TSTP Solution File: SWV697-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV697-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:52 EDT 2022
% Result : Timeout 300.05s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV697-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Wed Jun 15 10:30:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.12/1.55 *** allocated 10000 integers for termspace/termends
% 1.12/1.55 *** allocated 10000 integers for clauses
% 1.12/1.55 *** allocated 10000 integers for justifications
% 1.12/1.55 *** allocated 15000 integers for termspace/termends
% 1.12/1.55 *** allocated 22500 integers for termspace/termends
% 1.12/1.55 *** allocated 33750 integers for termspace/termends
% 1.12/1.55 *** allocated 50625 integers for termspace/termends
% 1.12/1.55 Bliksem 1.12
% 1.12/1.55
% 1.12/1.55
% 1.12/1.55 Automatic Strategy Selection
% 1.12/1.55
% 1.12/1.55 Clauses:
% 1.12/1.55 [
% 1.12/1.55 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.12/1.55 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.12/1.55 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.12/1.55 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.12/1.55 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.12/1.55 V5 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.12/1.55 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.12/1.55 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.12/1.55 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.12/1.55 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.12/1.55 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.12/1.55 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.55 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.55 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.55 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.55 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.12/1.55 V5 ) ) ],
% 1.12/1.55 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.12/1.55 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.12/1.55 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.12/1.55 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.12/1.55 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.12/1.55 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.12/1.55 V5 ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.12/1.55 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.12/1.55 , X, V4, V5 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.12/1.55 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.12/1.55 , V3, V4, V5, V6 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.12/1.55 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.12/1.55 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), T ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.12/1.55 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.55 ), Y ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.12/1.55 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.12/1.55 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.55 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.55 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.12/1.55 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.55 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.55 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( T, X ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.12/1.55 , X ) ) ), =( Y, Z ) ],
% 1.12/1.55 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.12/1.55 , X ) ) ), =( Y, Z ) ],
% 1.12/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.12/1.55 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.12/1.55 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.12/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.12/1.55 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.12/1.55 'c_lessequals'( Z, T, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.12/1.55 'c_lessequals'( Y, T, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.55 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.55 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.12/1.55 'c_lessequals'( Z, T, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.55 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.55 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.12/1.55 'c_lessequals'( Y, T, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.12/1.55 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.12/1.55 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.12/1.55 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.12/1.55 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.12/1.55 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.12/1.55 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.12/1.55 V1 ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.12/1.55 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.12/1.55 V1 ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.12/1.55 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.12/1.55 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.12/1.55 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.12/1.55 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.55 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.55 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.12/1.55 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.55 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.12/1.55 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.55 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.12/1.55 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.12/1.55 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.12/1.55 ), X ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.55 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.12/1.55 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.55 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.55 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.55 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.55 ), X ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.12/1.55 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.12/1.55 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.12/1.55 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.12/1.55 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.12/1.55 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.12/1.55 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.12/1.55 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.12/1.55 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.12/1.55 , Z ) ), Z ) ],
% 1.12/1.55 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.12/1.55 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.12/1.55 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.12/1.55 V6, T ) ) ],
% 1.12/1.55 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.12/1.55 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.12/1.55 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.12/1.55 V5, X, Y, Z, V6, T ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.12/1.55 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ) ), Y ) ) ],
% 1.12/1.55 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.12/1.55 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.12/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.12/1.55 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.55 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.55 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.55 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.55 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.55 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.12/1.55 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.55 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.12/1.55 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.12/1.55 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.12/1.55 Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.12/1.55 ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.12/1.55 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.12/1.55 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.12/1.55 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.12/1.55 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.12/1.55 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.12/1.55 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.12/1.55 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.55 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.12/1.55 ), X ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.12/1.55 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.12/1.55 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.12/1.55 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.12/1.55 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.12/1.55 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.55 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.12/1.55 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.55 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.12/1.55 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.12/1.55 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.12/1.55 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.12/1.55 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.12/1.55 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.12/1.55 , X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.12/1.55 ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.12/1.55 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.55 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.12/1.55 , X ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.12/1.55 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 T, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.12/1.55 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.12/1.55 , X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.55 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.12/1.55 'tc_nat' ) ), Y ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.55 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.55 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.55 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.12/1.55 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.55 Y ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.12/1.55 Y ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.12/1.55 Y ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.12/1.55 Y ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.55 Y ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.12/1.55 Y ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.12/1.55 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.12/1.55 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.12/1.55 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.12/1.55 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.12/1.55 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.55 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.12/1.55 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.12/1.55 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.12/1.55 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.12/1.55 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.12/1.55 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.12/1.55 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.55 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.12/1.55 ), X ), Y ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.55 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.55 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.12/1.55 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.12/1.55 ), Z ) ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.12/1.55 ), Z ) ), Y ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.12/1.55 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.12/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.12/1.55 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.12/1.55 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.12/1.55 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.12/1.55 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.12/1.55 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.55 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.55 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.12/1.55 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.12/1.55 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.12/1.55 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.12/1.55 