 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.19/1.62 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.19/1.62 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.19/1.62 , T, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.19/1.62 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.19/1.62 X ) ],
% 1.19/1.62 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.62 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.62 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.19/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.19/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), W ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.62 X, Y, Z ), T ), U ) ), W ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.19/1.62 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.19/1.62 U ), W ) ), hAPP( hAPP( Z, U ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z
% 1.19/1.62 , T ), U ), W ) ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, V2, X, T ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.19/1.62 , Z ) ), Z ) ],
% 1.19/1.62 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.19/1.62 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.19/1.62 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.19/1.62 V6, T ) ) ],
% 1.19/1.62 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.19/1.62 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.19/1.62 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.19/1.62 V5, X, Y, Z, V6, T ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( =( hAPP( 'c_NthRoot_Osqrt', X ), hAPP( 'c_NthRoot_Osqrt', Y ) ) ),
% 1.19/1.62 =( X, Y ) ],
% 1.19/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.19/1.62 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.19/1.62 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.19/1.62 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.19/1.62 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.19/1.62 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( =( hAPP( 'c_NthRoot_Oroot'( X ), Y ), hAPP( 'c_NthRoot_Oroot'( X )
% 1.19/1.62 , Z ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), X, 'tc_nat' ) ), =( Y, Z ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), W ) ), hAPP( hAPP( Y, hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~(
% 1.19/1.62 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.19/1.62 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.19/1.62 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.19/1.62 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.19/1.62 , X ) ), Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.62 Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ), hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), W ), U ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__semidom'( V0, V1, X, Y, V2, V3, Z ) ), =( T
% 1.19/1.62 , W ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.19/1.62 ), U, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( V2, V1 ), W ) ) ), ~( hBOOL(
% 1.19/1.62 hAPP( hAPP( V2, V1 ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.19/1.62 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.19/1.62 , 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.19/1.62 , 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.19/1.62 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.19/1.62 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.19/1.62 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 Y, X ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), X ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.19/1.62 , U ) ), hAPP( hAPP( Y, hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T
% 1.19/1.62 ), U ) ), T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.19/1.62 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.19/1.62 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.62 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.19/1.62 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), T ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), T ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.19/1.62 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.19/1.62 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.19/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.19/1.62 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.19/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, X, Z ), T )
% 1.19/1.62 , U ) ), T ), hAPP( hAPP( X, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.19/1.62 , X, Z ), T ), U ) ) ), ~( 'c_OrderedGroup_Omonoid__mult'( Y, X, Z ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.19/1.62 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.19/1.62 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.19/1.62 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.19/1.62 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), X ), X, 'tc_nat' ) ],
% 1.19/1.62 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), T ), ~(
% 1.19/1.62 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.19/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.19/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.19/1.62 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.19/1.62 ), X ), Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.19/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.19/1.62 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.19/1.62 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.19/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.19/1.62 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.62 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.19/1.62 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.19/1.62 , X ) ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.19/1.62 ), Z ), T, X ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ) ), =( Y, Z ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.19/1.62 ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.19/1.62 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.62 Y, Z, X ), X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, T ), Z ) )
% 1.19/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( U, W,
% 1.19/1.62 V0 ), Y ), hAPP( 'c_Suc', V1 ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.62 U, W, V0 ), Z ), hAPP( 'c_Suc', V1 ) ) ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__semidom'( V2, T, U, W, X, V3, V0 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.19/1.62 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 , Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.19/1.62 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.19/1.62 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.19/1.62 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.19/1.62 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.19/1.62 ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.19/1.62 ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.62 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.19/1.62 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.19/1.62 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.19/1.62 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.19/1.62 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.19/1.62 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.19/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.19/1.62 , X ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.19/1.62 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP(
% 1.19/1.62 'c_Suc', U ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), W ), hAPP(
% 1.19/1.62 'c_Suc', U ) ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1, X
% 1.19/1.62 , Y, V2, V3, Z ) ), =( T, W ), ~( hBOOL( hAPP( hAPP( V2, V1 ), W ) ) ),
% 1.19/1.62 ~( hBOOL( hAPP( hAPP( V2, V1 ), T ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.19/1.62 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.19/1.62 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.19/1.62 , V0, U, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.19/1.62 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.19/1.62 , V0, U, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.19/1.62 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 X, T, U, Y, W, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 X, T, U, Z, W, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.19/1.62 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, Y, W, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, Z, W, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, W, Y, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, W, Z, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.62 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.62 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.62 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.19/1.62 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.19/1.62 W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.19/1.62 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.19/1.62 W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.62 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.19/1.62 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.19/1.62 W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.19/1.62 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.19/1.62 W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 X, T, U, Y, W, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, Y, W, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, W, Y, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.19/1.62 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.19/1.62 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.19/1.62 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.19/1.62 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), V0 ), W ) ) )
% 1.19/1.62 , ~( hBOOL( hAPP( hAPP( X, V1 ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ),
% 1.19/1.62 V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V2, V1, Y, Z, X, V3
% 1.19/1.62 , T ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( T, Y, U ), Z ), W ) ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( T, Y, U ), Z ), W ) ) ), ~( hBOOL( hAPP( hAPP( X
% 1.19/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), Z ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__semidom'( V1, V0, T, Y, V2, X, U ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), Z ) )
% 1.19/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0,
% 1.19/1.62 V1 ), Y ), V2 ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0, V1 ), Z )
% 1.19/1.62 , V2 ) ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V3, U, W, V0, T
% 1.19/1.62 , X, V1 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.19/1.62 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.19/1.62 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.19/1.62 Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.19/1.62 T ), U ), hAPP( 'c_Suc', W ) ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) )
% 1.19/1.62 , ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, V2, X, T ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.19/1.62 ), Z ) ), T ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.19/1.62 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.19/1.62 Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__mult'( Z
% 1.19/1.62 , X, T ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__mult'( Y
% 1.19/1.62 , X, T ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.19/1.62 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ =( hAPP( 'c_NthRoot_Oroot'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ) ), X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.19/1.62 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.19/1.62 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.19/1.62 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.19/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.19/1.62 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.19/1.62 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.19/1.62 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.19/1.62 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.19/1.62 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.19/1.62 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.19/1.62 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.19/1.62 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.19/1.62 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.19/1.62 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.19/1.62 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.19/1.62 V6 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.19/1.62 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.19/1.62 , V2, V3, V4, Z, V5 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.19/1.62 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.19/1.62 , V2, V3, V4, T, V5 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.19/1.62 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.19/1.62 , V2, V3, V4, Y, V5 ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.19/1.62 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.19/1.62 , V2, V3, V4, T, V5 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.19/1.62 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.19/1.62 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.19/1.62 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.19/1.62 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.62 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.19/1.62 , X, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.62 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.62 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.62 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.62 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.19/1.62 , X, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.62 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.19/1.62 , Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.19/1.62 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.19/1.62 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__semidom'( T, Z, Y, U, W, X, V0 ) ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__semidom'( T, Z, Y, U, X, W, V0 ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.19/1.62 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.19/1.62 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.19/1.62 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.19/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.62 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.19/1.62 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.62 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.62 'c_Suc', Y ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( 'c_Suc', Y ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.19/1.62 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.19/1.62 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.19/1.62 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.19/1.62 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.19/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.19/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.62 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.19/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.19/1.62 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.19/1.62 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.19/1.62 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.19/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.19/1.62 ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.19/1.62 ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.19/1.62 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.19/1.62 ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.19/1.62 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.19/1.62 ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.19/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.19/1.62 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.19/1.62 , ~( hBOOL( hAPP( hAPP( X, U ), Y ) ) ), ~( hBOOL( hAPP( hAPP( X, V1 ), U