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 T, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.55 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.12/1.55 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.12/1.55 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.55 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.55 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.12/1.55 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.12/1.55 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.55 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.12/1.55 Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.12/1.55 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.12/1.55 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.12/1.55 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.55 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.12/1.55 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.55 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.55 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.55 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.12/1.55 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.12/1.55 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.12/1.55 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.12/1.55 , 'tc_nat' ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.12/1.55 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.12/1.55 , 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.55 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.55 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.55 Y, X ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.55 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Z ), Y ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Z ), Y ), X ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.12/1.55 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.12/1.55 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.55 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.55 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.12/1.55 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.55 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.55 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.12/1.55 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.12/1.55 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.55 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.55 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.12/1.55 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.12/1.55 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.12/1.55 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.12/1.55 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.12/1.55 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.55 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Z ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.12/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.55 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.12/1.55 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.12/1.55 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.55 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.12/1.55 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.12/1.55 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.12/1.55 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.12/1.55 ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.55 ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.12/1.55 ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.55 ), X ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.12/1.55 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.12/1.55 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.55 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.12/1.55 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.12/1.55 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.12/1.55 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.55 , X ) ), T ) ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.55 'tc_nat' ) ), =( Y, Z ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.55 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.55 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.55 X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.12/1.55 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.12/1.55 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.12/1.55 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.12/1.55 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.55 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.55 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 Y, Z, X ), X ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.55 'c_Suc'( X ), 'tc_nat' ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.55 'c_Suc'( X ), 'tc_nat' ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.12/1.55 ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.12/1.55 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.12/1.55 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.12/1.55 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.12/1.55 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.55 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.12/1.55 ), 'tc_nat' ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.55 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.12/1.55 ), 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.55 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.12/1.55 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.12/1.55 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ), X ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.55 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), U ), X ) ), Z ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.12/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.12/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 , X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.12/1.55 ), Z ) ), T ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' ) ) ],
% 1.12/1.55 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 'tc_nat' ), 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 'tc_nat' ), 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 Y, Z, 'tc_nat' ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.12/1.55 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.12/1.55 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.55 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.55 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.55 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.12/1.55 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.12/1.55 ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.12/1.55 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.55 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.55 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.12/1.55 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.12/1.55 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.12/1.55 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.12/1.55 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.12/1.55 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.12/1.55 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.12/1.55 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.12/1.55 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.12/1.55 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.12/1.55 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.12/1.55 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.12/1.55 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.12/1.55 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.12/1.55 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.12/1.55 V6 ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.12/1.55 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.12/1.55 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.12/1.55 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.55 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.55 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.12/1.55 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.55 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.12/1.55 , X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.12/1.55 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.55 ), T ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.12/1.55 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.55 ), T ), Z ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.12/1.55 , X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.55 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.12/1.55 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), T ), Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.12/1.55 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.55 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.55 ,
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.12/1.55 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.12/1.55 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.12/1.55 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.12/1.55 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.55 ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.55 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.55 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.55 Y, Z, X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.55 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.55 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.12/1.55 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.12/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.12/1.55 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.12/1.56 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.12/1.56 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.12/1.56 , V0, U, V1 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.12/1.56 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.12/1.56 , V0, U, V1 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.12/1.56 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 X, T, U, Y, W, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 X, T, U, Z, W, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.12/1.56 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 T, X, U, Y, W, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 T, X, U, Z, W, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 T, X, U, W, Y, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 T, X, U, W, Z, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.12/1.56 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.12/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.12/1.56 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.12/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.12/1.56 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.12/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.12/1.56 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.12/1.56 , V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.12/1.56 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.12/1.56 W, V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.12/1.56 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.12/1.56 , V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.12/1.56 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.12/1.56 W, V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.12/1.56 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.12/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.12/1.56 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.12/1.56 W, V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.12/1.56 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.12/1.56 W, V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.12/1.56 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.12/1.56 , V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.12/1.56 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.12/1.56 , V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 X, T, U, Y, W, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.12/1.56 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.12/1.56 , V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 T, X, U, Y, W, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.12/1.56 T, X, U, W, Y, V0 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.12/1.56 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.12/1.56 , V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.12/1.56 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.12/1.56 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.12/1.56 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.56 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.12/1.56 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.56 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.12/1.56 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.12/1.56 ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.12/1.56 'c_lessequals'( Y, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.12/1.56 'c_lessequals'( Y, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.12/1.56 ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.12/1.56 ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.12/1.56 ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.12/1.56 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.12/1.56 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.12/1.56 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.12/1.56 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ), T ) )
% 1.12/1.56 ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.12/1.56 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.56 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.12/1.56 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.12/1.56 , V2, V3, V4, Z, V5 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.12/1.56 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.12/1.56 , V2, V3, V4, T, V5 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.12/1.56 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.12/1.56 , V2, V3, V4, Y, V5 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.12/1.56 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.12/1.56 , V2, V3, V4, T, V5 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.12/1.56 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.12/1.56 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.12/1.56 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.12/1.56 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.12/1.56 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.12/1.56 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.12/1.56 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.12/1.56 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.12/1.56 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.12/1.56 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.56 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.12/1.56 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.12/1.56 , X, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.12/1.56 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.12/1.56 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.12/1.56 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.12/1.56 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.12/1.56 , X, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.12/1.56 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.12/1.56 , Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.12/1.56 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.12/1.56 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.12/1.56 , X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.12/1.56 , X ), X ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 Y ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.12/1.56 Y ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 Y ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.12/1.56 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.12/1.56 Y ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.12/1.56 Y ) ],
% 1.12/1.56 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 Y ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.12/1.56 Y ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.12/1.56 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.12/1.56 ), Y ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.12/1.56 ), Y ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.12/1.56 ), Y ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.56 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.12/1.56 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.56 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.12/1.56 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.12/1.56 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.12/1.56 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.12/1.56 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.12/1.56 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.56 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.56 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.12/1.56 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.56 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.56 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.56 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.12/1.56 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.56 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.12/1.56 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 T, X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.12/1.56 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.12/1.56 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.12/1.56 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.12/1.56 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.12/1.56 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.12/1.56 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.12/1.56 ) ), Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.12/1.56 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.12/1.56 Y ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.12/1.56 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.12/1.56 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ), 'tc_nat' ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.12/1.56 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.56 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.12/1.56 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.12/1.56 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.56 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.56 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.12/1.56 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.12/1.56 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.56 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.12/1.56 Z ), X ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.12/1.56 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.12/1.56 ), T ) ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.12/1.56 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.12/1.56 ), T ) ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.12/1.56 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.12/1.56 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.12/1.56 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.12/1.56 ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.56 ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.12/1.56 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.12/1.56 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.12/1.56 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.12/1.56 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.12/1.56 , X, V5 ) ) ],
% 1.12/1.56 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.12/1.56 V5 ) ) ],
% 1.12/1.56 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.12/1.56 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.12/1.56 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.12/1.56 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.12/1.56 X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.12/1.56 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.12/1.56 Y ) ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.12/1.56 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.12/1.56 ) ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.12/1.56 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.56 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.12/1.56 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.12/1.56 , U ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.12/1.56 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.12/1.56 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_lessequals'( Z, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.12/1.56 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( Z, Y, X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.12/1.56 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.12/1.56 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.12/1.56 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.12/1.56 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.12/1.56 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.12/1.56 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.12/1.56 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.12/1.56 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.12/1.56 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.12/1.56 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 Z, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.12/1.56 , X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.12/1.56 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.12/1.56 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.12/1.56 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.12/1.56 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.56 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.12/1.56 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.12/1.56 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.12/1.56 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.56 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.12/1.56 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.12/1.56 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 'tc_nat' ) ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.56 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.12/1.56 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.12/1.56 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.56 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.12/1.56 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.12/1.56 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.12/1.56 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.12/1.56 ) ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ),
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls'
% 1.12/1.56 ) ), Y ), X ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.12/1.56 'c_Int_OPls' ), X ), X ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ),
% 1.12/1.56 'c_Int_OPls' ), X ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.12/1.56 'tc_nat' ) ), Y ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.12/1.56 'tc_nat' ) ), Y ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.12/1.56 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.12/1.56 , X ) ), Z ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.12/1.56 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.12/1.56 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.56 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.12/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.12/1.56 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.12/1.56 ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.12/1.56 , Z ), Y ), 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.12/1.56 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.12/1.56 ],
% 1.12/1.56 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.56 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.12/1.56 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.12/1.56 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.12/1.56 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.12/1.56 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.12/1.56 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.12/1.56 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 X, T, 'tc_nat' ) ],