% 1.19/1.62 ) ) ), ~( 'c_HOL_Oord__class_Oless'( V0, W, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__semidom'( V2, V1, Y, Z, V3, X, T ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.19/1.62 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.19/1.62 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.19/1.62 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.19/1.62 , X, V5 ) ) ],
% 1.19/1.62 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.19/1.62 V5 ) ) ],
% 1.19/1.62 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.19/1.62 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.19/1.62 ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.19/1.62 ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.62 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.19/1.62 T ), U ), W ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), W, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, Y ), U ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1
% 1.19/1.62 , Y, Z, V2, X, T ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.19/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.19/1.62 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.19/1.62 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.19/1.62 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 X, T, 'tc_nat' ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.19/1.62 [ =( hAPP( 'c_NthRoot_Oroot'( X ), hAPP( 'c_NthRoot_Oroot'( Y ), Z ) ),
% 1.19/1.62 hAPP( 'c_NthRoot_Oroot'( Y ), hAPP( 'c_NthRoot_Oroot'( X ), Z ) ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.19/1.62 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.19/1.62 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.19/1.62 ), T ), U ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.19/1.62 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.19/1.62 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.19/1.62 X ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.19/1.62 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.19/1.62 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.19/1.62 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.19/1.62 Y ) ) ],
% 1.19/1.62 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.19/1.62 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.19/1.62 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.19/1.62 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.19/1.62 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ), Y ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.19/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.19/1.62 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.19/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.62 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.62 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.62 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.19/1.62 ), Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.19/1.62 ), Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.19/1.62 ), Y ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.19/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.62 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.62 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.19/1.62 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.19/1.62 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.19/1.62 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.19/1.62 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.19/1.62 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.62 Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.19/1.62 T, X ) ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.19/1.62 ) ), Z ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.19/1.62 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.19/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.19/1.62 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.19/1.62 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.62 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.19/1.62 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.19/1.62 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), V0 ), W ) ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), W
% 1.19/1.62 , 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( V1, V2 ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V3, V2
% 1.19/1.62 , Y, Z, V1, X, T ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.19/1.62 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.19/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.19/1.62 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.62 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.62 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.19/1.62 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.19/1.62 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.19/1.62 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.19/1.62 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 , X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.62 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.19/1.62 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.19/1.62 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.19/1.62 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.62 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.62 , Y ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 ) ), Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.62 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ), hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~( hBOOL( hAPP(
% 1.19/1.62 hAPP( V0, X ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2
% 1.19/1.62 , X, Y, V3, V0, Z ) ), =( U, W ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.19/1.62 Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.19/1.62 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.19/1.62 ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.19/1.63 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.19/1.63 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 'tc_nat' ) ) ) ],
% 1.19/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.63 , Y, X ) ) ],
% 1.19/1.63 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.19/1.63 , X ) ) ],
% 1.19/1.63 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.63 , Y, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.63 ), X ) ],
% 1.19/1.63 [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' )
% 1.19/1.63 ), Y ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.19/1.63 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.19/1.63 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.63 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.19/1.63 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.63 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.63 T, X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.19/1.63 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.19/1.63 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.63 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.19/1.63 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.63 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.19/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.19/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.19/1.63 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.63 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.19/1.63 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.19/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.63 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.19/1.63 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.63 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.19/1.63 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.63 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.19/1.63 , T ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.19/1.63 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.19/1.63 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.63 , 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.63 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.63 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.19/1.63 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.19/1.63 ) ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'(
% 1.19/1.63 Y, 'tc_nat' ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.19/1.63 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.19/1.63 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.63 Z, X ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.63 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.63 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.19/1.63 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.19/1.63 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.19/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.19/1.63 ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.19/1.63 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.19/1.63 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.19/1.63 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.19/1.63 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.63 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.19/1.63 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.19/1.63 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.19/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.63 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.19/1.63 ],
% 1.19/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.19/1.63 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.19/1.63 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.19/1.63 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.19/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.19/1.63 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.19/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.19/1.63 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.19/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.19/1.63 , Z ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.19/1.63 , Z ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.19/1.63 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.19/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.19/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.19/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.19/1.63 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.19/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.19/1.63 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.19/1.63 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 'tc_nat' ) ), Y ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.63 'tc_nat' ) ) ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.63 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.63 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.63 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.63 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.63 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.63 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.19/1.63 ), X ), Z ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 1.19/1.63 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool' ) ), T, U ) ), =(
% 1.19/1.63 Y, Z ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.19/1.63 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.63 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.19/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.63 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.19/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.19/1.63 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.19/1.63 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.19/1.63 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.19/1.63 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.63 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.63 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.19/1.63 ), Y ), Y ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.19/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.19/1.63 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.19/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, hAPP( hAPP( Y, T ), T ) )
% 1.19/1.63 , T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.19/1.63 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.19/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.19/1.63 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.19/1.63 W ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.19/1.63 U ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.19/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.63 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.19/1.63 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.19/1.63 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( hAPP( Y, T ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.63 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.19/1.63 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.19/1.63 hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( T, X ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.19/1.63 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.19/1.63 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.19/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.19/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.63 , X ) ), T ) ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.19/1.63 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.63 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OPls', X ) ), Y ) ],
% 1.19/1.63 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.19/1.63 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.19/1.63 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.19/1.63 ), X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.19/1.63 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.63 , X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.19/1.63 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.19/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.19/1.63 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.19/1.63 U ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.19/1.63 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.19/1.63 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.19/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.19/1.63 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.19/1.63 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.19/1.63 U ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.63 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.19/1.63 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.63 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.63 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.19/1.63 T ), U ), W ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, X, V2, T ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.19/1.63 U ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), W ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( V1, Y, Z, T, X, V2, U ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( Y, Z, U ), T ), W ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.63 X, Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z