% 1.12/1.56 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.12/1.56 ), 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.12/1.56 ), 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.12/1.56 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.12/1.56 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.12/1.56 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.12/1.56 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.12/1.56 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.12/1.56 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.12/1.56 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.12/1.56 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.12/1.56 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit0'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.12/1.56 [ =( 'c_Int_OBit0'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_Int_Oint' ), X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), T ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.12/1.56 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.56 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.56 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.12/1.56 Y ) ) ],
% 1.12/1.56 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.12/1.56 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.12/1.56 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 ), Y ), Y, X ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.56 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.12/1.56 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.12/1.56 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.12/1.56 , Z ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.12/1.56 , Z ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.12/1.56 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.12/1.56 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.12/1.56 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.12/1.56 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.12/1.56 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.56 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.12/1.56 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.56 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.12/1.56 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.12/1.56 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.56 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.12/1.56 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.12/1.56 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 'tc_nat' ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.12/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.12/1.56 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.12/1.56 , Y ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.12/1.56 ) ), Z ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.12/1.56 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z
% 1.12/1.56 ), 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), Y ), Z ), X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 X ) ) ],
% 1.12/1.56 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.56 X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.12/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.12/1.56 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.12/1.56 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.56 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.12/1.56 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.12/1.56 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.12/1.56 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.12/1.56 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.12/1.56 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.12/1.56 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 , X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.12/1.56 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.12/1.56 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.56 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.56 'c_Suc'( T ) ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.12/1.56 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.12/1.56 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.12/1.56 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.12/1.56 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.12/1.56 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.12/1.56 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.56 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.56 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.12/1.56 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.12/1.56 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), 'c_Suc'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.12/1.56 W ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.12/1.56 U ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.12/1.56 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.12/1.56 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.12/1.56 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.12/1.56 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.12/1.56 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.56 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.12/1.56 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.12/1.56 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Suc'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.12/1.56 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.12/1.56 U ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.12/1.56 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.12/1.56 ), Y ), Y ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.12/1.56 ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.12/1.56 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.12/1.56 ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.12/1.56 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.12/1.56 ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.56 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.12/1.56 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.12/1.56 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.12/1.56 , Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.12/1.56 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.12/1.56 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.12/1.56 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.12/1.56 ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.12/1.56 ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.12/1.56 [ =( 'c_FFT__Mirabelle_OFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.12/1.56 ), X ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.12/1.56 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.12/1.56 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.12/1.56 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.12/1.56 , T ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.56 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.12/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.12/1.56 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 'c_Int_OPls', X ) ), Y ) ],
% 1.12/1.56 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.12/1.56 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.12/1.56 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.12/1.56 ), X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.12/1.56 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.12/1.56 , X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.56 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.56 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.12/1.56 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.12/1.56 , Y ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.12/1.56 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.12/1.56 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.12/1.56 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.12/1.56 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.12/1.56 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.12/1.56 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.12/1.56 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.12/1.56 U ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.12/1.56 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.12/1.56 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.12/1.56 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.12/1.56 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.12/1.56 U ) ) ],
% 1.12/1.56 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.12/1.56 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.12/1.56 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.12/1.56 T ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.12/1.56 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.12/1.56 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.12/1.56 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.12/1.56 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.12/1.56 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.12/1.56 Z ) ) ],
% 1.12/1.56 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.12/1.56 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.12/1.56 T ) ) ],
% 1.12/1.56 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.12/1.56 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.12/1.56 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.12/1.56 U ) ) ],
% 1.12/1.56 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.12/1.56 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.12/1.56 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.12/1.56 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.12/1.56 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.12/1.56 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.12/1.56 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.12/1.56 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.12/1.56 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.12/1.56 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.12/1.56 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.12/1.56 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.12/1.56 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.12/1.56 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.12/1.56 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.12/1.56 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.12/1.56 V0 ) ) ],
% 1.12/1.56 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.56 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.12/1.56 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.12/1.56 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.12/1.56 V0 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.12/1.56 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.12/1.56 ) ), X, 'tc_nat' ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.12/1.56 ) ), X, 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.12/1.56 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.12/1.56 Z, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.56 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.12/1.56 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.12/1.56 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.12/1.56 ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.12/1.56 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.12/1.56 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.56 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.12/1.56 ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.56 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.56 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.12/1.56 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.56 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.56 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y )
% 1.12/1.56 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.12/1.56 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.12/1.56 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.12/1.56 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.12/1.56 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.12/1.56 X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.12/1.56 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.12/1.56 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.12/1.56 , X ) ],