% 1.19/1.63 , V2, X, U ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.19/1.63 U ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), W ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( V1, Y, Z, T, V2, X, U ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.19/1.63 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.63 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.19/1.63 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.19/1.63 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.19/1.63 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.19/1.63 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.19/1.63 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.19/1.63 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.19/1.63 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.19/1.63 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.19/1.63 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.19/1.63 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.19/1.63 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.19/1.63 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.19/1.63 V6 ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.19/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.19/1.63 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.19/1.63 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.63 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.63 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.19/1.63 ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.63 , Z ), Y ), 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.63 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.19/1.63 ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.63 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.63 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.19/1.63 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.63 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.63 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.63 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.63 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.19/1.63 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.63 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.63 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.63 'tc_nat' ) ) ) ],
% 1.19/1.63 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.19/1.63 , Y ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.63 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.63 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.63 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.63 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( W, V0, Y, Z, V1, X, V2 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( T, Y, Z, U, X, W, V0 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( Z, U, T, W, V0, X, V1 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( T, Y, Z, U, W, X, V0 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), T ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( Z, Y, T, U, W, X, V0 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.63 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, W ), T ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( Z, W, V0, V1, V2, X, V3 ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.63 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.63 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.63 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.63 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.63 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.19/1.63 ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.19/1.63 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.19/1.63 ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.63 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.19/1.63 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.19/1.63 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.19/1.63 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.63 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.63 Y, X ) ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.19/1.63 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.19/1.63 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.63 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.63 Z, X ) ) ) ],
% 1.19/1.63 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.63 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.63 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.63 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.63 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.63 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.63 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.63 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.19/1.63 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.19/1.63 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.19/1.63 T ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.19/1.63 [ =( 'c_Finite__Set_Ocard'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'(
% 1.19/1.63 'tc_bool', 'tc_bool' ) ), 'tc_bool' ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' ), ~(
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.19/1.63 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), X, 'tc_nat' )
% 1.19/1.63 ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.63 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.19/1.63 ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.19/1.63 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.19/1.63 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.19/1.63 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.19/1.63 Z ) ) ],
% 1.19/1.63 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.19/1.63 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.19/1.63 T ) ) ],
% 1.19/1.63 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.19/1.63 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.19/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.19/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), Z ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0,
% 1.19/1.63 V1 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( W, V0, V1 ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( V2, U, W, V0, T, X, V1 ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, T ), Z ) )
% 1.19/1.63 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( U, W,
% 1.19/1.63 V0 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( U, W, V0 ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( V1, T, U, W, X, V2, V0 ) ) ],
% 1.19/1.63 [ =( 'c_NthRoot_Osqrt', 'c_NthRoot_Oroot'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, T ), T ) ), ~(
% 1.19/1.63 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.19/1.63 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.19/1.63 U ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.63 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.19/1.63 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.19/1.63 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.19/1.63 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.19/1.63 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__semidom'( W, V0, X, Y, V1, V2, Z ) ), =( T
% 1.19/1.63 , U ), ~( hBOOL( hAPP( hAPP( V1, V0 ), U ) ) ), ~( hBOOL( hAPP( hAPP( V1
% 1.19/1.63 , V0 ), T ) ) ) ],
% 1.19/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.19/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.19/1.63 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.19/1.63 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.19/1.63 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.19/1.63 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.19/1.63 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.19/1.63 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.19/1.63 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.19/1.63 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.19/1.63 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.19/1.63 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.19/1.63 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.19/1.63 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.19/1.63 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.19/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.19/1.63 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.19/1.63 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.19/1.63 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.19/1.63 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.19/1.63 V0 ) ) ],
% 1.19/1.63 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.19/1.63 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.19/1.63 V0 ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), T ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.19/1.63 X, Y, T, U, Z ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.19/1.63 X, Y, T, U, Z ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.19/1.63 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.63 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.19/1.63 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.19/1.63 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.19/1.63 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.19/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.19/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), X ), ~(
% 1.19/1.63 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.19/1.63 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( X, Y, Z ), U ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, V0, T, V1, V2, Z ) ) ],
% 1.19/1.63 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.19/1.63 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.19/1.63 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.19/1.63 U ) ) ],
% 1.19/1.63 [ =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.19/1.63 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1'( X ) ) ), ~(
% 1.19/1.63 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.19/1.63 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.19/1.63 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.19/1.63 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.19/1.63 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.19/1.63 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.19/1.63 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.19/1.63 ), Y ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.63 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.19/1.63 ), Y ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.19/1.63 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.19/1.63 ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.19/1.63 ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.19/1.63 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.19/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.19/1.63 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.19/1.63 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.19/1.63 'tc_nat' ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.19/1.63 , X, Z, U, W, V0 ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.19/1.63 , Y ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 X ), Y ), Y ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.19/1.63 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.19/1.63 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.19/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.63 'tc_nat' ), X ), X ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.19/1.63 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.63 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.19/1.63 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.19/1.63 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.19/1.63 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.19/1.63 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.19/1.63 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.19/1.63 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.19/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.63 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.19/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.19/1.63 , Y ) ],
% 1.19/1.63 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.19/1.63 ,
% 1.19/1.63 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.19/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.19/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.19/1.63 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.19/1.63 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.19/1.63 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.19/1.63 [ ~( 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_A', 'tc_nat', 'tc_nat' ) ) ],
% 1.19/1.63 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.19/1.63 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.19/1.63 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.19/1.63 'class_Orderings_Opreorder'( Y ) ) ],
% 1.19/1.63 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.19/1.63 'class_Orderings_Oorder'( Y ) ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.19/1.63 ],
% 1.19/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.19/1.63 ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.19/1.63 ],
% 1.19/1.63 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.19/1.63 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.19/1.63 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.19/1.63 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.19/1.63 'tc_Int_Oint' ) ],
% 1.19/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.19/1.63 'tc_Int_Oint' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.19/1.63 'tc_Int_Oint' ) ],
% 1.19/1.63 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.19/1.63 ],
% 1.19/1.63 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.19/1.64 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.19/1.64 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.19/1.64 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.19/1.64 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.19/1.64 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.19/1.64 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 1.19/1.64 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 1.19/1.64 ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 1.19/1.64 ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 1.19/1.64 ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 1.19/1.64 ],
% 1.19/1.64 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 1.19/1.64 ,
% 1.19/1.64 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_RealVector_Oreal__normed__field'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oring__1'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Nat_Osemiring__char__0'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Ring__and__Field_Odvd'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Int_Oring__char__0'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Power_Opower'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'class_Int_Onumber'( 'tc_RealDef_Oreal' ) ],
% 1.19/1.64 [ 'c_fequal'( X, X, Y ) ],
% 1.19/1.64 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.19/1.64 ] .
% 1.19/1.64
% 1.19/1.64
% 1.19/1.64 percentage equality = 0.264409, percentage horn = 0.849126
% 1.19/1.64 This is a problem with some equality
% 1.19/1.64
% 1.19/1.64
% 1.19/1.64
% 1.19/1.64 Options Used:
% 1.19/1.64
% 1.19/1.64 useres = 1
% 1.19/1.64 useparamod = 1
% 1.19/1.64 useeqrefl = 1
% 1.19/1.64 useeqfact = 1
% 1.19/1.64 usefactor = 1
% 1.19/1.64 usesimpsplitting = 0
% 1.19/1.64 usesimpdemod = 5
% 1.19/1.64 usesimpres = 3
% 1.19/1.64
% 1.19/1.64 resimpinuse = 1000
% 1.19/1.64 resimpclauses = 20000
% 1.19/1.64 substype = eqrewr
% 1.19/1.64 backwardsubs = 1
% 1.19/1.64 selectoldest = 5
% 1.19/1.64
% 1.19/1.64 litorderings [0] = split
% 1.19/1.64 litorderings [1] = extend the termordering, first sorting on arguments
% 1.19/1.64
% 1.19/1.64 termordering = kbo
% 1.19/1.64
% 1.19/1.64 litapriori = 0
% 1.19/1.64 termapriori = 1
% 1.19/1.64 litaposteriori = 0
% 1.19/1.64 termaposteriori = 0
% 1.19/1.64 demodaposteriori = 0
% 1.19/1.64 ordereqreflfact = 0
% 1.19/1.64
% 1.19/1.64 litselect = negord
% 1.19/1.64
% 1.19/1.64 maxweight = 15
% 1.19/1.64 maxdepth = 30000
% 1.19/1.64 maxlength = 115
% 1.19/1.64 maxnrvars = 195
% 1.19/1.64 excuselevel = 1
% 1.19/1.64 increasemaxweight = 1
% 1.19/1.64
% 1.19/1.64 maxselected = 10000000
% 1.19/1.64 maxnrclauses = 10000000
% 1.19/1.64
% 1.19/1.64 showgenerated = 0
% 1.19/1.64 showkept = 0
% 1.19/1.64 showselected = 0
% 1.19/1.64 showdeleted = 0
% 1.19/1.64 showresimp = 1
% 1.19/1.64 showstatus = 2000
% 1.19/1.64
% 1.19/1.64 prologoutput = 1
% 1.19/1.64 nrgoals = 5000000
% 1.19/1.64 totalproof = 1
% 1.19/1.64
% 1.19/1.64 Symbols occurring in the translation:
% 1.19/1.64
% 1.19/1.64 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.19/1.64 . [1, 2] (w:1, o:145, a:1, s:1, b:0),
% 1.19/1.64 ! [4, 1] (w:0, o:72, a:1, s:1, b:0),
% 1.19/1.64 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.19/1.64 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.19/1.64 hAPP [41, 2] (w:1, o:170, a:1, s:1, b:0),
% 1.19/1.64 'c_Suc' [42, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.19/1.64 'c_Groebner__Basis_Ogb__semiring' [49, 6] (w:1, o:189, a:1, s:1, b:0)
% 1.19/1.64 ,
% 1.19/1.64 'c_Power_Opower_Opower' [54, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.62/1.99 hBOOL [56, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.62/1.99 'c_Ring__and__Field_Oordered__semidom' [60, 7] (w:1, o:190, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'class_Ring__and__Field_Oordered__semidom' [61, 1] (w:1, o:81, a:1
% 1.62/1.99 , s:1, b:0),
% 1.62/1.99 'c_HOL_Oplus__class_Oplus' [62, 1] (w:1, o:83, a:1, s:1, b:0),
% 1.62/1.99 'c_HOL_Oone__class_Oone' [63, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.62/1.99 'c_HOL_Oord__class_Oless' [64, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Oordered__field' [65, 1] (w:1, o:84, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'class_Ring__and__Field_Odivision__by__zero' [66, 1] (w:1, o:88, a:1
% 1.62/1.99 , s:1, b:0),
% 1.62/1.99 'c_HOL_Ozero__class_Ozero' [67, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.62/1.99 'c_HOL_Oinverse__class_Oinverse' [68, 2] (w:1, o:171, a:1, s:1, b:0)
% 1.62/1.99 ,
% 1.62/1.99 'class_Ring__and__Field_Ozero__neq__one' [69, 1] (w:1, o:90, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'class_Ring__and__Field_Ono__zero__divisors' [70, 1] (w:1, o:79, a:1
% 1.62/1.99 , s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Omult__zero' [71, 1] (w:1, o:78, a:1, s:1, b:
% 1.62/1.99 0),
% 1.62/1.99 'class_Power_Opower' [72, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.62/1.99 'c_Power_Opower__class_Opower' [73, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Oring__1__no__zero__divisors' [74, 1] (w:1
% 1.62/1.99 , o:117, a:1, s:1, b:0),
% 1.62/1.99 'tc_nat' [75, 0] (w:1, o:46, a:1, s:1, b:0),
% 1.62/1.99 'c_Ring__and__Field_Odvd__class_Odvd' [76, 3] (w:1, o:183, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'c_OrderedGroup_Omonoid__mult' [77, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Oidom' [81, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.62/1.99 'c_HOL_Otimes__class_Otimes' [82, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Ocomm__semiring__1' [85, 1] (w:1, o:86, a:1
% 1.62/1.99 , s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Oordered__idom' [89, 1] (w:1, o:120, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'class_Orderings_Olinorder' [90, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Ofield' [92, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.62/1.99
% 1.62/1.99 'c_HOL_Oinverse__class_Odivide' [93, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.62/1.99
% 1.62/1.99 'class_Lattices_Oboolean__algebra' [94, 1] (w:1, o:122, a:1, s:1, b:0
% 1.62/1.99 ),
% 1.62/1.99 'c_HOL_Ouminus__class_Ouminus' [95, 2] (w:1, o:172, a:1, s:1, b:0),
% 1.62/1.99 'class_OrderedGroup_Ogroup__add' [96, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.62/1.99