% 1.12/1.56 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.12/1.56 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.12/1.56 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.12/1.56 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.12/1.56 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.12/1.56 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.12/1.56 V6 ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.12/1.56 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.56 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.12/1.56 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.56 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_Int_Oint' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.56 'tc_Int_Oint' ), Z ), Y ), 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 X, Z, 'tc_Int_Oint' ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.56 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.12/1.56 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.12/1.56 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.12/1.56 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.12/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.12/1.56 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.12/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.56 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.56 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.12/1.56 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.12/1.56 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.12/1.56 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.12/1.56 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.12/1.56 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.56 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.12/1.56 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.12/1.56 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.12/1.56 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.12/1.56 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.12/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.56 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.12/1.56 ,
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.12/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.12/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.56 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.56 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.12/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.12/1.57 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.57 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.12/1.57 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.12/1.57 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.12/1.57 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.57 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.12/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.12/1.57 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.12/1.57 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.12/1.57 ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.12/1.57 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.12/1.57 ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.12/1.57 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.12/1.57 Y, X ), X ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.12/1.57 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.57 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.57 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.12/1.57 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.12/1.57 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.12/1.57 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.12/1.57 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.12/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.57 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.57 Y, X ) ) ) ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.12/1.57 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.12/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.57 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.12/1.57 Z, X ) ) ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.12/1.57 'c_lessequals'( Z, Y, X ) ],
% 1.12/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.57 'tc_nat' ), X ), X ) ) ],
% 1.12/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.12/1.57 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), T ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.12/1.57 X, Y, T, U, Z ) ) ],
% 1.12/1.57 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.12/1.57 X, Y, T, U, Z ) ) ],
% 1.12/1.57 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.12/1.57 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.12/1.57 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.12/1.57 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.12/1.57 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.12/1.57 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.12/1.57 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.57 ) ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.12/1.57 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.12/1.57 ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.12/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.12/1.57 Y, X ) ), Z ) ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.12/1.57 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.57 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.12/1.57 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.12/1.57 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.57 'tc_nat' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.12/1.57 X ), 'tc_nat' ) ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.57 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.12/1.57 hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) )
% 1.12/1.57 ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.12/1.57 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.12/1.57 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.12/1.57 [ =( 'c_Int_OBit0'( 'v_k' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.12/1.57 'tc_Int_Oint' ), 'v_k' ), 'v_k' ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.57 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.12/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.12/1.57 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.12/1.57 ,
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.12/1.57 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.12/1.57 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.12/1.57 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.12/1.57 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.12/1.57 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.12/1.57 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.12/1.57 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.57 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.12/1.57 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.57 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.12/1.57 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.12/1.57 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.57 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.57 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.12/1.57 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.12/1.57 ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.57 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.12/1.57 ), Y ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.12/1.57 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.12/1.57 ), Y ) ],
% 1.12/1.57 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.12/1.57 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.57 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.12/1.57 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.12/1.57 ) ],
% 1.12/1.57 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.12/1.57 ) ) ],
% 1.12/1.57 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.57 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.12/1.57 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.12/1.57 , Y ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.57 X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.12/1.57 X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.12/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.12/1.57 ],
% 1.12/1.57 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.12/1.57 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.12/1.57 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.12/1.57 ,
% 1.12/1.57 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.12/1.57 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.12/1.57 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.12/1.57 'tc_nat' ) ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.12/1.57 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.12/1.57 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.12/1.57 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.12/1.57 ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.57 'tc_nat' ) ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.12/1.57 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.12/1.57 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.57 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.12/1.57 ,
% 1.12/1.57 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.12/1.57 , X, Z, U, W, V0 ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.12/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.12/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.57 X ), Y ), Y ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.12/1.57 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.12/1.57 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.12/1.57 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.12/1.57 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.12/1.57 ,
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.12/1.57 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.12/1.57 ) ) ],
% 1.12/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.12/1.57 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.12/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.12/1.57 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.12/1.57 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.12/1.57 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.12/1.57 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.12/1.57 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.12/1.57 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.12/1.57 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.12/1.57 , Y, X ) ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.12/1.57 , Y, X ) ) ],
% 1.12/1.57 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.12/1.57 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.12/1.57 , X ) ) ],
% 1.12/1.57 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.12/1.57 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.12/1.57 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.12/1.57 ,
% 1.12/1.57 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.12/1.57 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.12/1.57 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.12/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.12/1.57 ), =( Z, Y ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.12/1.57 ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.12/1.57 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.12/1.57 ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.12/1.57 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.12/1.57 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.12/1.57 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.12/1.57 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.12/1.57 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.12/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.12/1.57 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.12/1.57 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.12/1.57 ,
% 1.12/1.57 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.17/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.57 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.17/1.57 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.17/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.57 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.17/1.57 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.17/1.57 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.17/1.57 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.57 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.17/1.57 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.17/1.57 [ 'c_HOL_Oord__class_Oless'( 'v_i', hAPP( hAPP(
% 1.17/1.57 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.17/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_k' ), 'tc_nat' ) ],
% 1.17/1.57 [ ~( =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP(
% 1.17/1.57 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.17/1.57 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.57 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_k' ), 'v_a', 'v_i' ), hAPP(