% 1.62/1.99 'c_Divides_Odiv__class_Omod' [97, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.62/1.99 'c_NthRoot_Oroot' [98, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.62/1.99 'class_Int_Onumber' [99, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.62/1.99 'c_Int_Onumber__class_Onumber__of' [101, 2] (w:1, o:174, a:1, s:1, b:
% 1.62/1.99 0),
% 1.62/1.99 'class_OrderedGroup_Opordered__ab__group__add' [102, 1] (w:1, o:95
% 1.62/1.99 , a:1, s:1, b:0),
% 1.62/1.99 'c_HOL_Oabs__class_Oabs' [103, 2] (w:1, o:173, a:1, s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Oordered__ring__strict' [104, 1] (w:1, o:80
% 1.62/1.99 , a:1, s:1, b:0),
% 1.62/1.99 'c_Ring__and__Field_Oordered__idom' [110, 11] (w:1, o:192, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'class_Ring__and__Field_Oordered__semiring__strict' [111, 1] (w:1, o:
% 1.62/1.99 125, a:1, s:1, b:0),
% 1.62/1.99 'class_OrderedGroup_Olordered__ab__group__add' [112, 1] (w:1, o:96
% 1.62/1.99 , a:1, s:1, b:0),
% 1.62/1.99 'c_Parity_Oeven__odd__class_Oeven' [114, 2] (w:1, o:175, a:1, s:1, b:
% 1.62/1.99 0),
% 1.62/1.99 'tc_Int_Oint' [115, 0] (w:1, o:57, a:1, s:1, b:0),
% 1.62/1.99 'class_OrderedGroup_Opordered__ab__group__add__abs' [117, 1] (w:1, o:
% 1.62/1.99 97, a:1, s:1, b:0),
% 1.62/1.99 'class_Ring__and__Field_Oabs__if' [118, 1] (w:1, o:126, a:1, s:1, b:0
% 1.62/1.99 ),
% 1.62/1.99 'class_OrderedGroup_Olordered__ab__group__add__abs' [119, 1] (w:1, o:
% 1.62/1.99 98, a:1, s:1, b:0),
% 1.62/1.99 'class_Int_Onumber__ring' [120, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.62/1.99 'class_Nat_Osemiring__char__0' [121, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.62/1.99 'c_Nat_Osemiring__1__class_Oof__nat' [122, 2] (w:1, o:176, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'class_Divides_Osemiring__div' [123, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.62/1.99
% 1.62/1.99 'class_Ring__and__Field_Osemiring__0' [124, 1] (w:1, o:133, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'class_OrderedGroup_Ocomm__monoid__add' [125, 1] (w:1, o:99, a:1, s:1
% 1.62/1.99 , b:0),
% 1.62/1.99 'c_NthRoot_Osqrt' [126, 0] (w:1, o:58, a:1, s:1, b:0),
% 14.37/14.74 'class_Ring__and__Field_Odivision__ring' [129, 1] (w:1, o:134, a:1
% 14.37/14.74 , s:1, b:0),
% 14.37/14.74 'class_Ring__and__Field_Osemiring__1' [130, 1] (w:1, o:135, a:1, s:1
% 14.37/14.74 , b:0),
% 14.37/14.74 'class_OrderedGroup_Oordered__ab__group__add' [131, 1] (w:1, o:94, a:
% 14.37/14.74 1, s:1, b:0),
% 14.37/14.74 'class_OrderedGroup_Omonoid__mult' [133, 1] (w:1, o:100, a:1, s:1, b:
% 14.37/14.74 0),
% 14.37/14.74 'class_Orderings_Oorder' [134, 1] (w:1, o:101, a:1, s:1, b:0),
% 14.37/14.74 'class_Orderings_Opreorder' [135, 1] (w:1, o:102, a:1, s:1, b:0),
% 14.37/14.74 'class_OrderedGroup_Oab__group__add' [136, 1] (w:1, o:103, a:1, s:1
% 14.37/14.74 , b:0),
% 14.37/14.74 'class_OrderedGroup_Oab__semigroup__add' [137, 1] (w:1, o:104, a:1
% 14.37/14.74 , s:1, b:0),
% 14.37/14.74 'class_RealVector_Oreal__normed__field' [138, 1] (w:1, o:136, a:1, s:
% 14.37/14.74 1, b:0),
% 14.37/14.74 'class_OrderedGroup_Opordered__comm__monoid__add' [139, 1] (w:1, o:
% 14.37/14.74 105, a:1, s:1, b:0),
% 14.37/14.74 'class_Divides_Oring__div' [140, 1] (w:1, o:128, a:1, s:1, b:0),
% 14.37/14.74 'class_Ring__and__Field_Ocomm__ring__1' [141, 1] (w:1, o:85, a:1, s:1
% 14.37/14.74 , b:0),
% 14.37/14.74 'class_OrderedGroup_Ocancel__ab__semigroup__add' [146, 1] (w:1, o:106
% 14.37/14.74 , a:1, s:1, b:0),
% 14.37/14.74 'class_OrderedGroup_Ocancel__semigroup__add' [147, 1] (w:1, o:107, a:
% 14.37/14.74 1, s:1, b:0),
% 14.37/14.74 'class_Ring__and__Field_Oordered__comm__semiring__strict' [148, 1]
% 14.37/14.74 (w:1, o:137, a:1, s:1, b:0),
% 14.37/14.74 'class_OrderedGroup_Omonoid__add' [149, 1] (w:1, o:108, a:1, s:1, b:0
% 14.37/14.74 ),
% 14.37/14.74 'class_Ring__and__Field_Oring__1' [152, 1] (w:1, o:130, a:1, s:1, b:0
% 14.37/14.74 ),
% 14.37/14.74 'class_Ring__and__Field_Oring' [157, 1] (w:1, o:131, a:1, s:1, b:0),
% 14.37/14.74
% 14.37/14.74 'class_Ring__and__Field_Oring__no__zero__divisors' [158, 1] (w:1, o:
% 14.37/14.74 132, a:1, s:1, b:0),
% 14.37/14.74 'class_RealVector_Oreal__normed__algebra' [159, 1] (w:1, o:138, a:1
% 14.37/14.74 , s:1, b:0),
% 14.37/14.74 'class_Ring__and__Field_Ocomm__semiring' [160, 1] (w:1, o:87, a:1, s:
% 14.37/14.74 1, b:0),
% 14.37/14.74 'class_OrderedGroup_Ocomm__monoid__mult' [161, 1] (w:1, o:109, a:1
% 14.37/14.74 , s:1, b:0),
% 14.37/14.74 'class_Ring__and__Field_Odvd' [162, 1] (w:1, o:139, a:1, s:1, b:0),
% 14.37/14.74 'class_Ring__and__Field_Osemiring' [163, 1] (w:1, o:140, a:1, s:1, b:
% 14.37/14.74 0),
% 14.37/14.74 'c_Int_Oiszero' [165, 2] (w:1, o:177, a:1, s:1, b:0),
% 14.37/14.74 'tc_bool' [166, 0] (w:1, o:62, a:1, s:1, b:0),
% 14.37/14.74 'tc_fun' [167, 2] (w:1, o:178, a:1, s:1, b:0),
% 14.37/14.74 'c_Orderings_Otop__class_Otop' [168, 1] (w:1, o:115, a:1, s:1, b:0),
% 14.37/14.74
% 14.37/14.74 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [169, 1]
% 14.37/14.74 (w:1, o:110, a:1, s:1, b:0),
% 14.37/14.74 'c_Int_OBit1' [171, 1] (w:1, o:142, a:1, s:1, b:0),
% 14.37/14.74 'c_Int_OPls' [172, 0] (w:1, o:63, a:1, s:1, b:0),
% 14.37/14.74 'c_Int_OBit0' [173, 1] (w:1, o:141, a:1, s:1, b:0),
% 14.37/14.74 'c_Fun_Oinj__on' [177, 4] (w:1, o:187, a:1, s:1, b:0),
% 14.37/14.74 'c_Ring__and__Field_Ocomm__ring__1' [178, 7] (w:1, o:191, a:1, s:1
% 14.37/14.74 , b:0),
% 14.37/14.74 'class_Int_Oring__char__0' [179, 1] (w:1, o:143, a:1, s:1, b:0),
% 14.37/14.74 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [180, 1]
% 14.37/14.74 (w:1, o:111, a:1, s:1, b:0),
% 14.37/14.74 'c_Finite__Set_Ocard' [181, 2] (w:1, o:179, a:1, s:1, b:0),
% 14.37/14.74 'c_Ring__and__Field_Osemiring__1' [182, 5] (w:1, o:188, a:1, s:1, b:0
% 14.37/14.74 ),
% 14.37/14.74 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1' [183, 1] (w:1, o:
% 14.37/14.74 144, a:1, s:1, b:0),
% 14.37/14.74 'class_OrderedGroup_Oab__semigroup__mult' [184, 1] (w:1, o:112, a:1
% 14.37/14.74 , s:1, b:0),
% 14.37/14.74 'class_OrderedGroup_Oab__semigroup__idem__mult' [185, 1] (w:1, o:113
% 14.37/14.74 , a:1, s:1, b:0),
% 14.37/14.74 'v_A' [186, 0] (w:1, o:66, a:1, s:1, b:0),
% 14.37/14.74 'tc_RealDef_Oreal' [189, 0] (w:1, o:69, a:1, s:1, b:0),
% 14.37/14.74 'c_fequal' [190, 3] (w:1, o:186, a:1, s:1, b:0).
% 14.37/14.74
% 14.37/14.74
% 14.37/14.74 Starting Search:
% 14.37/14.74
% 14.37/14.74 Resimplifying inuse:
% 14.37/14.74 Done
% 14.37/14.74
% 14.37/14.74
% 14.37/14.74 Intermediate Status:
% 14.37/14.74 Generated: 4047
% 14.37/14.74 Kept: 2042
% 14.37/14.74 Inuse: 114
% 14.37/14.74 Deleted: 2
% 14.37/14.74 Deletedinuse: 0
% 14.37/14.74
% 14.37/14.74 Resimplifying inuse:
% 14.37/14.74 Done
% 14.37/14.74
% 14.37/14.74 Resimplifying inuse:
% 14.37/14.74 Done
% 14.37/14.74
% 14.37/14.74
% 14.37/14.74 Intermediate Status:
% 14.37/14.74 Generated: 9867
% 14.37/14.74 Kept: 4104
% 14.37/14.74 Inuse: 184
% 14.37/14.74 Deleted: 4
% 14.37/14.74 Deletedinuse: 0
% 14.37/14.74
% 14.37/14.74 Resimplifying inuse:
% 14.37/14.74 Done
% 14.37/14.74
% 14.37/14.74 Resimplifying inuse:
% 14.37/14.74 Done
% 14.37/14.74
% 14.37/14.74
% 14.37/14.74 Intermediate Status:
% 14.37/14.74 Generated: 16601
% 14.37/14.74 Kept: 6255
% 14.37/14.74 Inuse: 257
% 14.37/14.74 Deleted: 4
% 14.37/14.74 Deletedinuse: 0
% 14.37/14.74
% 14.37/14.74 Resimplifying inuse:
% 14.37/14.74 Done
% 14.37/14.74
% 14.37/14.74 Resimplifying inuse:
% 14.37/14.74 Done
% 14.37/14.74
% 14.37/14.74
% 14.37/14.74 Intermediate Status:
% 41.57/41.95 Generated: 24022
% 41.57/41.95 Kept: 8754
% 41.57/41.95 Inuse: 326
% 41.57/41.95 Deleted: 5
% 41.57/41.95 Deletedinuse: 0
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 29372
% 41.57/41.95 Kept: 11003
% 41.57/41.95 Inuse: 366
% 41.57/41.95 Deleted: 5
% 41.57/41.95 Deletedinuse: 0
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 36288
% 41.57/41.95 Kept: 13153
% 41.57/41.95 Inuse: 381
% 41.57/41.95 Deleted: 5
% 41.57/41.95 Deletedinuse: 0
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 41016
% 41.57/41.95 Kept: 15206
% 41.57/41.95 Inuse: 410
% 41.57/41.95 Deleted: 8
% 41.57/41.95 Deletedinuse: 0
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 47144
% 41.57/41.95 Kept: 17290
% 41.57/41.95 Inuse: 446
% 41.57/41.95 Deleted: 11
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 55926
% 41.57/41.95 Kept: 20124
% 41.57/41.95 Inuse: 504
% 41.57/41.95 Deleted: 13
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying clauses:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 71086
% 41.57/41.95 Kept: 22834
% 41.57/41.95 Inuse: 529
% 41.57/41.95 Deleted: 340
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 85544
% 41.57/41.95 Kept: 25101
% 41.57/41.95 Inuse: 539
% 41.57/41.95 Deleted: 340
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 91820
% 41.57/41.95 Kept: 27349
% 41.57/41.95 Inuse: 559
% 41.57/41.95 Deleted: 340
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 99503
% 41.57/41.95 Kept: 29416
% 41.57/41.95 Inuse: 584
% 41.57/41.95 Deleted: 340
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 108036
% 41.57/41.95 Kept: 31924
% 41.57/41.95 Inuse: 614
% 41.57/41.95 Deleted: 340
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 115421
% 41.57/41.95 Kept: 34134
% 41.57/41.95 Inuse: 634
% 41.57/41.95 Deleted: 340
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 143235
% 41.57/41.95 Kept: 36242
% 41.57/41.95 Inuse: 654
% 41.57/41.95 Deleted: 340
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 157540
% 41.57/41.95 Kept: 39082
% 41.57/41.95 Inuse: 679
% 41.57/41.95 Deleted: 340
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying clauses:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 170075
% 41.57/41.95 Kept: 41444
% 41.57/41.95 Inuse: 694
% 41.57/41.95 Deleted: 420
% 41.57/41.95 Deletedinuse: 1
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 177938
% 41.57/41.95 Kept: 43451
% 41.57/41.95 Inuse: 720