% 1.17/1.57 'c_FFT__Mirabelle_OFFT'( 'v_k', 'v_a' ), 'v_i' ) ) ) ],
% 1.17/1.57 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.17/1.57 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.17/1.57 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.17/1.57 'class_Orderings_Opreorder'( Y ) ) ],
% 1.17/1.57 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.17/1.57 'class_Orderings_Oorder'( Y ) ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.17/1.57 ],
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.17/1.57 ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.17/1.57 ],
% 1.17/1.57 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.17/1.57 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.17/1.57 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.17/1.57 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.17/1.57 ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.17/1.57 ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.17/1.57 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.17/1.57 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.17/1.57 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.17/1.57 ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.17/1.57 ],
% 1.17/1.57 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.17/1.57 ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.17/1.57 ,
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.17/1.57 [ 'c_fequal'( X, X, Y ) ],
% 1.17/1.57 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.17/1.57 ] .
% 1.17/1.57
% 1.17/1.57
% 1.17/1.57 percentage equality = 0.198141, percentage horn = 0.824176
% 1.17/1.57 This is a problem with some equality
% 1.17/1.57
% 1.17/1.57
% 1.17/1.57
% 1.17/1.57 Options Used:
% 1.17/1.57
% 1.17/1.57 useres = 1
% 1.17/1.57 useparamod = 1
% 1.17/1.57 useeqrefl = 1
% 1.17/1.57 useeqfact = 1
% 1.17/1.57 usefactor = 1
% 1.17/1.57 usesimpsplitting = 0
% 1.17/1.57 usesimpdemod = 5
% 1.17/1.57 usesimpres = 3
% 1.17/1.57
% 1.17/1.57 resimpinuse = 1000
% 1.17/1.57 resimpclauses = 20000
% 1.17/1.57 substype = eqrewr
% 1.17/1.57 backwardsubs = 1
% 1.17/1.57 selectoldest = 5
% 1.17/1.57
% 1.17/1.57 litorderings [0] = split
% 1.17/1.57 litorderings [1] = extend the termordering, first sorting on arguments
% 1.17/1.57
% 1.17/1.57 termordering = kbo
% 1.17/1.57
% 1.17/1.57 litapriori = 0
% 1.17/1.57 termapriori = 1
% 1.17/1.57 litaposteriori = 0
% 1.17/1.57 termaposteriori = 0
% 1.17/1.57 demodaposteriori = 0
% 1.17/1.57 ordereqreflfact = 0
% 1.17/1.57
% 1.17/1.57 litselect = negord
% 1.17/1.57
% 1.17/1.57 maxweight = 15
% 1.17/1.57 maxdepth = 30000
% 1.17/1.57 maxlength = 115
% 1.17/1.57 maxnrvars = 195
% 1.17/1.57 excuselevel = 1
% 1.17/1.57 increasemaxweight = 1
% 1.17/1.57
% 1.17/1.57 maxselected = 10000000
% 1.17/1.57 maxnrclauses = 10000000
% 1.17/1.57
% 1.17/1.57 showgenerated = 0
% 1.17/1.57 showkept = 0
% 1.17/1.57 showselected = 0
% 1.17/1.57 showdeleted = 0
% 1.17/1.57 showresimp = 1
% 1.17/1.57 showstatus = 2000
% 1.17/1.57
% 1.17/1.57 prologoutput = 1
% 1.17/1.57 nrgoals = 5000000
% 1.17/1.57 totalproof = 1
% 1.17/1.57
% 1.17/1.57 Symbols occurring in the translation:
% 1.17/1.57
% 1.17/1.57 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.17/1.57 . [1, 2] (w:1, o:151, a:1, s:1, b:0),
% 1.17/1.57 ! [4, 1] (w:0, o:74, a:1, s:1, b:0),
% 1.17/1.57 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.17/1.57 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.17/1.57 'c_Ring__and__Field_Oordered__idom' [50, 11] (w:1, o:193, a:1, s:1
% 1.17/1.57 , b:0),
% 1.17/1.57 hAPP [51, 2] (w:1, o:176, a:1, s:1, b:0),
% 1.17/1.57 'class_Ring__and__Field_Ofield' [55, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.17/1.57 'class_Ring__and__Field_Odivision__by__zero' [56, 1] (w:1, o:83, a:1
% 1.17/1.57 , s:1, b:0),
% 1.17/1.57 'class_Int_Onumber' [57, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.17/1.57 'c_HOL_Ozero__class_Ozero' [58, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.17/1.57 'c_HOL_Otimes__class_Otimes' [59, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.17/1.57 'c_Int_Onumber__class_Onumber__of' [61, 2] (w:1, o:180, a:1, s:1, b:0
% 1.17/1.57 ),
% 1.17/1.57 'c_HOL_Oinverse__class_Odivide' [62, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.17/1.57
% 1.17/1.57 'c_Power_Opower_Opower' [63, 3] (w:1, o:186, a:1, s:1, b:0),
% 1.17/1.57 hBOOL [65, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.17/1.57 'tc_nat' [66, 0] (w:1, o:48, a:1, s:1, b:0),
% 1.17/1.57 'c_Suc' [68, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.17/1.57 'c_HOL_Oplus__class_Oplus' [69, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.17/1.57 'class_Ring__and__Field_Oordered__semiring__strict' [70, 1] (w:1, o:
% 1.17/1.57 97, a:1, s:1, b:0),
% 1.17/1.57 'c_HOL_Oord__class_Oless' [72, 3] (w:1, o:187, a:1, s:1, b:0),
% 1.17/1.57 'class_Ring__and__Field_Oordered__ring__strict' [73, 1] (w:1, o:96
% 1.17/1.57 , a:1, s:1, b:0),
% 1.17/1.57 'class_OrderedGroup_Olordered__ab__group__add' [74, 1] (w:1, o:99, a:
% 2.44/2.88 1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Oordered__idom' [75, 1] (w:1, o:100, a:1, s:1
% 2.44/2.88 , b:0),
% 2.44/2.88 'class_Ring__and__Field_Oring__no__zero__divisors' [76, 1] (w:1, o:
% 2.44/2.88 101, a:1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Ono__zero__divisors' [77, 1] (w:1, o:95, a:1
% 2.44/2.88 , s:1, b:0),
% 2.44/2.88 'class_OrderedGroup_Opordered__comm__monoid__add' [78, 1] (w:1, o:103
% 2.44/2.88 , a:1, s:1, b:0),
% 2.44/2.88 'c_lessequals' [80, 3] (w:1, o:188, a:1, s:1, b:0),
% 2.44/2.88 'c_HOL_Ouminus__class_Ouminus' [81, 2] (w:1, o:177, a:1, s:1, b:0),
% 2.44/2.88 'c_HOL_Oabs__class_Oabs' [82, 2] (w:1, o:178, a:1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Ozero__neq__one' [83, 1] (w:1, o:104, a:1, s:
% 2.44/2.88 1, b:0),
% 2.44/2.88 'c_HOL_Oone__class_Oone' [84, 1] (w:1, o:89, a:1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Oordered__field' [85, 1] (w:1, o:105, a:1, s:
% 2.44/2.88 1, b:0),
% 2.44/2.88 'class_OrderedGroup_Ogroup__add' [87, 1] (w:1, o:106, a:1, s:1, b:0)
% 2.44/2.88 ,
% 2.44/2.88 'class_Ring__and__Field_Ocomm__semiring__1' [88, 1] (w:1, o:81, a:1
% 2.44/2.88 , s:1, b:0),
% 2.44/2.88 'c_HOL_Oinverse__class_Oinverse' [93, 2] (w:1, o:179, a:1, s:1, b:0)
% 2.44/2.88 ,
% 2.44/2.88 'class_OrderedGroup_Opordered__ab__group__add__abs' [94, 1] (w:1, o:
% 2.44/2.88 107, a:1, s:1, b:0),
% 2.44/2.88 'class_OrderedGroup_Olordered__ab__group__add__abs' [95, 1] (w:1, o:
% 2.44/2.88 108, a:1, s:1, b:0),
% 2.44/2.88 'class_Lattices_Oboolean__algebra' [96, 1] (w:1, o:109, a:1, s:1, b:0
% 2.44/2.88 ),
% 2.44/2.88 'class_Orderings_Oorder' [97, 1] (w:1, o:110, a:1, s:1, b:0),
% 2.44/2.88 'tc_Int_Oint' [98, 0] (w:1, o:54, a:1, s:1, b:0),
% 2.44/2.88 'class_OrderedGroup_Opordered__ab__semigroup__add' [99, 1] (w:1, o:
% 2.44/2.88 111, a:1, s:1, b:0),
% 2.44/2.88 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [100, 1]
% 2.44/2.88 (w:1, o:112, a:1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Opordered__ring__abs' [101, 1] (w:1, o:116
% 2.44/2.88 , a:1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Oring' [103, 1] (w:1, o:117, a:1, s:1, b:0),
% 2.44/2.88
% 2.44/2.88 'c_Groebner__Basis_Ogb__semiring' [110, 6] (w:1, o:192, a:1, s:1, b:0
% 2.44/2.88 ),
% 2.44/2.88 'c_Int_OPls' [113, 0] (w:1, o:57, a:1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Oordered__semidom' [114, 1] (w:1, o:113, a:1
% 2.44/2.88 , s:1, b:0),
% 2.44/2.88 'class_OrderedGroup_Oab__semigroup__idem__mult' [115, 1] (w:1, o:118
% 2.44/2.88 , a:1, s:1, b:0),
% 2.44/2.88 'class_OrderedGroup_Opordered__ab__group__add' [116, 1] (w:1, o:119
% 2.44/2.88 , a:1, s:1, b:0),
% 2.44/2.88 'c_Power_Opower__class_Opower' [117, 1] (w:1, o:120, a:1, s:1, b:0),
% 2.44/2.88
% 2.44/2.88 'class_Power_Opower' [119, 1] (w:1, o:133, a:1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Omult__zero' [120, 1] (w:1, o:92, a:1, s:1
% 2.44/2.88 , b:0),
% 2.44/2.88 'class_Ring__and__Field_Osemiring__0' [121, 1] (w:1, o:136, a:1, s:1
% 2.44/2.88 , b:0),
% 2.44/2.88 'class_OrderedGroup_Ocomm__monoid__add' [122, 1] (w:1, o:121, a:1, s:
% 2.44/2.88 1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Omult__mono1' [123, 1] (w:1, o:93, a:1, s:1
% 2.44/2.88 , b:0),
% 2.44/2.88 'class_Ring__and__Field_Omult__mono' [124, 1] (w:1, o:94, a:1, s:1
% 2.44/2.88 , b:0),
% 2.44/2.88 'class_Ring__and__Field_Opordered__ring' [125, 1] (w:1, o:137, a:1
% 2.44/2.88 , s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Oabs__if' [126, 1] (w:1, o:138, a:1, s:1, b:0
% 2.44/2.88 ),
% 2.44/2.88 'class_Orderings_Olinorder' [127, 1] (w:1, o:122, a:1, s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Oidom' [128, 1] (w:1, o:139, a:1, s:1, b:0),
% 2.44/2.88
% 2.44/2.88 'class_Ring__and__Field_Oordered__semiring' [129, 1] (w:1, o:114, a:1
% 2.44/2.88 , s:1, b:0),
% 2.44/2.88 'class_Int_Onumber__ring' [130, 1] (w:1, o:140, a:1, s:1, b:0),
% 2.44/2.88 'class_Nat_Osemiring__char__0' [131, 1] (w:1, o:98, a:1, s:1, b:0),
% 2.44/2.88 'c_Nat_Osemiring__1__class_Oof__nat' [132, 2] (w:1, o:181, a:1, s:1
% 2.44/2.88 , b:0),
% 2.44/2.88 'class_Ring__and__Field_Olordered__ring' [135, 1] (w:1, o:91, a:1, s:
% 2.44/2.88 1, b:0),
% 2.44/2.88 'c_Int_OBit0' [137, 1] (w:1, o:141, a:1, s:1, b:0),
% 2.44/2.88 'class_OrderedGroup_Omonoid__mult' [138, 1] (w:1, o:123, a:1, s:1, b:
% 2.44/2.88 0),
% 2.44/2.88 'class_OrderedGroup_Ocomm__monoid__mult' [139, 1] (w:1, o:124, a:1
% 2.44/2.88 , s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Odivision__ring' [140, 1] (w:1, o:142, a:1
% 2.44/2.88 , s:1, b:0),
% 2.44/2.88 'class_Ring__and__Field_Osemiring__1' [142, 1] (w:1, o:143, a:1, s:1
% 2.44/2.88 , b:0),
% 2.44/2.88 'class_Ring__and__Field_Opordered__cancel__semiring' [143, 1] (w:1
% 13.87/14.29 , o:144, a:1, s:1, b:0),
% 13.87/14.29 'class_OrderedGroup_Oab__semigroup__mult' [144, 1] (w:1, o:125, a:1
% 13.87/14.29 , s:1, b:0),
% 13.87/14.29 'class_RealVector_Oreal__normed__algebra' [145, 1] (w:1, o:145, a:1
% 13.87/14.29 , s:1, b:0),
% 13.87/14.29 'class_Ring__and__Field_Ocomm__semiring' [150, 1] (w:1, o:82, a:1, s:
% 13.87/14.29 1, b:0),
% 13.87/14.29 'class_OrderedGroup_Oordered__ab__group__add' [151, 1] (w:1, o:102
% 13.87/14.29 , a:1, s:1, b:0),
% 13.87/14.29 'class_Ring__and__Field_Opordered__semiring' [152, 1] (w:1, o:146, a:
% 13.87/14.29 1, s:1, b:0),
% 13.87/14.29 'class_OrderedGroup_Oab__group__add' [153, 1] (w:1, o:126, a:1, s:1
% 13.87/14.29 , b:0),
% 13.87/14.29 'class_OrderedGroup_Oab__semigroup__add' [157, 1] (w:1, o:127, a:1
% 13.87/14.29 , s:1, b:0),
% 13.87/14.29 'class_Ring__and__Field_Osemiring' [158, 1] (w:1, o:147, a:1, s:1, b:
% 13.87/14.29 0),
% 13.87/14.29 'class_RealVector_Oreal__normed__field' [159, 1] (w:1, o:148, a:1, s:
% 13.87/14.29 1, b:0),
% 13.87/14.29 'class_OrderedGroup_Ocancel__ab__semigroup__add' [163, 1] (w:1, o:128
% 13.87/14.29 , a:1, s:1, b:0),
% 13.87/14.29 'class_OrderedGroup_Ocancel__semigroup__add' [164, 1] (w:1, o:129, a:
% 13.87/14.29 1, s:1, b:0),
% 13.87/14.29 'class_Ring__and__Field_Oordered__comm__semiring__strict' [165, 1]
% 13.87/14.29 (w:1, o:115, a:1, s:1, b:0),
% 13.87/14.29 'class_OrderedGroup_Omonoid__add' [166, 1] (w:1, o:130, a:1, s:1, b:0
% 13.87/14.29 ),
% 13.87/14.29 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [167, 1]
% 13.87/14.29 (w:1, o:131, a:1, s:1, b:0),
% 13.87/14.29 'c_Int_OBit1' [168, 1] (w:1, o:149, a:1, s:1, b:0),
% 13.87/14.29 'class_Orderings_Opreorder' [169, 1] (w:1, o:132, a:1, s:1, b:0),
% 13.87/14.29 'class_Ring__and__Field_Oring__1' [170, 1] (w:1, o:134, a:1, s:1, b:0
% 13.87/14.29 ),
% 13.87/14.29 'class_Ring__and__Field_Oring__1__no__zero__divisors' [174, 1] (w:1
% 13.87/14.29 , o:135, a:1, s:1, b:0),
% 13.87/14.29 'c_Int_Oiszero' [176, 2] (w:1, o:182, a:1, s:1, b:0),
% 13.87/14.29 'class_Ring__and__Field_Ocomm__ring__1' [177, 1] (w:1, o:80, a:1, s:1
% 13.87/14.29 , b:0),
% 13.87/14.29 'c_FFT__Mirabelle_OFFT' [179, 2] (w:1, o:183, a:1, s:1, b:0),
% 13.87/14.29 'class_Int_Oring__char__0' [180, 1] (w:1, o:150, a:1, s:1, b:0),
% 13.87/14.29 'c_Ring__and__Field_Osemiring__1' [181, 5] (w:1, o:191, a:1, s:1, b:0
% 13.87/14.29 ),
% 13.87/14.29 'v_k' [182, 0] (w:1, o:65, a:1, s:1, b:0),
% 13.87/14.29 'v_i' [184, 0] (w:1, o:67, a:1, s:1, b:0),
% 13.87/14.29 'v_a' [185, 0] (w:1, o:68, a:1, s:1, b:0),
% 13.87/14.29 'c_FFT__Mirabelle_ODFT' [186, 3] (w:1, o:189, a:1, s:1, b:0),
% 13.87/14.29 'tc_fun' [189, 2] (w:1, o:184, a:1, s:1, b:0),
% 13.87/14.29 'tc_Complex_Ocomplex' [190, 0] (w:1, o:71, a:1, s:1, b:0),
% 13.87/14.29 'c_fequal' [191, 3] (w:1, o:190, a:1, s:1, b:0).