% 41.57/41.95 Deleted: 422
% 41.57/41.95 Deletedinuse: 3
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 183807
% 41.57/41.95 Kept: 45787
% 41.57/41.95 Inuse: 729
% 41.57/41.95 Deleted: 422
% 41.57/41.95 Deletedinuse: 3
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 193553
% 41.57/41.95 Kept: 48619
% 41.57/41.95 Inuse: 759
% 41.57/41.95 Deleted: 422
% 41.57/41.95 Deletedinuse: 3
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 204861
% 41.57/41.95 Kept: 50945
% 41.57/41.95 Inuse: 769
% 41.57/41.95 Deleted: 422
% 41.57/41.95 Deletedinuse: 3
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 216362
% 41.57/41.95 Kept: 53075
% 41.57/41.95 Inuse: 798
% 41.57/41.95 Deleted: 424
% 41.57/41.95 Deletedinuse: 4
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 226467
% 41.57/41.95 Kept: 55152
% 41.57/41.95 Inuse: 823
% 41.57/41.95 Deleted: 424
% 41.57/41.95 Deletedinuse: 4
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 236228
% 41.57/41.95 Kept: 57154
% 41.57/41.95 Inuse: 857
% 41.57/41.95 Deleted: 434
% 41.57/41.95 Deletedinuse: 12
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 244048
% 41.57/41.95 Kept: 59904
% 41.57/41.95 Inuse: 866
% 41.57/41.95 Deleted: 434
% 41.57/41.95 Deletedinuse: 12
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying clauses:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 252769
% 41.57/41.95 Kept: 62098
% 41.57/41.95 Inuse: 895
% 41.57/41.95 Deleted: 1577
% 41.57/41.95 Deletedinuse: 12
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95 Resimplifying inuse:
% 41.57/41.95 Done
% 41.57/41.95
% 41.57/41.95
% 41.57/41.95 Intermediate Status:
% 41.57/41.95 Generated: 259707
% 41.57/41.95 Kept: 64134
% 41.57/41.95 Inuse: 917
% 41.57/41.95 Deleted: 1577
% 41.57/41.95 Deletedinuse: 12
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 268391
% 90.51/90.88 Kept: 66309
% 90.51/90.88 Inuse: 945
% 90.51/90.88 Deleted: 1577
% 90.51/90.88 Deletedinuse: 12
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 278358
% 90.51/90.88 Kept: 68556
% 90.51/90.88 Inuse: 970
% 90.51/90.88 Deleted: 1577
% 90.51/90.88 Deletedinuse: 12
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 287936
% 90.51/90.88 Kept: 70558
% 90.51/90.88 Inuse: 992
% 90.51/90.88 Deleted: 1577
% 90.51/90.88 Deletedinuse: 12
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 300787
% 90.51/90.88 Kept: 73098
% 90.51/90.88 Inuse: 1000
% 90.51/90.88 Deleted: 1578
% 90.51/90.88 Deletedinuse: 13
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 308125
% 90.51/90.88 Kept: 75108
% 90.51/90.88 Inuse: 1021
% 90.51/90.88 Deleted: 1579
% 90.51/90.88 Deletedinuse: 14
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 314609
% 90.51/90.88 Kept: 77147
% 90.51/90.88 Inuse: 1038
% 90.51/90.88 Deleted: 1579
% 90.51/90.88 Deletedinuse: 14
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 323919
% 90.51/90.88 Kept: 79262
% 90.51/90.88 Inuse: 1064
% 90.51/90.88 Deleted: 1583
% 90.51/90.88 Deletedinuse: 17
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying clauses:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 337032
% 90.51/90.88 Kept: 81269
% 90.51/90.88 Inuse: 1102
% 90.51/90.88 Deleted: 2334
% 90.51/90.88 Deletedinuse: 20
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 347024
% 90.51/90.88 Kept: 83336
% 90.51/90.88 Inuse: 1124
% 90.51/90.88 Deleted: 2334
% 90.51/90.88 Deletedinuse: 20
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 375734
% 90.51/90.88 Kept: 86842
% 90.51/90.88 Inuse: 1144
% 90.51/90.88 Deleted: 2334
% 90.51/90.88 Deletedinuse: 20
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 387446
% 90.51/90.88 Kept: 89599
% 90.51/90.88 Inuse: 1159
% 90.51/90.88 Deleted: 2334
% 90.51/90.88 Deletedinuse: 20
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 410378
% 90.51/90.88 Kept: 91611
% 90.51/90.88 Inuse: 1208
% 90.51/90.88 Deleted: 2335
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 425456
% 90.51/90.88 Kept: 93823
% 90.51/90.88 Inuse: 1214
% 90.51/90.88 Deleted: 2335
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 432890
% 90.51/90.88 Kept: 96176
% 90.51/90.88 Inuse: 1224
% 90.51/90.88 Deleted: 2335
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 441465
% 90.51/90.88 Kept: 98182
% 90.51/90.88 Inuse: 1242
% 90.51/90.88 Deleted: 2335
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 452016
% 90.51/90.88 Kept: 100409
% 90.51/90.88 Inuse: 1264
% 90.51/90.88 Deleted: 2335
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying clauses:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 461953
% 90.51/90.88 Kept: 102582
% 90.51/90.88 Inuse: 1279
% 90.51/90.88 Deleted: 2519
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 472047
% 90.51/90.88 Kept: 104649
% 90.51/90.88 Inuse: 1294
% 90.51/90.88 Deleted: 2519
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 485052
% 90.51/90.88 Kept: 107135
% 90.51/90.88 Inuse: 1314
% 90.51/90.88 Deleted: 2519
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 504334