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Starting Search:
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 5284
% 13.87/14.29 Kept: 2263
% 13.87/14.29 Inuse: 90
% 13.87/14.29 Deleted: 1
% 13.87/14.29 Deletedinuse: 0
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 12530
% 13.87/14.29 Kept: 4279
% 13.87/14.29 Inuse: 130
% 13.87/14.29 Deleted: 1
% 13.87/14.29 Deletedinuse: 0
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 18909
% 13.87/14.29 Kept: 6517
% 13.87/14.29 Inuse: 198
% 13.87/14.29 Deleted: 3
% 13.87/14.29 Deletedinuse: 0
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 26989
% 13.87/14.29 Kept: 8793
% 13.87/14.29 Inuse: 262
% 13.87/14.29 Deleted: 9
% 13.87/14.29 Deletedinuse: 0
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 34049
% 13.87/14.29 Kept: 10793
% 13.87/14.29 Inuse: 307
% 13.87/14.29 Deleted: 9
% 13.87/14.29 Deletedinuse: 0
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 41319
% 13.87/14.29 Kept: 12853
% 13.87/14.29 Inuse: 360
% 13.87/14.29 Deleted: 11
% 13.87/14.29 Deletedinuse: 0
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 45991
% 13.87/14.29 Kept: 14854
% 13.87/14.29 Inuse: 393
% 13.87/14.29 Deleted: 14
% 13.87/14.29 Deletedinuse: 0
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 53977
% 13.87/14.29 Kept: 17104
% 13.87/14.29 Inuse: 448
% 13.87/14.29 Deleted: 19
% 13.87/14.29 Deletedinuse: 1
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 60759
% 13.87/14.29 Kept: 19373
% 13.87/14.29 Inuse: 507
% 13.87/14.29 Deleted: 20
% 13.87/14.29 Deletedinuse: 1
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29 Resimplifying clauses:
% 13.87/14.29 Done
% 13.87/14.29
% 13.87/14.29
% 13.87/14.29 Intermediate Status:
% 13.87/14.29 Generated: 67700
% 13.87/14.29 Kept: 21454
% 13.87/14.29 Inuse: 554
% 13.87/14.29 Deleted: 367
% 13.87/14.29 Deletedinuse: 1
% 13.87/14.29
% 13.87/14.29 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 80065
% 39.93/40.28 Kept: 23856
% 39.93/40.28 Inuse: 584
% 39.93/40.28 Deleted: 367
% 39.93/40.28 Deletedinuse: 1
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 85077
% 39.93/40.28 Kept: 26101
% 39.93/40.28 Inuse: 624
% 39.93/40.28 Deleted: 367
% 39.93/40.28 Deletedinuse: 1
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 90157
% 39.93/40.28 Kept: 28145
% 39.93/40.28 Inuse: 634
% 39.93/40.28 Deleted: 367
% 39.93/40.28 Deletedinuse: 1
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 96665
% 39.93/40.28 Kept: 30150
% 39.93/40.28 Inuse: 662
% 39.93/40.28 Deleted: 367
% 39.93/40.28 Deletedinuse: 1
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 105346
% 39.93/40.28 Kept: 32244
% 39.93/40.28 Inuse: 703
% 39.93/40.28 Deleted: 369
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 115657
% 39.93/40.28 Kept: 35405
% 39.93/40.28 Inuse: 742
% 39.93/40.28 Deleted: 372
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 122124
% 39.93/40.28 Kept: 37424
% 39.93/40.28 Inuse: 771
% 39.93/40.28 Deleted: 372
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 132389
% 39.93/40.28 Kept: 40201
% 39.93/40.28 Inuse: 805
% 39.93/40.28 Deleted: 372
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying clauses:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 139672
% 39.93/40.28 Kept: 42413
% 39.93/40.28 Inuse: 830
% 39.93/40.28 Deleted: 558
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 146344
% 39.93/40.28 Kept: 44454
% 39.93/40.28 Inuse: 860
% 39.93/40.28 Deleted: 558
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 171573
% 39.93/40.28 Kept: 48207
% 39.93/40.28 Inuse: 890
% 39.93/40.28 Deleted: 558
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 191416
% 39.93/40.28 Kept: 50301
% 39.93/40.28 Inuse: 895
% 39.93/40.28 Deleted: 558
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 202291
% 39.93/40.28 Kept: 53218
% 39.93/40.28 Inuse: 905
% 39.93/40.28 Deleted: 558
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 209139
% 39.93/40.28 Kept: 55250
% 39.93/40.28 Inuse: 920
% 39.93/40.28 Deleted: 558
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 219442
% 39.93/40.28 Kept: 57389
% 39.93/40.28 Inuse: 955
% 39.93/40.28 Deleted: 558
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 232281
% 39.93/40.28 Kept: 59395
% 39.93/40.28 Inuse: 975
% 39.93/40.28 Deleted: 558
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying clauses:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 271183
% 39.93/40.28 Kept: 61400
% 39.93/40.28 Inuse: 984
% 39.93/40.28 Deleted: 672
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 285790
% 39.93/40.28 Kept: 63570
% 39.93/40.28 Inuse: 1005
% 39.93/40.28 Deleted: 672
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 297200
% 39.93/40.28 Kept: 65595
% 39.93/40.28 Inuse: 1035
% 39.93/40.28 Deleted: 672
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 318028
% 39.93/40.28 Kept: 68911
% 39.93/40.28 Inuse: 1045
% 39.93/40.28 Deleted: 672
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 331209
% 39.93/40.28 Kept: 70960
% 39.93/40.28 Inuse: 1075
% 39.93/40.28 Deleted: 672
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 340986
% 39.93/40.28 Kept: 73003
% 39.93/40.28 Inuse: 1095
% 39.93/40.28 Deleted: 672
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 352669
% 39.93/40.28 Kept: 75273
% 39.93/40.28 Inuse: 1120
% 39.93/40.28 Deleted: 672
% 39.93/40.28 Deletedinuse: 2
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 365061
% 39.93/40.28 Kept: 77365
% 39.93/40.28 Inuse: 1155
% 39.93/40.28 Deleted: 675
% 39.93/40.28 Deletedinuse: 5
% 39.93/40.28
% 39.93/40.28 Resimplifying inuse:
% 39.93/40.28 Done
% 39.93/40.28
% 39.93/40.28
% 39.93/40.28 Intermediate Status:
% 39.93/40.28 Generated: 378541
% 39.93/40.28 Kept: 81304
% 39.93/40.28 Inuse: 1169
% 112.29/112.69 Deleted: 676
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying clauses:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 397060
% 112.29/112.69 Kept: 83911
% 112.29/112.69 Inuse: 1174
% 112.29/112.69 Deleted: 1232
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 413198
% 112.29/112.69 Kept: 86632
% 112.29/112.69 Inuse: 1204
% 112.29/112.69 Deleted: 1232
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 428715
% 112.29/112.69 Kept: 89679
% 112.29/112.69 Inuse: 1214
% 112.29/112.69 Deleted: 1232
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 446031
% 112.29/112.69 Kept: 91687
% 112.29/112.69 Inuse: 1237
% 112.29/112.69 Deleted: 1232
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 457235
% 112.29/112.69 Kept: 93711
% 112.29/112.69 Inuse: 1261
% 112.29/112.69 Deleted: 1232
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 475072
% 112.29/112.69 Kept: 95975
% 112.29/112.69 Inuse: 1294
% 112.29/112.69 Deleted: 1232
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 484699
% 112.29/112.69 Kept: 98203
% 112.29/112.69 Inuse: 1304
% 112.29/112.69 Deleted: 1232
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 500810
% 112.29/112.69 Kept: 101504
% 112.29/112.69 Inuse: 1329
% 112.29/112.69 Deleted: 1232
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying clauses:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 510816
% 112.29/112.69 Kept: 103717
% 112.29/112.69 Inuse: 1339
% 112.29/112.69 Deleted: 1412
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 530769
% 112.29/112.69 Kept: 106578
% 112.29/112.69 Inuse: 1354
% 112.29/112.69 Deleted: 1412
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 546689
% 112.29/112.69 Kept: 109917
% 112.29/112.69 Inuse: 1374
% 112.29/112.69 Deleted: 1412
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 554162
% 112.29/112.69 Kept: 112024
% 112.29/112.69 Inuse: 1389
% 112.29/112.69 Deleted: 1412
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 561923
% 112.29/112.69 Kept: 114026
% 112.29/112.69 Inuse: 1405
% 112.29/112.69 Deleted: 1412
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 582379
% 112.29/112.69 Kept: 116185
% 112.29/112.69 Inuse: 1434
% 112.29/112.69 Deleted: 1412
% 112.29/112.69 Deletedinuse: 5
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 603840
% 112.29/112.69 Kept: 120198
% 112.29/112.69 Inuse: 1453
% 112.29/112.69 Deleted: 1424
% 112.29/112.69 Deletedinuse: 6
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 613725
% 112.29/112.69 Kept: 122249
% 112.29/112.69 Inuse: 1458
% 112.29/112.69 Deleted: 1424
% 112.29/112.69 Deletedinuse: 6
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying clauses:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 629705
% 112.29/112.69 Kept: 124962
% 112.29/112.69 Inuse: 1463
% 112.29/112.69 Deleted: 1792
% 112.29/112.69 Deletedinuse: 6
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 641456
% 112.29/112.69 Kept: 127309
% 112.29/112.69 Inuse: 1498
% 112.29/112.69 Deleted: 1793
% 112.29/112.69 Deletedinuse: 7
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 650280
% 112.29/112.69 Kept: 129327
% 112.29/112.69 Inuse: 1509
% 112.29/112.69 Deleted: 1793
% 112.29/112.69 Deletedinuse: 7
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 659587
% 112.29/112.69 Kept: 131844
% 112.29/112.69 Inuse: 1538
% 112.29/112.69 Deleted: 1793
% 112.29/112.69 Deletedinuse: 7
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 666401
% 112.29/112.69 Kept: 134238
% 112.29/112.69 Inuse: 1548
% 112.29/112.69 Deleted: 1793
% 112.29/112.69 Deletedinuse: 7
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 672274
% 112.29/112.69 Kept: 136621
% 112.29/112.69 Inuse: 1558
% 112.29/112.69 Deleted: 1793
% 112.29/112.69 Deletedinuse: 7
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 679185
% 112.29/112.69 Kept: 138994
% 112.29/112.69 Inuse: 1568
% 112.29/112.69 Deleted: 1793
% 112.29/112.69 Deletedinuse: 7
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 112.29/112.69 Done
% 112.29/112.69
% 112.29/112.69
% 112.29/112.69 Intermediate Status:
% 112.29/112.69 Generated: 685167
% 112.29/112.69 Kept: 141407
% 112.29/112.69 Inuse: 1578
% 112.29/112.69 Deleted: 1793
% 112.29/112.69 Deletedinuse: 7
% 112.29/112.69
% 112.29/112.69 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying clauses:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 692341
% 212.50/212.95 Kept: 143875
% 212.50/212.95 Inuse: 1588
% 212.50/212.95 Deleted: 1932
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 698446
% 212.50/212.95 Kept: 146324
% 212.50/212.95 Inuse: 1598
% 212.50/212.95 Deleted: 1932
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 719491
% 212.50/212.95 Kept: 148638
% 212.50/212.95 Inuse: 1608
% 212.50/212.95 Deleted: 1932
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 730505
% 212.50/212.95 Kept: 150641
% 212.50/212.95 Inuse: 1628
% 212.50/212.95 Deleted: 1932
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 740472
% 212.50/212.95 Kept: 152795
% 212.50/212.95 Inuse: 1648
% 212.50/212.95 Deleted: 1932
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 755369
% 212.50/212.95 Kept: 156276
% 212.50/212.95 Inuse: 1666
% 212.50/212.95 Deleted: 1932
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 763562
% 212.50/212.95 Kept: 158468
% 212.50/212.95 Inuse: 1668
% 212.50/212.95 Deleted: 1932
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 803969
% 212.50/212.95 Kept: 162931
% 212.50/212.95 Inuse: 1678
% 212.50/212.95 Deleted: 1932
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying clauses:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 822177
% 212.50/212.95 Kept: 166725
% 212.50/212.95 Inuse: 1698
% 212.50/212.95 Deleted: 2032
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 861436
% 212.50/212.95 Kept: 171991
% 212.50/212.95 Inuse: 1715
% 212.50/212.95 Deleted: 2032
% 212.50/212.95 Deletedinuse: 7
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 869370
% 212.50/212.95 Kept: 174328
% 212.50/212.95 Inuse: 1728
% 212.50/212.95 Deleted: 2033
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 880175
% 212.50/212.95 Kept: 178038
% 212.50/212.95 Inuse: 1738
% 212.50/212.95 Deleted: 2033
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 887939
% 212.50/212.95 Kept: 180399
% 212.50/212.95 Inuse: 1748
% 212.50/212.95 Deleted: 2033
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 897663
% 212.50/212.95 Kept: 182455
% 212.50/212.95 Inuse: 1763
% 212.50/212.95 Deleted: 2033
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying clauses:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 906362
% 212.50/212.95 Kept: 184563
% 212.50/212.95 Inuse: 1778
% 212.50/212.95 Deleted: 2251
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 916786
% 212.50/212.95 Kept: 186745
% 212.50/212.95 Inuse: 1788
% 212.50/212.95 Deleted: 2251
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 930706
% 212.50/212.95 Kept: 189823
% 212.50/212.95 Inuse: 1803
% 212.50/212.95 Deleted: 2251
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 943802
% 212.50/212.95 Kept: 192565
% 212.50/212.95 Inuse: 1818
% 212.50/212.95 Deleted: 2251
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 956289
% 212.50/212.95 Kept: 195842
% 212.50/212.95 Inuse: 1833
% 212.50/212.95 Deleted: 2251
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 970164
% 212.50/212.95 Kept: 198372
% 212.50/212.95 Inuse: 1858
% 212.50/212.95 Deleted: 2251
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 993663
% 212.50/212.95 Kept: 201216
% 212.50/212.95 Inuse: 1878
% 212.50/212.95 Deleted: 2251
% 212.50/212.95 Deletedinuse: 8
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 1011983
% 212.50/212.95 Kept: 203217
% 212.50/212.95 Inuse: 1883
% 212.50/212.95 Deleted: 2252
% 212.50/212.95 Deletedinuse: 9
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying clauses:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 1031623
% 212.50/212.95 Kept: 205231
% 212.50/212.95 Inuse: 1891
% 212.50/212.95 Deleted: 2776
% 212.50/212.95 Deletedinuse: 9
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 1050224
% 212.50/212.95 Kept: 207250
% 212.50/212.95 Inuse: 1897
% 212.50/212.95 Deleted: 2776
% 212.50/212.95 Deletedinuse: 9
% 212.50/212.95
% 212.50/212.95 Resimplifying inuse:
% 212.50/212.95 Done
% 212.50/212.95
% 212.50/212.95
% 212.50/212.95 Intermediate Status:
% 212.50/212.95 Generated: 1085151
% 212.50/212.95 KeptCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------