% 90.51/90.88 Kept: 110035
% 90.51/90.88 Inuse: 1339
% 90.51/90.88 Deleted: 2519
% 90.51/90.88 Deletedinuse: 21
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 527840
% 90.51/90.88 Kept: 112762
% 90.51/90.88 Inuse: 1349
% 90.51/90.88 Deleted: 2520
% 90.51/90.88 Deletedinuse: 22
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 551438
% 90.51/90.88 Kept: 115494
% 90.51/90.88 Inuse: 1359
% 90.51/90.88 Deleted: 2520
% 90.51/90.88 Deletedinuse: 22
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 567711
% 90.51/90.88 Kept: 118100
% 90.51/90.88 Inuse: 1369
% 90.51/90.88 Deleted: 2520
% 90.51/90.88 Deletedinuse: 22
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88 Resimplifying inuse:
% 90.51/90.88 Done
% 90.51/90.88
% 90.51/90.88
% 90.51/90.88 Intermediate Status:
% 90.51/90.88 Generated: 599814
% 90.51/90.88 Kept: 122587
% 90.51/90.88 Inuse: 1384
% 90.51/90.88 Deleted: 2520
% 90.51/90.88 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying clauses:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 609805
% 212.15/212.59 Kept: 125925
% 212.15/212.59 Inuse: 1399
% 212.15/212.59 Deleted: 2831
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 620978
% 212.15/212.59 Kept: 127947
% 212.15/212.59 Inuse: 1412
% 212.15/212.59 Deleted: 2831
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 630907
% 212.15/212.59 Kept: 130406
% 212.15/212.59 Inuse: 1419
% 212.15/212.59 Deleted: 2831
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 646779
% 212.15/212.59 Kept: 133418
% 212.15/212.59 Inuse: 1437
% 212.15/212.59 Deleted: 2833
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 657383
% 212.15/212.59 Kept: 135879
% 212.15/212.59 Inuse: 1457
% 212.15/212.59 Deleted: 2833
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 667345
% 212.15/212.59 Kept: 137914
% 212.15/212.59 Inuse: 1469
% 212.15/212.59 Deleted: 2833
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 677899
% 212.15/212.59 Kept: 139935
% 212.15/212.59 Inuse: 1492
% 212.15/212.59 Deleted: 2833
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 686224
% 212.15/212.59 Kept: 142129
% 212.15/212.59 Inuse: 1507
% 212.15/212.59 Deleted: 2833
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying clauses:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 695346
% 212.15/212.59 Kept: 144816
% 212.15/212.59 Inuse: 1517
% 212.15/212.59 Deleted: 3038
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 703348
% 212.15/212.59 Kept: 147504
% 212.15/212.59 Inuse: 1527
% 212.15/212.59 Deleted: 3038
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 712456
% 212.15/212.59 Kept: 150173
% 212.15/212.59 Inuse: 1537
% 212.15/212.59 Deleted: 3038
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 720568
% 212.15/212.59 Kept: 152888
% 212.15/212.59 Inuse: 1547
% 212.15/212.59 Deleted: 3038
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 729873
% 212.15/212.59 Kept: 155654
% 212.15/212.59 Inuse: 1557
% 212.15/212.59 Deleted: 3038
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 738138
% 212.15/212.59 Kept: 158404
% 212.15/212.59 Inuse: 1567
% 212.15/212.59 Deleted: 3038
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 747514
% 212.15/212.59 Kept: 161137
% 212.15/212.59 Inuse: 1577
% 212.15/212.59 Deleted: 3038
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 754586
% 212.15/212.59 Kept: 163325
% 212.15/212.59 Inuse: 1587
% 212.15/212.59 Deleted: 3038
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying clauses:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 763428
% 212.15/212.59 Kept: 165978
% 212.15/212.59 Inuse: 1602
% 212.15/212.59 Deleted: 3098
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 773823
% 212.15/212.59 Kept: 168314
% 212.15/212.59 Inuse: 1607
% 212.15/212.59 Deleted: 3098
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 784272
% 212.15/212.59 Kept: 170652
% 212.15/212.59 Inuse: 1612
% 212.15/212.59 Deleted: 3098
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 795037
% 212.15/212.59 Kept: 172677
% 212.15/212.59 Inuse: 1632
% 212.15/212.59 Deleted: 3098
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 805955
% 212.15/212.59 Kept: 174983
% 212.15/212.59 Inuse: 1642
% 212.15/212.59 Deleted: 3098
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 816195
% 212.15/212.59 Kept: 177440
% 212.15/212.59 Inuse: 1667
% 212.15/212.59 Deleted: 3098
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 827473
% 212.15/212.59 Kept: 179794
% 212.15/212.59 Inuse: 1682
% 212.15/212.59 Deleted: 3098
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 Resimplifying inuse:
% 212.15/212.59 Done
% 212.15/212.59
% 212.15/212.59
% 212.15/212.59 Intermediate Status:
% 212.15/212.59 Generated: 836190
% 212.15/212.59 Kept: 182025
% 212.15/212.59 Inuse: 1697
% 212.15/212.59 Deleted: 3098
% 212.15/212.59 Deletedinuse: 22
% 212.15/212.59
% 212.15/212.59 ResimplifCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------